An Experimental Study of a Stellar Neutron Source: ¹³C(α, n) ¹⁶O Citation Davids, Cary Nathan (1967) An Experimental Study of a Stellar Neutron Source: ¹³C(α, n) ¹⁶O. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1S8V-K872. https://resolver.caltech.edu/CaltechTHESIS:11232015-105123847 Abstract Described in this thesis are measurements made of the thick-target neutron yield from the reaction 13 C(α, n) 16 O. The yield was determined for laboratory bombarding energies between 0.475 and 0.700 MeV, using a stilbene crystal neutron detector and pulse-shape discrimination to eliminate gamma rays. Stellar temperatures between 2.5 and 4.5 x 10 8 o K are involved in this energy region. From the neutron yield was extracted the astrophysical cross-section factor S(E), which was found to fit a linear function: S(E) = [(5.48 ± 1.77) + (12.05 ± 3.91)E] x 10 5 MeV-barns, center-of-mass system. The stellar rate of the 13 C(α, n) 16 O reaction if calculated, and discussed with reference to helium burning and neutron production in the core of a giant star. Results are also presented of measurements carried out on the reaction 9 Be(α, n) 12 C, taken with a thin Be target. The bombarding energy-range covered was from 0.340 to 0.680 MeV, with excitation curves for the ground- and first excited-state neutrons being reported. Some angular distributions were also measured. Resonances were found at bombarding energies of E LAB = 0.520 MeV (E CM = 0.360 MeV, Γ ~ 55 keV CM, ωγ = 3.79 eV CM) and E LAB = 0.600 MeV (E CM = 0.415 MeV, Γ ˂ 4 keV CM, ωγ = 0.88 eV CM). The astrophysical rate of the 9 Be(α, n) 12 C reaction due to these resonances is calculated. 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): Fowler, William A. Thesis Committee: Unknown, Unknown Defense Date: 1 March 1967 Funders: Funding Agency Grant Number Imperial Oil Limited UNSPECIFIED Office of Naval Research UNSPECIFIED Record Number: CaltechTHESIS:11232015-105123847 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11232015-105123847 DOI: 10.7907/1S8V-K872 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9286 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 23 Nov 2015 19:33 Last Modified: 15 Mar 2024 21:39 Thesis Files Preview PDF - Final Version See Usage Policy. 18MB Repository Staff Only: item control page

AN EXPERIMENTAL STUDY OF 13 A STELLAR NEUTRON SOURCE: c(a., n) 16o Thesis by Cary Nathan Davids In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1967 (Submitte d March 1, 196 7) ii AC KNOVILEDG I\IBNTS The author would like to thank the entire staff of the Kellogg Radiation Laboratory for the assistance and encouragement provided during the course of this work. Especially appreciated were the aid given by Professor W. A. Fowler, who initially suggested the project, and discussions with Professor C. A. Barnes, which led to many clarifications. A Graduate Research Fellowship from Imperial Oil Limited of Canada is gratefully acknowledged, as is the support provided by the Office of Naval Research. iii ABSTRACT Described in this thesis are measurements made of the 16 13 thick-target neutron yield from the reaction c(a., n) o. The yield was determined for laboratory bombarding energies between 0. 475 and 0. 700 MeV, using a stilbene crystal neutron detector and pulse- shape discrimination to eliminate gamma rays. Stellar 8 temperatures between 2. 5 and 4. 5 x 10 °K are involved in this energy region. From the neutron yield was extracted the astro- physical cross-section factor S(E), which was found to fit a linear 5 function: S(E) == [ (5. 48 ± 1. 77) + (12. 05 ± 3. 91)E ] x 10 MeV. 13 16 barns, center-of-mass system. The stellar rate of the C(a.,n) 0 reaction is calculated, and discussed with reference to helium burning and neutron production in the core of a giant star. Results are also presented of measurements carried out 9 12 on the reaction Be(a.,n) c, taken with a thin Be target. The bombarding energy-range covered was from O. 340 to 0. 680 MeV, with excitation curves for the ground- and .first excited- state neutrons being reported. measured. Some angular d~stributions were also Resonances were found at bombarding energies of ELAB == 0. 520 MeV (ECM == 0. 360 MeV, r"'"' 55 keV CM, wy == 3. 79 eV CM) and ELAB = O. 600 MeV (EbM = 0. 415 MeV, r < 4 keV CM, 9 12 wy = O. 88 eV CM). The astrophysical rate of the Be(a., n) c reaction due to these resonances is calculated. iv TABLE OF CONTENTS PART PAGE I INTRODUCTION 1 II APPARATUS AND METHODS 5 (a) Alpha Beam 5 (b) Magnetic Analyse r, Current Regulator, and 5 Hall Probe (c) Energy Calibration 9 (d) Current Integration 11 (e) Target Chambe rs and Targets 12 (f) Stilbene Neutron Detector and Pulse-Shape I Discriminator (g) Detector Efficiencies and Yield Calculations (1) Yield of 13c (a, n)l6o 12 (2) Yield of 9 Be(a, n ) c and 0 9 12 Be(a, n ) C*(4. 43) · 1 m IV v 14 19 21 26 EXPERIMENTAL PROCEDURE 30 (a) 13C (a' n)160 12 9 (b) Be (a, n) c 30 32 RESULTS 35 (a) 13C(a , n)160 9 12 (b) Be(a,n) c 35 APPLICATIONS TO ASTROPHYSICS 39 36 v PART PAGE APPENDIX I Stilbene Response to Prot ons 48 APPENDIX II Pulse - Shape Discrimination 51 REFERENCES 54 TABLES 55 FIGURES 59 1 I. INTRODUCTION As part of the continuing program in the Kellogg-Sloan laboratories on the study of nuclear reactions in stars, the present 16 13 investigation was undertaken on the reaction c(a., n) o . . Greenstein (1954) and Cameron (1954) first proposed this reaction as a source of 8 0 stellar neutrons. At temperatures near 10 K the neutrons are thermalized in the dense stellar medium, and are captured by heavy "seed" nuclei in great numbers. The seed nuclei, principally members of the iron group, are present in small amounts as part of the material from which the star originally condensed. Jones and Wilkinson (1951) first experimentally observed 13 the reaction, by bombarding a thick separated c target with 1. 05 MeV alpha particles. They reported further work (Jones 1953) in the energy range 1. 0 to 2. 1 MeV. Rusbridge (1956) extended their work up to 2. 5 MeV, using better resolution. ·walton et al (1957) measured the 0° yield from 0. 8 to 3. 5 MeV, as well as yields at other angles at higher energies, and angular distributions above 1. 0 MeV. No experimental work has been reported at lower energies, because of the very low yield of the reaction. fu order to determine the rate of the 13 c(a., n) 16o reaction at stellar temperatures, one must know the cross-section below center-of-mass energies of about O. 3 MeV. Because of the high 13 coulomb barrier between alpha particles and c nuclei, the crosssection in this region is too low to measure at the present time. It is thus necessary to measure the cross- section in the laboratory down to as low a bombarding energy as is possible, and to rely on theory to predict the low-energy behaviour. reactions one can write For low-energy nuclear 2 ( ) 0 (E) =SE e -2m1 (1) E where S(E) is called the cross- section factor. Here we are assuming that no resoriances occur in the stellar thermal r egion. In this case S(E) is generally treated as a constant or as a constant plus a term linear in energy. If a r esonance exists in the thermal region equation (1) is still valid, but a dis persion form must be ascribed to S(E). If there are more resonances, with the possibility of interference, S(E) becomes more complicated, and a theoretical eA.-trapolation to lower energies becomes somewhat less reliable. In the present experiment the yield of the reaction 16 13 c(a, n) o has been determined for center-of-mass energies from O. 526 down to O. 373 MeV, and the cross-section factor has been fitted by the method of l east squares to a function of the form S(E) = S(O) + (dS/ dE)E. In the course of developing a counter for use in this experi- 9 12 ment, measurements were made on the reactions Be (a., n ) c and 0 12 9 Be(a, n ) c * (4. 43). These reactions provided a readily available 1 source of neutrons for testing purposes, and the second reaction also produces a 4. 43 MeV gamma ray. In this way the neutron-gamma discriminator (to be described later) could be adjusted for optimum elimination of gamma radiation. 9 12 The Be(a., n) c reaction has long been known as a prolific source of neutrons (Chadwick 1932). Bennett, Roys, and Toppel (1954) first observed the two l ow-energy resonances armmd O. 6 MeV bombarding energy with good resolution. However, their work was presented in abstract, and the only published figures depicting their 3 results appeared in Amaldi's article in the Handbuch der Physik They used a BF long counter to detect the neutrons, which 3 did not allow a separation of the n {ground-state) and n (first 0 1 excited-state) groups. James et al (1956) published the results of (1959). some of their earlier work, including analysis, but their data did not contain the two low-energy resonances. Instead, they observed a peak in the yield at a bombarding energy of about O. 650 MeV. They were able, on the basis of their angular distributions and the Bennett data, to tentatively assign a spin of (1/2+) to the 11. 01 MeV 13 level in c. This is the level responsible for the resonance at 9 12 O. 52 MeV bombarding energy in Be(a, n) c. No information has been available on the state producing the resonance at O. 60 MeV, 13 the 11. 08 MeV state of c. Before beginning the experiments, a completely new beam handling system for the 700 kV accelerator in the Kellogg Radiation Laboratory was designed and built. The existing electrostatic analyser was removed and replaced by a 90° magnetic analyser. Steering mag11ets, regulating and beam-defining slits, and cold traps were constructed and installed. An oil diffusion pump was obtained for use on the target side of the analyser, since the narrow beam tube of the analyser effectively isolated this area from the main accelerator vacuum. A Hall-Effect probe was incorporated for magnetic field measurements. Appropriate regulators and · controllers were designed and constructed for the Hall probe and for the DC generator supplying the magnetic analyser. Energy calibration of the magnetic analyser was carried out. Improvements were made in the beam current integrator and in the optical periscope viewing system of the accelerator. 4 A stilbene crystal was used as the neutron detector, and appropriate electronic circuits were built for analysis of the pulse shapes obtained. In parts IT and m of this thesis, the experimental details are described. The results of the measurements are presented in part IV, and some of the astrophysical considerations relating to 16 13 the c(a., n) o reaction are discussed in part V. 5 IT. APPARATUS AND METHODS (a) Alpha Beam For the series of experiments described h ere the 4 He+ beam from the Kellogg Radiation Laboratory 700 kV Electrostatic. accelerator was used. The machine uses an Oak Ridge type RF ion source, and has a maximum t erminal voltage of about 700 kV. After passing through the steering magnets, the beam enters the 90° analysing magnet. The analysed beam is collimated by regulating and beam-defining s lits, and then passes through a long cold trap. This trap, a 1. 5 cm diameter by 31 cm long tube C()mpletely immersed in liquid nitrogen, prevents condensible organic vapors from reaching the t a rget area. The usual gate valves and pump- outs are available for isolating various sections of the beam tube. The r est of the beam-handling facilities are related to the target area, and will be described separately. The maximum available beam m easured on the target was 38 µa, and for the 13 C (a, n) 16 . 