The elastic scattering of protons from He3 from 4.5 to 11.5 MeV

Nuclear Physics 50 (1964) 621--628; (~) Nm, th-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permissionfrom the publisher

T H E ELASTIC SCATTERING OF P R O T O N S F R O M He 3 F R O M 4.5 T O 11.5 MeV T. B. CLEGG, A. C. L. BARNARD, J. B. SWINT and J. L. WEIL t Bonner Nuclear Laboratories, Rice University, Houston, Texas tt Received 22 July 1963 Al~Lraet: HeS(p, p)He s cross sections have been measured for incident proton energies from 4.5 to 11.5 MeV using a tandem Van de Graaff accelerator. Excitation functions at centre-of-mass angles o f g 0 °, 125°18 ' and 161012' were measured from 4.5 to 10.4 MeV in steps of 200 keV, and no sharp structure was observed. Angular distributions were measured from 27038' to 166035' in the c~ntre-of-mass system at bombarding energies of 4.55, 5.51, 6.52, 7.51, 8.51,9.51, 10.38 and 11.48 MeV. A phase shift analysis has been made o f these data using one phase shift for each of the values o f ! through 1 = 2. The P-wave phase shift was found to be increasing with energy (in qualitative agreement with earlier analyses). Cross sections calculated from the phase shifts show large deviations from the experimental values in the region around 100° in the centre-ofmass system. This indicates that some spin-dependent splitting of the phase shifts is required to fit the data.

1. Introduction Recent p + H e 3 elastic scattering measurements from 2.0 to 4.5 MeV were made by Tombrello et al. 1) at Rice in an attempt to ascertain the existence and position of levels of the nucleus Li 4. This information is of interest because states found in Li 4 would correspond to excited states in the alpha particle. The p + He s scattering cross sections have been measured by other groups 2-6), and phase shift analyses have been made 1.7, s). Lowen's analysis of Famularo's angular distributions at 1.01, 1.60, 2.25 and 3.52 MeV has shown that a very good fit could be obtained by representing the two S-wave and the four P-wave phase shifts by only two independent phase shifts, one for each contributing value of/. Physically this is equivalent to assuming that there is no spin-orbit or spin-spin contribution to the nuclear force. The Rice group made a similar simplified phase shift analysis of their data from 2.0 to 4.5 MeV and of other isolated angular distributions. Their results show t~x to be increasing with energy up to 9 MeV but were inconclusive as to which of the four P-wave phase shifts caused the effect. There was an indication that at least two P-wave levels with different Jvalues contributed. The calculated fits of Tombrello et al. 1) to their two highest energy angular distributions begin to show departures from the experimental data around 90 °. This is an t Now at the University of Kentucky, Lexington, Kentucky. ** Work supported in part by the U. S. Atomic Energy Commission; work based on a thesis submitted by one of the authors (T.B.C.) in partial fulfillment o f the requirements for the M. A. degree, Rice University. 621

622

T.a. CIJU30 et al.

indication that even at 4 MeV the assumption o f only three phase shift parameters is no longer good, and that, as expected, there is some spin-dependent contribution to the nuclear force. The present work extends the p + He s elastic scattering measurements from 4.5 to 11.5 MeV. Excitation functions were measured at centr~of-mass angles of 90 °, 125°18 ' and 161°12 ' from 4.5 to 10.4 MeV. Angular distributions were measured at approximately 1.0 MeV intervals from 4.5 to 11.5 MeV. An attempt has been made to reproduce the experimental angular distributions from the phase shifts making the simplifying assumptions mentioned above.

