The (p, 2p) reaction on 2H, 3He and 4He

Volume 46B, number 2

PHYSICS LETTERS

17 September 1973

T H E (p, 2p) R E A C T I O N O N 2H, 3 H e A N D 4 H e * H.G. PUGH**, P.G. ROOS, A.A. COWLEY***, V.K.C. CHENG and R. WOODY Umverstty of Maryland, CollegePark. Maryland 20742, USA Received 31 July 1973 The (p, 2p) cross sections on 2H, 3He and 4He were measured at 65, 85 and 100 MeV. The experimental data show rather strong energy and target mass dependence, particularly for 4He. The (p, 2p) cross sections for 2H, 3He and 4He have been measured at 65, 85 and 100 MeV At bombarding energies above 100 MeV an impulse approxxmatlon treatment of the (p, 2p) reaction is generally accepted [ 1], whereas in the range 2 0 - 5 0 MeV such a treatment is known to be madequate, even for the 2H(p, 2p) reaction. The present data provide the opportumty to investigate systematically the energy and target mass dependence of the (p, 2p) reaction m the intermediate energy range. The understanding of these dependences Is Important, so that one can extract the important wave function information which ts m principle available from the study of knockout reactions [1] This study is especmlly faclhtated by the choice of three target nuclei from the 1s shell. The experiment was performed with proton beams from the University of Maryland cyclotron. The beam was focused on a 12.5 cm diameter gas target filled to a pressure of approxmaately one atmosphere and positioned m the center of a 150 cm diameter scattering chamber Two detector telescopes, each consisting of a sxllcon surface barrier ~ detector and a 5 cm thick × 2.5 cm dmmeter Nal E detector, were placed m the chamber coplanar with and on opposite sides of the beam. The detector shts subtended approximately 2.5 ° (m the scattering plane) × 2 0 ° (out of the plane). Wlth standard electronics the four coincident linear energy signals were fed to an IBM 360/44 on-hne computer through 2048-channel

* Research supported in part by the U S. Atomic Energy Commission. ** On leave for the academic year 1972-1973 to CERN, Geneva, Switzerland *** Visitor from CSIR, Pretona, South Africa. 192

analogue-to-digital converters (ADC). The z2~E-E addition and particle Identification were performed in the computer. In addition, a time-to-amphtude converter (TAC), with Its output sent to a fifth ADC, was employed to measure the time difference between the two detected charged particles. The tlmmg signals were obtained from the z5£" detectors. The use of a TAC allowed the storage of both real and accidental coincidences simultaneously. The basic experimental reformation (four energy signals plus the time difference for each event) was written on magnetac tape for subsequent detaded analysis. In addition, numerous hve displays were generated during data accumulation [2]. The beam intensity was hmited to the range of 25 to 100 nA to keep the number of random coincidences small. Coincidence data were taken for coplanar symmetric angles such that zero recoil momentum was klnematlcally allowed, thus providing a measurement of the moment distribution of the knocked out proton. The experamental differential cross sections for 100 MeV are presented in fig. 1 The results for the 65 and 85 MeV are qualitatively slmdar [3] The error bars are statistical only. The cross-section scales are accurate to approximately 5% relative to each other, and the absolute scale is accurate to approximately 10%. As a means of correlating the energy and target mass dependence of the (p, 2p) reaction, we have compared the experimental cross sections to calculations carried out in the plane-wave impulse approximation (PWIA), i.e. d3o d~Id~2dE 1

= (PSF) X d~tpp X Nplq~(q)12

(1)

where the phase space factor (PSF) represents known

Volume 46B, number 2

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d (p,2p)n F~=IO0 MeV

17 September 1973

Table 1 The ratios of expertmental cross sectmns to PWIA calculations. The errors are relatwe errors Target nuleus

OJI

~

I

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I

Ep (MeV)

0

E. =100 MeV

%

I

1

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Ep (MeV) *He(pp2p)3H

E.=IO0 MeV ~ . . ~ ~

. ( PWlAx.092 )

I

J

I

1

~

I

20

30

40

50

60

70

Eo

(MeV)

Fig. 1. Experimental cross sections for the (p, 2p) reaction at 100 MeV. The solid curves are PW1A calculations (see text) normalazed by the factors in the figure

kinematical quantities; do/dI2lpp is the free p-p cross section [4] appropriate for the final state of the two detected protons; Np is a factor due to spin and antisymmetrization which is effectively the spectroscopic factor (1 for deuterium, 3/2 for 3He, and 2 for 4He);

Eo(MeV)