0 expernnent, beams of 25-30 µa were common_ l y used. (b) Mag11etic Analyser, Current Regulator, and Hall Probe Momentum analysis of the accelerator beam was provided by a 41 cm 90° d ouble focusing analysing magnet. With a coil resistance of O. 30, nearly 60 amperes are required to defle ct a 4 O. 700 MeV He + ion. For energy resolution of± O. 5 keV, current stability of better than 1 part in 500 is required. 6 The magnet current regulating system employed was patterned after that described by Garwin (1959), using an 18-volt 200-ampere DC welding generator. In this system (see figs. 1-4), the magnet current flows through a Constantan shm1t of very low resistance, and the ':oltage drop so produced is compared with a stable, adjustable reference, in this case a portion of the voltage across a mercury cell. Any error signal is converted to AC by means of a chopper, amplified, and re-converted to DC. The correction sig11al of the proper polarity is sent to a bank of 3 parallel- connected transistors in series with the magnet and generator (see fig. 2). The conductance of these pass transistors is thus modulated in such a way as to hold the current constant to 4 better than 1 part in 10 . In addition, a sensing circuit was desig11ed (see fig. 3) which supplies only enough current to the generator field to provide a l·· or 2-volt drop across the transistors, plus the required voltage across the magnet. In this way the power dissipation of the pass transistors is kept to an absolute minimum. The entire circuit is transistorized, with the exception of the first stage of the error amplifier. This is a high-gain DC chopper amplifier, modified from a commercial "Brown chopper amplifier". There are only two controls: an on-off switch, and a ten-turn potentiometer for adjusting the current. In nearly 3 years of operation the system has been stable and trouble-free. The 3 pass transistors plus one driver transistor are mounted on a water- cooled copper heat sink. Safety precautions include a thermoswitch which opens the generator field if the cooling water is shut off, and Zener diodes protecting the pass transistors from transients and overvoltage. Current is divided 7 equally among the 3 transistors by the inclusion of O. 06 o nichrome resistors in each emitter lead, Magnetic field measurements are carried out by means of a Hall-Effect probe placed between the pole pieces of the magnet. Because of the very narrow gap, the installation of a more conventional NMR system was not attempted. This would have required the use of compensating coils to offset the r-·l/ 2 dependence of the mag11etic field, making for too large a probe. A Hall _probe offers several advantages over an NMR system for magnetic field measurements. output is a DC voltage. It is small and compact, and the The disadvantages are its low output signal (tens of millivolts) and moderate temperature sensitivity. With the proper equipment, however, these two factors can be overcome to permit the desired degree of precision. The Hall probe is a thin wafer of semiconducting material {in this case Indium Arsenide) with electrical contacts made at four edges. A constant control current is passed through two opposing contacts. Applying a mag11etic field perpendicular to the face of the probe causes a potential difference to appear across the other two contacts. This potential difference, whose magnih1de is proportional to the product of field and control current, is typically several hundred millivolts for a ten kilogauss field and several hundred milliamperes of control current. The device has a very low output impedance, and termination of the output by a resistor specified by the manufacturer gives the best linearity of response to applied mag11etic field. The device used in this application was the Siemens Field Probe SA 23. The manufacturer states that the mean temperature coefficient of the Hall voltage is -0. 1%/deg C. between 0° and 100°C. 8 Room ambient temperature varies as much as five degrees over the year, and the temperature inside the magnet depends on the current being passed through it. Due to these variations, temperature compensation of the Hall probe was necessary in order to achieve the desired precision in the mag11etic field measurements. A copper heat sink 6. 4 x 2. 5 x 1. 3 cm was fashioned to completely enclose the probe. In addition, holes were provided for a 2000 O glass- enclosed bead thermistor and a 470 carbon resistor. The thermistor serves as one arm of an AC-excited bridge, and the 470 resistor is the heat:il1g element. A simple transistor circuit (see fig. 5) supplies current pulses to the heater when the b::.'idge is unbalanced, thus keeping the temperature of the copper block at a constant value. temperature was chosen to be 42°C. The normal operating Maintain:il1g this temperature requires a steady DC input power of 0. 3 watts. . A sensitive mercury thermometer was inserted in the block to serve as a temperature monitor. Over a period of two years, the temperature has remained within ± O. 2°c. of the desired value. The tempe rature controller is operated continuously. A very stable control current is required for precise field measurements. To this end a constant current source was designed and fabricated, utilizing a high-gain DC chopper amplifier in the feedback loop (see fig. 6). The rest of the circuit is transistorized. Hourly stability is better than 10 parts per million. A 20 manganinwire resistor is used as the current sensing element, and a mercury cell as the reference voltage. The current is automatically held at a low value when the source is initially turned on. This is accom- plished by the 100µf-470kO network at the input of the 2N1309 9 transistor. During this interval the chopper amplifier has time to warm up, and it then takes over and stabilizes the output current at 225 ma. · Typical values of Hall voltage, with a terminating resistor of 90, range up to lOOmv at the field required to bend a O. 765 MeV 4 He+ ion.· A Rubicon potentiometer is used to measure the Hall voltage, with precision equal to ± 0. 02%, or about ± O. 1 keV. {c) Energy Calibration Calibration of the 41 cm analysing magnet and Hall probe has been accomplished by means of resonances in the reactions 12 19 16 11 B(p, y) c* and F(p,a.y) o. In the following table, the reaction, mass of bombarding particle, bombarding energy, resonance width, and gamma energy are given. In all cases the charge of the incoming particle is 1, and the energy per nucleon is the resonance energy. Mass EB(MeV) r(keV) E (MeV) y 1) llB(p,y )12C* 1 0.1631 6. 3 11. 68 2) 19F(p,a.y )16 0 1 0.3405 2. 7 6-7 3) 19F(p, a. y )160 1 0.4836 1. 8 6-7 4) llB(p,y )12C* 2 0.3262 12.6 11. 68 5) llB(p,y )12C* 3 0.4893 18. 9 11. 68 Reaction The values of resonance energies and widths were taken from the article by Marion on accelerator energy calibration (1961). 10 The 11 B target was a pellet of separated 11 . B isotope pressed into a stainless steel holder. It served as an infinitely 19 thick target. The F target consisted of a layer of CaF 2 evaporated onto a O. 005" Ta backing. Its thickness was approximately 7. 5 keV to O. 480 MeV protons, essentially a thick target. Gamma rays were detected by a 2" x 2" Nal(Tl) scintillator, with a Hamner DDL amplifier serving as an integral discriminator, accepting all pulses with an energy greater than 3 MeV. A computer program (CNDCAL) was written to accept the five values of Hall voltage (V H) vs energy (E) and beam atomic number (A), and to fit these points by the method of least squares to a function of the form 1 2 V H(millivolts) = V + c(AE) / + d(AE), with E in keV. 0 Each point was weighted according to the precision of measurement. When the parameters V 0 , c, and d are obtained, V H is calculated for beams of mass 1 to 4 and energy from ·o. 000 to O. 998 MeV in O. 002 MeV steps. In addition, the program computes the uncertainties in the coefficients V , c, and cl. 0 Since the calibration points were derived from resonances of finite width, the weights were set equal to the inverse square of the width of the resonance involved. The stability and reproducibility of the system has been shown to be excellent by repeated measurements of thick target 14 13 13 excitation curves using c targets. The reaction c (p, y ) N has 11 a very sharp resonance at 0. 4485 MeV (Vogl 1963), and every measurement made on this resonance has been within 0. 5 keV of the correct value. The presence of the offset term V is due to the difficulty 0 in placing the Hall voltage leads exactly opposite one another. An ohmic voltage drop i s present with no mag11etic field, caused by 2 the flow of the control current. The term c(AE) l/ is what one would expect from the fact that the energy of the analysed particle varies with the square of the magnetic field. If the response of the Hall probe were linear with magnetic field, only these two terms should appear in the expression for V H. The term d(AE) represents non- linearity due to intrinsic limitations of the device itself and also changes in field shape as the field is increased. Because the Hall probe occupies a finite area in a region where the field is varying like r- 112 , any changes in the field gradient caused by saturation effects will be reflected in the total integrated output of the device. In the most recent calibration taken 1 month before the 13 c(a., n) 16o experiment was run, the following values of V 0 , c, and d were obtained: V d = o. 0032 ± o. 0003. 0 = -0. 545 ± O. 169, c = 1. 652 ± O. 015, and (d) Current Integration Charge measur ements were made with the 700 kV accelerator current integrator, considerably modified for these experiments. (19 52). The original circuit is described in Wenzel 's thesis A high-stability capacitor is charged to a predetermined voltage by the beam current. The voltage is read by a low- leakage 12 Acorn vacuum tube connected as a cathode follower. When the preset voltage is reached, the capacitor is discharged in a very short time, and the discharge is recorde d on a counter. Thus the total charge is given by the product of the capacitance, the number of discharges, and the discharge voltage. In the present series of experiments a 0. 944µf capacitor was charged to 98. 6V. A 300V battery connected between target and current integrator provides secondary electron suppression. In addition, a 2MO resistor has been inserted in series with the current lead. A high impedance Field-Effect transistor voltmeter was designed to read the voltage across this resistor, and it ~rives a 25µa meter serving as a beam current indicator (see fig. 7). The usabl e r ange eA.1:ends from O. 25 to 250µa full scale in seven ranges. Upstream from the target an electron suppressor ring completely surrounds but does not touch the beam. It is biased to - 300V, and prevents any electrons produced in the beam tube from reaching the target. (e) Target Chambers and Targets For 13 Two types of target chamber were used in the experiments. 16 c(a,n) o, where the yield is very low, a chamber permitting maximum solid angle in detection was used. In this case the target itself served as the end of the vacuum chamber, and the counter could be placed immediately adjoining the back face (see fig. 8). 