Most of the experimental procedures were described in the preceding paper 9), thus only details pertinent to this experiment will be discussed. For the excitation function measurements the scattering chamber was sealed off from the accelerator vacuum system by a SiO entrance foil, and for the ang~_~!~r distributions by a 63 × I0 -s mm Ni foil. The energy thicknesses of these foils were determined from the apparent energy shift of the 4.8 MeV C12(p, p)C 12 resonance between measurements using differential pumping 9) and measurements using the foils. The SiO foil was found to be I 0 ± 3 keV thick and the Ni foil 3 2 + 5 keV thick to 4.8 MeVprotons. Silicon junction and surface barrier detectors were used in taking all data except the 161°12 ' excitation function, for which a scintillation counter was used. During the excitation function measurements there was considerable difficulty with slow gas leakage through the SiO foil and with water vapour from outgassing of the chamber walls. The loss of He s was corrected for by assuming that the difference o f up to 7 ~o in cross section as measured with old and new samples o f He s in the chamber arose from a linear decrease in the He 3 partial pressure with time. For the angular distribution measurements precautions were taken to reduce chamber outgassing, a new sample of He s was placed in the chamber for each ang~l~r distribution so the contamination never became very large, and the thicker Ni entrance foil was used to reduce the He s leakage. In this case repeating cross section measurements with a fresh gas sample showed no conclusive evidence of gas loss, so no correction was made. For both the excitation functions and the angular distributions, impurity groups could be separated out at all angles. The impurity content of the He s gas used was determined by mass spectroscopic analysis to be 1.86+0.30 ~o for the excitation functions and 0.38_0.I0 ~o for the angular distributions. Counting loss corrections were made, as described in the preceding paper 9), with l(R)-channel spectra and five-step integral bias curves. An experimental check with p-p scattering showed agreement with the work of Knecht et al. I°) to better than 1 ~o for all detectors.

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ELASTIC

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available. The solid curves were calculated from the phase shifts derived using the analysis described in sect. 4. Sources o f e r r o r are similar to those in the preceding paper 9) with the exceigion o f the possible error in the gas loss correction. The rms probable error for the excitation functions is ± 3.4 % at 90 ° and 125°18 ' and ±2.7 % at 161°12 '. For the angular distributions the rms error is ±2.8 % for angles between 90 ° and 135 ° and ± 2.2 ~o at all other angles. Tables 1 and 2 give all the cross sections measured in Q25

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the present experiment. At higher energies several forward angle points on the angular distributions were measured by counting the He 3 recoils, since the elastically scattered protons were too energetic to be stopped in the detector used in this angle range. The He 3 recoil peaks were low in pulse-height, and there was a greater uncertainty in the background correction for them than for the elastic proton peaks used. For this reason, it is estimated that the rms error for these points (indicated b y ' ) table l) is about + 3 . 0 % . The data of Tombrello et aL 1) at 4.54 MeV are stated to be accurate to ± 3 %. Discrepancies between that experiment and the present one are not larger than the combined errors quoted for the two experiments. The data of Brolley et al. 5) taken with the Los Alamos cyclotron are shown on the 6.52 and 8.51 MeV distributions. The cross sections of the present experiment agree well with the Los Alamos cross sections meas-

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626

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TABLE 2

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229.0 230.6 227.9 219.0 220.4 208.7 204.2 199.2 191.5 184.8 180.1 174.1 171.7 173.6 165.6 160.0

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ured by counting the elastically scattered protons, but the Los Alamos points measured by counting the recoil He s nuclei do not agree to within the quoted errors with the elastically scattered proton data of either that experiment or the present one. It is interesting to note the Coulomb-nuclear interference dip observed at forward angles in both experiments. At 9.51 MeV the data of Lovberg 4) are plotted for comparison. Agreement is good except at forward angles. Lovberg indicates that large corrections were made in his data in this region to account for double Coulomb scattering in the 0.0012 cm Dural walls of his target cell. Using a scintillation counter and a 10-channel analyser he was unable to separate out protons scattered from impurity nuclei for angles smaller than about 45 ° in the centre-of-mass system. Thus an inaccurate estimate of the effect of double scattering of the proton beam or an unknown impurity contribution could account for his disagreement with the present measurements at forward angles. 4. Phase Shift Analysis t Tombrello et aL l) give a complete expression for the centre-of-mass cross section in terms of the phase shifts for the scattering of spin ½ particles by spin ½ particles. With the assumption of no spin-spin or spin-orbit interaction this reduces to _ ~Op

