Comparison of the β-α Angular Correlations in the Beta Decays of Li⁸ and B⁸

Citation

Nordberg, Martin Emery, Jr (1961) Comparison of the β-α Angular Correlations in the Beta Decays of Li⁸ and B⁸. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/00je-ft97. https://resolver.caltech.edu/CaltechTHESIS:07152025-213640159

Abstract

This thesis describes a comparison of the β-α angular correlations of the beta decays of Li ⁸ and B ⁸ to the 2.90-Mev α-unstable state of Be ⁸ . The data are fitted to the angular correlation function in the laboratory system, W(ϴ _βα ) = 1 + A cos ϴ _βα + B cos ² ϴ _βα , where A and B are independently determined for each decay from measurements at ϴ _βα = 0°, 90°, and 180°. The coefficient, A, is due to the recoil of Be ^8* and has the same sign for both beta decays. The coefficient, B, arises from the interference of forbidden vector matrix elements with the allowed axial vector matrix element and changes sign in the two decays. The correlation for the Li ⁸ decay is measured with average total β-energies of W _β ≃ 5, 8, and 11 Mev. Both A and B are approximately linear in the energy. The correlation for the B ⁸ decay is measured only with average total β-energy of W _β ≃ 11 Mev. From the data with W _β ≃ 11 Mev, the difference of the coefficients, B(Li ⁸ ) - B(B ⁸ ), is equal to (0.0069 ± 0.0011)W _β . This result is compared with theoretical predictions based on the older Fermi and the newer Conserved Vector Current theories of beta decay. The experiment agrees with the prediction of the latter theory.

Item Type:

Thesis (Dissertation (Ph.D.))

Subject Keywords:

(Physics)

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Physics

Thesis Availability:

Public (worldwide access)

Research Advisor(s):

Barnes, Charles A. (advisor)
Weidenmuller, Hans A. (advisor)
Fowler, William A. (advisor)

Thesis Committee:

Unknown, Unknown

Defense Date:

1 January 1961

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Funding Agency	Grant Number
Office of Naval Research (ONR)	UNSPECIFIED
U.S. Atomic Energy Commission	UNSPECIFIED

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CaltechTHESIS:07152025-213640159

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https://resolver.caltech.edu/CaltechTHESIS:07152025-213640159

DOI:

10.7907/00je-ft97

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17529

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CaltechTHESIS

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Benjamin Perez

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17 Jul 2025 18:08

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17 Jul 2025 18:23

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COMPARISON OF THE f3-a. ANGULAR CORRELATIONS IN THE BETA DECAYS OF Li 8 AND B 8 Thesis by Martin Emery Nordberg, Jr. In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena~ California 1961 ACKNOWLEDGMENTS It is a pleasure for the author to acknowledge the assistance offered him by all of the personnel of the Kellogg Radiation Laboratory. The author is especially indebted to Professors C. A. Barnes, H. A. Wei9-enmuller ~ and W. A . Fowler for discussions aiding the performance of this experiment. The collaboration of B. Povh and F. B. Morinigo in the execution of the experiment is gratefully acknowledged. The author also wishes to express his appreciation for a fellowship offered by the General Electric Company and for the financial support of this research by the joint program of the Office of Naval Research and the U. S. Atomic Energy Commission. ABSTRACT This thesis describes a comparison of the lations of the beta decays of Li 8 state of Be . 8 to the 2. 9 0 -Mev a-unstable W(8l3n) = 1 + A cos 0 2 130 + B cos 8l3n' where A are independently determined for each decay from measure0 0 0 ments at 8l3a, = 0 , 90 , and 180 . recoil of Be ficient, and B The data are fitted to the angular correlation function in the laboratory system, and B 8 l3-a. angular corre- The coefficient, A, is due to the s* and has the same sign for both beta decays. The coef- B, arises from the interference of forbidden vector matrix elements with the allowed axial vector matrix element and changes sign in the two decays. The correlation for the average total l3 -energies of 8 decay is measured with 13 Both A and B The correlation for the decay is measured only with average total 8 8 w ==- 5, 8, and 11 Mev. are approximately linear in the energy. From the data with Li 13- energy of B 8 Wl3:::::.. 11 Mev . w : : :. 11 M6!v, the difference of the coefficients, 13 B(Li ) - B(B ), is equal to (0. 0069 ± 0. 00ll)Wl3. This result is com- pared with theoretical predictions based on the older Fermi and the newer Conserved Vector Current theories of beta decay . ment agrees with the prediction of the latter theory. The e x peri- TABLE OF CONTENTS Page Section I 1 INTRODUCTION Fermi Theory of Beta Decay Universal V-A Theory Tests of the Conserved Vector Current Theory II APPARATUS 11 14 15 16 17 PROCEDURE 21 Measurement Analysis Results IV 5 11 Target Chamber Counting Cycle n-Particle Detector 13-Detector Electronic Circuitry III 1 4 21 24 31 DISCUSSION 13-Spectrum a-Spectrum Counting Rate Effects Symmetry of the Counting Arrangement Discussion of Results 35 38 43 46 49 APPENDIX A Semiconductor Surface Barrier Detectors 56 APPENDIX B Integration Ov er Detector Solid Angles 64 APPENDIX C Solution for the Coefficients, 69 APPENDIX D The Transformation From the Be 8 ,:, Rest System to the Laboratory System A and B 73 REFERENCES 81 FIGURES 84 -1- I. INTRODUCTION Although many of the features of beta decay have been satisfactorily understood since the 19 30' s , much effort in the past few years has been devoted to extending and refining the theoretical and experimental understanding of the weak interactions (1-5). The theoretical prediction of Lee and Yang that the weak interactions do not conserve parity (6) has especially stimulated much of the activity in the field . Experimentally it was promptly verified that indeed parity is not conserved in nuclear beta decay (7) nor in muon decay (8, 9). At a time when experiments posed some doubt as to the actual form of the coupling , Feynman and Gell-Mann (10), Sudarshan and Marshak (11), and Sakurai (12) proposed a universal vector-axial vector theory of the weak interactions . Many aspects of the theory have since been experimentally verified, including the vector and axial vector forms, the degree of parity violation, the helicity of electrons and neutrinos , and effects in muon decay (1, 2, 5, 13, 14) . Feynman and Gell-Mann (10) also proposed as a feature of the theory, the idea of a conserved vector current ( C . V. C. ). about the This experiment tests a prediction of the C. V. C. theory j3-a angular correlation in the beta decays of Li 8 8 and B . Fermi Theory of Beta Decay In the conventional Fermi theory of beta decay (1-4) the most general relativistically invariant forms of a four ferm.ion point interaction are the five types described as scalar (S), vector ,('[ ), axial vector (A), tensor (T) , and pseudoscalar (P). The allowed S and V interac- tions obey the Fermi selection rules (b.I = 0 but no 0 ._ 0, b.J = O, -2- no parity change) while the allowed A Gamow-Teller selection rules but no and T (61 = 0,, .±. 1 but no 0 -- 0, 0-+ 0, no parity change), where is the total angular momentum. interactions obey the 6J = 0, + 1 I is the isotopic spin and J Both types of allowed beta decays are observed. The P A priori" all five interactions could occur in nature with various ampli- 11 interaction does not contribute to allowed transitions. tudes, but the experimental absence of the "Fierz" interference terms was assumed to indicate on the basis of.the parity conserving Fermi theory that either S or V is present and either or A T is present. On the basis of a general, parity non-conserving theory this conclusion is not justified, For some time it was believed the interactions were S and T, but more recent data definitely indicate that the interactions are V A (5, 13, 60). and Furthermore, the experimental amplitudes of the coupling (-GA)/ GV .!::! 1. 2. constants are in the ratio, A parity conserving Hamil- tonian for nuclear beta decay would be written= >:< where p = p y , 4 e = e *y coupling constants, GS' 4 and p., n, e, v GT, and GP' represent wave functions. The are zero in the Fermi theory only on the basis of experimental evidence. The five interactions can be written in the Fermi theory either in parity conserving or parity non-conserving form. The violation of parity can be expu;essed by replacing . the lepton operator, yµ (1 + cy ). 5 yµ , by Lee and Yang (15 ),. Landau (16 ), and Salam (17) predicted that c is real and equal to tl, in which case the product of Parity times Charge Conjugation is conserved and the neutrino is 100% polarized. In experiments on the asymmetric distribution of electrons from -3- oriented nuclei , the longitudinal polarization of electrons from unoriented nuclei , and the asymmetric distribution and polarization of -y-rays following beta decay , the maximum effect is found indicating c = +l (2, 14). The Hamiltonian for nuclear beta decay is thus: The idea that nuclear beta decay is but one facet of a universal wea'.k: interaction has been .c onsidered for many years. The Hamiltonian may easily be extended to the following: H = {p-yµ ( GV-GAy 5 )n}(eyµ(l+y )v) + h. c. 5 beta decay + G µ (µy µ (l+y 5 )v}(ey µ {l+y 5 )v) + h. c . muon decay + {pyµ{GV-GA-y 5 )n}{µyµ<l+y 5 )v) + h. c . muon capture + •• strange particle decays 0 0 • • • • • • • • • I) • Recently universality has been given a quantitative basis in the measurement of the muon decay rate and in the measurement of the ratio of 1T + - tude, µ + +V to rr +- e + + -v decays. In fact, it happens that the ampli- G , associated with muon decays is, within a few per cent, equal µ to the vector amplitude, Gy, of beta decay (18, 19). Although this re- sult is not impossible in the Fermi theory it is rather surprising. Large renormalization effects arising from strong interactions would be expected to be present in nuclear beta decay which are not present 1n muon decay. In the older theory it would be a coincidence that the cou- pling constants , Gµ and Gy, are almost identically equal and that GV and -GA are approximately equal. -4- Universal V-A Theory The theory of a universal vector-axial vector interaction (10, 11, 12, 20) explains all the features of beta decay discussed above and also the equality of Gµ and GV. The approximate equality of -GA and GV is still not understood. Historically, the theory was proposed at a time when experiments were not yet clear on the form of the weak interactions. There ?,re two separate ideas advanced in this theory, the idea of a current-current interaction and the idea that the vector part of this current contains terms arising from pions and is thus conserved in strong interactions (10). In the universal V-A theory it is assumed that "bare II nucleons couple exactly as do leptons, that is, with the 1 + '( term. This has the effect that the S, T, and P and the V and A 5 interactions vanish couplings are necessarily equal. The current-current hypothesis proposes that the various matrix elements of '( µ (1 + '( ) are 5 Gummed to form a vector plus axial vector quantity which interacts with itself to form the weak interactions. If the symbols (np), (ev), etc. are used to abbreviate the matrix elements, (n'(µ(l + '( )p), 5 ('e'(µ(l +'( )v), 5 etc. , the weak current is the sum: J µ -{np)+(ev)+{µv)+ ... The Hamiltonian for the weak interactions of universal strength, H wea k:: GJ J µ µ G, is: + The cross terms are those leading to beta decay, muon decay, muon capture, and strange particle decays. The product also contains squared -5terms of order G ==- 10 -7 , such as (ve)(ev) which can lead to neutrino- electron scattering, and (pn)(np) which can lead to weak, parity non- conserving forces in the neutron-proton interaction. Experimental techniques are not yet sensitive enough to observe these effects but may be in the future. order G 2 ==- 10- 14 The older theory also leads to such effects but of the . Feynman and Gell-Mann {10) also advanced the hypothesis that the vector part of the current, J µ' contains a contribution from pions analagous to the pion contribution in the electromagnetic current, j . µ The difference is that the electromagnetic intera·cti on ccnit ains - the z- component of the isotopic spin current whereas the weak interactions contain the (x ± iy)-components. The addition of the pion term results in a conserved quantity in the weak interactions analo.gous to the conserved current in the electromagnetic interaction. The strong interactions are thus arranged not to renormalize the vector beta decay coupling constant; that is, G = GV within the accuracy of electromagnetic corrections. The axial vector coupling is apparently renormalized by the strong interactions, resulting in the ratio (-GA) / GV = 1. 2 . Tests of the Conserved Vector Current Theory In searching for other predi.ctions of the conserved vector current theory, Gell-Mann (21) suggested an effect in beta decay which he called 11 weak magnetism. 11 In the electromagnetic interaction the pion terms result in the anomalous magnetic moments of the proton and neutron which enhance the nuclear matrix elements for magnetic dipole emission of a -y-ray. Therefore the pion terms of the weak interaction -6would be expected to enhance the analogous matrix elements for 13-emis sion. In other words, the Dirac magnetic moment operator is replaced by the total magnetic moment operator, Dirac plus anomalous. Gell- Mann suggested that the best situation to look for such an effect is in the interference of a second forbidden vector matrix element with an allowed axial vector beta decay. In mirror beta decays the interference effect changes sign in the positron and electron emissions and the magnitude of the effect can be predicte,d from the matrix element of the analogous of the B 12 -v- ray transition. and N 12 with matrix element, He considered the effect on the spectra decays. X, For an allowed a x ial vector 13-transition Gell-Mann defines the quantity, a= where M is the nucleon mass and A = 1. 2 is the ratio of The effect on the spectrum is a correction factor, matrix element of the magnetic dipole operator, 1 + 8 -GA to 3 a W[3. GV. The µ, is obtained from the analogous -v-ray transition: r '( (Ml) = where w is the energy of the -v-ray . element, 0 14 2 3 µ w X, The allowed Gamow-Teller matrix is obtained from a comparison of the ft-value with that of , which is a pure Fermi transition with a matrix element equal to -fz . Then: lal -7- Bernstein and Lewis have considered the effect of "weak magnetism" in other mass systems (22). In particular, they calculated the angular c o rrelation of the electron from the beta decay B 8 of Li 8 or and the a-particles from the breaku p of the 2. 9 0 Mev daughter . Be8. state 1n The energy levels of this system are shown in figure 1'(2 ~} . The angular correlation in the center of mass system for either decay is shown to be: Since the sign of ~ changes between the Li 8 and B 8 decays, a com- parison of the two correlations measures twice the effect. Indeed, it is imperative to make a comparison measurement in an experiment because there are many terms which can lead to a small asymmetry with the same sign in both decays (24, 25). The Ml '{-ray transition rate has not been e x perimentally measured from the J = 2 +, T = 1 state in Be 8 . Therefore Bernstein and Lewis (22) assumed an average value of I' 'Y (Ml) is the Weis skopf unit. = 0 . 15 r W' where I' W For this estimate, I' (Ml) equals 8. 2 ev. 'Y 5 From the ft-value, 5 ·x 10 , and the approximately known '{-ray energy, 13. 7 Mev, the quantity, 0. 0073 per Mev. a, is given by, /a / = 0. 00 25 [ r 'Y {Ml)(ev)] ~/ 2 = Therefore, if 6 is defined as the difference of the coefficients of the 8 8 (Li -B ) 2 cos ef3a term in the angular correlations, Bernstein and Lewis predict 6 = (±0 . 015) W f3'· ("\i\T f3 in :W.:e.v,: ). The sign is undetermined since the sign of a cannot be determined from the ft-value. At this point, chronologically, the first part of the experiment -8- described in this thesis was performed by B. Povh, Dr. C. A. Barnes, and the author {26). The preliminary result then was 6= {0. 002±0. 004)Wl3 {statistical error only), which temporarily, at least, appeared to dis agree with the C. V. C. theoretical prediction. At this time Dr. H. Weidenmuller calculated the various wave functions and matrix elements by the intermediate coupling model of the nucleus {27). By fitting parameters so that the model gave the correct values of the energy splitting, the log ft-value, and the magnetic moment 8 of the ground state of Li , Weidenmuller was able to put limits on the matrix elements in question. Since the magnetic dipole operator con- tains a contribution from the nucleons' orbital momenta which is not enhanced by the pion current terms, the older Fermi theory (i. e. with no If TT-corrections at all) may also lead to an appreciable asymmetry. is the orbital angular momentum operator and CT Fermi theory predicts an effect proportional to f.. the spin operator, the < JJ.. + CT J > and the C. V. C. theory predicts an effect proportional to < Ji. + 4. 7CT J >. Quanti- tatively the calculation predicts: Fermi theory {0. 001) W l3 < 6 < {0. 004) Wl3 C. V. C. theory {0. 005) W l3 < 6 < (0. 009) Wl3 The calculation can give the sign and predicts a and thus is positive for 6, as defined above, is also predicted to be positive. C. V. C. theoretical asymmetry is a factor of 2 8 Li , The smaller than the origi- nal estimate of Bernstein and Lewis {22), and the two theories predict similar effects differing in magnitude by about a factor of 2. Both of these facts make a positive test for the C. V. C. theory more difficult. -9The limits for r '{ (Ml) in this calculation are 1 to 4 ev with the inclusion of estimates of the spin-orbit-coupling term in the Hamiltonian. value of r y (E2) is estimated to be negligible. The Kurath has made a simi- r '{ (Ml) (28). lar calculation and finds essentially the same result for In view of this calculation no definite conclusion may be drawn from the small result of the first part of the experiment, Therefore it was decided to repeat the experiment to obtain better statistical accuracy and better control of possible systematic errors. This second ex- periment, which is described in this thesis , was carried out by the author, with F. B. Morinigo and Dr. C. A. Barnes (29). The result is o= (0. 0069 ± 0. 00ll)W f3 (statistical error plus estimates of systematic errors), which is a positive indication for the C. V. C. theory. Various other experiments have been suggested, and some have been attempted in order to verify or disprove the C. V. C. theory (21, 22, 24, 30-34). N 12 An experiment at this laboratory measuring the spectral shapes is so far inconclusive (32). relation experiment in the beta decay of F 2 f3-y A B 12 and angular cor- 0 is consistent with the theory but is not definitive since the mirror decay cannot be used for comparison ( 33 ). Muon absorption experiments are also consistent with the theory but are not accurate enough to be considered positive evidence ( 34). More accurate comparisons of the 0 14 and muon coupling constants still do not resolve the few per cent discrepancy between them (18, 19). This may indicate a deficiency of the theory or may be resolved by refined calculations of other small effects that are in:volved. The experiment described here is perhaps the most positive ·experimental confirmation of the validity of the C. V. C. theory, which -10- has been carried out up to the present time. Figur-e 1 illustrates the pertinent energy levels of the mass-8 isotopic triplet. Li 8 decays by electron emission and B 8 decays by posi- 8 tron emission to the 2. 90-Mev excited state of Be , with half lives of 0. 85 and 0. 77 second, respectively {23). The 2. 90-Mev state is un- stable and immediately breaks up into two a- particles. 16. 1 Mev, in 8 8 the case of Li , and 17. 0 Mev, in the case of B , are the energies available to be shared by the electron, neutrino, and two a-particles. The a-particle energy spectrum peaks at 1. 5 Mev and is about 0. 8Mev broad. Therefore the electron and positron spectra do not have simple allowed shapes, but approximate end points of 13.1 and 14. 0 Mev are characteristic of the decays. J = 2 + ground states of Li 8 The state in Be and B Mev or the one at 16. 63 Mev. 8 8 analogous to the • is probably either the one at 16. 94 The -y-ray widths of these states are not known, but experiments are proceeding in several laboratories in an attempt to measure these widths. The present experiment involves measuring coincidences between a-particles in a fixed direction and electrons or positrons at an angle, 0R , relative to this direction. ~Cl • 0 0 0f3a, = 0 , 90 , and 180 0 Some data were taken with three angles, . and the rest were taken with 0 130 = 90 0 0 and 180 , The general features of the first and second phases of the experiment are similar but they differ in detail. The discussion to follow will refer to the second phase of the experiment unless the first phase is specifically mentioned. -11- II. APPARATUS The parent radioactive nuclei, Li 8 8 and B , are produced in the nuclear reactions: L/(d,p)Li 8 Q = -0.192 Mev, Eth::: 0. 247 Mev 3 6 8 Li (He , n)B The beams of deute rons and He Q::: -1. 