12 9 For Be(a, n) c, chambers with cylindrical symmetry about a vertical axis were used, allowing angular distribution measurements to be made (see fig. 9). Since power dissipations in the 10 watt region were commonly encountered, all the chambers were fo rcecooled by an air blast. It was desirable to keep the targets themselve s 13 at an elevated temperature to reduce carbon buildup. were cooled to preserve the vacuum seals. The chambers Both teflon and un- greased viton 0- rings were used. Immediate ly in front of the target and concentric with the beam was placed a long cold sleeve cooled to liquid nitrogen temperature (see fig. 8). The target volume, extending to the cold trap mentioned in section (a), was kept at high vacuum by a 9 liters/ sec titanium-getter ion pump (manufactured by Ultek Corp.). Pressures read on the ion pump gauge during bombardment ranged - -7 from 3 to 4 x 10 torr. The precautions taken to keep the vacuum system free from organic vapors were necessary to hold the amount of carbon deposited o:;_ the targets to an absolute minimum. Pearson (1963) has found that the carbon deposition rate is proportional to the beam current and a l so to the target pressure. Any carbon buildup 13 on the c target would be especially noticeable because of the high beam currents and long bombardments. A natural carbon layer 13 (1% c) would reduce the energy of the particles incident on the 13 c layer, and thus reduce the neutron yield, since the yield is a very steep function of the bombarding energy. P eriodic checks of the yield at O. 625 MeV showed that carbon deposition was not a problem. Thick 13 c targets were made by heating 1/16" x 7/8" 13 diameter copper discs to red heat in an atmosphere of c-enriched methyl iodide vapor. The pressure used was about 10 cm of mercury. 13 Methyl iodide (CH I) enriched to 54% in c was obtained from Bio3 Racl Laboratories, Richmond, Calif. As deduced from measurements 13 14 made on a narrow resonance in the reaction c (p, y ) N, the targets had thicknesses near O. 200 MeV for O. 600 MeV alpha particles, 14 corresponding to about 200µg/cm 2 (see fig. 10 for typical thick target excitation curve). 9 Thin Be targets were made by evaporating Be metal from tantalum boats onto clean polished 1/16" copper blanks. 2 Target thicknesses. were of the order of 25µ g/ cm , giving an energy loss of,....., O. 015 MeV for O. 600 MeV alpha particles. Both the Be and C targets withstood long bombardments with ·little deterioration except for some discoloration. (f) Stilbene Neutron Detector and Pulse-Shape Discriminator Because of the low yields expected in the 13 c(a, n) 16 o reaction, it was necessary to choose a neutron detector possessing a very high efficiency. In addition, the detector chosen had to be insensitive to gamma rays. There are no gamma rays produced 16 13 in c(a , n) o, but a 4. 43 MeV gamma ray accompanies each 9 12 neutron in the Be(a, n ) C* (4. 43) reaction. Howeve r, even room 1 . 13 16 background exceeds the C(a, n) 0 count rate by several orders of magnitude at low bombarding energies, so gamma-ray elimination became a major consideration. For these reasons a scintillation counter employing a stilbene crystal was chosen. In this type of detector the neutron undergoes n-p scattering, and it is actually the recoiling proton that is detected. Stilbene, an organic compound with chemical formul a C H , is available only in small crystalline sizes, and 14 12 the crystal used in these experiments was 1 1/ 2" in diameter by 1 1/2" long, mounted in an aluminum enclosure. If high efficiency alone were desired, a large plastic scintillator (main requirement: high percentage of hydrogen) could have been used. However, 15 stilbene possesses the additional characteristic of providing different pulse shapes for events due to electrons from those due to protons. This phenomenon was first noticed by Wright (1956), who measured the decay times of pulses from stilbene ·(see Appendix II). Since 1958, circuits have been published which enable efficient discrimination of neutrons over a wide range of energies. The discrimination circuit used here was developed by Daehnick and Sherr (1961), and all the subsequent analysis circuits were developed by the author (see block diagram of system, fig. 11). The crystal was optically coupled by Dow Corning C-20057 Compound to a RCA type 6810A 2" photomultiplier tube. Layers of "Netic" and "Conetic" foil were wrapped around the assembly to provide shielding from stray magnetic fields. The tube anode voltage was 1940V, provided by a Fluke model 412B regulated power supply. Included in the phototube base are an integrating-type preamplifier for the linear signal and the initial pulse- shape discrimination circuit (see fig. 12). The linear signal (L) passes on directly for further analysis, while the pulse- shape discrimination (PSD) pulse undergoes preliminary amplification and shaping in the phototube base. This PSD pulse (see Appendix II) is positive for protons, and its amplitude is roughly proportional to the corresponding linear signal of the proton recoil. It is delayed by 2 to 3µs with respect to the L pulse, a characteristic of the time constants and operating mode of the circuit. The discriminating circuit contains no active elements, and has three variable capacitors which are adjusted so that an electron produces zero or negative 16 output. Three stages of amplification, biased to clip negative pulses, ensure that only positive (proton) pulses are amplified and passed on for further analysis. The circuits in the phototube base receive their power through the L signal lead. Both the L and PSD pulses are sent to the main electronics, where each event is subjected to various tests which determine whethe r it i s an acceptable neutron event (see figs. 13-15). If so, it is stored in the pulseheight analyser, and a lso recorded in a decade scaler. In order that an event be attributed to a neutron, several criteria must be satisfied. Firstly the L pulse must be above a preset minimum level. If this is the case, the lower level discriminator generates a 14µs "GO" pulse. Then both the L and PSD pulses are amplified and stretched. Each pulse stretcher produces a rectangular pulse whose amplitude equals that of the input and whose length is 14µs • . Action of the stretchers is terminated by the falling edge of the GO pulse. Stretched L and PSD pulses are applied to the X and Y plates of an oscilloscope, for display purposes. In addition, the L pulse is sent to an upper level discriminator. If the amplitude exceeds the l evel set there, a "V" veto pulse is generated. The second criterion which must be satisfied is that the amplitudes of the L and PSD pulses must bear a certain relation to one another. More specifically, the two stretched pulses are applied to the inputs of a differential amplifier. It computes the function (f . PSD - L), where f can be varied from 0 to 1. For a proton r ecoil, PSD is very closely proportional to L, whereas for an electron event PSD is very much smaller and is essentially 17 independent of L. If I f · PSD I is greater than ILI , the circuit allows a gate pulse "G" to be generated. The final test that the event must pass is a time coincidence test. G and GO are fed to a coincidence mixer, along with V in anticoincidence. If G and GO appear simulta11eously without the presence of V, the event is accepted as a neutron event. In this case a 7µs pulse is generated by the brightener trigger pair and applied to the Z axis of the display oscilloscope. This axis controls the intensity of the display. The timing of this pulse is such that it appears and disappears while the stretched pulses are still at their peak values. Thus an event appears on the oscilloscope as a brightened dot in the 2-dimensional L-PSD field. fall on a diagonal line. All proton recoils Electron events also appear, but their traces are not intensified, and they fall entirely on the X axis. If desired, the oscilloscope intensity control can be adjusted to make electron events just barely visible or completely invisibl e. After an event has been accepted, a coincidence pulse "C" is generated to be used in the Delayed Coincidence input of a RIDL 34-12 400- channel pulse- height analyser. The L pulse is suitably amplified and passed through a O. 8µs delay line, in order that the timing relations be correct. Positive outputs are provided to record the GO and C pulses on decade scalers. Adjustment of the circuit is extremely simple with the help of the display oscilloscope. The intensity is turned up so that both electron and proton events are visible when the counter is exposed to a source of neutrons and gamma rays. The cmmt rate should net be in excess of several thousand counts/sec. Variable capacitors . R, C, and F are adjusted so that the proton recoil locus i s separated from the electron locus as much as possible. The best setting will be 18 cleady seen if the count rate is high enough to provide a continuous display of events. During the course of runs with 13 c(a, n) 16 o it was discovered that sparks causing mi.nor fluctuations in the accelerator terminal voltage were registering as events, which could not be discriminated from neutrons. Efforts were made to shield out this RF energy, but they were unsuccessful. The reason for this is clear when one considers that the energy had to penetrate the thick grounded pressure tank of the accelerator. It must be a very low impedance source indeed! However, these fluctuations could be detected as sudden changes in the column current flowing down the bleeder chain resistors. Accordingly a circuit was devised which produced a V pulse only upon the appearance of a very fast transient on the resistor column current (see figs. 16 and 17). The timing of the pulses is such that the V pulse arrives in time to cancel an event due to a machine spark. These fluctuations were random in nature, sometimes occurring every few minutes and sometimes not at all. In order to check the efficiency of the spark detector, the C scaler pulse was connected to a beeping device, also audible in Room 101 Kellogg. Every time an event was registered, the audio tone thus produced could be correlated with any fluctuation appearing in the column current. The spark detector worked well enough to relieve the author of having to continuously watch for such spurious events on the column current meter. With the variable upper and lower thresholds, and the variable L/PSD ratio, the circuit is effective in eliminating about 99. 97% of all gamma rays, while counting proton recoils down to an energy of O. 9 MeV (see figs. 18 and 20). The gamma-ray elimination can be improved by raising the lower level of 19 discrimination to 1. 