2H

3He

4He

65 85 100

0.56 ~: 0.03 0 72 ± 0 05 0 77 -+ 0.04

0.36 ± 0,03 0 49 ± 0,03 0.56 ± 0 04

0,024 +- 0.003 0,049 -+ 0.005 0.092 ± 0.007

and ~ q ) is the Fourier transform of the overlap integral between the spatml wave function of the target nucleus and the residual nucleus. It should be noted that the integral fl(o(q)12d3qis generally less than 1. For the three reactions the following wave functions were used to calculate the overlap integral. a) 2H(p, 2p)n: A Hulthen wave function for the deuteron. b) 3He(p, 2p)d' An Irvmg-Gunn wave function for 3He overlapped with a Hulthen wave function for the deuteron. c) 4He(p, 2p)t: A 1s oscillator wave function I¢(q)l 2 = Nexp(-q2/q 2) with qo = 90 MeV/c which fits the width of the 600 MeV 4He(p, 2p)t data [5]. The normalization constant N was chosen so that the integral fl¢(q)i2d3q equals unity [6]. The results of these PWlA calculations, normalized to the experimental peak cross sections, are presented in fig. 1 for the I00 MeV data. The PWlA calculations are too large, and have been multiplied by the factors shown in the figure. The normalization factors for these data and the 65 and 85 MeV data are presented in table 1. In addition to the necessity of renormahza, tion, for deuterium the theoretical distribution is significantly broader than the experimental distribution while for 3He the agreement in width is reasonable. In the 4He(p, 2p)t reaction relatively little of the wave function in momentum space can be measured at these energies, and the primary comparison must be to the peak cross section. The discrepancies between experiment and the PWIA.calculations are typical of (p, 2p) reactions in this energy range [ 1]. In fig. 2 we present the ratio of the experimental cross sections to the PWIA calculations as a function of energy for the present data, as well as other data m the same energy range [7-12]. Two results can be seen from this figure. First, there is a smooth mcrease in the ratio as the mcident energy is increased. This effect is most pronounced for the 4He(p, 2p) reaction for which the proton is most tightly bound 193

Volume 46B, number 2

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_i ---'

/ / /~r / I

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"*'-

C.LThlsWork 3Help,2p){ aRef II ~.~Ref 12

I 60

I 80 E.

I 4He(PI'2P)(iThls W°rk J I00 120 140 160 {MeV)

Fig. 2. The ratio of the experimental (p, 2p) cross sections to the PWlA calculations as a function of energy. The error bars include the absolute errors in the expermaental data. The solid curve is a smooth curve drawn through the data The dashed curve is obtained when the ratios represented by the solid curve are corrected for the approprmte off energy shell cross section. [6]. Second, the ratio systematically decreases as the number of target nucleons is increased. The reduction in the ratio for 4He is quite dramatic. Part o f this effect is probably due to the use o f an oversimplified ¢(q). It would be quite useful to compare the data to a more accurate 4He wave function. The ratios presented in fig. 2 were obtained using for do/d~21pp in eq.(1) the experimental free p-p cross section appropriate for the final state of the two outgoing protons. However, properly calculated off-energy-shell cross sections can differ appreciably from on-shell values [13]. We have therefore made a correction for off-shell effects using the computer code o f ref. [13]. We calculated, for the Reid softcore potential, the ratio between the off-shell and on-shell cross sections. This ratio, which IS found to be much less model dependent than the cross sections themselves, was then used to correct the PWlA calculations. To avoid confusion with data points we have corrected the ratio o f the experimental cross section to the PWlA calculation, represented by the solid lines m fig. 2, resulting in the dashed curves o f fig. 2. The corrections introduced by the proper treatment o f the off-shell cross sections are negligible for deuterium, small for 3He, and quite large for 4He, although by no means sufficient to bring the theory into agreement with experiment. 194

17 September 1973

The results displayed m fig. 2 clearly show inadequacies of the PWlA theory as a function o f energy and mass number. A l ~ o u g h some improvement is obtained through the use of a more correct treatment of the twO-body cross section, the major source o f the disagreement must be due to multiple scattering or distortion effects. In order to obtain useful reformation about the wave functions for these light nuclei, a proper treatment of the multiple scattering series must be made. Recently claculatlons by Wallace [ 14] which sum the multiple scattering series for the 2H(p, 2p)n reaction produce very good agreement with the data presented in this paper. It would be desirable to carry out such calculations for 3He and 4He to see if they predict the behavior shown in fig. 2, particularly the increased energy dependence for the 4He(p, 2p)t reaction. The large extent and rapid energy dependence of the discrepancy between PWlA and experimental data for 4He will provide an extremely severe and useful test of more sophisticated theories. F o r this nucleus it would also be desirable to have additional measurements above 100 MeV. The authors gratefully acknowledge the electronics support provided by J.E. Etter and the computer support provided by N.R. Yoder. We would also like to express out thanks to the entire cyclotron staff. [1] G. Jacob and T.A.J. Maris, Revs. Mod. Phys. 38 (1966) 121; G. Jacob and T.A.J. Marls, Revs. Mod. Phys. 45 (1973) 6. [2] P.E. Frisbee and N.R. Yoder, Univ. of Maryland Tech. Rep #73-043. [3] All data are presented in the 1972 University of Maryland Progress Report. [4] From interpolation of the results complied in R. Wilson, N-N interaction, experimental and phenomenological aspects (Interscience, N.Y., 1963, John Wiley). [5] C.F. Perdrisat et al., Phys. Rev. 187 (1969) 1201. [6] With this normalization the ratio of experiment to PWIA for the 600 MeV data is 0.37. [7] J.L. Durand et al., Phys. Rev. C6 (1972) 393. [8] D.J. Margaziotis et al., Phys. Rev. C2 (1970) 2050. [9] P.J. Pan and J.E. Crawford, Nucl. Phys. A150 (1970) 216. [10] M. Morlet et al., Nucl. Phys. A129 (1969) 177. [11] I. Slaus et al., Phys. Rev. Lett. 27 (1971) 751. [12] R. Frascaria et al., Nucl. Phys. A178 (1971) 307. [13] E.F. Redish, G.J. Stephenson and G.M. Lerner, Phys. Rev. C2 (1970) 1665. [14] J. Wallace, Phys. Rev. C7 (1973) 10.