976 Mev, Eth= 2. 966 Mev 3 ions are accelerated to 0. 7 5 Mev and 3. 2 Mev, respectively, in a Van de Graaf£ electrostatic generator, and are analyzed in a 90° double focusing magnet. After pas sing through vertical and horizontal defining slits the beam hits the target. The horizontal slits, which define the vertical motion of the beam, also serve to regulate the Van de Graaf£ voltage. The beam energies are held constant to better than 1/2 %, although this is not an important parameter for the experiment. Target Chamber The target chamber consists of a 3 "-diameter by 1/8 "-wall lucite tube mounted vertically on an angular distribution table scribed with angle marks at 10° intervals. in figure 2. The The chamber and table are shown ~-detector is the plastic scintillator shown in the foreground and is mounted inside the lead shield during the experiment. The scintillator, lead shield, photomultiplier, and preamplifier can all be rotated precisely about the axis of the lucite target chamber and can be positioned by the scribed scale to within about 1/10°. The lucite vacuum chamber contains a concentric cylindrical liquid nitrogen cold trap, the target shield, and a lead container for the shield mounted from -12- below. A 5 -mil aluminum target backing is fastened to a movable 1/ 4 11 - diameter brass rod which is mounted from above. A tube containing the retractable lithium furnace is mounted 2-3 / 4" above the plane of the detectors. The target rod can be pulled up to allow the target backing directly to face the furnace for the lithium evaporation. The beam enters the target chamber through the lucite tube mounted from the rear right-hand side in figure 2. Actually three different lucite chambers have been used in the course of the experiment. only at 0/30, In the first two, where data can be taken = 90° and 180°, the gold-silicon a-detectors are mounted through holes in the side of the chamber. In the third which is shown in figure 2, data can be taken at 0/3a = 0°, 90°, and 180°, and the a-de- tectors are mounted from the top. The chamber is covered with black paper during the experiment since the detectors are slightly light sensitive. As in all angular correlation experiments, symmetry is of prime importance. The target chambers have been designed with this in view. The walls of all chambers are milled to a uniform thickness to minimize the variation of electron energy loss with angle. In all cases the lithium evaporating furnace is positioned as symmetricaily as possible to minimize variation in the number of scattered electrons with angle, although it is at a different height than the detectors and should have a negligible effect. The target has been placed at a 45° angle with respect to the detector positions except in the ment. . 8 B case of the first part of the experi- Dummy a-detectors are symmetrically placed to prevent dif- ferences in the number of scattered or transmitted electrons. The -13- beam entrance tube cannot be placed symmetrically. However it is a thin walled lucite tube and should produce a negligible number of scattered electrons. The target consists of either natural lithium (92, 6% L/ 6 7.4%Li ) forthe case. Li 8 caseorenrichedLi 6 and 6 8 (99.7%Li )forthe B In both cases the lithium is evaporated in metal form on a 5-mil aluminum backing. In the first phase of the experiment the lithium was· evaporated on the whole width of the aluminum backing and the target spot was thus defined by the width of the beam, target at an angle of 45° in the case of Li 8 The beam hit the 8 and 30° in the case of B . This arrangement could allow some inaccuracy and possibly some systematic error in the position of the target spot. For this reason and also to minimize the recoil into the target backing (this will be dis cussed later), an improved arrangement is used in the second phase of the experiment. In this arrangement the beam hits the target at the glancing angle of 15 °. vertical strip. 2. The Also the lithium is evaporated only on a 2-mm wide 2-mm aperture of the furnace can be seen in figure The projection of the lithium strip on the plane perpendicular to the direction of the beam (2 mm sin 15° = 1/ 2 mm) is narrower than the beam width. lithium strip . Therefore the target spot is defined by the evaporated This arrangement defines the target position more ac- curately than the previous arrangement and minimizes the possibility of systematic error arising from lateral motion of the beam . Also a signal from the vertical beam defining slits can be used to regulate a magnet which can hold the beam fixed in the center of these slits and thus in a well defined position on the target . The magnet has been used -14- only during part of the experiment. No significant systematic beam movement is observed either with or without the magnet. Counting Cycle Several aspects of the experiment dictate certain features of the apparatus. For example, the 0. 848-second Li 8 half life and the . 8 0. 77-second B half life allow delayed counting while the beam is turned off. Two systems are common for this purpose, either synchro- nous motor choppers and gate signals phased with 60 cycle line voltage, or mechanically controlled choppers and gate signals phased with cam driven relays. The second system with a period of 1 second was chosen because it facilitates the operation of a target shield with a vertical solenoid-activated movement. This shield maintains symmetry within the sensitive target region during the counting period by dropping out of the way. functions: As seen in figure 3 the chopping mechanism has four (1) to gate the 100 channel analyzer, (2) to gate the scalers, (3) to activate the solenoid for the beam chopper, and (4) to activate the solenoid for the target shield, The chopping mechanism consists of the two solenoid power supplies and four switches driven by three cams on one shaft turning at 1 cycle per second. Both gate switches are driven by the same cam and are shorted except during the counting period. The beam chopper also has a vertical movement activated by a solenoid and is located about 20 11 ahead of the target. Starting with the beam cut off, the gates off and the target shield down, the complete counting cycle is the following: -15at t::: 0 the target shield rises to surround the target t = 0.05 sec. the beam is turned on = 0.45 sec. the beam is cut off t = o. 50 sec. the shield drops t t ::: 0.5 5 sec. the gates are turned on for the start of the counting period t ::: 0.95sec. the gates are turned off =1. 0 sec. the target shield rises. t a-Particle Detector At the time of the start of this experiment it was not known whether a suitable gold-silicon semiconductor a-detector could be constructed. Gold-germanium semiconductor detectors (35, 36, 37) had been constructed and had operated satisfactorily when cooled to liquid nitrogen temperature. Therefore the first target chamber was designed to accommodate either:;type of semiconductor detector or a CsI(Tl) scintil- lator and photomultiplier, whichever proved the most satisfactory. A CsI(Tl) scintillator has the disadvanta.ges •of slow,.ri,se±ime,., sensitivity to electrons, and extreme light sensitivity, thus requiring a light shield through which the a-particles have to pass. A silicon surface barrier detector was constructed (38) and found to operate satisfactorily at room temperature. (See Appendix A for a full description of the opera- tion of semiconductor detectors.) A gold-silicon detector was compared with a CsI(Tl) scintillator by exposing both counters to the a-particles following the Li 8 beta decay. Both spectra showed pulses from electrons, and noise, at low pulse heights. However the silicon detector displayed a much cleaner spectrum and altogether was very well suited for the -16- experiment . A typical response to the a-particles following the Li 8 decay is shown in figure 4 and the response to the 5 . 3 Mev a-particles of P o 212 . s h own 1n . f 1gure ' 5. 1s The pulse height vs. energy of gold- silicon detectors was also measured and found to be quite linear. There is no evidence of an appreciable dead layer on the surface of the detectors. The noise of the silicon detectors increases with age and for this reason new detectors have to be constructed periodically. size is a 5 / 16 11 wafer with a 1/ 4 11 -diameter aperture. The usual The detectors are located approximately 7 /8 11 from the target. The most useful data have been taken with the system allowing the 13-detector to be placed at all three angles, 0 0 0 0l3a. = 0 , 90 , and 180 . This system would not be possible without a semiconductor a-detecto:r because at 0° the electrons pass directly through the a-detector before reaching the 13-detector. The problem of light collection would make a similar scintillator and photomultiplier system very awkward. The sili- con dete,ctor in this case consists of an etched wafer only about 3 / 4-mm thick in which the electrons lose a negligible amount of energy. The thin a-detectors, electrical leads, and apertures are visible in figure 2. 13-Detect.or For the 13-detector both a plastic and a Nal(Tl) scintillator were tested. It was known from a previous experiment that a plastic scintil- lator shows good 13-spectra {13), but the plastic has the disadvantage of no convenient means of energy calibration with available y-ray sources. Although the Nal(Tl) scintillator can be calibrated with y-ray sources because of its sharper response, it produced a poorer 13-spectrum of the Li 8 decay than the plastic scintillator. This was due to increased -17 - sensitivity to background radiation (mostly neutrons) , slightly poorer crystal geometry , with higher Z which allowed more electrons to scatter out of the crystal , and to greater bremsstrahlung loss from the crystal. For this reason , and also to avoid the longer pulse rise time of Na!, the plastic scintillator has been used in the e x periment. the electrons from the Li 8 The response to decay is shown in figure 6 and the response to the 2. 6 Mev '{-ray from ThC II is shown in figure 7 . The calibration of the energy scale by means of the 13-spectrum is d i scussed in the next sections . The plastic scintillator is fastened to a 2 11 -diameter RCA type 6655 photomultiplier with a 1 11 -long lucite light pipe. The scintillator which is shown in figure 2 is in the shape of truncated cones with a 2-3 / 4"-maximum diameter and a 2 11 -minimum diameter. The aperture in the lead shield is only 1-3 / 8 11 in diameter thus reducing the probability that electrons scatter out of the sides of the scintillator. The photo- multiplier is shielded from stray magnetic fields by layers of high µ material and a steel case. The 3 / 4" -thick lead shield protects the scintillator from background -y-radiation. Electronic Circuitry A block diagram of the electronic system is ,s hown in figure 3. The general s y stem is that of a II slow-fast II coincident arrangement . The fast resolving time is 80 mµsec . and the slo w resolving time is the 1 µsec . resolving time of the coincidence mixer of the 100 channel analyzer . The coincident a. - spectrum is recorded in the 100 channel analyzer in order to e x trapolate the spectrum to zero pulse height with reasonable confidence. This point is discussed in the next sections . .-18- The preamplifiers used with the surface barrier detectors produce an output voltage pulse which is linearly dependent on the input charge. 40. A low noise 417 A triode on the input provides a gain of about This is followed by a cathode follower and the signal is fed back to the input grid by a 20-µµf capacitor. The output voltage in this configura- tion is approximately the input charge from the detector divided by the feedback capacitor. millivolt. A 1/2-Mev particle gives an output of only about 1 Thus a large amount of amplification is needed in order to analyze the pulses. Therefore, in the slow system, another preamplifier with a stabilized voltage gain of about 40 is used. This is followed by a standard laboratory type 10T2 linear amplifier of gain up . to about 5000, the output of which goes to the input of the 100 channel analyzer. In the fast system five Hewlett-Packard 'delay line amplifiers are used to provide the necessary gain. Special precautions, such as extra shielding on the connecting cables and separation of the amplifiers, are needed to prevent this system from oscillating when the gain is turned up. Several pulse shaping and coincidence mixer systems have been used in the course of the experiment. In the first part of the experiment the pulses were clipped and limited after the Hewlett-Packard amplifiers by a delay line plate load on an El80F pentode. time was used in the case of Li 8 A 40-mµsec . resolving 8 and 80-mµsec . in the case of B . The limiters were followed by a 6BN6 coincidence mixer~ In the second part of the experiment the pulses are clipped by a shorted cable following the second Hewlett-Packard amplifier as in figure 3. The resolving time with a 16' cable is about 80 mµsec. for both Li 8 and B . 8 The El80F limiters and 6BN6 mixer have been used in collecting -19about half of the data. For the · remaining data a circuit employing tun- nel-diode limiters and coincidence mixer has been used. This circuit has the advantage of increased sensitivity which allows use of somewhat less gain in the chain of Hewlett-Packard amplifiers. The output of the coincidence mixer goes into the "gate II of the 100 channel analyzer. The electronic circuits for the 13-detector are similar to those for the a-detector except that the extra preamplifier is not needed and only 2 or 3 (depending on the [3-energy) Hewlett-Packard amplifiers are needed. Following the linear amplifier is a single channel differential discriminator. This is used to select the portion of the 13-spectrum de- sired to be in coincidence with the a.-particles, such as the shaded portion of figure 6. The output of this discriminator goes to the "delayed coincidence II input of the 100 channel analyzer. Both an electron sensitive plastic scintillator and an a-particle sensitive gold-silicon detector have been used at different times as a monitor counter. The monitor is used only as a check on the consistency of the a-detector counts. The electronic circuits for the monitor con- sist of a preamplifier, a 10T2 linear amplifier and a scaler. Scalers are used to count the a.-pulses, the 13..:pulses, the 13- pulses passed by the single channel discriminator, the monitor pulses, and the output pulses of the fast coincidence mixer. These scalers and the 100 channel analyzer are gated on and off by the gating mechanism described previously. The 100 channel analyzer requires the presence of four conditions 1n order to register a coincident count: (1) the gating switch is open for the 0. 4 sec. counting period, (2) the fast coincidence mixer produces an -20- output pulse, (3) the [3-discriminator produces an output pulse, and (4) the a-amplifier produces an output pulse. The presence of (2) would indicate the presence of (4) if it were not for excess noise in the fast amplifiers. In such a case the 100 channel analyzer records a count in channel 1, 2, or 3. These counts are discarded in analyzing the data. -21- III. PROCEDURE Several tests have been carried out to insure the proper operation of the various components of the equipment. Estimates of the possible systematic errors based on these tests are summarized in the next section. This section outlines the procedure of accumulating and analyzing the data after the apparatus has been adjusted and is operating properly. Measurement The first step at the beginning of a group of runs is to evaporate a fresh Li 6 or Li 7 target in metal form on the aluminum backing. The evaporation is done inside the target chamber under high vacuum. New spots of the 2-mm strip are bombarded periodically in taking data. Next, the beam is aligned by adjusting the defining slits so that the beam enters the target chamber at the correct vertical position and precisely on the chamber axis. The beam spot and the shadow of the target backing on a quartz disc can be viewed for this adjustment. disc is pulled out of the way for taking data. This At this stage of the second part of the experiment, care has been taken not to expose the silicon a-detectors to sputtered material from the target or quartz. However, in the first part of the experiment some material may have sputtered on the detectors during the beam alignment for the B 8 decay, and thus caused a further degradation of the a-particle energies. The intensity of the O. 7 5-Mev deuteron beam for the is adjusted to about 0. 1 µa rate to 2-5%. 3. 2-Mev He 3 For the B 8 Li 8 decay average value in order to limit the random decay randoms are not a problem and the beam is adjusted to about 1 µa average value which is -22- nearly the maximum the distortion. 5-mil aluminum backing will stand without The beam is purposely not sharply focused on the target so that it uniformly bombards the width of the 2-mm lithium target strip. In the third target chamber where the [3-detector can be positioned at all three angles, the target is grounded since the a-detectors are mounted from the brass top which also holds the target rod. beam current cannot be read directly. Thus the For this case the target shield is biased 300 volts positively and is connected to ground through a microammeter . The shield collects the secondary electrons knocked out of the target by the beam and indirectly monitors the beam intensity. secondary He 3 A emission factor of about 20 is observed for the 3 . 2 Mev beam on the Li 6 target, for the geometrical arrangement of this experiment . With the system aligned and operating, the spectra of the various detectors are inspected on the 100 channel analyzer, and the counter voltages and amplifier gains are adjusted. The scaler biases are set to correspond to definite channels of the 100 channel analyzer spectrum. The f3-single channel discriminator bias is set by observing the cutoff of the f3-spectrum in coincidence with the discriminator output. the various spectra are recorded. Then The recorded spectra include those of (1) the f3-detector, (2) background in the f3-detector found by reversing the target so that the beam hits the bare aluminum , {3) the f3- dete u: tor in coincidence with the single channel discriminator, (4) the monitor detector, (5) the a-detector, and (6) the a-detector with the alimiter pulses going to both inputs of the fast coincidence mixer and its output gating the 100 channel analyzer. The last spectrum, called "a-a -23gate, 11 checks on the proper operation of the fast circuit. These spectra are recorded occasionally throughout each group of data runs and again at the end of the group . Finally coincident data are recorded. Runs of either a definite charge collected on the target or a fixed time are recorded for each angle of the f3-detector. The time of a run is usually about 10 to 20 minutes and about 2 minutes are required to record the scalers and to print out the memory of the 100 channel analyzer. The f3-detector is rotated to a new position while the memory is printing out. of angles in positioning the The order f3-detector is varied frequently throughout a group of runs so that sequential or time-dependent effects do not appear as angle-dependent effects. For part of the three angle data the f3-detector is set in the 90° position twice as often as at the other angles since the error in the coefficient, B, is more dependent on the error in the number of 90° coincidences. In the Lis decay about one out of four runs measures random coincidences from the fast coincidence mixer. For these runs 120' of extra RG-114 / U cable is put in the f3-side of the fast coincidence mixer to delay the f3-pulses beyond the resolving time. For the BS decay random coincidences are neglected b ut an occasional random coincidence run is taken in which zero counts insures the proper operation of the equipment. With the f3-detector at the 0 ° position runs are also taken with the target reversed so that the aluminum backing stops the a-particles which would normally reach the a-detector. The backing only minutely affects the f3-spectrum. In this way a coincident spectrum is obtained from the electrons which produce a small pulse in the a-detector and a normal large pulse in the f3- -24- scintillator. 