25 MeV, at which point about 7 counts per hour were recorded as background, all at low energy. In fact, this was 13 16 the lower level setting used in the c (a, n) 0 exp.eriment. At higher count rates the circuit performance is slightly degraded. Because of the dead time of the GO trigger circuit, charge tends to pile up on the pulse stretchers if pulses come at less than 14µ s intervals. A reasonable count rate is 5000 counts/ sec. (g) Detector Efficiencies and Yield Calculations It is a fairly straightforward procedure to calculate the detection efficiency of a neutron counter such as is described above, for a parallel beam of incident neutrons. The neutrons scatter off hydrogen and carbon, but it is only the proton recoils that produce a scintillation large enough to elicit a response at the photocathode. Due to scattering, the beam of incident neutrons is attenuated on passing through the crystal. These considerations can be expressed mathematically in terms of the n-p scattering cross- section and the n- carbon total cross- section. However, in the present experiment, the beam of neutrons cannot be considered to be parallel. Angular factors must be employed when calculating the efficiency, because the path length in the crystal is a function of the angle of incidence of the neutron. In addition, the neutron energy depends on the arigle of incidence, and thus the n-p scattering cross-section is different for every angle. Another consideration is the fact that only protons whose energies lie above the lower level discriminator setting are. accepted for analysis. In Ap;?endix I it is shown that the energy distribution 20 of proton recoils from a neutron beam of energy E 11 is of the form: dN constant for 0 < E ::;. E p - { p n dE p 0 for all other E p This means that if the number of proton recoils between some cutoff energy E 0 and the maximum energy E is known, the total number c 11 of protons is given by that number inultiplied by the factor En/(E 11-Ec 0 ). It is only necessary to know the energy Eco corresponding to the cutoff channel chosen in the pulse-height spectrum, to be able to determine the true number of proton recoils from zero energy to E • Since this factor is a function of neutron n energy as well, it must be included in the efficiency calculation for each angle of incidence. In practice, all the above mentioned effects are included in one integral, and the integ1~ation is carried out over the geometry of the crystal. A computer program has been written which produces the detector efficiency, including the solid angle, as a function of target nucleus, bombarding particle, crystal dimensions, angle made by crystal axis with the beam direction, target-to-detector distance, and low-energy cutoff. on the IBM 7094 computer. The integration is done numerically Provision is also made for inserting corrections due to absorption by the target backing. 21 . 13 16 (1) Yield of C (a, n) 0 This reaction has an extremely low yield at low energies, so that to determine the total cross- section by conventional methods is impossible, i.e. thin target excitation functions and angular distributions. Several crude angular distributions using moderately thick targets were measured and showed that an assumption of isotropy was consistent within about 25 percent. Thus the total 0 cross-section could be obtained from the o yield, measured with as great a solid angle as possible. The front face of the counter was placed 3 mm from the front face of the target (see fig. 19). A 2 thick target (~ 200µg/ cm ) was used, and the yield of neutrons was measured at bombarding energies from 0. 475 to 0. 700 MeV in 0. 025 MeV steps. As it turned out, the yield essentially doubled 13 12 every O. 025 MeV. For a thick target, containing c and c, the yield is given by EB Y(E ) = (nCV) • p • B q 1· C(EL)a(EL)dEL e (EL) where is yield at alpha-particle bombarding energy EB, in the laboratory system nCV q n is number of incident alpha-particles is number of current-integrator discharges . 22 c is current-integrator capacitance = O. 944µf v is current-integrator discharge voltage = 98. 6V q is charge per incident alpha-particle = 1. 6 x 10- 19 coulomb is fraction of target which is 13 c = O. 545 is alpha-particle energy in MeV in the laboratory system is efficiency of counter for isotropic source including solid angle factor is total cross-section at energy EL in barns is stopping cross- section for 4 He beam particles in carbon at energy EL in MeV-barns eT is target thickness in MeV in laboratory system ~ O. 200 MeV. The efficiency c;:(EL) is obtained from the following integral: · 211 c;:(EL) = frr J dcp J o crystal (A)(B)(C)(D)sin e de where A= ex p(-x'( e ). 1bu cbu) = exp(-0. 047sece) (2) 23 D = 1 - h25 E n and is number of H atoms in stilbene/cm 3 x n-p scattering cross- section . !. is number of C atmns1 cm 3 x total neutron cross- section for carbon nCti°"Cu i s number of Cu atoms/ cm 3 x total neutron cross- section for copper x(e) is path length for neutron in stilbene crystal (see fig. 19) x'(e) is path length for neutron in target backing E is neutron energy in MeV in laboratory system n = En(EL,e). Both nHcrH and nccrc are functions of neutron energy En. Term A accounts for the absorptive effect of the copper target backing. Term B gives the fraction of neutron interactions in the crystal which lead to a detectabl e recoil proton. Assuming that any interaction whatever r emoves a neutron from the beam, t erm C describes the attenuation of the beam in passing through the crystal. Fina lly, t erm D provides the fraction of proton recoils accepted, due to their 24 energies being greater than the lower level discriminator threshold, set in this case at 1. 25 MeV. The integral over cp can be evaluated, since there is cylindrical symmetry about the crystal axis. Then the yield is given by where IC(EL) is a slowly varying function of EL, ranging from O. 0733 at O. 4875 MeV to O. 0751 at 0. 6875 MeV. Since a low-energy nuclear reaction is involved, the substitution S(EL)exp(-2m1) EL Then is useful. (3) 25 where S(EL) is the astrophysical cross-section factor introduced in equation (1), page 2. Its units are Me V - barns, in the laboratory system. The evaluation of equation (4) to obtain S(EL) is best accomplished by substituting expressions for IC(EL) and e(EL), and postulating a functional form for s. Since \(EL) and e(EL) are slowly varying with EL' power series expansions up to terms in EL 2 are sufficient. Differentiation of the yield curve showed that S(EL) was well represented by a two-term linear function where SL (0) and a. are unknown constants. Also required for the integral is the target thickness S.· However, the exponential term so dominates the integrand that less than 1% of the integral is due to energies more than O. 200 MeV below EB. The target is thicker than O. 200 MeV in all cases. Using O. 300 MeV as a suitable thickness, Y(EB) = 1. 59n • 10 14 E JB {SL (0) ~-.300 EB + a I ~.300 26 The stopping cross-section c:(EL) has been taken from Porat and Ramavataram (1961), who state the precision of their absolute measurements to be 5%. Integrals I and I have been performed 1 2 on the IBM 7094 computer, and are found in Table 1. The constants SL (0) and a. are found from a least-squares fit of all the yields taken at the various bombarding energies. Errors used in this fit are the statistical uncertainties in the yields. Other uncertainties are applied to the final answers. To convert the value of S(EL) from the laboratory to the center- of- mass system, we notice that the ratio $(E)/E is the same in both systems (see equation (3)). Thus . = 0. 76464SL (0) + a.E MeV-barns, CM (5) system where the coefficient a. is unchanged since S(E)/S(EL) = E/EL. These reactions have a significantly higher yield than the 13c (a, n) 160 reaction, so thin target excitation functions and angular distributions were measured. Both neutron groups are present in the pulse-height spectrum, and they can be separated to obtain d.i fferential cross- sections (see fig. 20). The procedure is as follows: A cutoff energy Eco is chosen (refer to fig. 20) such that only ground- state neutrons are present above it. The counts are 27 summed from there up to an energy which is definitely higher than the energy of the group. Let this sum be i:: 0 . If N0 is the number of ground- state neutrons emitted into 4rr if the source were isotropic, then J Eco No J do = - r 0 Eno 4n f (o) [ 1 - - crystal where f(o) = (A)(B)(C) as defined in section (g), (1), part II, except that the variable e is replaced by a dependence on the cp-direction in the crystal and the angle made by the · crystal axis with the beam direction. The target-backing correction term (A) is used only when the backing comes between the target surface and the counter. Next a lower cutoff energy Eel is chosen such that it is slightly above the lower level discriminator bias. The counts between this cutoff energy E ' c 1 and the upper cutoff E c 0 are summed. Included here are both ground- and first excited- state neutrons. Let this sum be I: 1 , and let the number of ground- state neutrons contained in i:: 1 be !: • But 2 J f(O) [ crystal E cO - E Eno cl ]dO 28 E 1 E 0 f(o) [ (1 - __£__ ) - (1 - __£__ ) ] dO I Eno crystal Eno where I crystal E f(o) [ 1 - Eel J do • nO Subtracting r. from ~l gives the number of first excited-state 2 neutrons in the energy interval (Eco - Ec 1), or equivalently, the number of first excited-state neutrons between the lower energy cutoff E cl and the maximum neutron group energy Enl. Let this number be 'El . J Eel Nl J do = - I Enl 4rr 1 f(o) [ 1 - - crystal where N is the number of first excited- states neutrons emitted 1 into 4n if the source were isotropic. We have 29 But . N L: 0 4rr - I 0 0 ' so 4n = The quantities of interest are N /4n and N /4n, which are related 0 1 to the differential cross- sections at the angles concerne d. the known stopping cross-section of 4 From He particles in Be (Whaling 1958) and the measured width of a very narrow resonance obtained from the excitation function (see fig. 24), the target thickness was 18 2 obtained. This was fo~nd to be (0. 514 ± O. 037) x 10 atoms/cm • So ~ = (~~) x (number of incident particles) x (thickness) in appropriate units. Putting in the correct constants, we obtain ( da ) = O. 00335 dO n ( B_) 4rr where n is the number of integrator discharges. Finally da ( dO )n 0 1 L:o µb = 299 n ( I ) sr , laboratory system 0 µ b , laboratory system. sr The integrals I 0 , Il' and I have been calculated numerically 2 on the IBM 7094 computer. 30 ill. EXPERIMENTAL PROCEDURE Before performing any runs on the 13 c(a., n) 16 o reaction it was necessary to establish an energy calibration for the s.tilbene neutron counter. This enabled the lower level discriminator to be set at 1. 25 MeV, the value selected as giving good detection efficiency combined with a low background count. The calibration was carried 12 9 out using the reaction Be(a., n) c at three different energies: 0. 4, O. 5, and O. 6 MeV. Before the runs, the equipment was allowed to warm up for 24 hours. Supplementing the neutron energies as calibrations, three gamma rays were used as independent checks on linearity and gain. 137 22 . They were Cs (0. 66 MeV), and Na (0. 51 and 1. 28 MeV) . . Smee stilbene is an organic material, with very low- Z constituents (carbon and hydrogen), its response to low- energy gamma rays is entirely due to Compton scattering. The gamma rays were also used for recalibration purposes at a later data, allowing the overall gain to 9 12 be reset at the Be(a. , n) c calibration value. Gain stability over a day's run was found to be excellent, and with the low yields encountered, gain shifts due to count-rate were nonexistent. Before each day's run, the linearity and zero level of the RIDL model 34-12 400-cha.nnel pulse-height analyser were checked using a mercury pulser, which was provided with a motorized amplitude control. This allowed the amplitude to be raised or lowered at a linear rate with time. Establishment of the zero level to within one channel was important, since zero volts = zero channel 31 was used as one of the energy calibration points. The internal amplifier of the RIDL was not used, but instead the pulses from the previously described electronics were fed directly to the analogue-to-digital converter by means of the DIRECT CONV input. Coincidence gate pulses (C) w,ere applied to the DELAYED COINCIDENCE input. Each run was recorded in 100-channel segments, and the number of coincidence pulses was recorded on two separate decade scalers conne~ted in parallel. The runs were terminated after approximately 20, 000 µC of charge had been accumulated on the current integrator. At regular intervals during the running day, a check-was made on the condition of the target. This was accomplished by measuring the yield of the reaction at O. 625 MeV bombarding energy. Approximately 475 counts were obtained for 20, 000 µC, the time · taken being about 12 minutes. Al1y deposit of carbon caused by the bombardment would have shown up in the yield, since the energy of the incident particles would have been slightly degraded upon passing 13 through the carbon layer. This layer contains only 1% c, so there will be negligible ·contribution to the neutron yield. During the entire 16-hour bombarding period, no deviation in the yield at O. 625 MeV outside the statistics was noticed. As mentioned pre- 7 viously, target area pressure was .4xl0- tor~,and both liquid nitrogen traps were kept constantly filled during the run. Half-way through the running day the beam was removed from the target and a background run was taken. was set at 0. 