This technique, described in the Charged Particle Section (page 62) I, provides the majority of the cross-sectional data. The Neutrons section (page 141) describes a determination of the neutron production cross section using a flat response detector.
TARGET CHAMBER
The energy loss of the beam before reaching the target area was determined experimentally using elastic scattering. The laboratory angle at which the number of counts of pure Rutherford scattering in a gas target is independent of angle is plotted against the ratio of the incident to the target masses 1\~ (see the text page 26 and Figure 7).
RUTHERFORD SCATTERING OF PROTONS ON ARGON
BEAM
In order to reduce the effect of small changes in beam angle on The numerical values of the data presented in the paper by Bromley et al.
COUNTS
A suitable thickness for a solid target is about 1 I.l gm/cm • A difference of 2. Since solid targets cannot be made of pure oxygen, they are susceptible to the production of unwanted '(I from reactions with other nuclei in the target.
63 - another counter
One reason is that in the remaining cores, regions of excitation energy with a high density of states are energetically accessible. Furthermore, the low particle yields required large angular apertures for the counter telescopes, resulting in kinematic broadening of the peak from a given excited state. Finally, the three body channels produce a continuum of particle energies for a given state in the residual core.
The beam intensity was not limited by the entrance foil required for a "closed" gas target, and the beam energy loss and straggling were well under control. Gas flowing through the target chamber swept out any impurities that had degassed in the system to prevent build-up. of target contaminants.
65 - Elastic Scattering Section (page 21)
Alpha and proton spectra were obtained with a counter telescope (Figure 12) consisting of a proportional counter to measure 0.6E and a 2 mm thick (110 mm2 area) lithium silicon detector to measure particle E. The gas-tight housing of the telescope was tightly connected to a lucite flange that rotated on an O-ring in the delivery chamber lid. The high voltage electrode was a length of 0.1 mm diameter piano wire on the shaft of the proportional counter.
It was supported by a cylindrical glass insulator at the end closest to the E counter, and by a Kovar glass bushing at the other end, providing the electrical connection to the wire from the counter housing. This counter telescope consisted of a proportional counter for measuring 6E and a 2 mm thick Si(Li) counter for measuring E.
COUNTER TELESCOPE I "
Electrical breakdown occurred at approx. 300 V in the oxygen gas (at 3 torr chamber pressure) when the high-voltage connection was made without the hose, whereas it happened at approx. 600 V in the counter gas (120 torr) with the cable at atmospheric pressure. An experimental check of the solid angle factors was performed by scattering 1.8 MeV protons from pure argon gas in the differentially pumped system at a chamber pressure of 2.0 torr. The ratio between the number of counts in the counter telescope and in the monitor counter gave
After amplification, the 6E and E pulses were stored in the two coordinate directions of a 64 X 64 Nuclear channel analyzer. The 6E pulse processing ADC was randomly determined by a low-level discriminator placed on the E pulses, thus eliminating much of the noise inherent in the proportional counter.
DATA - PREAMP AMPLIFIER ADC ---_.-L_
NUCLEAR DATA ANALYZER
The performance and potential noise contributions of the .6E - E two-dimensional coincident pulse recording system were verified using different gains. The energy scale in the E direction was calibrated with protons and alphas corresponding to the lowest lying levels in 31 P and 28 Si, respectively. The two two-dimensional spectra were compared in the .6E direction to obtain the particle spectra as shown in Fig. 16 .
For example, the 1.8 MeV protons used for the space angle factor ratio Ineassurement provided one control. The peaks in the alpha spectrum are not the result of statistics (see figure 17 and text page 79).
CHARGED PARTICLE
E COUNTER CHANNEL
MeV. Data from spectra taken at several different angles are presented in each figure to show that the peaks
The range of extrapolated counts is also given. corresponding channels and linear interpolation of the counts at the ends of the interval. The factor is correct (as for both body reactions). well, show the structure in the angular distributions. The value of A and its error of fit are also shown in Table 6. When there were only three angles or less. the angular distribution was isotropic, and the average was used for the differential cross-section A. The attributed error at such values of A was taken to cover the individual values of da-jdn) or to be 20%.
To obtain total production cross-sections, the number of low-energy particles in the target chamber gas was stopped. 900 • The hydrogen recovery peak was easily identifiable in the proton 16 16 . spectra. and the number of protons from 0 + 0 reactions below the peak was also determined by a linear extrapolation.
CHARGED PARTICLE YIELDS FROM
The beam was then turned off and the f3 particles from 31S and 30p were detected in the scintillator as a function of time. A build-up of oxygen in the trap sheet from background-contributed beam bombardment. 5 J.L gm/cm • The pollutant yield was somewhat decreased 2 by installing a cold trap below the SiO sheet.