11 This spectrum is called 0° f3 . 11 Analysis The primary data of the experiment consist of the scaler readings, the non-coincident 100 channel analyzer spectra, and the coincident 100 channel analyzer spectra. A systematic procedure has been adopted to analyze this data. Roughly one day 1 s set of runs is grouped together for the analysis. A group consists of 5 to 10 runs with a total of about 2 x 10 3 B 8 coincidences or 2 x 10 4 Li 8 coincidences at each angle. The coincident a-spectra and the scalar readings of all the runs with the f3-detector at a particular angle are added together. Since there are relatively few counts per channel in the coincident spectra, the channels are grouped together by threes for the analysis. The coincident a-spectra at each angle of the f3-detector are normalized by dividing by the corresponding total number of f3-single channel discriminator output counts. The normalization corrects the number of coincidences for differences in the total amount of Li 8 or B 8 produced in the target, for variations in the f3-detector solid angle or gain, and for some counting rate effects . Normalization in this fashion is right if the solid angle of the a-detector is a constant independent of the position of the f3-detector. This is discussed in the next section. The re- sulting coincident a-spectra are illustrated by figures 8, 9, 10, and 11. 0f3 a = 0° is extrapolated to zero pulse height by sub- The. curve for tracting the 11 0 0 f3 "-spectrum. The 11 0° f3 11 -coincidences are arbitrarily normalized because the usual normalization would produce a negative net number of counts in the 0° spectrum below channel 10. This means that the a-detector is slightly more sensitive to the electrons when the -25- flux of a-particles is not present than when it is . No explanation has yet been discovered for this behavior of the a-detector. In the decay of Li 8 the number of random coincidences from the fast coincidence mixer , NR' is calculated for each data run from the formula: N R -- N where: N 11 a 13 t T 11 = the net time of the run t N a Nf3 ::: the ::; number of counts in the the number of counts in the scaler "T n = the f3-dis c riminator effective resolving time . 11 For each group a best value of all angles of the a - scaler 13-detector. 7' 11 is found from the random runs with 11 is defined by the same NR is known. It is not the true re- Essentially formula from those cases where 11 7' solving time since it depends on the fraction of the whole a-spectrum which is counted by the a-scaler . 11 7 11 i s used to calculate the random coincidences in each data run s _e parately. These number s of random coincidences are summed and normalized in the same way as the real coincident spectra, and subtracted from the totals of the real coincident spectra. 0 The result is a set of three numbers of coincidences, 0 n(0 ), 0 n(90 }, and n(l80 }, or two numbers for those runs where the f3-detector 0 could not also be placed at 0 . The statistical uncertainties of the ran- o dom runs add small contributions to the statistical errors of n(0 }, etc. Other effects which depend on the counting rate are neglected in the analysis of the data. These effects can be categorized as random coinci- -26- dences from the slow coincidence mixer, pile up of pulses in the 13-discriminator, and dead time in the 13-discriminator. They are discussed more fully in the next section. Also all the n.on-coincident spectra of a particular type, such as 13-detector, background in the 13-detector, etc., are added together and plotted. Plots of the and 13. The spectra of the 13-detector in coincidence with the single a,- and 13-spectra are shown in figures 4, 6, 12, channel discriminator are also summed for each group of runs . The sum spectrum is similar to the shaded portion of figure 6 or 13 for the case where Wl3 Wl3 z.. 5 and W l3 z.. 8 Mev, this spectrum consists of the portion from is approx imately 11 Mev. channel 25 to 40 or 40 to 55, respectively. For the cases where In order to estimate the actual average energy of this spectrum, the average channel is first calculated. This is compared to the channe_l corresponding to the half maximum point of the whole 13-spectrum, for example, channel 61. 5 • 8 in figure 6. From the Li 13-spectrum obtained by Hornyak and Lauritsen in a magnetic spectrometer (39, 40), the half maximum point is known to be 9. 5 Mev kinetic energy. in figure 6. Their spectrum is also plotted In the absence of a similar standard for the B 8 spectrum, the corresponding point is considered to be the ratio of end points times 9. 5 Mev,or 10 . 2 Mev. With the assumption of a linear scale, the average channel is easily converted to kinetic energy or total energy with the addition of 1/2 Mev. w z.. 5 and 8 Mev data. 13 Slight corrections are applied to the The accuracy of this procedure is discussed in the next section. At this point, the data has been reduced to the value of Wl3 and -27- either the three numbers 0 0 n(90 ) and n{l80 ) . Li 8 and B 8 n{0°), n(90°), and n(180°) or the two numbers Tables I and II list all of the data in this form for respectively. The number of coincidences are normalized to 200, 000 electrons analyzed by the single channel differential discriminator. The nmnbers are corrected for randoms in the fast coincidence mixer and for the 11 0 0 (3 11 -spectrum due to electrons. The variations in the numbers in a particular column are caused by the variations in the sizes of the various a.-detectors which have been used. The three numbers of coincidences are sufficient to find both coefficients, A and B, of the angular correlation function, W. The number of normalized coincidences at any angle is proportional to the integral of W over the detector solid angles with the detector arrangement at that angle. In the experimental apparatus the f3- and a.- solid angles are fixed by circular apertures of 19° 40' and 9° half angle, respectively. The integration over these solid angles is carried out in Appendix B. There result three equations in three unknowns, where one unknown is a proportionality factor. n(l80°) where £ 1 = 0. 965, f 2 = 0. 932, and f 3 = 0. 034. solved in Appendix C for the coefficients, deviations of A and B A These equations are and B. Also the standard found in terms of the statistical errors of the -28TABLE I Normalized and Corrected Number of Coincidences for Li Group Date No. (1960) 8 wl3 n(90°) n(l80°) (Mev) 27 20 61 ± 18 2286 ± 18 11. 4 2 Feb 27 2013 ± 16 2258 ± 16 11. 1 3 Mar 15 2493 =!= 14 2768 ± 20 11. 1 4 Mar 18 2406 ± 15 2669 ± 1 7 10. 7 1 Feb n{0°) 5 Mar 15 2397 ± 20 2502 ± 21 2813 ± 20 1 o. 7 6 Mar 16 224 7 ± 19 2384 ± 20 2713 ± 20 10.9 7 Mar 18 2239 ± 25 2409 ± 25 2780 ± 20 11. 1 8 Mar 19 2311 ± 3 2 2367 ± 32 2637 ± 32 1 o. 9 9 Apr 28 2660 ± 45 2789 ± 34 3051 ±41 11. 0 10 Jun 25 2305 ± 25 2480 ± 25 2738 ± 27 10.4 11 Jun 28 2341 ± 30 2445 ± 24 2804 ± 31 10. 8 12 Jun . 28 2227 ± 23 2433 ± 22 2744 ± 24 1 0. 5 13 Jun 30 2376 ± 27 2482 ± 23 27 50 ± 29 10, 5 14 Jul 1 237 2 ± 20 2535±15 2791 ± 22 1 o. 4 15 Jul 1 2371 ± 20 2459 ± 14 2664±19 8. 1 16 Jul 22 2341 ± 18 2410 ± 12 2601 ± 16 , 8, 2 1 7 Jul 21 2271 ± 14 2355 ± 10 2469 ± 1 5 5. 8 18 Jul 25 2373 ± 12 2427 ± 2552 ± 12 5. 5 8 -29TABLE II Normalized and Corrected Number of Coincidences for B8 Group Date No. (1960) w/3 n{0°) n{90° n(180°) {Mev) 1 Feb 17 1935 ± 31 1953±30 1 o. 9 2 Feb 28 1848 ± 42 1949 ± 44 11. 0 3 Feb 29 1854 ± 39 1986±39 11. 2 4 Feb 29 1790 ± 33 1942±35 10.8 5 Mar 1 1848 ± 30 1943 ± 31 10. 7 6 May 4 1820 ± 47 2003 ± 45 2213 ± 50 11. 9 7 May 5 1866 ± 42 2127 ± 40 2287 ± 46 11. 6 8 Jun 3 2079 ± 45 2394 ± 45 2564 ± 53 1 o. 9 9 Jun 4 2090 ± 56 2456 ± 56 2536 ± 63 11. 1 10 Jun 4 2095 ± 53 2469 ± 56 2487 ± 66 11. 1 11 Jul 15 2148 ± 53 2413 ± 39 2554 ± 60 11. 4 12 Jul 17 2031 ± 42 2381 ± 29 2485 ± 48 1 o. 6 13 Jul 19 2089 ± 40 2426 ± 32 2547 ± 43 10.6 -30- numbers of coincidences. 0 B= 0 0 n(O ) + n(l80 ) - 2n(90 ) .6.B = For each group of runs with data at all three angles, the quantities, A, B, .6.A, and .6.B, are calculated with these formulas. For the groups of runs with data at only two angles, only the quantity, B - A, may be calculated. B Therefore, these groups are analyzed for average value of A from the three angle data. case are the following: by using the The formulas in this -31- Results The coefficients, A W l3 in order to and B, are both divided by average together the several groups of data and for comparison with theory. Although the theoretical predictions are that A is proportional to the 13-momentum, proximation, p, and B 2 is proportional to p /Wl3' the ap- Wl3 = p, is adequate for these purposes since it is ac- curate to within 1/2% even at the coefficients, Wp = 5 Mev. In the averaging procedure A/w and B/w , are weighted with the inverse square 13 13 of the statistical error. Possible systematic errors are not considered in the averaging procedure. The results from the three angle data are listed in the top entries of table III. The two angle data are analyzed with the assumption that A= (-0. 0087)w , as indicated by the three angle data. 13 The weighted averages are listed in the middle entries of table III. Attempts to take data in the B 8 decay at lower 13-energies are frustrated · by the large amount of background which is present in the 13-spectrum, as is evident in figure 13. This background makes the nor- malization procedure unreliable at the lower energies. The possibility of allowing coincidences over the lower energy portion of the 13-spectrum but normalizing to the high energy portion was considered but was discarded as unreliable. of the Li 8 and B 8 The best values for comparing the difference beta decays of the coefficient, B/w , are the 13 weighted averages of the three angle and the two angle data with Mev. W l3:::. 11 These are listed in the bottom entries of table III. Also the clif8 8 ) - B(B ) = W o , is . given. · N o val'd · · h f erence, B(Li W i comparison wit the B 8 13 13 8 data can be made of the lower energy Li data. -3 2- TABLE III Weighted Averages of the Coefficients, wf3 (Mev) A/Wf3 and B/Wf3 Coefficient Weighted Average Statistical Error A/Wf3 -0.0073 ±0.0006 B/Wf3 o. 00 23 ±0.0008 A/Wf3 -0.0072 ± 0.0006 B / Wf3 0.0033 ±0.0008 A / Wf3 -0.0087 ±0.0002 B/Wf3 0.0034 ±0.0004 A/Wf3 -0.0088 ±0.0005 B / Wf3 -0.0039 ±0.0008 11 B/W • f3 0.0020 ±0.0006 4 11 B/Wf3 - 0.0044 ±0.0012 5 11 B / Wf3 o. 0029 ± 0.0003 14 B8 11 B/Wf3 -0.0040 ± 0.0007 13 8 8 Li -B 11 o/Wf3 0.0069 ±0.0008 Beta Decay Li Li Li 8 8 8 B8 Li 8 B8 Li 8 5 2 2 8 11 11 Number of Groups 10 8 -33- A histogram of all the results is given in figure 14. For com- parison purposes, normal distribution curves are drawn with the averages of the where n Wf3:::::.. 11 Mev data. The widths are equal to /n6., is the number of groups and 6. of the weighted mean. is the standard deviation The histograms of the Li Wf3 :::::. 5 and 8 Mev groups. 8 data also contain Also some data which may be inaccurate because of known faulty operation of the equipment or other known reasons has been included in the histogram but not in the averaging procedure. The f3-a. angular correlation of the beta decay of Li 8 has been . 2 studied for asymmetries of the cos 0f3a form by other workers. In general they have not obtained data with comparable statistical accuracy. In 1953 D. StP. Bunbury measured the correlation with a pro- portional counter and f3-spectrometer (41). He found the asymmetiries: {0.004 ± 0,020)Wf3 for Wf3 = 9. 8 Mev (0. 016 ± o. 012) W f3 for Wf3 = 7. 5 Mev Since he does not mention compensation for the cos 0p_ ,-,a term and he . 0 only took data for angles greater than 90 , these results are probably equivalent to the difference, B - A, in this experiment. In 1954 S. S. Hanna, E. C. La Vier, and C. M. Class measured the correlation with scintillation detectors (42). They made measurements at 0f3a, and rr - 0f3a. in order to compensate for the result is; B = {0. 002 ± 0. 006)Wf3' cos 0f3a term. Their average - 34- with the assumption of an average energy of about 6 Mev. In 1959 K. Krebs, H. Riesenberg, and V . Soergel measured the correlation with a proportional counter and a ment measures 13-spectrometer (43). Their experi- B - A and they correct for A with its first order theoretical form in order to find B. The results are: + o. 0029 B = (0. 0 0 5 7 _ O. OOl 9 ) Wl3 for Wl3 = 7. 0 Mev B = (0 0054 + O. 00 74 ) W • - o. 0066 13 for Wl3 = 3 . 5 Mev These results, although less accurate, are generally consistent with the present experiment and all give a positive sign of the coefficient, B, for the Li 8 correlation. -35- IV. DISCUSSION Since the statistical errors of the coefficients, A and B , are less than (0. 001) W l3 :::::. 0. 01, it is imperative to consider effects of similar size in the data arising from the apparatus or method of analysis . . These can be subdivided into effects associated with the !3- spectrum, with the a-spectrum, with counting rate, and with symmetry. /3-Spectrum The coefficients are divided by W l3 in order to average the groups together and to compare the results with theory. some estimate of the accuracy of W 13 , or in other words of the cali- bration of the /3-spectrum, is called for. the Therefore, As described previously, /3-detector is a plastic scintillator and does not have particularly good re~rnlution for y-rays. Mev y-ray from ThC 11 • Figure 7 shows the spectrum of the 2. 6- There is no particularly sharp feature of this curve which "a priori" can be associated with the energy, 2. 6 Mev. A calibration accuracy of only about 10% can be expected from this spectrum. Therefore the by comparison with the Li /3-spectrum itself is used as the calibration 8 /3-spectrum measured by Hornyak and Lauritsen in a magnetic spectrometer (39, 40) . A convenient calibra- tion point is the upper half maximum point, which occurs at an energy of 9. 5 Mev kinetic energy on their curve. The spectrum from the !3- spectrometer is compared to one from the scintillation counter in figure 6. The experimental and standard curves are normalized to have the same area and the half maximum points have the same abscissa . For the B 8 spectrum, the half max imum energy is considered to be -36- 9. 5 Mev times the ratio of the end points, or 10. 2 Mev. {The end points ,., 8 for production of 2. 90 Mev excitation energy in Be ,, are used.) Negligible distortion of the shape arises from Coulomb corrections at these high /3-energies. Vedder has measured both the Li 8 and B 8 spectra and finds both half maximum points about 3% lower in energy (44). In the analysis of the data, the average /3-energy of the spectrum passed by the single channel discriminator is found by the comparison with the point of half maximum. For the cases where Mev, the discriminator passes all pulses above a fixed height. (See figure 6 or 13.) In these cases an ind~pendent but approximate procedure is available to calculate the average energy from the number of pulses above the fixed height and also the total number. If one as- sumes an allowed fermi spectral shape of known end point and a one-toone correspondence of pulse height to energy, there is a definite, calculable energy associated with the fraction of pulses in the upper end of the spectrum. In several cases the mean energies have been calcu- lated by both methods and on the averages are equal within 4%. differences are not always in the same direction. The From a similar comparison with the integral of the Hornyak and Lauritsen curve, the average energy may also be found and again agrees within about 4%, but this method is not completely independent of the first. From these comparisons it is estimated that the systematic error in W /3 is less than 5% for the high energy groups, when the energy is calculated by the procedure used in the analysis of the data. The correspondence between the standard and experimental -37- curves of figure 6 is not unreasonable, but there is a definite difference of slope in the upper portion. To try to account for this differ- ence in shape, and also to try to estimate the number of small pulses originating from high energy electrons, an attempt has been made to fold in the resolution function of the plastic scintillator. It is assumed that the scintillator used in the equipment has the same resolution function as a different · 2" x 3" plastic scintillator. Figure 15 shows the response of the latter scintillator to 7 . 1 Mev monoenergetic electrons as obtained by Dr . H. Hilton and Dr . V. Soergel in a meter (45). 13-spectro- This and similar curves at other energies are approxi- mated by the triangular areas shown in the figure. A graphical analysis has been made by dividing the standard spectrum into 1/ 2 Mev intervals and for each interval plotting a curve like that of figure 15 of equal area. The smoothed over sum spectrum is shown in figure 16 along with the experimental and standard spectra. height as the standard. It is normalized to the same peak As seen in this figure, the derived curve has nearly the shape of the experimental curve in the upper energy region. The important feature is that the half maximum point of the derived curve is very nearly equal to that of the standard, which would indicate the calibration procedure is valid. The shape at lower pulse height indicates an excess number of counts. From a similar graphical analysis, the contamination of the 5 and 8 Mev groups by higher energy electrons is determined. The result is to raise the average energies of these groups by 15% and 5%, respectively. Since the derived spectrum contains too many low pulses to fit the experimental spectrum, this may be an over estimate. Therefore, -38- the data are analyzed with energies corrected by 10% and 5%, respectively. The limits of systematic error for these cases can reasonably be set at 10%, but this is not as important as in the cases of the higher f3-energy groups since the statistical accuracy oi the data is poorer. An improved f3-detector system could have been achieved with the use of an anticoincidence scintillator around the f3-detector scintillator. This would prevent the counting of electrons which scatter out of the scintillator and also would cut the background rate . a-Spectrum The accuracy of the integration over the whole coincident a.spectrum is pas sibly the severest limitation on the accuracy of the results. This problem arises from two intrinsic features of the Be 8 >:< breakup and one feature of the experimental arrangement: the 2. 