475 MeV. Bombarding energy One cow1t was observed in 1, 000 seconds. 32 Beam current on the target varied throughout the running period from 20 - 27 µa. Air blast cooling was used on the target chamber, and was adjusted such that the target was visibly reddish in color under bombardment. This heating of the target by the beam helped to keep the deposition of contaminants at a very low level. The thick target neutron yield for the 13 c(a., n) 16 o reaction was measured in 0. 025-MeV steps from 0. 475 MeV to O. 700 MeV. Data used for analysis were the scaler counts, with the pulse-height spectra used only as stand-by. At bombarding ~nergies below 0. 625 MeV, the runs were sufficiently long and the count-rate sufficiently low that background corrections were made, based on the length of the run. Above this energy the background was negligible. In fact, at the higher energies the statistics were good enough to allow less charge to be ·accumulated for each run. The total charge registered for the running period was 1. 3 coulombs. (b) 9 Be(a., n) 12 C The presence of two neutron groups in this reaction made energy calibration of the counter a routine m atter. Before each day's run began, the same precautions and checks on the apparatus that 16 13 9 16 were performed for the C(a., n) o were repeated for Be(a., n) o. Because ·of the higher count-rates encountered, a lower level discriminator setting of O. 9 MeV could be tolerated, allowing a larger fraction of the low-energy first excited-state neutron group to be detected. All data analysis was performed on the pulse-height spectra, · with the scaler counts serving as a monitor during the experiment. 33 0 Excitation functions were recorded at o and 90° in the laboratory system, between the energies of 0. 340 arid 0. 680 MeV. The charge accumulated for the majority of the runs was 2, 000 µC. A 4. 5 cm diameter brass target chamber was used (see fig. 9), and the front face of the detector was 2. 3 cm from the target center. In this position the front face of the detector subtended an angle of just under 40 0 at the target. In addition to the excitation functions, angular distributions were measured at O. 480, 0. 520, 0. 5925, and O. 608 MeV. In this case a stainless steel target chamber of diameter 2. 5 cm was used, and the front face of the detector was placed at a distance of 8. 1 cm from the center of the target. Data were taken at nine angles: 0, 20, 40, 60, ~O, 100, 120, and 140 degrees in the laboratory system. During these runs, ta.ken about 1 1/2 months after the excitation functions, the zero level of the RIDL 400-channel pulse-height analyser was malfunctioning, and a shift of nearly 10 channels was observed over the course of the running period. Corrections to each. run have been applied to remove this shift, based on the mercurypulser calibration made at the beginning of the running day. An angle of just w1der 14° was .s ubtended by the front face of the counter at the target, permitting. good angular resolution. The target was placed with its outward normal at an angle of -13 5° to the focident beam direction. ..Angles below 90° thus required a targetbacking correction, while those greater than 80° did not. The angle 80° was measured w1der both conditions, in order to supply a check for the correction. was used. For these measurements a beam current of 12 µa 34 At the same time, two spectra were taken with reduced photomultiplier voltage and amplifier gain, in order to demonstrate the effect of the neutron- gamma discriminator. These spectra clearly show that the 4. 43 MeV gamma ray from the decay of the 12 first excited state of c does not appear when the neutron-gamma discriminator is operating (see fig. 18). The same target that was used for the excitation functions was used in the angular distribution measurements. The spark 9 12 detector veto circuit was not used in any of the Be(a., n) c runs. 35 iV. RESULTS The thick target neutron yield for the reaction is shown in fig. 21, in counts per 2.J, 000 µC. 13 c (a., n) 16o The observed numbers are found in Table 1. Along with the normalized experimental points is a solid curve computed from the least- squares fit to the yield. 5 The results from this fit give SL(O) = (7. 165 ± 2. 118) x 10 MeV5 barns, and a. = (12. 047 ± 3. 623) x 10 MeV-barns. Uncertainties are due solely to the statistics. Equation (5) enables S(E) to be calculated, and this function appears in fig. 22, along with the stellar temperature scale associated with the center- of- mass energies. 8 These are given in units of 10 °K (T ). Knowing S(E), the total 8 cross- section o(E) can be calculated, and this is shown in fig. 23. Also found in Table 1 are the calculated values of the yield and of the total cross- section at each energy point. Before stating a final value for S(E), . the sources of uncertainty must be considered. Besides the statistics, there exist uncertainties in the number of incident particles, the stopping crosssection e:(EL), and the efficiency integral IC(EL). An error of ± 5% can be assigned to the number of incident particles determined from the current integration. of ± 5%. The stopping cross- section has an uncertainty Systematic errors appear in the efficiency integral IC(EL). These are due to uncertainties in the crystal dimensions, detector-totarget distance, beam spot size and centering, as well as errors in determining the lower cutoff energy 1. 25 MeV, and small errors in the n-p and n-carbon cross-sections. These latter quantities were 36 obtained from "Neutron Cross-Sections" (Hughes 1958), and were fitted to simple functions in the energy range concerned, in order that the calculations be done entirely by computer. From all of these factors, an uncertainty of 10% is _assig110d to the quantity \(EL). _ The total uncertainty in the final expression for S(E) is thus: least-squares fit (statistics) < 30% (see p. 101) current integratfon 5% stopping cross- section 5% .efficiency integral 10% Total < 32% (see p. 101) So 5 S(E) = [ (5. 48 ± 1. 77) + (12. 05 ± 3. 9l)E] x 10 MeV-barns. If E is measured in keV the expression becomes 8 S(E) = [ (5. 48 ± 1. 77) + (0. 012 ± 0. 004)E] x 10 keV-barns. On figures 24 and 25 are found the excitation ·functions for 9 12 the ground- and first excited-state neutrons from the Be(a., n) c 0 reaction, taken at o and 90° in the laboratory system. The yield has been converted to a differential cross- section by the method 37 outlined in Section (g)(2), part II. Angular distributions for both neutron groups are shown in figs. 26 and 27. The experimental points have been fitted by the method of least squares to combinations of Legendre polynomials, and normalized to the calculated value at 90°. All distributions are in the center- of- mass system. Terms up to and including P 4 (cos e) were used when necessary. Table 2 gives the coefficients found for each Legendre polynomial, normalized to the coefficient of P (cose) taken equal to 0 1. The four bo-m barding energies at ·which angular distributions were ta.ken were 0. 480, 0. 520, 0. 593, and 0. 608 MeV. From the excitation function measurements the lower resonance at 0. 520 MeV bombarding energy (11. 01 MeV state in 13 c) is seen to have a laboratory width of 80 keV. The upper resonance 13 at O. 600 MeV (11. 08 MeV state in c) can be assigned a laboratory width of less than 5 keV. A very thin Be target is required to further investigate the properties of this level. An analysis of the experimental excitation functions and angular distributions by an R-matrix calculation is in principle feasible. However, as is obvious by the shape of the excitation functions, more than two levels are involved. In fact, the two broad 13 ~ states in C at 11. 97 MeV [ t.1 = (7/2) ] and 12. 87 MeV tJ > (5/2)] are almost certainly affecting the data in the energy range measured. In view of the unknown characters of these upper states, and in the limited interest in the lower states in 13c, it was decided not to pursue the calculation. 9 In the energy range studied, the reaction Be(a, n) to populate equally the ground- and first excited- states of 12 c appears 12 c. An · 38 uncertainty of about ± 15% can be assigned to the absolute differential cross- sections. Relative errors in the angular distributions are of the order of ± 5%. For further discussion 9 12 of the resonance parameters applied to the Be(a., n) c reaction in a star, see the following section on astrophysical applications. 39 V. APPLICATIONS TO ASTROPHYSICS Once expe rimental cross- section data are available for a thermonuclear reaction, it is useful to present the information in a format which enables the computation of variables of interest in astrophysics. A recent review article (Fowle r et al 1967, henceforth referred to as FC Z) presents a compilation of experimental results from many thermonuclear reactions, and provides a series of numerical coefficients with which the reader may construct quantities pertinent to nuclear astrophysics. These are the reaction rates, nuclear lifetimes, and energ·y generation rates, as a function of stellar paramete rs like temperature, density, and abundances of the constituent nuclei. Two types of reactions are dealt with: those involving resonances in the compound state, usually occurring at 8 stellar temperatures greater than 2 x 10 °K, and those exhibiting a slowly-varying non-resonant behavior with energy, typical of 8 0 stellar temperatures below about 10 K. 16 13 For the present application of the c (a., n) o reaction, we are concerned only with the non- resonant region, which in this case 9 extends from T (T = 10 °K) = 0 to 1. A short summary of the 9 notation in FC Z will be in order. The reaction rate between two nuclei 0 and 1 is given by P 01 0 1 ( 01 ) reactions- cm = 11 11 -3 - sec -1 where (01) ; (av ) in cm 3-sec-l is the product of cross-section and velocity averaged over the velocity distribution. The particle 3 number densities are given by n and n in cm- . If the atomic 0 1 abundances by mas s x and x are used, n 0 = p NAx 0; A0 and 0 1 40 3 = p NAXl/ A , where p = matter density in gm-cm- , NA= 1 1 Avogadro's number, and A and A are the atomic mass numbers 0 1 of 0 and 1. With respect to the laboratory, A is the target 0 nucleus and A is the projectile. 1 The mean lifetime of the nucleus 0 for interaction with n nucleus 1 is xl 1 = A.1(0) = ,.1 (0) n (01) = - [ 01] sec 1 Al [ 01 J = pNA (01) sec where -1 -1 so Energy generation by the exoergic reaction 0 + 1 _. 