Cross sections as a function of energy for the scattering of protons from 12C

Nuclear Physics 86 (1966) 119--129; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

C R O S S S E C T I O N S AS A F U N C T I O N O F E N E R G Y FOR THE SCATTERING OF PROTONS

F R O M 12C

J. B. SWINT, t A. C. L. BARNARD, T. B. CLEGG tt and J. L. WEIL ttt Bonner Nuclear Laboratories, Rice University, Houston, Texas

Received 5 November 1965 Abstract: The scattering of protons from carbon in the range of incident energies 4.7 to 12.8 MeV has been investigated using a tandem Van de Graaff accelerator and a differentially pumped gas scattering chamber. Absolute differential cross sections for elastic scattering and for the inelastic scattering reactions l~C(p, p')I~C* (Q = -4.43 MeV) and ~C(p, p")t~C* (Q = -7.66 MeV) were measured at laboratory angles of 25.54°, 85.22°, 105.23°, 121.16°, 137.52° and 159.45° as a function of energy in steps of 2.5 to 20 keV. Of particular interest is the splitting of the known resonance at 9.14 MeV, indicating a previously unknown level.

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NUCLEAR REACTIONS I~C(P'P)' E = 4"7-12"8 MeV; 12C(p, p'), E = 6.0-- 12.8 MeV; measured or(E, 0). X3N deduced levels. Natural target. 1. Introduction

The scattering o f protons by 12C in the energy range below 12 MeV has been investigated by several groups 1-9). I n the present w o r k absolute cross sections for elastic scattering and for the inelastic scattering reaction lZC(p,p')12C* (Q = - 4 . 4 3 MeV) have been measured at six scattering angles in the energy ranges 4.7 to 12.8 M e V and 6.0 to 12.8 MeV, respectively, with g o o d energy resolution and precision. The reaction 12C(p, p")12C* (Q = - 7 . 6 6 MeV) was observed f r o m 10.2 to 12.8 MeV. A complete analysis o f the 1 2 C + p elastic scattering experiment would entail finding the phase shifts (complex t h r o u g h m o s t o f the energy range) as a function o f energy and relating them to the eigenstates o f the 1 2 C + p system. This is reported in the following paper 1 o). 2. Experimental Methods A type E N t a n d e m Van de Graaff accelerator was used to accelerate protons which entered a differentially p u m p e d gas scattering c h a m b e r described in detail by Jones et aL 11). The b e a m energy value was k n o w n to better than 0 . 1 % 12). The gaseous target was 99 % pure methane on which a mass spectrometric analysis was performed. The scattering c h a m b e r has four detector ports, and during this experiment eight detectors (six silicon surface barrier detectors, one silicon diffused j u n c t i o n detector and a CsI(Tl) scintillator) were used at various times. M a n y o f the experimental procedures have been described previously 13), so only details specially pertinent to this experiment will be discussed. t Now at the University of Florida, Gainesville, Florida. tt NASA Fellow in Physics, now at the University of Wisconsin, Madison, Wisconsin. ttt Now at the University of Kentucky, Lexington, Kentucky. Supported in part by the U.S. Atomic Energy Commission. 119