90 Mev state is quite broad, the energy distribution of the a-particles changes with angle, and the a-particles lose some energy in the target and dead layers on the detectors. The fact that the a-particles lose some energy in the target is the most serious because this energy loss is different for the B 8 decays. Li 8 and The spectra from an infinitesimally thin target would con- tain essentially no a-particles below about 1/ 2 Mev and there would be little difficulty in detecting all energies with 100% efficiency. or Li 8 The B 8 ions recoil into the target backing from the momentum of the incident 3. 2-Mev He 3 beam or the 0. 7 5-Mev d beam. Therefore, the a-particles must lose some energy in travelling back out of the target. The mean recoil energies are approximately : x 0. 95 Mev for B 8 and 8 9 2 x '1 x 0. 75 Mev = 0.15 Mev for ~ x 3. 2 Mev = .8 L1. Since -39- the beam enters at 15 0 • 0 to the target and the a.-particles leave at 45 , the a-particles must penetrate a distance corresponding to the range of the 0 . 95 Mev B 8 ions or the 0 . 15 Mev Li sin 15° / sin 45° = 0. 36. 8 ions times the quantity, Although the a-particle energy loss depends on the energy, the energy loss is approximately 100 to 300 kev for the B 8 decay and 0 to 50 kev for the Li 8 decay. In the first part of the e x periment there was even a greater lo.ss since the target was at a 30° angle to the beam and the a-dete .e tor may have had a dead layer on the surface during the measurements of the B 8 correlation . Figure 17 shows a comparison of the 90 ° coincident spectra of the first and second parts of the experiment. The second spectrum has been greatly improved by placing the target at 15° to the beam and protecting the detector during the beam alignment procedure. a.- However, even in the second part of the experiment the spectrum e x tends down to zero pulse height because of the energy losses and the limited resolution of the a.- detectors. The change in the energy distribution of the a-particles with the angle of the f3-detector stems from the recoil of the from the beta decay . Be 8* nucleus The electron-neutrino correlation has been in- directly measured from this effect and shows that the form of the interaction for the Li 8 decay is a x ial vector (13, 46). The effect prevents one from using a fi x ed lower cutoff of the a-spectrum because the fraction of the total counts above the cutoff is dependent on the angle . Therefore in this experiment the entire a-spectrum is recorded o n the 100 channel analyzer . Nevertheless, the problem still exists of recognizing an elec- -40- tronic cutoff of the a-spectrum at low pulse heights. The problem is aggravated by noise produced in the silicon detector which causes an increase in the spectrum at low pulse heights, as in figures 4 and 12. This noise is not passed by the a.-a. coincidence gate because the fre- quency of the noise spectrum is generally much lower than that required by the 80 mµsec. fast resolving time. Yet it is the fast coincidence mixer that is most suspect as producing an electronic cutoff. methods have been used to test the coincidence mixer. Several The spectrum of a pulser in place of the a-detector can be displayed on the 100 channel analyzer. With the a.-a. gate, the pulser registers down to channel 8 with about 100% efficiency and counts below that with reduced efficiency. Full limiting occurs for pulses larger than channel 12. A criticism might be offered that the pulser produces better shaped pulses than the a-detector, and therefore these are detected more easily by the coincidence mixer. However, no difference can be seen in the shape of large pulses from the a-detector and pulser. The shape of the small pulses from the a-detector cannot be seen accurately because of the great number of larger pulses. On the other hand, the a-a gate system may be a too stringent test of small pulse performance because it requires . the coincidence mixer to sense two small pulses, whereas in the actual experiment the 13-pulses are all fully limited. Another check has been made by reducing the a-detector output by shunting it with a small capacitor. Then the a-spectrum with the a-a gate is recorded and the gain of the fast amplifiers lowered. A factor of two lowering in gain is needed to reduce appreciably the coincidences 1n channel 10. Thus with reasonable certainty, the system can -41- be considered 100% efficient down to channel 10 under normal operating conditions. Less than 1% of the total counts of the 90° and 180° curves are of smaller pulse height. region. However the 0 0 About 2% of the 0 ° curves lie in this curve is complicated by the fact that some electrons passing through the a-detector produce small pulses. These small pulses from the a-detector are naturally in coincidence with the f3-detector output. tracted from the 0 Therefore the small uo f3 "-spectrum must be sub0° curve. The "0°f3 11 -spectrum is arbitrarily adjusted in size because normalization by the usual procedure consistently produces a negative number in the subtraction. 11 0 0 f3"-spectrum and the shapes of the 90 extrapolate the 0 0 0 The general shape of the and 180 0 curves are used to spectrum to zero pulse height. The error in the coefficient, B, associated with this extrapola- tion is in the same direction for both Li 8 8 and B . Thus the differ- ence, 6, should be less susceptible to this extrapolation. The three angle data with W f3 ::::::. 11 Mev has been treated as two angle data in an attempt to estimate the possible errors involved. B for Li 8 (0. 0005)Wf3 increases by (0. 0003) Wf3 The result is that and B for B 8 increases by giving only a net decrease in 6 of (0 . 0002)Wf3. The fact that two different coincidence mixer and limiter systems have been used with no noticeable change in results is also an indication that the low energy portions of the a-spectra are reliable. The data taken with Li 8 f3-energies of ~5 and ~s Mev are much less susceptible to error in the extrapolation to zero pulse height 8 >:< because the Be these cases. recoil is less. Figures 8 and 9 show the spectra in They also show an interesting change in shape at the high -42- energy portion of the spectrum. Figure 18 shows a comparison of the 90° data at all three energies normalized to the same area. As seen in this figure, the high energy region of the a-spectrum in coincidence with electrons of ~11 Mevis much lower. conservation of energy. cles is 16. 1 Mev. This can be explained by the The mass difference of Li 8 and two a-parti- If the electron is required to take 10 or more Mev there is left 6 or less Mev to be shared between the two a-particles and neutrino. spectrum. Thus there should be a cutoff at about 3 Mev in the a.- On the other hand, 5 Mevis less energy than the average of the whole [)-spectrum and so one expects a higher than average number of counts at the high energy portion of the corresponding a.spectrum. The ~3 Mev a-energy cutoff associated with the ~11 Mev [3-group does have the advantage of few counts over channel 100. For part of the runs the counts have been summed from channel 100 to 120 and stored in channel O of the analyzer. carded. Above this the counts are dis- For the rest of the ~11 Mev runs and all of the ~s and ~3 Mev runs the counts are summed up to channel 160. For the ~11 Mev data the extension to channel 160 adds less than 1% to the number of coincidences and the error in A is less than (0. 000l}Wf3. or B from neglecting these counts For the lower [)-energies, 8 to 12% of the total number of counts are over channel 100, which makes the extension to channel i60 imperative. The a.-spectra of random coincidences do not show the high energy cutoff which is evident in the coincident a-spectra. Figure 19 represents the sum of several groups of random coincident spectra from the data with W f3.:;:;, 11 Mev. The coincident curve of figure 10 and -43- the non-coincident curve of figure 4 are drawn for comparison. random coincidences fit the non-coincident curve. The This is to be expected because random coincidences are caused by the association of an electron from one Li 8 beta decay with an a.-particle from another, unre- lated decay. Counting Rate Effects Effects associated with the counting rate are appreciable only for the Li 8 decay since for the B ten times smaller. 8 decay the counting rate is at least The major effect is that of random coincidences in the fast coincidence mixer. These random coincidences are experi- mentally measured and subtracted from the real coincidences for the Li 8 measurements as discussed previously, but other effects are neg- lected. For the B 8 measurements all counting rate effects are neg- lected. The other effects dependent on counting rate are (1) random coincidences in the slow coincidence mixer, (2) pile up of pulses into the discriminator, and (3) dead time in the f3-discriminator circuit. 13- All three sources are present in the measurement of coincidences, while the last two are also present in the measurements of the electron counts to which the coincidences are normalized. These effects can be ex- pressed in the following equation for the ratio of real coincidences to non-coincident electrons of the correct energy: N (true) C = Nf3 (true) Nc(measured)[l-(RCS)-(PUP)+(DTL)] - NR Nf3 {measured)l 1-(PUP) 1 + (DTL) 'J -44- N (true) C N C (measured) Nl3 (measured) [ 1 - (RCS) - (PUP) +(PUP)' + (DTL) - (DTL) '] - Nl3 {measured) where: (RCS) = Random Coincidences in the Slow coincidence mixer, expressed as a fraction of the real coincidences (PUP) = Pile Up of two Pulses into the 13-discriminator, one of which isalso in fast coincidence with an a-particle (DTL) = Dead Time Losses of coincidences because the fj-discriminator did not have sufficient time to recover from a previous pulse {PUP)'= Pile Up of two Pulses into the 13-discriminator, expressed as a fraction of the non-coincident electrons of correct energy. In this case neither pulse must be in coincidence with an a-particle (DTL) 1 = Dead Time Losses of non-coincident electrons because of dead time in the 13-discriminator circuit = Number of random coincidences from the fast coincidence mixer (not a fraction) The fractional dead time losses are necessarily equal (and thus cancel) for the coincidences and normalization numbers since the dead time is caused by the same group of pulses in the same circuit. Frac- tional pile up can be slightly different in the two cases since the fast coincidence requirement imposes additional restrictions on some of the pulses, but they approximately cancel. For the case of w ~ n Mev, estimates of these fractions have 13 been developed from the experimental parameters ( 7' s = L 2 µs e c . , -45- 7'DT::: 6 µsec., Nf3::: 1000 per sec.) and approximations to the f3-spec- trum and f3-pulse shape (the spectrum is assumed trapezoidal and the pulse shape is assumed a pure exponential with 1 µsec. decay constant). The results are the following: = 0.006 {PUP) = 0.030 -(PUP) = -0. 032 -{DTL) = - 0.006 (DTL) = 0..006 (RCS) I I 0.004 Since NR is about O. 03 times Nc' the neglected effects, {RCS), etc. , add up to less than 20% of the measured randoms . However, neg- lecting these effects can also be justified for another reason. The reason is that the fractions, {RCS), etc., are only depe_n dent on counting rate and thus, the numbers of spurious coincidences, have the same angular dependence as the number, N C alone. N x (RCS), etc. , C On the other hand, NR' is only dependent on counting rate and thus, the angu- lar dependenee of NR is isotropic. This means that for a fixed counting rate, ignoring the effects, (RCS), etc., would have no effect on the measurements of the angular correlation of Nc' whereas ignoring NR would make the angular correlation of N C . tropic than it actually is. appear more nearly iso- Of course in the experimental measurements, the counting rate is not fixed but the variations with angle of the f3detector in general are less than 5%. The smallness of these effects does not justify a detailed estimate for the cases with W f3::::.. 5 Mev or 8 Mev. Qualitatively, it can be seen that {RCS) would remain about the same for the same counting rate, {PUP) -46- would decrease, and (DTL) would increase . about the same as for the case with The net result would be W ~ ==- 11 Mev so that corrections for only the measured numbers of random coincidences is quite adequate. Second order effects such as a simultaneous random coincidence in both slow and fast coincidence mixers are truly negligible. Also the dead time of the 100 channel analyzer produces a negligible effect (N C ==-10 per sec., T ==- 50 µsec.). Pile up of two a-particle pulses during the time scale of the slow coincidence mixer may exist, but would not add nor subtract from the recorded number of coincidences. However, it could produce a slight distortion of the coincident a-spectrum. Symmetry of the Counting Arrangement Symmetry conditions are of prime importance in this experiment. Four sources of asymmetry may be present: (1) variation in the number of scattered electrons with angle, (2) variation in the detector gain with angle, or B 8 ~- ions recoiling out of the target and decaying on the walls of the target chamber, and (4) variation in the a-detector solid angle with the position of the ~-detector. The first source has been minimized by the design of the target chamber. It should be negligible, especially for the 11-Mev electrons. Electrons which scatter out of the solid angle of the ~-detector do not affect the results. The second source of asymmetry would arise from the sensitivity of the photomultiplier . to stray magnetic fields. been checked with the the ~ -detector ThC" y-ray source. The gain has The source is fastened to and the number of counts above a fixed bias is recorded -47- as the detector assembly is rotated. The bias is equivalent to about channel 65 in figure 7, so that a small change in gain shows up as a larger change in the number of counts. With the beam analyzing magnet turned on, the variation in the number of counts with angle is less than 1/ 2%. Also with the detector in a fixed position, the varia- tion in counts is less than 1/2% while turning the magnet off and on. These measurements would indicate that the systematic change in gain with angle is negligible for the purposes of the experiment. Any effects on the number of counts because of gain changes are compensated by the normalization procedure. The third source of asymmetry, L 1.8 or B8 ions recoiling out of the target, makes the target shield a nee es sity. the cone of recoiling Li 8 target at 15° some of the B 8 ions do not. These ions is 33° , of the Li Li 8 8 B 8 The half angle of ions 8° . With the ions recoil out of the target while the ions are caught by the target shield which drops into its lead container during the counting period. To test this system, the target is fastened to the shield and the ratio of electrons detected with the shield moving up and down in its normal cycle to the number of electrons with the shield always up is measured. This ratio is about O. 1%, and there is small variation in the ratio with the angle of the 13-detector. This indicates that the shield is completely effective in catching the escaping Li 8 ions. The fourth point, variation in the a-detector solid angle, is potentially the most serious . A variation in solid angle could occur if the weight of the 13-detector assembly warped the table enough to cause a change in relative position of a-detector and target or of the beam -48- position and target. Mounting the target and a-detector in the same mount should reduce the chance · of relative motion between them and evaporating the lithium targets in the form of a narrow strip should reduce the possibility of motion of the target spot caused by lateral motion of the beam . The purpose of the monitor counter, which in part of the experiment is an electron detector and in the other part is an a-particle detector, is to check on this point. From the ratio of its counts to the non-coincident a-particles the solid angle of the a.detector varies on the average less than 0 . 2%. This would indicate that the a-detector solid angle is suitably constant, and that the correct procedure is to normalize the coincidences by the number of electrons analyzed by the experiment. i3-discriminator, as has been done in the There is one indication that signifies that the system is slightly asymmetrical. The difference in the Li 8 and B 8 cases of the variation with angle of the ratio of a-particles to electrons analyzed by the differential discriminator averages over all groups to about 0. 01. This means that .the final result for (0. 001) Wr'3 6 would be decreased by about if the coincidences were normalized to the single a-particle counts instead of to the electron counts. However, the i3-detector can have a different efficiency at the different angles for various reasons. For example, the dummy a-detectors may be slightly different in thickness or the target may not be exactly on the axis of rotation of the r'3detector . If the a-dete.ctor solid angle is constant, the normalization procedure compensates the data for changes in the i3-detector efficiency. -49- Discussion of Results The sources· of systematic error discussed above must be quantitatively estimated in a form compatible with the stated statistical errors, in order to evaluate the overall reliability of the results, and especially o. of the quantity, Although this is a somewhat arbitrary procedure, table IV lists estimates of the limits of possible errors associated with (1) statistics, (2) calibration of the f3-spectrum, {3) integration over the a.-spectrum, (4) counting rate effects, and (5) symmetry conditions. The column marked "RMS Sum" is the square root of the sum of the squares of the numbered columns. In the cases where W i3:::::. 11 Mev, a significant number of groups of data are averaged together to give the final results. The groups are illustrated in the histogram of figure 14. It is instructive to compare the experimental RMS deviation of these groups with the other errors.. The RMS deviation of the mea:p., found by weighting the data samples in the same way as they are weighted to calculate the mean, is given in the column marked "Exp. RMS. " The numbers in this column are very nearly equal to the statistical errors alon.e . This is an indica- tion that the systematic errors are relatively constant for all groups of data or that the systematic errors average out to zero over the number of runs in a group. In the previous sections, the angular correlation has been discussed in its general form: where A and B are functions of the momentum of the a-particle and electron. The actual functional dependence of A ~or B contains terms 8 11 11 11 8 8 Li Li Li BB 8 8 Li -B 6/Wf:i 0.0069 -0.0040 0.0007 0.0008 0.0007 0.0005 0.0003 -0.0088 A/Wf:i B/Wf:> 0.0003 0.0003 0.0002 0.0029 -0.0087 A/Wfj 0.0008 B/Wf:> 0.0033 B/Wf:i 0.0006 -0.0072 A/Wfj 0.0006 ( 1) 0.0008 0.0003 Exp. RMS o. 0023 -0.0073 Exp. Result B/Wf:> A/Wf:i Coe£ficient 0.0004 0.0002 0.0005 0.0002 0.0004 0.0004 0.0008 0.0004 0.0008 ( 2) 0.0003 0.0004 0.0004 0.0003 0.0003 0.0002 0.0002 0.0001 0.0006 0.0004 0.0004 -- -- 0.0002 0.0002 0.0003 0.0003 0.0004 0.0004 ( 5) 0,0001 0.0001 0,0001 0.0001 0.0001 0.0001 0.0001 0.0001 (4) (3) For detailed description of the various errors listed, see accompanying text. 5 8 ,:, wf:> (Mev) Beta Decay ,:, and B/Wfj Errors Estimates of Errors of the Coefficients, A/W f:i TABLE IV 0.0011 0.0009 0.0009 0.0005 0.0006 0.0010 o. 0011 0.0010 0 . 