2 + 3 + Q is given by Poi e01 = -p- Q(erg) = 9. 6487 x 10 where Q 6 17 xx 0 1 - - [ 01] Q AO Al is the reaction Q in MeV. 6 -1 -l erg-gm -sec 41 Before the previous quantities can be calculated, ( av) must be determined. With the expression for cr(E) given in equation (1) page 2, and using a Maxwellian velocity distribution, we obtain for charged particles s · [ 01 J = { 7. 8327 x 10 9 (ZoZ1/ A) 1/3 S(O)J ~ eff 8(0) p T 9 - 2/3 exp(- T) • The reduced mass number A is given by A= A A /(A + A ), and 0 1 1 0 the factor in curly brackets is the numerical coefficient listed in Table III of FC Z. The quantity Sef/S(O) is a function of temperature: Seff _ 1/3 2/3 4/3 5/3 S(OJ - 1 + (a)T 9 + (b)Tg + (c)Tg + (d)T + (e)Tg • 9 Coefficients (a) - (e) for the various powers of T are given in FC Z, 9 3 Table III, as is the quantity ,- T l/ . For the lifetime, 9 and the energy generation _ { 17 9 1/3 S(O) } e01 - 9.6487 x 10 x 7.8327 x 10 (ZoZ1/ A) A A Q6 0 1 42 In the case of the 9 Be(a., n) 12 C reaction, it may be important in high temperature- high density situations where the primary constituents are alpha- particles and neutrons. In analogy 9 to the 3- a process, some Be could be produced in equilibrium 12 9 12 quantities, forming c via Be(a., n) c. In a normal star, any 9 Be that is produced is quicldy consumed by the reaction 8 Be(p, d) Be _, 2a.. Several resonances exist in the T = 1 region 9 9 12 for Be(a., n) C, and the parameters needed to compute the astro9 physical lifetime of Be can be obtained from the experimental data. 9 FC Z give, for a resonance at E r in the center-of-mass system, [ 01] = { 1. 540 x 10 }. -3/2 -1 11 -3/2 A (wy )r pT exp(-E/kT)sec 9 where ( wy) wrlr2 = ( -r - )r r Me V w = (2Jr + 1)/(2J + 1)(2J + 1) • 0 1 The J's are the spins of the resonant state, target nucleus, and projectile, while the r 1 s are the widths associated with the BreitWigner cross-section (see FC Z). Two methods for obtaining (wy) r are .given by FC Z: one for "poor" resolution experiments, and one for "good" resolution experiments, where the quantities E , cr , r and r r are obtained from the experimental measurements. fir st case we have r For the 43 (wy)r = ~ • 3807(AEr) J crdE center-of-mass system r r In the second case, A 3 0 . (wy )r = • 3807( A +A ) A1 (rrEr)L ar center-of-mass system. 0 1 Referring to figs. 26 and 27, the total cross-section can be obtained from the 90° excitation function with little error, because the average of each angular distribution is approximately the differential cross-section at 90°. Because of the high neutron energies involved, conversion to center-of-mass angle from the lab angle of 90° introduces negligible error. Taking the area under the yield curve for the narrow resonance yields for the two neutron groups: (wy) . = O. 51 x 10 r (wy) r -6 MeV (CM) ground-state group = O. 37 x 10- 6 MeV (CM) first excited~state group. . For the lmver, broader resonance the parameters are: E r = 0. 520 MeV (LAB) E r = 0. 360 MeV (CM) · 44 a = 92 µb ground- state group a = 89 µb first excited- state group r r rr = O. 080 MeV (LAB) rr = O. 055 MeV (CM). Adding the cross- sections for both groups, we obtain (wy) -6 = 3. 79 x 10 r MeV (CM). 9 4 The lifetime of the Be nucleus to inte raction with He via 9 16 Be(a., n) o may now be computed. Using numerical coefficients 9 given in FC Z, .including (Er/k) (degrees x 10 ), the result is 9 1 1 pT ---,9,____ = _ x 5 4 9 T4 ( Be) 3. 17 x 10 He He -3/2 exp(-4. 179/ T ) sec -1 9 (0. 520 MeV resonance) 1 x 4 pT9 -3/2 exp(-4. 822/ T 9) sec -1 = ----_-= 9 5 ( Be) 1.39 x 10 He 1 ,4 He (0. 600 MeV resonance) . These times are in the nanosecond range for T 9 c. 1 and p ~ 10 gm-cm -3 5 45 Using the table we may construct the various expressions . 13 16 for the react10n C(a, n) 0. For the non-resonant case we have [01] = 6. 769 x 10 15 (1 + O. 013T 1/3 + 2. 04T 2/3 + O. 184T ) 9 9 9 ( -1/3 )sec -1 x pT 9 - 2/3 exp-32.329T 9 3 2 l _ 1 (1 + 0.013T l/ + 2.04T g 13 + 0.184T ) 9 6 9 5.913 x 10 x x 4 HepT 9 e13 4 C He - 2/3 ( -1/3 -1 exp -32.329T 9 ~ sec (6) -- 2. 779 x 1032 (1+O.013T 1/3 + 2. 04T 2/3 + O. 184T ) 9 9 9 x x4 He x 13 pT 9 -2/3 exp(-32. 329T 9 -1/ 3) erg-gm C -1 -sec . -1 13 The quantity log 10 [ pX T 4 ( c)] has been plotted in fig. 28, as a 4 . He He function of T , with the lifetime in years. As expected, the lifetime 9 is a very sensitive function of temperature, especially for T < O. 2o 9 See Table 3. 16 13 The rate of the c(a, n) o reaction in stars has been discussed by several authors (Cameron 1955, Burbidge 1957, Caughlan and Fowle r 1964, and Re0ves 1966). The re are two 46 temperature regions in which it plays a part in neutron production. While hydrogen is burning via the CNO-cycle, an equilibrium 13 concentration of c exists. Just before .the onset of helium burning, at a temperature around T = O. 08, the possibility exists 9 13 16 . that the C(a, n) 0 reaction could produce neutrons. However, the conditions prevailing in the core of the star are such that very few neutrons are made available for capture by the heavier elements. 13 c nuclei ("' 1% of all CNO This is because of the low abundance of 14 nuclei), and because of the presence of N (,..., 95% of CNO nuclei). . . 14 14 Many neutrons are absorbed by the reaction N(n, p) C. Regener16 12 13 13 ation of the neutrons by c (p, y ) N _, c (a, n) o is not sufficiently 14 rapid to act as an antid.o te to the N. If we assume the nmnber of iron group "seed" nuclei to be 1/ 70 of the number of CNO nuclei, then less than 1 neutron is available for capture by each heavy metal 16 13 nucleus. For these reasons, the reaction C(a., n) o only supplies neutrons for capture on a very long time scale during the hydrogenburning phase. However, the situation changes after the hydrogen in the center of the star has been converted to helium, and the helium core 4 12 heats up sufficiently to begin burning via the 3 He _, c process. The star has now reached the giant stage, and its core temperature = O. 1. It is now possible for a small number 9 of protons from the inner edge of the hydrogen envelope to be is in the vicinity of T introduced into the core, where they are immediately captured by 12c nuclei and thus form 13c. Since there are only a limited number 14 13 of protons available in this region, the reaction c(p, y ) N is 16 13 inhibited. Instead, the c(a, n) o reaction now takes place unimp2ded, supplying a large number of neutrons which are captured by the heavy elements. 47 Equation (6) of this section may be used to compute the 13 c lifetime under: the two conditions specified above. For .the first case , at the termination of the CNO-cycle in the core, take 4 3 T : O. 08, and p ,..., 10 grn-cm- • Since most of the hydrogen in 9 the core has been consumed, x :::::= 1. The lifetime obtained He 5 is,..., 10 yr, demonstrating that the neutrons are indeed produced 4 on a slow time scale. Secondly, allow protons to be mixed into the helium4 burning core at T 9 : O. 1, and assume a density of,.._, 5 x 10 gm-cm- 3• A lifetime of,..., 100 yr results. It is important to note that these temperatures and densities are .only rough estimates. In fact, the density is changing very rapidly near the core boundary, and since the lifetime is such a sensitive function of temperature, a wide range of equilibrium situations will prevail 13 wherever the c is burning. However, it is clear that under these conditions the neutrons will be produced on a rapid time scale, . permitting the formation of the heavier elements, i.e. those with A 2 100. It appears that above a temperature of T ,..., O. 25, the 9 13 c(a., n) 16o reaction will no longer be an important neutron source in the dense helium core, because the rate offor mati on of 13 C is limited 13 by the 10-min 13-decay of N. Other reactions without this 21 24 limitation, like Ne(a, n) Mg, will become prevalent at the higher temperatures. 48 APPENDIX I Stilbene Response to Protons Treating only single neutron-proton interactions in the stilbene crystal, the energy distribution of recoil protons from a monoenergetic neutron beam can be obtained in a straightforward mam1er. If the neutron energy is below 14 MeV, the elastic scattering in the center-of-m:-iss system is isotropic. From this fact it is easily shown that the number of recoil protons is independent of proton energy, up to the maximum energy available to them. This energy is simply the neutron energy. In other words, ::p p = { constant for 0 < Ep ~ En 0 for all other E p The observed pulse-height spectrum differs from the theoretical rectangular shape for several reasons. It turns out that the luminous output of the stilbene is not proportional to the energy that the proton leaves in the crystal. A semi-empirical formula due to Birks (1953) allows us to write 1 dP dE = ----="dE= p 1 +kB dx where P is the pulse height, and kB is a constant. For electrons of reasonable energy, dE/dx is very small, and can be neglected. This produces a direct proportionality between pulse height and 49 energy loss. For protons in the MeV region, dE/dx ca1mot be neglected, and the pulse height is not a linear function of the energy loss. In various measurements made by the author, the observed pulse height dependence on proton energy could be closely fit by a function of the form P = A(E )m, where A is p a constant of normalization, and m is a number in the vicinity of 1. 4. The effect of the non-linear response of stilbene is to compress the pulse-height spectrum at lower energies. This is illustrated by fig. 20, which shows the pulse-height spectrum on a semi-logarithmic scale obtained from the two reactions 9 12 9 12 . . . Be(a., n ) C and Be(a., n ) C*(4. 43). The higher energy 0 1 group has an energy of 6. 24 MeV and the lower energy group has an energy of 1. 88 MeV. A second factor which causes distortion of the pulseheight spectrum is statistical fluctuations. These occur in both the number of photons produced by the decaying lattice molecules, a.rid in the number of photoelectrons emitted at the photocathode. As a result of these fluctuations, the pulse-height spectrum no longer has a sharp upper limit, but instead is folded with a gaussian. The width of this gaussian is usually several tenths of an MeV. It is common practice to assign the point at which. the "r2ctangular" distribution drops to one-half its value as the energy corresponding to the maximum proton energy. For the reasons stated above, the energy. resolution of a stilbene crystal used as a fast neutron det2ctor is quite poor. For precise determinations of neutron energies, other methods such as time-of-flight and (n, p) and (n,a.) reactions in silicon detectors 50 are far supe rior. The advantage of stilbene lies in its high efficiency and its ability to discriminate against gamma rays {see Appendix II). In all the efficiency calculations done in this thesis, effects such as (a) loss of protons from the end of the crystal, (b) loss of protons from the sides of the crystal, (c) scattering from carbon nuclei, and (d) double scattering from hydrogen, have all been neglected. It turns out that neglecting these factors usually causes only a small error. The reasons for this are: (1) some of the effects actually work to cancel one anothe r, i.e. (a) and (c) with (d), and (2) the total integrated number of counts does not change. Counts may be shifted from lower to higher energies and vice-ve rsa. Since the quantities determined from these experiments involved adding up the total number of counts between