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627

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6~ is the phase shift for the partial wave o f angular momentum L In these formulae k = ~ v ) / h , ~/= (Zt Zze2)/hv, COo= 0 and cet = ~_~=1 tg-101/s), where v is the relative velocity o f the two particles and ~t is the reduced mass of the system. The phase shifts in this expression were determined using Method B described in the preceding paperg). The curves in figs. I-2 were calculated using only three partial wave contributions. Acomparison of the angular distribution data and the curves calculated from the phase shifts show that the fits became increasingly worse at higher energies. The 60, 61 and 62 contributions are too small at 100° to allow for improving the fit with these parameters alone. At 8.51 MeV adding a small amount of 63 was found to improve I

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forward angle agreement, but to increase the discrepancy near 120 °, leading to a curve with a slightly larger percentage deviation from the data than the present fit. This line of investigation was not pursued at other energies. The "best fit" phase shifts are plotted in fig. 3 together with the phase shifts o f Tombrello et al.1). The solid line on the plot of the S-wave phase shift is the "hard sphere" phase shift for an interaction radius of R = 3.5 fin. The positively increasing P-wave parameter would seem to indicate at least one 1 = 1 state in the Li 4 nuclear configuration. Tombrello et al. 1) found that in terms of single-level dispersion theory their l = 1 phase shift corresponded, for R = 3.5 fro, to a level at E,®s (c.m.) = 26 MeV with a reduced width of 3.2 times the Wigner limit. Their calculated curve using these parameters is shown in fig. 3. 5. Conclusion The increasing P-wave phase shift indicates an 1 = I state in the Li 4 nuclear configuration, but evidence for such a level is not conclusive from this simplified analysis.

628

T.a.

CLEOO et al.

At the higher energies the larger discrepancy observed between the experimental and calculated angular distributions in the mid-angle region seems to indicate enough spin dependence o f t h e nuclear force t o m a k e a m o r e complete phase shift analysis n__~ces-_ sary. Other possible sources for the discrepancy are two open reaction channels. A b o v e 5.493 MeV the reaction He3(p, 2p)d is energetically possible, a n d above 7.718 M e V the reaction He3(p, 3p)n m a y occur.

Note added in proof." A complete phase shift analysis, giving evidence for the existence o f several states in Li 4, has recently been reported by Tombrello xx). References

I) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

T. A. Tombrello, C. M. Jones, G. C. Phillips and J. L. Weft, Nuclear Physics 39 (1962) 541 K. F. Famularo, R. J. S. Brown, H. D. Holragrcn and T. F. Stratton, Phys. Rzv. 93 (1954) 928 D. R. Swcctman, Phil. Mag. 46 (1955) 358 R. Lovberg, Phys. Rev. 103 (1956) 1393 J. E. Brollcy, Jr., T. M. Putnam, L. Rosen and L. Stewart, Phys. Rev. 117 (1960) 1307 K. P. Artcmov, S. P. Kalinin and L. N. Samoilov, JETP (Soviet Physics) 10 (1959) 474 R. W. Lowen, Phys. R©v. 96 (1954) 826 R. M. Frank and J. L. Gmnra©l, Phys. Roy. 99 (1955) 1406 A. C. L. B ~ a r d , C. M. Jones and J. L. W¢il, Nuclear Physics 50 (1963) 604 David J. Knecht, S. Mcsselt, E. D. Bcrncrs and L. C. Northcfiffc, Phys. Rev. 114 (1959) 550 T. A. Tombrolio, Topical Conf. on Compound Nucleur States, Gatlinburg, Tenn., Oct. 1963