0011 RMS Sum I u, I 0 -51- arising from kinematic considerations of the transformation from the * Be ~ rest system to the laboratory system and from interference of forbidden transition matrix elements with the allowed axial vector matrix element. The complete transformation has been carried to second order in the electron momentum. in Appendix D. A description of the transformation is given This transformation was first worked out by F . B. Morinigo after B . Stech and J . Eichler {47) pointed out the form employed in the reduction of the data for the first part of the experiment was inaccurate . Only the interference terms of interest with respect to the C. V. C. theory are included in the correlation. The result from Appendix D is: 1 0 3 2 1 0 :: 1 - [(p<- (90 )> + 2 ap K-p (90 )>] c o s 0Ra Pa a ~ 5 2 + [ap + 13P 1 o ~ 2 <p (90 ) > J cos 0~a Q, where a is the quantity defined in the introduction which is enhanced in the C . V. C . theory relative to the Fermi theory . the Li 8 and B 8 decays. It changes sign in If the terms arising from interference of forbidden axial vector with allowed a x ial vecto r matrix elements were included, they would be similar to the terms with the quantity, a, but would not change sign (21) . Including all such terms into the completely I unknown quantities, b the coefficients, and B, are the following : A and b , and with the approximation, A= - [ < - l Pa B = 3 ap) + b ] WR (90 o ) > {l + 2 [a + ~ p ~ <fa (90°) > 2 + b 1] W~ W~ .:::::. p, -52- and therefore, Since the quantity, o, is a difference, all of the small terms which do not change sign in the two decays cancel. calculation {27) of the quantity, Weidenmuller' s o, shows that it is given in the two theories of beta decay by: p Fermi theory C. V. C. theory o = 0.012 <11 +4.70"1> <IO"I> 2 p 2 where < 11 I> and < 10" I> are dimensionless matrix elements of the orbital angular momentum and spin. With Weidenmuller 's quantitative limits for these matrix elements the predictions are: Fermi theory , (0. 001) Wl3 < o < (0. 004) Wl3 C. V. C. theory (0. 005) w < o < (0. 009) w 13 The experimental result, C. V. C. theory. 13 o = (0. 0069 ± O. 0011) W!3' definitely favors the Even if all the estimates of systematic errors happened to be in the same direction, the estimated total error would be ((±0. 0022)~!3" and the result would still slightly favor the C . V. C. theory. However, it must be emphasized that the theoretical predictions depend on a calculation of the analogous model. this Ml y-ray transition by an intermediate coupling It clearly would be advantageous to determine experimentally y-ray transition rate. If the C. V. C . theory is assumed valid, the -53- present experiment predicts a width, r '{ (Ml) = (1. 9 ± 0. 6) ev. Although the errors of the experimental results are about the same size as the second order terms of the theoretical forms for A and B, a comparison may give some indication of the size of the terms arising from interference of forbidden axial vector with allowed axial vector matrix elements, Frqm a previous magnetic analysis of the a.- spectrum by C. A. Barnes, et al (13), the average of the reciprocal = of the a-momentum is calculated to be < _l_ (90°)> 0, 0093 ( Mev ) -l Pa c for a 13-energy about 11 Mev. This times (-)Wl3 is the leading term in (-0. 0093) w . 13 Pa The second order term, [- ~ ap < :a {90°)>] W13' changes sign in the two decays. is (-0. 0005)Wl3 . for For p = 11 Mev /c Li 8 and a and (+ 0. 0005)Wl3 for ical values are A = (-0. 0098-b) Wl3 for 8 B . .E.... , A = Therefore, to first order in the theoretical form of A. Li 8 =0. 003 5, this term 8 B . Thus, the theoret- and A = (-0 . 0088- b) W l3 for These are to be compared with experimental values of A= (-0.. 0087 ± 0. 0006)Wl3 for Li 8 and A= (-0. 0088 ± 0, 0009)Wl3 for 8 B . The experimental errors are about the same size as the expected difference between the two determinations of A. would indicate that b is about Using an average value -0. 0005. The first order term in the theoretical expression for B quantity, a W l3' which is. the major point of the experiment. is the The second order term, [ 5 p < - 1 (90 o ) > 2] WA• equals ( +0. 0006) Wl3 for p = 11 Mev / c. 8 Pa 1--' 8 8 One half of the sum of the theoretical expressions for the B and Li I cases is equal to the second order terms, (+ 0, 0006 + b )W . 13 One half of the sum of the experimental measurements, B = (0. 0029 ± 0. 0005) Wl3 for Li 8 8 and B = (-0. 0040 ± 0. 0009)Wl3 for B , is equal to {-0. 0005)Wl3. -54This would indicate b measuring the 1 is about -0. 001. V-A interference Thus, the experiment, besides (a), suggests that A-A interference I (b or b ) is present but is smaller. In the cases of the Li 8 data with the lower f3-energies, the theoretical value of the coefficient, A, is slightly smaller because of the change in the shape of the a-spectrum, and resulting change in value 1 of <-- {90°) >. The changes in the spectra are illustrated fo figure 18. Pa A numerical integration of J_ over these spectra give the results, Pa < {90°) > 0. 0083 { ~ev)-l for WP..:::::. 5 Mev and < - 1- (90°)> = 0. 0088 f = Pa, t-' < _l (900)> = 0. 0093 (Mev fl ( i.fev ) -1 for Wf3.:::::. 8 Mev, based on the value, C for w 13 .: : :. 11 Mev. p a, The experimental results for C A are both smaller than the values predicted by the theoretical forms using the above results for 1 < - - (90°) >. The experimental results are A Pa, = (-0. 0073 ± 0. 0011) WP. for t-' w13 .: : :. 5 Mev and A= (-0. 0072 ± 0. 00ll)W/3 for w .: : :. 8 Mev. 13 While the differences of these results from the theoretical values are statistically not very significant, they again are an indication of the term, order b, of -0. 001. The main reason for taking data at the various show that the coefficient, B, is linear in energy, f3-energies is to Wf3. The experimen- tal results do show this within the experimental errors. B ::: (0. 0023 ± 0. 0010) W f3 for Wf3.:::::. 5 Mev = (0. 0033 ± 0. 0010) Wf3 for Wf3.:::::. 8 Mev B = (0. 0029 ± 0. 0005) Wf3 for Wf3.:::::. 11 Mev B This checks that the measurement is of the quantity, is independent of energy. aw13, since a The size of the experimental errors does -55not warrant any statement about the second order terms in the theoretical form of B at the lower 13-energies. To improve the accuracy of the present experiment would require redesign of the experiment in almost every detail, in view of the comparable size of the various estimated systematic errors. cular run the statistics are the major source of error. For any parti- However , when many runs are averaged together, the other effects become relatively more important. more data. The statistical error can be improved only by taking The energy calibration of the /3 .- spectrum possibly could be improved by a more elaborate scintillation counter and certainly by use of a 13-spectrometer. Ideally the integration over the a.-spectrum ~ould be no problem if a really thin target could be made, and noiseless, electron insensitive a.-detectors were available.. Counting rate effects already are small but can be reduced to any desired degree by slower counting rates. Symmetry is possibly the hardest point to improve and is also very difficult to check. It may be that with a thin enough target, the a.-detector could be rotated relative to a fixed 13-detector to achieve more nearly symmetrical conditions. Most of the suggested improve- ments would require a sacrifice of counting rate, which in the present experiment is already rather low. -56- APPENDIX A Semiconductor Surface Barrier Detectors ( 35- 38, 48-54) The operation of a semiconductor detector is based on the creation of electron-hole ion pairs in the semiconductor by an energetic charged particle. In an applied field these ion pairs are free to drift and they result in a sudden charge at the contacts of the detector after the passage of the particle. The detectors' usefulness arises from the facts (1) that the regfon of applied field is thick enough to stop particles of a few Mev, (2) that the output charge is linearly dependent on the particle energy, ( 3) that the output pulse rise time is of the order of one :mµ sec.~ and ( 4) that the nu,mber of ion pairs created is of an order of magnitude greater than the number in a gas ionization chamber. For the generation of the high field region two techniques are available: surface barriers and diffused p-n junctions. Both silicon and germanium are used to con- struct detectors of large sensitive areas. Germanium detectors must be cooled to near liquid nitrogen temperature while silicon detectors operate 0 well at temperatures up to at least 45 C. The present experiment was performed with gold-silicon surface barrier detectors but both gold-silicon and gold-germanium detectors have been constructed and tested. This Appendix outlines the general properties of semiconductor detectors. compares measurement with theory, and describes the steps in their construction. The particles to be detected enter the surface barrier detector after passing through the thin gold surface contact. This gold layer is deposited by evaporation and can be made thin enough (less than O. 1 -57- micron) so that a negligible amount of energy is lost in it. In n-type material the particle-sensitive depletion layer is formed by biasing the gold surface negative with respect to the bulk material. If its range is less than the thickness of the depletion layer, a particle of ener,gy, ,E, produces a charge, Q, on the contacts, where Q = eE / E. e is the electron charge and E is the mean energy required to create an electron-hole pair. The effective value of E in silicon and germanium has been measured with 5. 3 Mev a-particles. as a function of the applied bias voltage. It is plotted in figure 20 For a bias above a certain voltage the depletion layer thickness is greater than the range of the aparticles and negligible recombination of the electron-hole pairs occurs. In this region E • is constant, and is measured to be 3. 0 ev for ger- manium and 3. 8 ev for silicon with estimated errors of 5%. values are 3. 0 ev and 3. 6 ev (54). The accepted Experimentally it has been shown that E is independent of the value of dE / dx for the particle, even for particles of extremely different dE/dx such as fission fragments and electrons (54). The result of E being constant is that the output pulse height is proportional to the incident energy. Figure 21 shows the general form of results obtained with various silicon detectors for protons and a-particles. For a particle energy up to the point where its range equals the depletion layer depth the curve is linear. The pulse height shows a fur- ther increase as the range exceeds the depletion layer depth because of diffusion of the electron-hole pairs in the bulk semiconductor back to the high field depletion layer. This portion of the curve is sensitive to the decay time of the electronic circuitry since the diffusion is a relatively slow process. Above a certain energy the pulse height falls because of -58- the decreasing stopping f?Ower with increasing energy. Two properties of interest, the thickness of the depletion layer and the capacitance of the surface barrier detector, are s.atisfactorily described by a theory devised by W. Schottky (55, 56, 57, 35 ). Because the surface and bulk fermi levels must adjust to the same level, the surface charge is compensated by a region of opposite charge extending into the semiconductor. This region is called the depletion layer since it is devoid of free electrons and is thus left with a net density of charged donor impurities. The thickness of the depletion layer, 2KE x= { 1/2 o) ~ { ;1, 'i's + V) x, is given by: 1/2 where: = the difference of the surface and bulk fermi potentials {approximately half the band gap) V = the applied bias voltage N = the net density of donor impurities K = the dielectric constant €0 - the permittivity of free space µ n = the electron mobility p 1 = the resistivity = eNµ n For silicon detectors at bias voltages large enough to neglect l); , the s thickness, x, is approximately given in microns by: x:::::. o. 5{pV) 1/2 This result shows that thicker depletion layers can be obtained with higher bias voltages, higher resistivity material, or both. -59- The small signal behavior of a surface barrier detector is approximately that of a capacitor. The capacitance is that of a parallel plate capacitor with plate separation , x, and dielectric constant , K. The capacitance per unit area is given by: C = and thus: 1/ c2 = 2pµ (L(; + V) n s Kc 0 In figure 22 measured values of l / C vs the bias voltage, s·i stivity of 170 fkm. V. 2 for a silicon detector are plotted The slope of the line is calculated with a re- For this sample of silicon 10 volts bias results 2 in about 500 µµ£ per cm . The above formula indicates that the energy in the output pulse, which equals yoltages . a 2 / 2C, increases appro x imately as (pV) 1/ 2 for high bias However the bias voltage cannot be increased indefinitely without causing a large leakage current which produces increased noise . Also the resistivity, p, cannot be increased indefinitely because the maximum available resistivity in silicon is about 10 , 0 0 0 fkm, although intrinsic silicon would have a resistivity of about 230, 000 fkm (58) . Some useful quantities for germanium and silicon are given in the following table. -60- TABLE V Properties of Silicon and Germanium Property Unit Silicon Dielectric Constant, K Band Gap Energy, E Electron Mobility, µ ev g n Hole Mobility, µp Germanium 12 16 1. 1 0.7 2 cm /volt-sec. 1300 3900 2 cm /volt-sec. 480 1900 Energy Loss per Ion Pair ev Density gm/cm 3 3. 6 3.0 2.33 5. 3 2 The order of magnitude of the rise time of the pulse produced by an incident particle can be calculated from the electron and hole mobilities and the depletion layer thickness and field in which the ion pairs are created. 7::::. X Y ~ 2 X µ (V/x} n X µ V n ~ 2KE 0 p Note that this expression is independent of bias voltage. For silicon 'T is approximately given by: 'T - 2 x 10 -3 p m µsec. Although high resistivity materials have the advantage of thicker depletion layers and smaller capacitance, they have the disadvantage of longer rise -61- times. Also the situation is more complicated for high resistivity ma- terial because of the rise time associated with the series resistance of the bulk material and the input capacitance of the preamplifier. When the range of the incident particle is greater than the depletion layer thickness, a slowly rising pulse is superimposed on the fast pulse . The slower rise time is ofthe order of.i;iev.er:al hundred mµsec. Figure 5 shows the response to 5. 3 Mev a-particles of a typical detector used in this e x periment and also that of a smaller detector. Since the number of generated electron-hole pairs is large (n = E/E = 6 6 5. 3 x 10 /3. 6 ::; 1. 47 x 10 ). the statistics of this process do not determine the resolution (n / b.n =n / /n =-fn = 1. 2 x 10 3 ). If the response is gaussian, the full width at half maximum is given by 2. 35cr and the resolution is defined as the energy of the peak divided by er. workers have obtained resolutions o f O. 7 x 10 riers {49). 3 Other for gold-silicon bar- It is mainly the noise in the counter generated by excess surface current which limits the resolution. Amplifier noise also con- tribute s but::is,_of an urde:r of magnitude smaller. than the noise of the detector with 5% full width at half maximum. Crystal inhomogeneities and defects also tend to reduce the resolution. Figure 23 shows the direct current characteristics of several silicon and germanium detectors. The reverse current is mainly sur- face leakage except at low bias voltages. A qualitative relationship has been observed that a detector with lower reverse current exhibits a higher resolution. time . The reverse current and the resolution vary with Generally a detector deteriorated in vacuum but sometimes could be improved temporarily by washing the surface , heating slightly , -62or just standing in air. When a detector became too noisy to use it ex- hibited a large amount of noise with a low frequency spectrum. The noise passed by the 80 mµsec. clipping time did not increase so much. No particular routine has be-e n rigorously adhered to in the construction of gold-silicon detectors , but the general procedures are listed below. (1) A sample of silicon is sliced to ~ 1 mm thickness with a diamond embedded sawo the desired size. {2) The wafers are cut into squares of (5/16 11 is usual for the present experiment.) The wafers are lapped with # 600 carborundumo A few detectors have been further polished with fine garnet but no definite improvement in results is foundo (3) The lapped wafers are etched in a polyethylene beaker of CP-4 for about 1 minute. The beaker is agitated to remove bubbles from the silicon. The CP-4 heats up from the reaction with silicon. CP-4 consists of the following: 1 part concentrated hydrofluoric acid by volume 1 part glacial acetic acid 1-1/2 parts concentrated nitric acid. (4) The etch is diluted with distilled water before removing the silicon wafer. The wafer is then washed in distilled water and dried on tissue paper. After etching, care is taken not to handle the wafer with the fingers. (5) The crystal is mounted. Generally silver conducting paint is used to make the back contact for silicon detectors and indium solder is used for germanium. Some detectors have been -63- potted in e,poxy resin and others have been left exposed to air. (6) a mask. The gold surface is evaporated onto the crystal through The thickness of the gold roughly cuts the transmission of light by 1/2. For the epoxy mounted detectors the gold is also evaporated on the epoxy and thus makes contact to a pin beside the wafer. For the open detectors the contact is made by a narrow strip of 1-mil gold foil stuck to the gold surface with silver conducting paint. -64APPENDIX B Integration Over Detector Solid Angles In the laboratory system the f3-a angular correlation can be written as: = 1 + A cos 0 130 + B cos where the coefficients, a.-particle momenta. A 2 8f3a and B, are functions of the electron and The experimentally measured distribution repre- sents the average of this correlation over the finite solid angles of the 13- and a.