widely spaced limits, the effects of the above-mentioned secondary or geometrical factors are minimized, and are therefore neglected here. 51 APPENDIX Il Pulse- Shape Discrimination Within the last decade a new technique for detecting fast neutrons has evolved, based on a phenomenon peculiar to certain organic scintillators. It is found that the decay times of the scintillations from these materials increases with the specific ionization of the detected particle (Wright 1956). Actually, it has been shown that the decay consists of a slow and a fast comp-: ment, and _it is the relative amounts of each which is determil1ed by the nature of the ionizing particle. Thus the scintillations due to protons (caused by recoil from a neutron) and to electrons (produced when an incident gamma ray undergoes Compton scatteril1g or pair production) may be separated electronically using their clifferent scintillation pulse shapes (Owen 1958). Some scintillators which are useful for pulse- shape discrimination are stilb2ne, quaterphenyl, and anthracene. The se are solid crystals. Certain liquid scintillators exhibit the same decay-time characteristics, provided that all dissolved oxygen is first removed (Brooks 1959). Circuit Details The c~rcuit chosen was one devised by Daehnick and She rr (Daehnick 1961) (see upper left corner of figo 12). The op2ration of the pulse- shape discriminator is as follows. The current pulse through the photomultiplier may be approximated by the sum of two components: 52 where 'ff is a fast decay time, .5 10 ns, and 'fs is a slow decay time, usually several hundred ns. The coefficient a(E) depends on dE/dx of the charged particle which is actually detected. For electrons, a(E) is small (ab'Jut O. 011 for several MeV), and increases for more heavily ionizing particles (about O. 021 for protons of similar energy) (Daehnick 1961). It is the excess of slow compo:ient possessed by proton pulses which enables them to be separated from electron pulses. The photomultiplier current pulse is integrated by stray capacities at the anode and at the second-last dyno:le. The anode capacity is discharged through a low resistance R :::: 3. 9 ko 1 (integrating time ,..,., 10 ns), whereas the dynode capacity sees a 1 Mo resistance R 2 {integrating time several µs). As a consequence, the voltage pulse obtained from the anode consists of only a sharp negative spike. The dynode pulse is a positive pulse which contains a slowly decaying tail. Both pulses are stretched by means of diodes CR1 and CR2, and added together on a common load resistor R • Time constants controlled by capacitors R, C, and F are 3 adjusted so that electrons produce a zero or negative output, while protons pro1uce a positive output pulse. This is the PSD p'J.lse referred to in the main bo:ly of the text. An additional feature of this circuit is the coupling networl{ between the fast (anode) channel and the slow (dynode) channel. This network consists of trimming capacitor C, diode CR3, and resistor R • It acts to effectively short-circuit the slow channel to ground for 4 the first few hundred ns after the arrival of a pulse. In this way the 53 pulse derived from the slow channel is proportional only to the amount of slow decay component. 54 REFERENCES Amaldi, E. 1959, Handbuch der Physik (Fltigge) Vol. XXXVID/2, 115. Bennet, W. E., Roys, P.A., and Toppel, B. J. 1954, Phys. Rev. 93, A924. Birks, J.B. 1953, "Scintillation Counters", 93. Brooks, F. D. 1959, Nucl. Instr. and Meth. 4, 151. Burbidge, E. M., Burbidge, G. R., Fowler, W. A., and Hoyle, F. 1957, Rev. Mod. Phys. 29, 547. Cameron, A.G. W. 1954, Phys. Rev. 93, 932 1955, Ap. J. 121, 144. Caughlan, G. R., and Fowler, W. A. 1934, Ap. J. 139, 1180. Chadwick, J. 1932, Proc. Royal Soc. London A136, 692. Daehnick, W., and Sherr, R. 1951, Rev. Sci. Instr. 32, ·666. Fowler, W. A., Caugh1an, G. R., and Zimmerman, B. A. 1957, Annual Review of Astronomy and Astrophysics (to be published). Garwin, R. L., Hutchinson, D., Penman, S., and Shapiro, G. 1959, Rev. Sci. Instr. 3·) , 105. Greenstein, J. L. 1954, "Modern Physics for the Engineer", First Series, 267. Hughes, D. J. 1958, "Neutron Cross-Sections", 2nd Ed., 74, 97. James, D. B. , Jones, G. A., and Wilkinson, D. H. 1956, Phil. Mag. _!, 949. 55 Jones, G. A., and Wilkinson, D. H. 1951, Proc. Phys. Soc. A64, 756. 1953, Proc. Phys. Soc. A66, 1176. Marion, J.B. 1961, Rev. Mod. Phys. 33, 139. Owen, R. B. 1958, IRE Trans. in Nucl. Sci. NS-5, 198. Pearson, J. D. 1953, Thesis, California Institute of Tech.11ology. Porat, D. I., and Ramavataram, K. 1961, Proc. Phys. Soc. 78, 1135. Reeves, H. 1966, Ap. J." 146, 447. Rusbridge, M. G. 1956, Proc. Phys. Soc. A69, 830. Vogl, J. L. 1963, Thesis, California Institute of Technology. Walton, R. B., Clement, J. D., and Boreli, F. 1954, Phys. Rev. 107, 1065. Wenzel, W. A. 1952, Thesis, California Institute of Technology. Whaling, W. 1958, Handbuch der Physik (FlUgge) Vol. XXXN, 13. Wright, G. T. 1956, Proe. Phys. Soc. B69, 358. 56 TABLE 1 Quantities used in computing the yield of the 13 c (a, n) 16o reactim1, . discussed in Section (g) (1), part II, and Section (a) part V. n EB 200 y e.hrp y calc cr(EL) (nb) (MeV) • 475 1. 15 • 519 18 88 83. 1 2.93 • 500 2. 81 1.33 21 245 241. 5 6.83 • 525 6.43 3. 19 8 238 215. 1 14.9 • 550 13. 9 7.23 4 225 237. 8 31. 0 • 575 28.7 15.6 3 384 375. 2 61. 2 • 600 56.6 32. 0 2 492 503.2 116 . . • 625 107• 63. 1 4 1884 1945.9 211. • 650 196 • 120. •5 474 453.6 371. • 675 348. 221. .5 826 819. 0 632 • • 700 599 • 393. • 25 744 717. 9 1047. 57 TABLE 2 Coefficients of Legendre polynomials required to fit angular 9 9 12 12 distributions from the reactions Be{a, n ) c and Be{a., n ) c* 1 0 (4. 43). All are normalized such that the coefficient of P {cose) = 1. 0 9 Be(a., n ) 0 12 C EB Ao Al A2 A3 • 480 1 -. 09 ± . 03 -. 09 ±. 04 +. 35 ± . 05 • 520 1 -. 05 ± . 02 -. 09 ± . 02 • 593 1 -.41+.02 +. 01 ± . 03 -. 56 ± . 04 +. 19 ± • 03 .608 1 -. 41 ± • 02 -.01+.03 - • 40 ± . 04 +. 26 ± . 03 A3 A4 9 Be(cr1 n ) 1 EB AO Al • 480 1 - • 09 ± . 02 • 520 1 -. 21 ± • 02 • 593 1 -. 24 ± • 01 .608 1 -.04±.02 12 A4 C* (4. 43) A2 +. 08 ± • 02 - • 06 ± • 02 -.06...± .02 58 TABLE 3 13 Lifetime of the c nucleus to interaction with 4 He via the reaction 13 c(a., n) 16 o. The lifetime is g·iven in years, and the density is . . gm-cm - 3 s ee page 45 • given m T9 log10CpX4 He 'f4 (13C)] He • 02 +27.80 . 04 +17.30 • 06 +12.20 • 08 +8.98 • 10 +6.69 • 12 +4.94 • 14 +3.54 • 16 . +2.39 • 18 +1. 42 . 20 +0.57 • 25 -1. 11 . 30 -2.40 • 40 -4.28 • 50 -5. 62 Fig. 1 Schematic diagram of the regulating system for the magnetic analyser, 700 kV accelerator. Individual circuits are given for the transistor panel (fig. 2), the coarse regulator (fig. 3), and the DC amplifier and driver (fig. 4). See page 6. CJ'1 tO MAGNETIC ANALYSER CURRENT SUPPLY 10µ. r----------, I RM 200 I I THERMOSWITCH ON TRANSISTOR PANEL"'.! AND REGULATOR FAST FEEDBACK I .,._...,_._~ 4µ. I I I 1.5K ±...... 750 I F DC u~ =r 10.000µ. BROWN CHOPPER CONSTANTAN SHUNT 0.01.0. .. µ.+r I 750 AND DRIVER x x O'J 0 D A ~ - _f - - - - _,_ - J A A fooo ::L ~AMPLIFIER I I E x x COARSE ~ REGULATOR xx 33K 0 .5µ. 125V EXCITER 18V 200A GENERATOR PANEL D : 2K HP L ....---A"', 1'3~4't(p :. 1.34V Ho '---- -------, I I I HEAVY LINE INDICATES MAGNET CURRENT 1-:tj ..... c;q i:::; "1 CD 1-l IOOK Fig. 2 The pass transistors and the driver transistor for the magnetic analyser regulating system. These transistors are mounted on a water- cooled copper heat sink. See fig. 1 for complete circuit details, and also page 6. O') '"""' <{ 62 (.Q 0 0 U) q 0 Figure 2 ~ z (/) t- w _J 0 :c <{ _J q w Cl) z ~ 0 I (.) 0 0 (/) Q: t- z z ~ :::> <.\I 0 z IO t- w 0 0 z ?;: <! t- l!J t- 0:: <! (/) 0 Q: I.LI (" 0 Fig. 3 Coarse regulator for field winding of DC generator, magnetic analyser regulator system. The voltage across the transistor panel, fig. 2, appears between points A and B. This is compared with the voltage at the emitter of the 2N388 transistor, which is set in the vicinity of 1-2 volts by the 2N525 transistor. The output is taken from points C and B to the base of the 2N277 transistor, fig. 1. Current in this transistor passes through the field windings. If the voltage across the transistor panel rises above 2 volts, the coarse regulator decreases the generator field current, and thus its output voltage. See page 6. m ~ COARSE REGULATOR 2 .2K 20VCT xlll 150 2W IN2069 I x_J - rr-~~ IN2069 IK '> I IU - 150 20µ. I 400 ·- IZG.80.Z µ. T m )~ 2.2K~ I r--+t ~ 20µ.+I I 12K I +1 I ~ c *150 8 . ~ ..... ~ Ii <D v A ~ Fig. 4 DC amplifier and driver, magnetic analyser regulator for 700 kV accelerator. This circuit amplifies the DC error signal received from the chopper amplifier and raises it to a level sufficient to drive the transistors of the transistor panel, fig. 2. See fig. 1 and page 6. O') 01 DC AMPLIFIER AND DRIVER 20Q.h 200 µ. -r+ µ. + 47 F 47 I I I ....~ aa1-1 (1) ~ E Fig. 5 Temperature controller for Hall probe. The thermistor RT is one arm of an AC- excited bridge. Current pulses are supplied by the 2Nl3 95-2N277 combination to the heater when the bridge is unbalanced. Equilibrium is reached at 42°C. See page 8. O') -:J HALL PROBE TEMPERATURE CONTROLLER RT: FENWAL GLASS-ENCLOSED BEAD THERMISTOR GB31 P2 R25 .c = 1000.0. HEATER I 47 2W TRIAD F-91X A- 470 15K RED 1~2069 20V RMS 500 w ----·-----·-, YELLOW lllf Cl)" I fll~BLACK OJ BLACKYELLOW I !_N_2JQ _ SHORT -~~-J 2N 1039 ~·,'.~.~~S LONG! BLACK WITH TAPE r 1111111mm I BLACK ll cp ~-- -1'~ I t 100 K : 1-rj 1~ 110 VAC 01 (SOLA) Fig. 6 Current supply for Hall probe. Supplies 225 ma very highly regulated. See page 8. O') co HALL PROBE PRECISION (4) 1810 CURRENT SUPPLY 0-500mo INl510I >I ~27~ .Jlooµ.~ LOAD --e 50 IOW l.34V Hg ,, R 9KP VVVV' IKWW 200WW 2KWW 2KWW 1soµ I_ + 1 ~N1306 ~~4.7Kf _b_oo 1 I -J 0 T 4 .7K 2.7K TO GALV. BROWN IN2069S2 ..:.L500µ. +r 2.7K lcHOPPERI I I >-rj ,_.. uq ~ 1-j I) 225 mo OPERATION: R = 4 70 K (!) Ci) 2) 100 mo OPERATION: R = 68K CONNECT A,B OF HELIPOT TO C, D Fig. 7 Beam current indicator. The two field-effect transistors are connected in a voltmeter configuration. Since the entire circuit must be isolated from DC ground, it is built on an insulating circuit board, which is then mounted on a lucite panel. See page 12. -:I ~ FIELD EFFECT TRANSISTOR BEAM CURRENT INDICATOR INTEGRATOR 2MP ~ J'O f.S. ~.25 IOMP r. 5 8MP -::r ~ IMP 2MP '? BOOKP ~ IOOKP 5 .01 IOK 15KP 25 r--o 50 SOKP 0 - 25µ.o 12KP t--° 11 ZER0 11 .01 IOK -- I I 2.68V THQ •, I I ~ l 2.sav Hc;i 20KP l"rj ~· aq ~ >i ro -::r TARGET Fig. 8 Target holder used for the reaction 13 c (a., n) 16o. The target itself serves as the end vacuum seal. Also seen is one end of the cold sleeve surrounding the beam, which keeps carbon deposition during bombardment to a negligible rate. A viewing port is provided so that the beam spot can be observed during bombardment. See pages 12 and 13. -::r ~ 13 C(a,n) 16 0 TARGET HOLDER KOVAR-GLASS VIEWER STAINLESS STEEL COLD SLEEVE TARGET BACKING ' -:? ~~ VITON/ 0-RING . f.rj ...... r . BRASS TARGET HOLDER lcm1 ~ Ii ([) co 75 Fig. 9 Brass target chamber used for excitation function 9 12 measurements on the reaction Be(a., n) c. The large mass of copper used as the target support provided a heat. sink which was cooled by an air blast. See page 12. 76 TARGET 12 CHAMBER USED FOR 9 Be (a ,n) c FUNCTION MEASUREMENTS Figure 9 EXCITATION Be TARGET ~I cm-..j 77 . Fig. 10 12 Excitation function measurement on a thick c 13 . 13 14 and C target of the reaction C (p, y) N. The sharp resonance at 448. 5 keV is seen as a steep step in the yield. See page 13 for details. 