The counter spectrum from the plastic scintillator used in the activation measurements is shown for E = 9 MeV. The !3 spectrum correction allowed for the missing count in the decay curve due to the discriminator setting.
40 CROSS SECTION FOR
Cross sections obtained by the activation method for the production of 30p from 160 + 160 reactions are plotted.
NEUTRON AND DEUTERON YIELDS
The activation data showed that carbon build-up on the target was slow enough to keep the neutron yield from this reaction lower than the yield from 31 8 + n at. Even with the usual uncertainties. in the measurement of absolute neutron cross sections. the large factor between the two alternatives made the experiment feasible. Low detector efficiency and difficulties in localizing the target region for obtaining angular distributions precluded the use of the gas target.
The angular distribution of the neutrons was taken at a constant distance of 26 cm from the target to the front of the long counter's inner wax. The neutron counter efficiency was determined with a "calibrated" (to about ± 10%) Pu-a-Be source in place of the target.
OM. NEUTRON SPECTRUM
From an average of the two sources, and the number of neutrons counted, the I.ency was efficient. The error was ascertained by introducing a 15% uncertainty in the graphical integration and extrapolation of the angular distribution at posterior angles (see Figure 37). The conclusion is that the three body compartments are responsible for the ITlation of 30p.
Laboratory differential cross sections for neutron production measured with the long counter are plotted as a function of laboratory angle. Even with the large active volume of the long counter, it had to move quite close to the target due to its low absolute efficiency and low neutron yield.
Measurements were limited at some angles by energy loss and multiple scattering in the SiO foil target, and at others by high elastic scattering count rates. Two solid state detectors were used, one mounted on each IUpremable arIU in a 61 CIU scattering chamber. The beam intensity and target thickness s were related to the integrated current in the cup by measuring the efficiency of Mott scattered 160 cores at e cm = 900 with two semiconductor counters.
The pulses from the two counters were amplified and fed into the Nuclear data analyzer used in the two dimensional 64 X 64 channel mode. The energy scale for each counter is calibrated using elastic scattering peaks at several angles.
LLI Z
Z I.&J
48 BACKWARD
COUNTER 32
CHANNEL
N is the nUInber of counters in the top of 12C + 20Ne and 0 is the integrated current in the Faraday cup. The effect of multiple scattering of the reaction products in the film was difficult to assess. Assuming that the angular distribution after .. scattering in the foil is purely Gaussian .. and that the laboratory angular distribution was approximately isotropic over an area larger than the counter, the ratio is.
These errors come from statistical uncertainties in the number of scores N, and from deadline en. In addition, an overall error of ± 15 % is estimated for the finite beam. spot size, for changes in the incident beam. angle, and for the charge integration.
We attempted to determine the overall angular distribution from these measured values alone. Since all the particles involved have spin 0 and since the incoming and target particles are identical, the angular distribution must be of the form (see DeBenedetti (1964). The values of X 2 for the three parameter fits are very large, indicating that lTIore two values of L .
L = 4 seems likely to be present, but this is to be expected because the zeros of P 4 (cos e) occur at. Spectrometer data were used to select between two cross sections from the fits.
CMF MON •
The error on the fitted section was chosen to cover the sections predicted for the best fit (except for the L = 2,4,6 solution). Estimates of the 32S, 31S, 30p, and 12C + 20Ne production cross sections are required to obtain the full reaction cross section at the lowest bombardment energies. The first two assumptions will not seriously affect the extrapolation of the total reaction cross section to lower energies, since the branching ratio for the output channels is 31S + n, 30p + d and 30p + p + n srn.all.
Not only is the absolute percentage of three-body reactions important, but the variation of this percentage with bombardment energy can significantly affect the extrapolation of the total reaction cross section to energies below those measured. These are the first measurements of the total reaction cross section for the most complicated astrophysical nuclear reaction ever studied.
APPENDIX I
Energy loss in the gas has been subtracted and gives a total uncertainty in the energy scale of ~ 50 keV (C.M.).
SCATTERING
The combined beam intensity and target thickness were monitored by elastic scattering at a ::: 900 t using the results of Appendix I. This allowed a direct comparison of the S variation with Ecm for the -y yield and for the measurements of charged particles. from Patterson,. The energy loss of the beam in the foU was estimated at 60 keV (laboratory).
The agreement between the -y yield measurements and the charged particle data could have been worse if a different discriminator cutoff had been used.
BIBLIOGRAPHY
See also Proceedings of the Second Conference on Reactions Between Complex Nuclei, Gatlinburg, (John Wiley and Sons, New York), p.297.
191 - Table 5