-detectors. perimental data, Hence, in order to relate A W(8f3a) and B to the ex- must be integrated over the solid angles. Both detectors have solid angles defined by circular apertures. The finite size of the target spot also tends to smear the experimental angular correlation, but this effect is negligible compared to that from the detector apertures. For each position, 0 0 0 8f3a = 0 , 90 , and 180 , the number of coincidences is proportional to the value of the normalized double integral: r )ro wceA ) dn dnA Jn t--'a f3 a t--' a Figure 24(a) illustrates the geometry and defines the appropriate angles for the 0° and 180° configurations. and YJ Let <J" be the azimuthal angle be the polar .a ngle of the infinitesimal solid angle dO detector, which has a maximum polar angle 80.. a in the a - Let X. be the azi- -65muthal angle and 6 be the polar angle of the infinitesimal solid angle d0f3 in the [3-detector, which has a maximum polar angle 0[3. dO a. Then = -der d( cos rJ); From a theorem of spherical trigonometry: . cos ef3o. (0°) = - cos ef3a. (180°) =cos 6 cos rJ + sin 6 sin rJ cos(:>--. +er) =cos 6 cos rJ + sin 6 sin rJ(cos A cos er - sin A sin er) where cos 0[3o. (0°) means \ \ Jn J n f3 0 Thus for the rangement. a, cos 0f3a measured in the O and 180 0 0° -detector ar- arrangements: W(0p, ) dO . dOR :: sef3 \ Zrrse a. SZrr {1 ± A[ cos 6 cos YJ t-'o. a. t-' o Jo o o 2 2 + sin 6 sin rJ(cos A cos er - sin A sin er)] + B[ cos ocos Y) + 2cos :>--. cos YJ sin 6 sin rJ(cos :>--. cos er - sin :>--. sin er) . 2~ . 2 ( 2, 2 , . , . + sin u sin Y) cos I\. cos cr - 2 cos I\. cos er sin I\. sin er 2 2 + sin :>--. sin er)]} der d(cos Y)) d:\. d{cos 6) where the + sign applies to 0° and the integration over er and A yields: and the integration over Y) and 6 yields: - sign applies to 180°. The -66- Dividing by the solid angles of the detectors gives the following expression for the normalized integral: Figure 24(b) tion. The angles, illustrates the angles involved in the 90° configurao-, r,, A, and o, are defined as before. Also cf, is de- fined as the angle between (1) the line joining the target and the center of the Cl-detector and (2) the line joining the target and the infinitesimal solid angle dO f3 . Then: cos cf, = cos o cos 90° + sin A sin 90° sin A = sin o cos A Also define s as the projection of the angle o on the plane parallel to the surface of the cos o.-detector. It can be shown: cos o s = (1 - sm . 2 2 1/2 o cos A) -67Applying the theorem of spherical trigonometry a second time yields : cos 0f3a. ::: cos cf> cos r, + sin cf> sin r, cos (<r- s) :,; sin 6 cos X. cos r, + sin r, {cos <r cos 6 + sin <r sin 6sin X.) Thus, for the 90 Sn Sn f3 0 arrangement: W(0 a )dQ dQ = 13 f3a. • a. ef3 ~ 2rrs 0 a. r\ 2rr {1 + A [sin 6 cos X. cos r, So • o o ,)o 2 2 2 + sin r,{cos <r cos 6 + sin <r sin 6 sin X.)] + B[ sin 6 cos X. cos n + 2 sin 6 cos X. cos r, sin r,(cos <r cos 6 + sin <r sin 6 sin X.) 2 2 2 + sin r,(cos <r cos 6 + 2 cos <r cos 6 sin <r sin 6 sin A. The integration over <r and X. yields: + B 4 2 2 2 2 ·· [l+cos r, +cos 6-3cos r,cos o]}d~cosr,)d{cos 6) And the integration over rJ \s Jn o f3 Cl and 6 yields: 2 W{0p_ )dQ dQP- ::: {2rr) (1 - cos 0p_}{l - cos 0 ) { 1 l'-'o. a I'-' I'-' a. -68- Normalization gives the following expression for the 90° configuration: ( ( Jn Jn f3 dO dOR a. t-' a In the experimental apparatus, 0 0[3 = 19 40 I 0 and 0 a = 9 . Using these values results in the following numbers for the integrals of W(0f3a) over the detector solid angles: 0°: l+0.965A+0.932B 90°: 1 180°: l-0.965A+0.932B +0.034B -69- APPENDIX C Solution for the Coefficients, The number of [3- a. A and B coincident counts in each configuration (0°, 90°, 180°) is proportional to the angular distribution function, W{0f3a), integrated over the detector solid angles, as in Appendix B . function of the unknowns, A This is a and B, which are to be determined, and also an unknown proportionality factor, I n. 0 0 Let n(0 ) , n{90 ) , and n{l80°) be the normalized number of coincidences measured at each angle. Then: I (1) n{0°) = n (1 + f 1A + f 2 B) (2) n{90°) = n (1 (3) n{l80°) :;: n (1 - f A + f B) 1 2 I where f 1 2 3 ' ' £ = 0. 034. 3 + f 3 B) I are the integrals of Appendix B, £ = 0. 9 65, £ = 0. 9 32, 2 1 Rewriting equation (2): Adding and subtracting equations {l) and (3) yields equations for A B respectively: B = n{0°) + n{l80°) - 2n(90°) 2f n(90°) - £ n(0°) - £ n(l80°) 3 3 2 A __ n{0°) - n{l80°) [ n{0°} + n{l80°) - 2n(90°) 1 + £3 ----"--'---....;o'-o o o 2£ n(90 ) 2£ n(90 )- f n{0 ) - £ n(180 ) 3 3 2 1 A:::::.. n(0°) - n(l80°) 0 2£ n(9 0 ) 1 ] and -70For the purpose of calculating the standard deviations of the coefficients, A and B, arising from the statistical errors in n{0°) , n{90°), and n{l80°), the various partial derivatives are needed : 2{£ - f )n{90°) 2o_ _3 _ _o_ _ _ _ _o_]-=-2 _[ _ _ __ --- = ---- = 8n{0°) 8n{l80°) 2f n{90 ) - f n{O ) - f n(l80 ) 2 3 3 oB aB -2(£ oB 2 - f )[ n{0°) +n{l80°)] 3 8n{90°) The approximation, n(90°)::::. ~ [ n(0°)+ n{l80°)], is accurate enough for this purpose and simplifies the partial derivatives to the following: 8B oB = 8n{l80°) 8n(0°) 1 = 2{£ 0 2 - f )n(90 ) 3 -1 8B = {£ - f )n(90 ) 0 8n(90°) 2 3 The standard deviation of B is found by using the general rule for the combination of independent errors: AB = { [ 2 8B ] 8n{0°) A2n(Oo) + [ 2 +[ AB = oB ] 8n(l80°) 2 8B ] A 2n(90o) 8n{90°) A 2 n{l80°)} 1/2 l [ A 2 n(0°) + 4A 2 n(90°) + A 2 n{l80°)] l/ 2(£ - f )n{90°) 3 2 Similarly for A: 2 -71- 8A -8A = 8n{0°) 8n{l80°) 2£ n{90°) 1 8A =n(l80 ) - n(0 ) 0 0 2 2f n {90°) 1 8n{90°) !::J.A z.. 1 = 0 0 2 { !::J.. 2n(Oo) + [ n{l80 ) - n{O ) ] !::J..2n{ 9 0o) 1 0 n{90°) 2f n{90 ) 1 + !::J. 2 n {18 0 °) } 1/ 2 These expressions for the standard deviations, A.A and C:J.B, take into account only the statistical accuracy of the data. An{ 0°); , etc. cannot be replaced simply by However , 2 [ n{0°)] l/ , etc . since each number of coincidences is normalized by the corresponding number of non-coincident 13-counts. For the data with the 13-detector placed only in the 90° and 180° positions there result only equations (2) and (3). considered a known quantity. B In this case A is Then: = n{l80 ) - {l - f1A}n{90 ) 0 0 0 0 f n{90 ) - f n(l80 ) 3 2 The partial derivatives in this case are the following: 8B 8n{l80°) f n{90°) - f n(l80°) - (-f )[ n{l801- (1 - f A)n{90°)] 3 _ _o_-=-2------2 _ _ _ _[3_ _ _o_ _ _ 1 = _ f2n(90 ) - f n(l80 )] 3 = 1 + f B 3 () 0 f n{90 )- f n{l80 ) 3 2 -72-{l-fl A)[ f n{90 °) -f n{l80 °)] -f [ n(l80 °) -{l-f A)n(9 0 °)] = - - - -2-[- - ( - 3- o - - - - -2o--:::2_ _ _ _1_ _ __ 8n(90°) f n 90 ) - f n(l80 1 ) ] 2 3 = - (1 - f A + f B) 1 2 Therefore: The dependence of the error in B on the error in A has been neglected. It is an order of magnitude smaller than the statistical errors, -73APPENDIX D ~❖~ The Transformation From the Be 8 Rest System to the Laboratory System The angular correlation in the rest system of the daughter nucleus, of Li 8 Be 8 ,:-: , of the electron, neutrino, and a-particles in the decays 8 or . B . can be derived from the theory of beta decay. In order to calculate the angular correlation in the laboratory system of the electron and a-particle, one must multiply the correlation in the Be 8 rest system by the purely geometric solid angle transformation and then integrate over all directions of the unobserved neutrino. Figure 25 shows superimposed diagrams of the directions of the electron, neutrino, and a-particles in the two systems. In the Be 8 rest system the particles are denoted by ~' ~' ~ and the angles between them by ~ ' ~ ' ~· Similarly in the laboratory system the particles and angles are denoted by £, 2::_, a and f3v, [3a, va.. Then the following general identity can be written: W{en, ea, na)dQ dQ dQ e n a dQ dQ dQ = W[ en([3v, [3a, va), ea{[3v, [3a, vo.), na{[3v, [3a, va)] dO; dO n dO a dQ[3 dQ v dQ a. V Thus the problem is to express the angles angles 0. en, ea, and~ in terms of the E• [3a, and vo., to solve for the ratio of solid angles, and finally to integrate over the neutrino solid angle. First the ratio of solid angles is solved. Since the neutrino has velocity, c, and the electron has a velocity nearly equal to c, while the recoil velocity is very much less than c, the angles and momenta 8 >'< of the electron and neutrino are very nearly equal in both the Be ' rest system and the laboratory system. dQ n /dQ V = 1, Thus to a very good approxima- en = [3v. The remaining ratio, -74- dO a / dO a, , can be solved with the aid of equations for the conservation of momentum. In figure 2 5 the electron defines the polar axis and the neutrino defines the y dO a. = -d(cos -!30.)dq> . = 0 plane. Then: dOa = -d{cos ea)dljJ, Writing the ratio of solid angles in terms of the Jacobian: o(cos ea, lj;) = ..,...,----;s--..,..... o{cos l3a, cf>) Define p of the neutrino, o{cos ea) 04) o{cos ~) olJi oc/> o(cos ~a) = o(cos ~a) sq;- as the momentum of the electron , q as the momentum ,:c 8 pa as the momentum in the Be rest system of the detected a.-particle and p a of the detected a-particle. as the momentum in the laboratory system A second a-particle is emitted with equal and opposite momentum in the Be 8* rest system. An approximation is made by neglecting the conservation of energy equation and using only the conservation of momentum (3). This neglects the kinetic energy of ,:c 8 the recoiling Be , which is at most 15 kev. In this approximation q is independent of the direction of the a-particle. The momentum equa- tions for the three directions of figure 25 are: 1 2 q sin 13v = - Pa, sin 13a cos q> + pa sin ea cos lj; p sin 13a sin q> = pa sin ea sin lj; "?:1 q cos~ + 21 p = -pa, cos l3a + pa cos ea Solving for the variables of the tory variables yields: Be 8* rest system in terms of the labora- -75I cos ea= [ cos j3a. + p I I [1 +p + q cos 13v] I 12 +q 12 I + 2p cos j3a. I + 2p q cos j3v + 2q cos j3v cos j3a. • • P. ] -1/2 + 2 q I cos 'I',I.. sin .t'P..2:. sin~ I = cot¢ + q sin E csc ¢ csc j3a. where, p = p/2p , q =q/2p . Then p z.. 1/20 and q ~ 1/100 for the a. a. cot 41 I I I •experimental case with W p ==- 11 Mev. I Taking the partial derivatives I yields to first order in q : 841/ 8¢ ==- 1 - q sin j3v cos¢ csc j3o. I 841/8(cos !30.) ==- - q sin E sin¢ cos j3a. csc 3 !30. I I 8(cos ea)/8¢ ==- [ q sin¢ sin j3v sin j3a.(cos j3a. + p )] [ 1 + p I I I 12 +q 12 I + 2p cos j3a. + Zp q cos j3v + 2q cos E cos j3a. • • P. ] - 3 / 2 + 2 q I cos 'I',I.. sin .t'P..2:. sin~ 8(cos ea} / 8(cos j3a.) z.. [ 1 + q 12 I I J + p cos j3a. + p q cos¢ sin j3v cos j3a. I I + q cos j3v cos 13a. + ~q cos ¢ sin j3v sin j3a. I + q cos ¢ sin j3v cot j3a. cos !30.] [ 1 + p I I I 12 +q 12 I + 2p cos 13a. + 2p q cos E + 2q cos E cos j3a. • • P. ] -3 / 2 + 2 q I cos 'I',I.. sin .t'P..2:. sin~ Ideally the procedure would be to multiply these partial deriva- -76- tives together to form dn a / dn a W, and integrate over dingly complicated. and then multiply this by the function, The algebra of this procedure is forbid- Instead, the procedure used here is to carry out the multiplication and integration for the simplified case with q = 0 and then show that all of the integrals in which q appears to first order are identically zero . ,;c Next the correlation function of the Be pressed in terms of laboratory coordinates. Weidenmuller, the correlation in the W{ea, en, na) = (1 - .!_ap) - (L 3 WP Be 8 rest system is ex- As derived by Dro Ho a* rest system is (59): 1 3 ap) cos ea cos na - ap cos en + ap cos 2 ea where the quantity, a, is the interference term arising from the vector Ml type matrix element in the two theories of beta decay. order (o.Z) 2 Terms of have been neglected for the allowed transition and the ap- proximations, m e =0 and aZ = 0, have been assumed for the forbidden transition. In the q = 0 approximation: COS p + cos pa, ea.::::. tz t l/Z (1 + p + 2p cos pa) , cos 41 .: : . cos ¢ From a theorem of spherical trigonometry: cos na = cos en cos ea + sin en sin ea cos Lj; Therefore, the correlation function in terms of the laboratory variables is: -77I W P + cos pa p 1 ][ - ( - - - ap) 3 2 1 +p + 2p cos pa. WP =(1 - 3 ap) - ap cos pv + 1 I :x cos p v {p - c; p - t I + cos po.) + ap{p + cos pa.) ap)sin pv sin pa. cos <I>] This is to be multiplied by the ratio of solid angles, which in the q =0 approximation is: t dO /dO a a = 1 + p cos po, (1 + p 1 2 I + 2p cos po.) 3/2 This ratio is independent of the neutrino direction and thus is a constant for the integration over the neutrino solid angle. The laboratory angu- lar distribution function of the electron and a-particle is the normalized integral: \ (W dO /dO )dO Jn a a V V dO V ·: 1 s 2rrr +l j { W dQ /dO ) d(cos pa) dc/> • 0 -1 a a = :41r The only variable terms in the integral are cos E and sin pv cos </>. However, the integrals of these functions are identically zero. +l S -1 cos E d(cos E) = 0, s 2 rr cos </> dcp 0 =0 -78- Thus 1 W((3a) = [(l-""3ap)+ 1 2 ap(p + cos (3a) 1 + p'cos (3a . ] ,2 , ][ ,2 , P.a)3/2 1 t p t 2p COS (3a 1 + p + 2 p cos f-' This is approximated by expanding the denominators, keeping only terms 2 3 up to order p' , combining the cos ~ term. with the cos and renormalizing the constant term to be 1. is replaced by its definition, (3a term, t Also the quantity, p , p/2p . . a 2 9 2 + -1:.,. )cos (3a W((3a) 8 c., - Pa Next, it is shown that this same result also applies when q =f: O. ,., s· rest This can be seen from the expressions for the angles of the Be system in terms of the laboratory variables, and also from the expressions for the partial derivatives. Note that pressions only when multj.plied by either Thus the general form of the product, first order dependence on q t q cos t appears in these ex- (3v or sin (3v cos ¢. W dS1 / dS1 , indicating only the a a and the dependence on the neutrino angles, is the following: . 1 + Vq sin (3v cos ¢)(X + Y cos (3v + Z sin (3v cos ¢) (Uq' cos (3v For each product of two terms at least one of the integrals over the neutrino angles, (3v and ¢, is equal to zero. order terms in q . Thus there are no first Second order terms are negligible. Another effect large enough to be considered is the variation of pa with angle, arising from the recoil of Bes*. The Be 8 >!< recoil -79averaged over the neutrino direction is: q/ 3 Precoil = p - Half of this m .omentum is received by each a-particle. I£ the 0 9o a- ,::: ppectrum is used as an approximation to the spectrum in the Be 8 rest system, the 180° and 0° spectra are replicas of the 9 0° spectrum but shifted by .± -12 p recoil p , over the a 0 Therefore, averaging a function of the momentum, a-spectrum at angle, l3a, is approximately equivalent to - averaging the same function of pa - i(P - j)cos l3a over the 90° aspectrum. The angular distribution, which is to be averaged over the 1/(1-x) .!:::! 1 + x,. function, W{l3a), contains the £unction 1/p , a a-spectrum. Using the approximation, where x is small, gives the following average of the ljp {l3a): a This correction is appreciable only for the leading cos l3a term in W{l3a). The final expression for the angular correlation in the laboratory system is the following: The quantity, a,. as discussed in section I, includes the inter- ference effect of the vector Ml type matrix element. be about a factor of 2 larger in the It is expected to C. V. 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Series II, 5, 355 (1960). 53. Proceedings of the Seventh Scintillation Counter Symposium, Transactions on Nuclear Science 7, No. 2- 3, 178 (19 60). 54. Proceedings of the Semiconductor Detector Confer e nce, Transactions on Nuclear Science 8, No. 1, 1 (1961). 55. W. Schottky, 56. J. Bardeen, Handbook of Physics, Edited by Condon and Odishaw 8-52 (1958 . 5 7. E. Spenke, 58 . E. M. Conwell, Proc. I. R. E. 59 . H . A . Weidenmuller (private communication). 60. W. B . Herrmannsfeldt, R. L . Burman, P. Stahelin, J. S . Allen, and T. H. Braid, Phys . Rev. Letters 1, 61 (1958) . U. C . R. L. Phys. Rev. 95, ll0 Zeitr. F . Physik 159, Rept. No. 8324 (1958). A. E. R. E . Rept. No . 3437 Nuclear Instr. and Methods, Bull. Am. Phys. Nucleonics , Zeitr . F. Physik 113, 367 (1939). Electronic Semiconductors, McGraw-Hill (1958). 46, 1281 (1958). - 84a- Figure 1 illustrates the energy levels of the mass-8 isotopic triplet . Li 8 Either electrons from the beta decay of or positrons from the beta decay of B 8 are detected in coincidence with a-particles from the breakup of the 2. 9 O-Mev state of Be 8 as a function of the angle , 0f3a" Both beta decays are primarily allowed axial vector but second forbidden vector matrix elements affect the angular distribution of coincidences by an amount depending on the magnitude of the analogous dashed in the figure. Ml y-ray transition rate shown The effect on the angular distribution may be used as a check of the validity of the conserved vector current theory of beta decay. Li 8 is produced in the 7 8 Li (d, p)Li reaction by a deuteron beam of O. 75 Me v . is produced in the of 3. 2 Mev. and 10. 6 Li (He B 8 3, n)B 8 reaction by a He 3 beam Figure 1 is discussed in Section I, pages 7 -84- g8 Li -0.192 8 17.64 1+, (T= I) 16.63 16.94 17.980 J=2+ 2.966 2 moc threshold -__,,.lt-.....~ 16.002 J=2+ -1. 976 Li7+d-P Lis+He3-n -0.094 J=O~T=O Be 8 Figure 1 -85a- Figure 2 illustrates the 3 11 -diameter target chamber and associated apparatus. The incident beam from the Van de Graaf£ generator enters the tube at the right rear and strikes the target at a 15 ° angle . Four gold-silicon surface barrier a-particle detectors are placed at 45 target. The 0 angles to the a-detector furthest to the right in the figure is used as a monitor, the one towards the right foreground detects a-particles in coincidence with electrons, and the other two detectors are dummy detectors for the purpose of symmetry. wide, Li 7 A furnace, which is used to evaporate thin, 2-mm or Li 6 targets on the 5-mil aluminum backing is shown in the rear of the chamber about 3 11 above the plane of the detectors. A tantalum cup with a cut through which the beam enters is shown surrounding the target backing. This shield drops into the 1-1/2"-diameter lead container during the counting period. The lead container is supported by the cold trap which can be filled with liquid nitrogen from below. The plastic scintillator which detects electrons is shown in the foreground. It is mounted inside the movable lead shield to the left during the course of the experiment. discussed in Section II, pages 11-17. Figure 2 is -85- TARGET CHAMBER Figure 2 -86a- Figure 3 outlines a block diagram. of the electronic circuitry used in this experiment. A 11 fast-slow 11 coincidence system is used with a fast resolving time of about 80mµsec. and a slow resolving time of about 1. 2 µ sec. The coincident a.-spectra are displayed on the 100 channel analyzer. A single channel discriminator selects the The /3-energy. gating supply regulates the 1 sec. delayed counting cycle; the beam is on the target 40% and off 60% of the time, the scalers and 100 channel analyzer are off 60% and on 40% of the time, the target shield is up 50% and down 50% of the time. Figure 3 is discussed in Section II~ pages 14 and 17-20. -86- high vol tage su ppl y ,, preamp preamp ~z choppe r linear amplif ier --- beam bias monitor,....._____ voltcge counter .....___ ___. supply ream photomultiplier X preamp (\J cou~ler preamp 13 .