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A T M C 400-channel pulse-height analyser was used in the 4 x 100 channel mode. The counting loss correction was made by the first method described in ref. 13), using fast scalers in parallel with the analyser. The largest counting loss correction was 7.7 ~ , the average correction being 2.2 ~ . The 100-channel spectra were examined to identify those proton groups due to scattering from 12C, as well as groups due to scattering from the impurities, to determine the upper and lower channel limits on the groups of interest and to make background corrections. In the reduction of the elastic data, small corrections were made for the elastic scattering from the 13C, 14N and 160 impurities. The elastically scattered protons from the three impurities are close in energy to protons elastically scattered from 12C. When the impurity peaks were unresolved, it was assumed for the purpose of making these small corrections that the proton scattering cross sections of the impurities and 12C were equal. This assumption should introduce negligible errors into the cross sections. At the more backward angles some of the impurity peaks were well resolved and could be ignored in the data reduction. The groups from inelastic scattering were summed between upper and lower channel limits chosen in a consistent manner. Since there were no impurity groups close in energy to the inelastic groups, the only correction necessary was for the "fiat" spectral background. For inelastic scattering to the first excited state, the number of counts per channel above and below the peak of interest was typically less than 1 of the peak counts, so that any change in the choice of upper and lower limits would have had only a small effect on the total number of counts. Since the second inelastic group was located on the upper side of low-energy noise, a plot of counts/channel versus channel number for each spectrum was drawn in order to obtain the best corrected peak count. The number of molecules per unit volume of target was determined by measuring the temperature and pressure of the gas once every few data points. The molecular composition of the gas was known from the mass spectrometric analysis so that various effective pressures could be obtained. For instance if scattering from 12C was resolved from scattering from all other nucleides, the effective pressure used was for 12C alone. If scattering from 13C was unresolved, the effective pressure was higher by the factor (total carbon)/~2C, and so on. The length of the target volume was known from the chamber geometry so that the number of scattering centers per cm 2 of target was obtained. The target thickness depends mainly on gas pressure, beam energy and angle of observation. For 5 MeV protons, at the chamber pressure used, the smallest target thickness was 0.9 keV at 90 ° and the largest thickness was 6.8 keV at 161 °. The energy loss of protons in traversing the differential pumping system and first half of the scattering chamber cannot be accurately calculated since the pressure distribution along the proton path is not well known. An empirical formula obtained by Jones et al. 11) gave the energy loss at proton energy Ep = 5 MeV as 22 keV for the chamber pressure used. Extreme assumptions concerning the pressure distribu-

PROTON SCATTERING FROM 12C

121

tion in the system change the energy loss by 4- 10 keV, so that 4- 30 7ooseems a reasonable estimate of the accuracy of the energy loss. At Ep -- 5 MeV the beam energy uncertainty arising from the uncertainty in the 90 ° bending magnet calibration is about 4- 5 keV. These two systematic errors compound to approximately ___12 keV. There is also a random error in the beam energy due to possible different paths through the 90 ° magnet with different lens and deflector settings. Since the energy of sharp resonances was usually repeatable to within a few keV, this is estimated as the random energy uncertainty. The energy spread of the beam is also estimated as a few keV. At higher energies the beam energy uncertainty increases, but the energy loss before the target decreases, leaving the total systematic uncertainty approximately constant. Thus this uncertainty should be less than 4- 15 keV at all energies used in this experiment. The peak cross section of the 4.8 MeV anomaly in the elastic scattering cross sections appeared at 4.803 MeV at 0.... -- 161.14 ° and 4.809 MeV at 0.... = 140.76 ° in this experiment. An absolute measurement 2) at 180 ° has placed the peak at 4.806___0.005 MeV. The data-taking and data reduction procedures and geometrical features of the scattering chamber have recently been checked by scattering protons from differentially pumped hydrogen gas 13). The differential centre-of-mass cross sections agreed to within 0.57oo on the average with the results of Knecht et al. 14).

3. Experimental Results Absolute differential cross sections for elastic scattering of protons by 12C and inelastic scattering to the 4.43 MeV first excited state of 12C were measured at six angles in the energy ranges 4.7 to 12.8 MeV and 6.0 to 12.8 MeV, respectively. Inelastic scattering to the 7.66 MeV second excited state of 12C was observed at five angles from 10.2 to 12.8 MeV. The data at 0~b = 85.22 °, 121.16 ° and 159.45 ° were taken at one time and the data at 0tab = 25.54 °, 105.23 ° and 137.52 ° at a later time. F r o m the close agreement between the positions of the 4.8 MeV m a x i m u m in the elastic scattering cross sections at 0.... = 161.14 ° and 140.76 °, the two energy scales are in satisfactory agreement. The elastic and inelastic scattering excitation functions are shown in figs. 1-3. The energy steps were generally 6 to 9 keV, except that over narrow resonances 2.5 to 4 keV steps and above 12.3 MeV approximately 20 keV steps were taken. Counting statistics, which are the largest source of error, and overall r.m.s, errors of the excitation functions are given in table 1. Contributions to the r.m.s, error from sources other than statistics are given in table 1 ofref. 1a). Experimental points from the angular distributions of Reich, Phillips and Russell 2), Moss and Haeberli 15), and Barnard, Swint and Clegg 1o) are also plotted on figs. 1 and 2 for comparison.