78 F igure 10 1800 1600 1400 u ~ 1200 0 0 ...... ~ 1000 z · :::> 0 0 800 600 400 200 0 ,__~--L~~-'-~~-'-~~-'--~---'~~--'-~~--L..~~-'-~~-'--~~ 420 430 440 450 460 470 480 490 500 510 520 Ep(keV) LAB Fig. 11 Block diagram of neutron counter electronics. The left-hand block is contained in the probe (fig. 12), and the schematic diagrams for the remaining blocks are found in figs. 13- 15. See circuit description beginning page 15. -:J co . Bp.e L ----,..() DELAYED UPPER LEVELllif DISCRIM INATOR l 1..J• ~K • DET. f. I _f_ -.:;:- LOWER LEVEL ~>----II DISCRIMINATOR 1J GO l I-••--_;;_---••------• ,.._ J L co TERMINATE STRETCHER 0 ----+----' ~ PSD ....___ __, L STRETCH I ) ' I x DIFF. AMP. TRIGGER PAIR co1Nc. 1m1 • MIXER BRIGHTEN TR IGGER PAIR ii! ~ - I PSD STRETCH I ' GATE AXIS · I """" >:tj ..... ELECTRONICS BLOCK DIAGRAM ~ .... 'i ('!) ...... ...... Fig. 12 Circuit diagram of pulse-shape discrimination probe, contained in the photomultiplier tube base. Included are the n-y discrimination circuit, linear pulse preamplifier, and PSD pulse output circuit. Description of circuitry is given on pages 15 and 16. °' ....... PULSE-SHAPE DISCRIMINATOR PROBE [] @, < ' - ' > ~ .I ~2.7K H IK f S.6K "'f 'f ~""" ~ 4"" 4.7K 3 .9K 4 1 ~ ~I I AAA ~ .02 3KV ~.t .1 :::::: IOOJL --.... l 15 - TEST .!. .=E 50JL !i ~ I °' !.'-' -f- I 2 .2K I -··· (' I ~ 22K 100 -= -= DISC ~ 'l LIN T1/i 17 LINEAR (To -2ov THROUGH IK) 0 OISC IT.I !-'• ~ 1"'$ (i) .L = 4 20 RCA 6810 A T }--1. l:'V Fig. 13 Pulse- shape discrimination pulse analysis circuitry including linear pulse amplifier, lower level discriminator, linear pulse stretcher, delay line, and linear output amplifier. See block diagram (fig. 11) and description on page 16. co ~ PULSE - SHAPE G • -10 OISCRIMIN.ATOR PULSE ANALYSIS G • - IS LOWER (I) LEVEL OISCRIMINATOll "<i~---r-r-~-~~~-.._. r t r i ~~,~I~L--1:----r-~___. ·' I ~ f l ~IX\ <BID ·'r t •20V .... - I 'CJ .I •~~n _ II( -2ov • 100 2 .2K 27K TEST L !501' _i.: ~~ l!IK'!> I ~93 I lf~ l l ~ 1 I_ S ' •- LIN 22K ~V'N 15Kww .___,-~ .. )\jl;·~I , 10K! ± 2.2 K L .I -sl' 1 L:@ 4;-- OISC]CW IOOK I. NEG t [ INIOO:zs- ~33K ~ rKP 1 ~@ ('!) ~ SCALER ::r: - 47 t-@ @ ·'I_J_ ~ 22K 2K~----. .01 2KP ISKP NIOO IK 220K~ .01 IOK 22M 500 IOK T · ~ __r_o1 02on50 ~ 2.2M5: _ L PULSE STllETCHEll I "'F 5,.. (!) I DELAY C . ,..... I 51' A I G • - I TO -5 ~ citj• IOK NEG STllETCH, - @ I ,!; "1 ~ (D D~~~y "" Fig. 14 Pulse- shape discriminator pulse analysis circuitry including PSD pulse amplifier, PSD stretcher, and linear pulse upper level discriminator. See block diagram (fig. 11) and description on page 16. °' c:.n PULSE - SHAPE DISCRIMINATOR G •-20 UPPER PULSE ANALYSIS (2) LEVEL DISCRIMINATOR @ 2.5KP TEST '"Ji~ ! 3K WW_ cw331< s 47 / \ INIOO . 50P 22K - .I @--4 15KP 7 t5µ 93 + 22K .001 2.21( ..I.'I -- -- NEG PSD IOK t5µ 00 (.:J) ® 47 47 @ IOOK THRESH .:c·I © .01 ~ I < IK .01 ~ IOK ~o 020/250 220KS INIOO ~ !>!>U~ - @ I -5fl T®, y AXIS 1-Tj ..... °211 (1) PSO I ..... ,;.. Fig. 15 Pulse-shape discriminator pulse analysis including differential amplifier, trigger pair, coincidence mixer, brightener trigger pair, and scaler and gate output. co -::i See block diagram (fig. 11) and description on pages 16 and 17. PULSE-SHAPE DIFFERENTIAL AlilPLIFIER TRIGGER DISCRIMINATOR PAIR PULSE ANALYSIS (3) COINCIDENCE MIXER SCALER ANO GATE OUTPUT -2ov .... ~~~~~~~~~~p.--~~~~~~~~~~~~~-.~~~~~~...-~--<t~~~~~~~~~~~~~~...-~~~~~~~~~~~~--~~~~~~ 3 . 9K IOOK IK 220K 22K HK ® © <r-5. . IOK l . 5M tOOK © •IOV ··---- I l SCALE~ JI'" co co GATE ® . -· SPA~K OfT. cvWE~ LEVEL DISC. n , u 2 .2K 4·' l AXIS ~ ..... cr.s ..... 11 CD ._. -tOY 01 !IRIGHTENER TRIGGER PAIR Fig. 16 Spark detector schematic. The input of this circuit is connected to the bleeder chain of the 700 kV accelerator, and it detects fast transients appearing there. The output is connected to the gate generator (upper circuit, fig. 17), which generates the "V" veto pulse. See page 18. 00 tO SPARK DETECTOR IOK <: IM~ UHF ~ 0.01 I I 0.1 - - 4.7K . I I ' \ (.0 0 0.001 150 - - 4 .5V ,, BNC IOK 2.5mh • r I ~ 0.1 ~ ..... ~ 'i ('!) ~ CJ) Fig. 17 Modular circuit which includes spark detector gate generator and a count-rate meter. The. gate generator takes a signal from the spark detector (fig. 16) and converts it into a pulse capable of blocking the analysis of a pulse in the pulse- shape discriminator (figs. 13-15). Any pulse whose amplitude exceeds O. 5V will drive the cow1t-rate meter, seen below the gate generator. Full-scale ranges of 20, 200, 2k, 20k, and 200k counts/ sec are provided. Details of gate generator are found on page 18. (.0 I-" SPARK DETECTOR GATE INVERT ANO GENERATOR TRIGGER OIFF. OUTPUT PAIR +2ov--""""""""-.-~~~~~~~~~~--,r-~~r-~r-~~~~~~---, 100 .I.1 15 6.8K IK 220K + 22K INIOO ii t VVV... t IOOK 15~ ' 1.!IM 47 GATE o® CD [:\.:> -2ov--~~~-l.~~~~~~~_.__~~~~~~~~~~~COUNT RATE METER (POSITIVE OR NEGATIVE INPUT) +20V ____,,.._~~~~~~"NV\/l__,~~~~-t-~---:~~~~r-~~~~~~--,r-~~~~~~~~~~~~~~~~~~~1""~~~~"1 220~ I IOK I. -= 3.3K 39K 47 20 200J 2 K 20K ZOOK .I @-j 100 S 10 5 I 5 100 KP<:KP <:KP<: IOK P COUNTS PER SECOND 47K IOK IOK 1-rj ..... ~1--j -2ov--1-~-1~~~~~~-L~~~~~~~~~~~~~~~~~~~~~~~~~~--~~~ ro ...... -.J 93 Fig. 18 Illustrating the elimination of the 4. 43 Me V gamma 12 9 ray from the reaction Be(a, n ) c*(4. 43). The lower 1 curve shows the spectrum with the ·n eutron-gamma discriminator in operation, and the upper curve shows the same spectrum when the discriminator is removed. Neutrons 12 9 from the reaction Be(a, n ) c appear in both spectra in 0 the same number. See page 34. 94 10 4 Figure 18 i \ A- 9 Be(a,n) 12 c PULSE HEIGHT SPECTRUM IN STILBENE Ea= 520 keV LAB BLAB = oo WITHOUT n- y DISCRIMINATOR WITH n- y DISCRIMINATOR U) t- 102 z :::> 0 (.) 10 1 A 0 CHANNEL NUMBER A 95 Fig. 19 Target-detector geometry for the reaction. See page 12. 13 C(a., n) 16 0 96 13 c (a, n }16 o TARGET TARGET Figure 19 GEOMETRY BACKING BEAM l-1 cm-c:-1 STILBENE CRYSTAL 97 Fig. 20 Pulse-height spectrum in stilbene of recoil protons 12 9 from the reaction Be(a, n) c. Two neutron groups are 12 seen, one leading to the grow1d state of c (n ), and the 0 other leading to the first excited state (n ). Also shown on 1 the figure are the cutoff energies Eco and Eel as described on pages 26 and 27. 93 .5 2 1.5 9 ae (a,n) 12 c PROTON E 0 s612 .5 keV E '• 2 .5 3 Figure 20 3.5 RECOIL PULSE 4.5 HEIGHT 5 5.5 6 6.5 SPECTRUM IN STILBENE LAB BLAB = 0 • J,~ En, <P"oct>o ' 0 0 0 0 0 0 Ul I- 0 ~ 102 0 'booct>a> o o o o of o o 'boo oo o cP oo ~ °"-- oo o ooo a9 a>o o o o E"o o <ti oCl'cP~ oooq,o v-q,o oocfb oo cP cP o o cP cfb o cP oo oo d'o o o o<X>coo o I 0 0 O 0 O t oO 00 cP 00 0 0 0 00 0 0 10 1 0 00 0 0 0 CHANNEL NUMBER 99 Fig. 21 Thick-target yield from the reaction 13 c(a., n) 16o, in the bombarding energy range O. 475-0. 700 MeV. Taken with the geometry shown in fig. 19. The solid curve is computed from the values of S(O) and a. obtained from the least-squares fit of the expe rimental data. and Table 1. See page 32 100 13 c (a,n .) 16 0 IN THICK TARGET Figure 21 YIELD NEUTRONS /20,000 µ C - l.) ::I... 0 0 o_ 0 (\J ....... 0 - 102 ~ _J w >- z 0 0:: ~ :::> w z - 100'--~~~~'~~~-'-'~~~---Ll~~~--'l~~~--'l'--~~~L--l~~~..____l---J .400 .450 .500 .550 .600 .650 .700 .750 Ea (MeV)LAB Fig. 22 Astr ophysical cross-section factor S(E) in the center-of-mass system, 5 calculated from the equation S(E) = [ 5. 48 + 12. 05 E] x 10 MeV-barns. The region delineated by arrows indicates the energy range covered in the measurements. See page 26 and Table 1. Errors on the function S(E) are shown by the light curves, as computed from the least- squares fit error matrix. ........ 0 ........ CENTER-OF-MASS Ts 0.1 0.2 0.4 0 .6 0.8 13 C(a I n) 16 o ASTROPHYSICAL . CROSS-SECTION FACTOR 1.0 2.0 1.5 S(E) 2 .5 3.0 3. 5 4.0 4 .5 5 .0 I 14.0 12:0 ~ ~ ..... 0 tv 10.0 . 0 .D I >d> 8.0 ~ S(E) =(5.48+12.05E) x 10 5 MeV-borns I() 0 6.0 w Cf) 4.0 1-.j 2.0 I-'• cr~ ~ 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~-'-~~~~~~'--~~~~~--' 0 .100 .200 .300 .400 .500 .600 ECM(MeV) 0 l'-' N 103 Fig. 23 Total cross- section in the laboratory system for the 16 13 reaction c(a., n) o, calculated fro'm equation 1, page 2. See also page 3 5 and Table 1. 101 Fig.ire 23 104 13 c(a,n) 16 o TOTAL CROSS - SECTION b 10 1 100 0 .400 0.500 0.600 Ea (MeV)LAB 0.700 105 Fig. 24 Excitation functions at 0° measured for the reactions 12 9 12 . Be(a., n ) C and Be(a., n ) C*(4. 43). The yield has been 0 1 converted to an absolute differential cross- section by the 9 method outlined in Section (g) (2), part II. See page 3 3. 106 Figure 24 22 A 20 18 16 11 ·\ Be (a, n) 12 C THIN TARGET EXCITATION FUNCTION 0° LAB 9 o GROUND. STATE A FIRST EXCITED STATE A \ A ~~~ 14 0 -... 12 ~ .Cl 15 keV ::t. ~ "O 01 10 'b ~ I \l ;-~, 8 6 \ if'\, 4 0 ......-.,.._,/ 0 ~A-A ~o 2 ~=====-9~ ~40 400 500 600 Ea (keV) LAB 100 107 Fig. 25 Excitation functions at 90° measured for the reactions 12 9 12 . Be(a, n 0) C and Be(a, n 1) C*(4. 43). The yield has been converted to an absolute differential cross- section by the 9 method outlined in Section (g) (2), part II. See page 33. 108 Figure 25 9 12 Be(a,no> c THIN TARGET EXCITATION FUNCTION 90° LAB 16 o 14 GROUND STATE -;::- 12 ~ .&> :l. ~ 10 ..., ..... b ..., 8 6 4 2 300 400 500 600 700 Ea< keV) LAB 14 12 9 Be (a,n, ) 12 c· (4.43) EXCITATION .. -10 ... ..... o THIN FUNCTION FIRST EXCITED TARGET 90° LAB lI 0 STATE .&> :l. ~ 1 ov 8 ...,..... ...,b 6 4 2 300 400 500 Ea< keV) LAB 600 700 109 Fig. 26 9 12 Angular distributions for the reaction Be(a, n ) c. 0 Shown are the experimental points and the computed fits to Legendre polynomials. See page 33 and Table 2. 110 9 12 Be(a,n ) 0 C ANGULAR 2.2 2 .2 1.0 1.0 1.8 (/) I- :::> 1.4 0 0 1,i " :50.0 w o:::0.6 1.2 1-1" LLJ l I- i"' I..._1/ ~ 1.0 :5 0.8 L - 1 - - I 0.6 0.4 0 .2 0.2 0.0 _ _ _..___ _ 40 0 80 ..____.__.._____.__..____.__..L..-__.__..L..-~ 40 80 120 .._____.__...._____.__....__~ 160 2.2 2.2 2.0 2.0 1.8 1.8 0.5925 MeV ~ 1.6 160 0.608 MeV (/) 1.6 z 1- 0 0 z :::> 1.4 12 I 1.0 .J 0 .8 w 0::: I LLJ 0::: 0 ~ ....-.-'-r -1-•---i 0.4 0 .0 u 0.520 MeV u u 12 ~ 1.0 I- 1.6 z ~ 1.4 • DISTRIBUTIONS 1.8 0.480 MeV (/) 1.6 w Figure 26 :::> 1.4 u 1.2 w > 1.0 /,..-•-..-... ....... / ~ ~ 0 .8 0.6 i 0.4 ,/ 0::: 0.6 0.4L--I 0.2./ / i I /I / ' • ............_ .......... I / 0.2 40 120 160 0.00 40 120 160 111 Fig. 27 9 12 Angular distributions for the reaction Be(a., n ) c* 1 (4. 43). Shown are the experimental points and the computed fits to Legendre polynom~als. See page 33 and Table 2. 112 Figure 27 9 Be(a,n ) 12 C*.(4.43) ANGULAR 1 2.2 2.2 2 .0 2.0 1.8 U> ..... z ::> 0 u _J z ::> 1.4 1.4 0 u I. 2 0.8 0 .5 20 MeV ~ ·r.6 1.6 > 1.0 w a:: 1.8 0.480 MeV w ..... <( DISTRIBUTIONS I I I _1-1-i-I 1 w -I > 1.0 ..... <( w a:: 0.4 0 .2 0.2 80 120 0.00 160 I 0.6 0.4 40 I • _J 0.8 0.6 0.00 i/l 1.2 40 BcM 2.2 2.0 2.0 1.8 0.5925 MeV 1.6 ~ 1.6 ~ 1.4 ::> 1.4 U> ..... 160 0 .608 MeV z 0 0 u 120 BcM 2.2 1.8 80 u 1.2 1.2 . ._ ' -I-w > 10 <( _J w a:: 0.6 0.4 0.4 0.2 0.2 _.____,'--_.___J...._--J...____J 120 160 ~lI - I - - - , 0.8 0.6 0.0 ._____.__...._____,__ 0 40 1 - 1 - 1... 1 • 0 .00 40 120 160 113 Fig. 28 Lifetime of the 13 c nucleus to interaction with 4 He. 13 c)], with ,4 He He given in years, pin gm-cm-3, and x is the mass 4 He 4 fraction of He. See page 45 and Table 3. The quantity plotted is log 10 [ pX 4 ,- ( 114 Figure 28 28 26 LIFETIME THE 13 NUCLEUS TO 4 He VIA 13 C(a,n) 16 WITH c OF INTERACTION o 24 22 20 18 16 II) .... 14 0 4l> >. c 12 ~ 10 .... ..,__.. 0 • 8 % ....v • 6 % v x ~ 0 4 2 Cl" 0 0 -2 -4 -6 -8 -10 0 2 4 5