----......... scintillator targ~ield y bias voltage supply delay box type A 16' 16 RG-62/U type A Hewlett Packard Amplifiers type B linear amplifier limiter ~---.--clipper type B type A type B coincidence mix r scaler scaler X X single channel analyser scale ,---,........, of 1 ,..........,-...... RG-62/U type A clipper type A sca ler . linear amplifier inverter gate --delayed coincide nee ~__,..,__----'-------1 input 100 channel prompt analyser coincidence 8 X scaler scaler -+-X X y z gating supply ELE CTRONIC CIRCUITRY Figure 3 8 beta decay. From an ideally thin target The points marked Noise and This mode of operation is less (See Section II, page 15; Section III, page 26; and Section IV, page 40.) channel 10. mixer reliably detects pulses from a-particles to somewhat below sensitive to noise but the spectrum indicates that the fast coincidence same a-particle pulses in both inputs. 100 channel analyzer being gated by the fast coincidence mixer with the tra.-a coincidence gaterr represents the same spectrum but with the pulses from electrons appear in the low channels. the target and the limited resolution of the detectors. Actually the peak is lowered and broadened by the a-particle loss in the peak would occur at about 1. 5 Mev and be about 0. 8-Mev wide. particles following the Li the response of a gold-silicon surface barrier detector to the a- Figure 4 is a spectrum from the 100 channel analyzer showing I 00 I Pl .._J 1000 2000 Fig ure 4 u 0 ~ 3000 Cf) .._ a.. u o:: 4000 w I <{ z ~ 5000 _J 6000 10 20 8 30 40 50 CHANNELS 60 NON-COINCIDENT a-SPECTRUM Li 0 70 80 90 WITH a-a C0INC. GATE e WITHOUT GATE I I -.J CP The wider curve is from a typical detector used A Appendix A, page 61. discussion related to figure 5 can be found in Section II, page 16 or a.-particles is greater than for the case of 5. 3 Mev a-particles. energies of figure 4, the full width at half maximum for monoenergetic At the lower The amplifier gain used for obtaining figure 5 is about half of that for figure 4. selected counter of superior resolution. in this experiment while the narrower curve is from a smaller, polonium source. surface barrier detectors to monoenergetic a.-particles from a Figure 5 shows the pulse height response of two gold-silicon I I Ill 00 00 ...J 500 u 0 100 200 Figure 5 :::) z ~ 300 ~ (l_ w 0:: u 400 :I: <{ z z w 600 \ 10 30 ~ 5 % Full Width at Half Ma,timum 50 60 70 80 90 111 \ 20 mm 2 ~ 1.2% Full Width at Half Maximum 50mm 2 a-PARTICLE SPECTRUM CHANNELS 40 SELECTED COUNTER O 20 TYPICAL COUNTER e 5 . 3 Mev POLONIUM I I 00 I Cl:) 8 The shaded portion of the Figure 6 is also page 35. discussed in Section II, page 17; Section III, page 26; and Section IV, for the case of an average 13-energy about 11 Mev. spectrum represents pulses selected by the single channel analyzer scale) to kinetic energy (upper scale). equivalent to 9. 5 Mev, kinetic energy, thus converting channels (lower This abscissa is A magnetic spectrometer 13-spectrum of equal area is plotted with equal abscissa for the point of half maximum. points. the beam on only the aluminum backing, is subtracted from the open To obtain the solid points, background, measured with decay to the analysis of the pulse height response of the plastic scintillator. Li Figure 6 illustrates the relation of the 13-spectrum from the I Ct:) I Ill ...c, 4000 5000 u 0 1000 2000 Fi gure 6 :::) z Cl) 3000 ..,_ w a.. 0::: ~ <! z z w _J 6000 10 2 20 Li 8 4 30 8 10 12 14 50 60 70 80 90 0 EXPERIMENTAL PLUS BACKGROUND - --STANDARD ( MAGNETIC SPECTROMETER) e EXPERIMENTAL (SCINTILLATION COUNTER) CHANNELS 40 ~ /3 -- SPECTRUM 6 KINETIC ENERGY (Mev) I OJ -.D I As is evident the response is This figure is mentioned in Section II, page 17 and Section IV, page 3 5. the 13-energy scale . quite poor and therefore this spectrum is not used to calibrate 13- detector to 2. 62 Mev ":y-rays. Figure 7 illustrates the response of the plastic scintillator I '°Pl0 I 2500 u 0 ::) z ~ Figure 7 500 1000 en 1500 ~ Q. a:: w ~ 2000 z <r z w ...J 3000 10 20 \._ 30 50 CHANNELS 40 60 70 80 90 2.62 Mev Th C"y-SPECTRUM IN PLASTIC SCINTILLATOR I I I '°0 decay of total energy about 5 Mev. 0 11 This shift aggravates nucleus 9, 10 and 11.) Figure 8 is discussed in Section III, page 24. (Also compare figures the problem of accurately measuring the areas under the curves. from the momentum of the electron and neutrino. 8 The shift in the position of the peaks is caused by the recoil of the Be is done in the dashed extrapolation to zero pulse height. This 0°13 11 spectrum which must be subtracted from the measured numbers of coincidences to yield the true numbers. pulses, called the of 0/3a = 0 , electrons traverse the a-detector and produce small For the case The total numbers of coincidences of pulse height greater than 100 channels are also known. angular distribution function. The integrals of the curves are used to calculate the coefficients of the The curves are normalized to a fixed number of non-coincident /3-counts. 8 0f3a, for the particular case of coinci- dences with electrons from the Li data as a function of the angle, It represents the sum of the coincident a-spectra from two groups of Figure 8 is an example of the essential data of the experiment. '°Ill I I t--' 100 Figure 8 u 0 u z w o 200 u z w en 300 10 20 30 COi NCIDENT 8 • 50 CHANNELS 40 a-SPECTRUM Li ti 0 ~ • 70 0013 180° 90° 0° ~ 5 Mev 60 W/3 80 90 I I 1---' --SJ decay {Compare figures 10 and 11, and see the discussion in Section III, page 24. } as in figure 8 . 8 The details are essentially the same 0f3a.' for the case of electrons from the Li of total energy about 8 Mev. of the angle, Figure 9 illustrates the coincident a.-spectra as a function '°Pl I I N 100 200 I L Figure 9 u -0 z u - 0 w z 300 u w (/) 400 500 I- 10 20 30 rl . / / COINCIDENT 8 '\. """'- 40 50 CHANNELS '\. a-SPECTRUM Li 60 b. 0 •A 70 0°/3 oo 180° goo w/J ~8 Mev 80 90 I N I -..D 8 from the mo- Figure 10 Section III, page 24. ) 8 decay. (Also see Figure 10 should be compared to figure 11, which is the analogous data from the B 14 similar groups of data. represents the sum of the data from two groups out of a total of figure 8, since the electron momentum is greater. mentum of the electron and neutrino is greater in this case than in 8 decay of average total energy about 11 Mev. The shift of the peaks caused by the recoil of Be electrons from the Li Figure 10 shows the coincident a-spectra for the case of '°Ill I I (.,J JOO 200 300 Figure 10 u 0 2 u Cl w U400 z w Cl) 500 600 10 20 8 30 50 CHAN NELS 40 COINCIDENT a-SPECTRUM Li 60 0 70 80 oo /3 oo ~ l:J. 180° 90° • w11 ~ 11 Mev 90 I I w --D 8 decay. decay and figure 10 The increased widths of 8 3 8 applies to figure 11. nuclei Figure 11 is discussed in Section III, page 24. The description of figure 8 also 8 nuclei recoil from the beam deeper into the target than do the Li The B from the 0. 75-Mev deuteron beam. 3 . 2-Mev He of the a-particles in the target. the spectra of figure 11 are caused by the additional energy loss applies to electrons from the Li positrons of about 11 Mev total energy from the B Figure 11 is analogous to figure 10, where figure 11 applies to I I ,i:,. '° PJ - 94 - 0 O') 0 (X) <ll. 0 0 0 0 0,..._ 0000 (X) (1) > Q) e ◄ O<l ~ 0 <D 2 ~ 0 (/) I{) ...J (X) (D LLJ z z ~ => n:: I- u w CL <t • o:i: V U (/) I cs I- 0 z t0 w 0 u -0z 0 C\J u 0 0 0 <D 0 0 I{) 0 0 V 0 0 I"'"> S3:>N301:>NIOJ 0 0 C\J 0 0 (1) L. ::J O'l LL 8 beta 8 decay. In figure 12 there is a larger Also the curve is broadened by the energy loss in the target. This spectrum indicates that the fast as channel 6 to 10, (See Section III, page 26 and Section IV, page 40.) coincidence mixer is sensitive to pulses from a.-particles as small particle pulses in both inputs. the 100 channel analyzer gated by the fast coincidence mixer with a.- The points marked 11 a.-a. coincidence gate II represent the operation of lower. contribution from noise since the counting rate of a.-particles is Li This spectrum can be compared with figure 4 which is the a.-spectrum following the decay. of the gold-silicon detector to a.-particles following the B Figure 12 represents the pulse height analysis of the response '°p., I I \.Tl 100 200 Figure 12 u 0 ::) z 300 ~ a. en w o:: 400 u <t: ::i: z ~ 500 _J 600 10 20 30 o Clb 0 40 50 CHANNELS 0 e 60 70 80 90 WITH a -a C0INC. GATE WITHOUT GATE NON-COINCIDENT a-SPECTRUM Ba 0 I I lJl '° beta decay obtained The solid points are obtained from the 8 The abscissa of the half maximum 8 8 The increased back- Figure 13 is discussed in Section III, pages 26 and 31; and Section IV, page 3 5. trons. ground does not permit reliable coincidence data with low energy posi- and corresponds to a total energy of about 11 Mev. spectrum represents the pulses selected by the single channel analyzer The shaded portion of the This is caused by the greater incident beam energy and much lower yield of B . electron spectrum in figure 6. The background of this spectrum is much greater than that of the Li point is taken to be 10. 2 Mev, to determine the kinetic energy scale. only the aluminum target backing. open points by subtracting background measured with the beam striking with the plastic scintillator. Figure 13 is the positron spectrum of the B I I lll --D 0-- I I I I I I I 20 30 40 50 14 16 60 70 80 90 EXPERIMENTAL PLUS BACKGROUND EXPERIMENTAL 12 400 800 Figure 13 (.) 0 I- ILi 10 CHANNELS 1 ~ 1200 I 0 e 10 I I 8 8 8 ,8+-SPECTRUM 6 '°0-- 4 a:: 1600 a.. en (.) :r <( z ~2000 ..J 2400 2 KINETIC ENERGY (Mev) -97a- Figure 14 is a histogram of all the data reduced to the values of the coefficients of the angular distribution function, W( 8f3a) = 1 + A cos 8f3a + B cos 2 8f3a" Since the theoretical forms of the coefficients are proportional to the electron total energy, W f3' the coefficients are divided by W f3 in order to average the various groups of data together. Each group of data is represented by a rectangle whose height is proportional to the inverse square of the statistical error of that group. Normal distribution curves are plotted about the mean of each coefficient. The data marked unreliable are not used in com- puting the mean values. The widths of the normal curves are equal to the square root of the number of groups times the statistical error of the mean. The coefficients, Lis and BS decays are very nearly equal. B, for the two decays are different. A, for the The coefficients, The magnitude of this difference is a positive indication for the conserved vector current theory of beta decay. The histogram is discussed in Section III, page 33; and Section IV, page 49. -9 7- ~ ~ A/W. '/3 Be ;] 4 W1, ~ 11 Mev Wp ~ 8 OR 5 Mev UNRELIABLE DATA 6 ,8 L, -12 - IO -8 -6 -4 10 8 i'w/3 -2 COEFFICIENT 8 0 X 2 10 4 3 HISTOGRAM OF RESULTS Figure 14 6 8 10 It is assumed that the scintil- Estimates of the distortion of the Li 8 13-spectrum and of {See figure 16 and Section III, page 3 7. ) made from this and similar response curves at different energies. the number of small pulses arising from high energy electrons are figure. be adequately approximated by the triangular areas shown in the lator used in this experiment has a similar response and that it can to 7.1 mev monoenergetic electrons. Figure 15 shows the response of a 2 11 x 3 11 plastic scintillator '°Pl I I CX) CJ) 400 800 • • Figure 15 . 0 0 ::> z 1200 .... 1600 2000 2400 10 20 30 50 CHANNELS 40 60 IN A PLASTIC SCINTILLATOR 70 SPECTRUM OF 7.1 Mev MONOENERGETIC ELECTRONS 80 90 1 I co --.D 8 f3- spectrum. The dashed The third curve has been The third curve is plotted pulse heights. Reference is made to figure 16 in Section IV, page 37. It closely approximates the experimental spectrum for the higher with the same peak height as the magnetic spectrometer spectrum. function of the scintillator as in figure 15. graphically derived from the second curve assuming a resolution abscissa for the points of half maximum. curve is a magnetic spectrometer spectrum of equal area and equal counter to the f3-spectrum and is identical to figure 6. The solid curve represents the response of the plastic scintillation Figure 16 consists of three graphs of the Li I I Pl -.D -.D 4000 1000 I- II 2000 f- Figure 16 (.) 0 :::> ~ 3000 en 0... a:: w (.) .J: <{ z z ~ 5000 I 6000 [ I I I 10 20 j/ / I Li 8 30 I 6 I I I 12 I 14 \ I 60 70 I ~ \. \, ' \. 80 90 - - - DERIVED FROM STANDARD - - - STANDARD EXPERIMENTAL I I I 10 8 50 I CHANNELS 40 "'~ /3- SPECTRUM I //~ 4 I I 2 4/ }/ I KINETIC ENERGY ( Mev) ,~ decay in the new counting arrangement The primary changes are (1) that the target 8 (See Section I, pages 7 and 8; and Section IV, page 38.) during the beam alignment procedure in the new arrangement. gold-silicon a.-detectors are protected from sputtered material was changed from 30° to 15° to the beam, thereby reducing the 8 effect of the recoil of the B into the target, and (2) that the relative to the old. a.-spectra following the B Figure 17 illustrates the improvement in the coincident I f--' I PJ 0 0 u -u -0z Lu 0 u z Lu (/) I ~ I I Figure 17 100 200 300 4 00 500 600 I 10 I ;' j 20 J 30 50 ~ CHANNELS 40 f\ OLD /J. 60 NEW _. 70 80 90 COMPARISON OF 90° a-SPECTRUM FOR OLD AND NEW ARRANGE MEN TS 88 I I >--' I 0 0 Li 8 • t-'Q beta decay at 0A The suppression of high energy discussed in Section IV, page 42.. restriction imposed by the conservation of energy. The figure is a-particles in coincidence with high energy electrons is due to the and have very nearly equal areas. are all normalized to equal numbers of non-coincident electrons The curves = 90° for The three curves are the average total electron energies of 11, 8 and 5 Mev. coincident spectra fro1n the caused by the energy of the electrons. Figure 18 displays the effect on the coincident a-spectra I Ill .....I 0 ..... 100 200 Figure 18 (.) 0 z 300 (.) Q w o 400 z w en 500 600 10 20 30 8 50 60 • 6. ~ a-SPECTRUM CHANNELS 40 90° COINCIDENT Li 70 80 w~ ~ 11 Mev w~ ~ a Mev w~ ~ 5 Mev 90 I I ,__ ...... 0 beta decay with average total electron As expected, the random coincidences fit 8 IV, page 42. ) a-spectrum of figure 10. (See the discussion of figure 19 in Section the non-coincident a.-spectrum of figure 6 rather than the coincident energies about 11 Mev. groups of data from the Li Figure 19 represents the random coincidences of several I Pl N I ..... 0 25 50 75 Figure 19 u 0 ~ z 1-- Cf) w 125 z z <( ::c u 100 a: w a.. _J 150 10 20 30 • ~ \ \ \ 50 \ CHANNELS 40 8 \ \ \ RAN DOM COINCIDE NC ES \ \ '\. " 60 \ '-. 70 ''' 80 90 -- ------ ---COINC. a-SPECTRUM - - NON-COi NC. a-SPECTRUM e RANDOM a-SPECTRUM Li I N 0 I ,_. With the high bias voltages that are discussion of figure 20 appears in Appendix A, page 57 . (3) the response of the amplifier to a known charge input. The of the amplifier with 5 . 3 Mev a. - particles hitting the detector , and ments of (1) the detector and preamplifier capacitance , ( 2) the output The experimental points are determined from measure- silicon. approaches 3 . 0 ev for germanium and 3 . 8 ev for E value of necessary for effi e ient collection of all generated ion pairs , the by 5. 3 Mev a.-particles. tectors at 77°K and gold-silicon detectors at room temperature energy required to produce an ion pair in gold-germanium de- Figure 20 demonstrates measurements of the effective I I p.l w 0 >-' 4 2 Figure 20 \JJ - w _J w u t- 3 a:: 0 z > 0 ..J en t- Q.. a:: 5 w -0 z Q.. <t ~ 6 - 2 4 6 vs 10 0 e 12 14 GERMANIUM SILICON 16 BIAS FOR 5.3 Mev a-PARTICLES BIAS VOLTAGE 8 E 18 I I (.,.J 0 f-' As a result energy up to the point where the incident particle penetrates the output pulse height bears a linear relation to the input pair being independent of incident energy and particle type , of the mean energy required to release an electron-hole silicon detectors to protons and a-particles . Figure 21 illustrated the general behavior of gold- I Pl ~ 0 I ...... 20 40 ~ I Figure 21 a.. ::::, ...J Cl) w I w - (.!) I .,_ 60 u - <l I z z w 80 ...J - 100 2 / 3 4 ENERGY (Mev) 5 HEIGHT vs ENERGY PROTO NS PULSE 6 ~ 7 8 a - PAR T ICLES 9 l J,. 0 I ,_, -105a- Figure 22 shows that the inverse square of the capacitance varies approximately linearly with the bias applied to a gold-silicon detector, This relation is expected from the theoretical prediction that the depth of the depletion layer increases as the square root of the applied bias plus a surface potential. silicon. The slope of the line represents a sample of 170 !Jcm (Also see Appendix A, page 69. ) -105- I/ /c2 vs BIAS VOLTAGE 6 U) I • 0 X -- 5 • N =t. =t. v 'E 4 0 N I <( w a:: 3 <( ~ z ::::::> ' >- 2 ~ u <( Cl. <( u / / / 2 0 -2 -4 -6 BIAS VOLTAGE Figure 22 -8 -10 -12 -106a- Figure 23 represents the direct current characteristics of various gold-germanium detectors at 77°K and gold-silicon detectors at room temperatures operated in near darkness. Empirically it is found that detectors with larger reverse currents exhibit poorer resolution. None of the characteristics illustrated represent detectors of outstanding resolution. ment are about Typical bias voltages for this experi- - 8 volts. The reverse current of the de- tectors is slightly light sensitive and thus for best results the detectors are operated in near darkness. Further dis- cussion of figure 23 is contained in Appendix A, page 61. - 106 - .20 DIRECT CURRENT CHARACTERISTICS .16 OF VARIOUS COUNTERS - - - GERMANIUM .12 SILICON .08 .04 BIAS VOLTAGE -24 -16 -20 -12 -8 -4 4 / -.04_ I U) w w a.. I ll: I I -.08 ~ <l'. 0 I ll: I u I ~ I I I I I I -.12 - .,_ z w ll: ll: -.16::::, u -.20 Figure 23 -107a- Figure 24 represents the solid angles accepted by the f3-detector and the 180° configurations. 24a the 0 a.-detector in the 0 0 , 90 , and The figure is not to scale. In figure 0° configuration is merely the inversion of the a-detector in the 180° configuration through the origin at the target spot. Both detectors have solid angles defined 1 by circular apertures, of half angle 19°40 in the case of the f3-detector and 9° in the case of the a-detector. The figure illustrates the definitions of the various angles used in Appendix B, page 64, for the purpose of integrating the 2 functions, cos 8f3a and cos 8f3a' over the solid angles. -107 - 0°or 180° Configuration ,8-DETECTOR a-DETECTOR Target Spot d .O.a {a) 0 90 Configuration ,8-DETECTOR Target Spot a-DETECTOR (T {b) DETECTOR SOLID ANGLE CONFIGURATIONS Figure 24 -108a- Figure 25 shows the directions of the electron, neutrino and a-particles and the angles between them in the rest system of Be 8 :.:< and in the laboratory system. The particles and angles in the laboratory system are denoted by Greek letters. The drawing is not to scale. The Be 8 :::c nucleus, which is not shown, recoils from the momentum of the electron and neutrino. This recoil imparts an addi- tional momentum in the laboratory system to the a-particles which are emitted in opposite directions in the rest system. The corresponding directional changes of the electron and neutrino are neglected. The result of the transformation is that several terms are added to the theoretical angular distribution function. Appendix D, page 73 , The transformation is discussed in - 108 - z /3 ,e v,n I I I I I I I I I ,- -,- I I I _, L:- ::::::-_::-- _I.--- \ \ \ \ \ \ \ ~ a' TRANSFORMATION TO LABORATORY ANGLES Figure 25