4. Discussion The level structure of 13 N is quite well known and most of the anomalies in the elastic scattering cross sections have the shapes and positions expected. However,

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TABLE 1 Errors in the excitation functions Average counting statistics

r.m.s, overall error

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Laboratory ~tngle ~ elastic 25.54 ° 85.22 ° 105.23 ° 121.16 ° 137.52 ° 159.45 °

' ' 0.9(1.4) 1:8(4.0) 1.6(3.0) 1.8(4.1) 1.2(4.1) 0.8(5.8)

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second inelagtic

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3.1(7.9) 6.4(16.0) 5.3(8.0) 6.0(16.0) 3.3(9.0)

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elastic • 2.0 2,6 2.4 2.6 2.2 2.0

first second ineias~tlc " inelastic : 4.0 4.1 3.8 3.4 3.2 2.4

3.8 6.8 5.8 6.4 4.0

Extreme values of the counting statistics are given in the parentheses. t h e s p l i t t i n g o f t h e r e s o n a n c e at Ep = 9.14 M e V , w h i c h c a n b e seen in t h e 90 ° a n d 140 ° elastic s c a t t e r i n g e x c i t a t i o n f u n c t i o n s (figs. l c a n d l d ) , has n o t b e e n r e p o r t e d p r e v i o u s l y . T h i s i n d i c a t e s a n e w state v e r y close to t h e k n o w n ~7 - - state at a n excitat i o n e n e r g y Ex( 1 a N ) = 1 0 . 3 8 M e V . I n t h e d a t a s h o w n in fig. 2 at a n i n c i d e n t p r o t o n e n e r g y o f a p p r o x i m a t e l y 10.74 M e V , t h e r e is a n i n d i c a t i o n o f a level seen p r e v i o u s l y o n l y b y A d a m s et aL 16). T h e a u t h o r s g r a t e f u l l y a c k n o w l e d g e a s s i s t a n c e f r o m D r . C. M . J o n e s in t a k i n g t h e e a r l y d a t a , a n d f r o m M i s s P e g g y Sue R o b i n s o n a n d Messrs. R . A . M o y e r a n d J.S. D u v a l in d a t a r e d u c t i o n .

References 1) H. L. Jackson, A. I. Galonsky, F. G. Eppling, R. W. Hill, E. Goldberg and J. R. Cameron, Phys. Rev. 89 (1953) 365; H. L. Jackson and A. I. Galonsky, Phys. Rev. 89 (1953) 370 2) C. W. Reich, G. C. Phillips and J. L. Russell, Jr., Phys. Rev. 104 (1956) 143 3) H. Schneider, Helv. Phys. Acta 29 (1956) 55 4) F. L. Bordell, G. E. Mitchell, P. B. Weiss, J. W. Nelson and R. H. Davis, Bull. Am. Phys. Soc. 5 (1960) 404 5) G. Dearnaley and A. B. Whitehead, private communication and Proc. Int. Conf. on Nuclear Structure, Kingston, Canada (1960) 6) Y. Nagahara, J. Phys. Soc. Jap. 16 (1961) 133 7) G. G. Shute, D. Robson, V. R. McKenna and A. T. Berztiss, Nuclear Physics 37 (1962) 535 8) F. C. Barker, G. D. Symonsl N. W. Tanner and P. B. Treacy, Nuclear Physics 45 (1963) 449 9) N. Nikolic, L. J. Lidofsky and T. H. Kruse, Phys. Rev. 132 (1963) 2212 10) A. C. L. Barnard, J. B. Swint and T. B. Clegg, Nuclear Physics 86 (1966) 130 11) C. M. Jones, G. C. Phillips, R. W. Harris and E. H. Beckner, Nuclear Physics 37 (1962) 1 12) G. C. Phillips, Proceedings of the Second International Conference on Nuclidic Masses 1963, Springer-Verlag, Vienna, 1964; B. E. Bonner, J. Rickards and G. C. Phillips, to be published 13) A. C. L. Barnard, C. M. Jones and J. L. Weil, Nuclear Physics 50 (1964) 604 14) D. J. Knecht, S. Messelt, E. D. Berners and L. C. Northcliffe, Phys. Rev. 114 (1959) 550 15) S. J. Moss, P h . D . Thesis (University of Wisconsin, 1961); S. J. Moss and W. Haeberli, to be published 16) H. S. Adams, J. D. Fox, N. P. Heydenburg and G. M. Temmer, Phys. Rev. 124 0961) 1899