Proton polarization from the 40Ca(d, p)41Ca reaction at 5 MeV

Proton polarization from the 40Ca(d, p)41Ca reaction at 5 MeV

2.B [ Nuclear Physics A l l 5 (1968) 108---112; (~) North-Holland Publishin9 Co., Amsterdam I Not to be reproduced by photoprint or microfilm with...

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Nuclear Physics A l l 5 (1968) 108---112; (~) North-Holland Publishin9 Co., Amsterdam


Not to be reproduced by photoprint or microfilm without written permission from the publisher


FROM THE 4°Ca(d, p)41Ca REACTION AT 5 MeV H. G. LEIGHTON, G. ROY and D. P. GURD Nuclear Research Center, Physics Department, University of'Alberta, Edmonton, Alberta, Canada t Received 19 March 1968 Abstract: The polarization of the protons from the ground state 4°Ca(d, p)41Ca reaction has been measured for an incident deuteron energy of 5 MeV and in the angular range from 25 ° to 115°. The polarization showed the same trends found in higher energy experiments, namely small and negative in the forward direction with an indication of a negative peak in the vicinity of 100°. DWBA calculations, including a vector type spin-orbit potential, predicted in all cases polarizations opposite in sign to those observed experimentally. E



NUCLEAR REACTIONS 4°Ca(d, p), E : 5 MeV; measured a(0), polarization P(O).

1. Introduction In recent years, some limitations of the D W B A theory as applied to deuteron stripping reactions have become more apparent. F o r cases in which the deuteron optical potential has been determined from elastic scattering experiments, the agreement to experimental (d, p) and (d, n) angular distributions and particularly polarization distributions has often been quite p o o r ~- 5). The inadequacies of the theory have led to different approaches. On the one hand, there have been efforts to improve the present form of D W B A theory such as the inclusion of the deuteron D-wave in the calculations by J o h n s o n and Santos 6), and, on the other hand, entirely new stripping theories have been proposed such as the W B P model 7-9) and B H M M theory 10). In testing such theories against experiment, it is useful to have large amounts o f data from the same target nucleus and covering a wide range of energies. The studies of the 52Cr(d, p)53Cr reaction in the energy range 8-11 MeV by Alty et al. ~t) and from 4.3 to 6.3 MeV by Legg et al. 1) comprise one such large body of data. A n o t h e r extensive study is that of the 4 ° C a ( d , d ) 4 ° C a and 4°Ca(d, p)4~Ca reactions by Bassel et al. 12) and Lee et al. 3) and at 14.3 MeV by H j o r t h et al. 4). Various experimental groups at the University of Alberta have cooperate to extend in energy and scope the information from deuteron-induced reactions on calcium. The elastic scattering and the (d, p) and (d, n) stripping distributions have already been reported 2) and a preliminary report of the (d, p) and (d, n) polarization distributions t This research work was supported in part by the Atomic Energy Control Board of Canada. 108

4°Ca(d, p)41Ca REACTION


has also been given a 3). In this paper, we present the results of the measurements of the proton polarization and a comparison of the data with some predictions of D W B A theory is made. While there is no reason to expect more successful agreement to the polarization data than was obtained by Hjorth at 14.3 MeV, the additional data may help eventually to establish a more successful stripping theory or to determine details of the deuteron optical potential.

2. Experimental method and results The proton polarization was measured using a carbon polarimeter coupled to a 50 cm magnetic spectrometer. The polarimeter has been described in detail by Gurd et al. 14). It consists of two silicon detectors in which the left-right asymmetry of the elastic scattering from a carbon foil was measured. The carbon foil was 17 mg/cm z thick which represents an energy loss of 1.1 MeV to 6 MeV protons. Background in the side counters was reduced by first passing the protons through a thin fully depleted silicon detector, thereby providing a gating condition for these counters. The polarimeter was calibrated using the measured polarization of 6.18 MeV protons I



I ./







I "\~'~',t J " ~"#






























i__ 120

l 140

OJCM t d e cj~

Fig. 1. T h e p r o t o n p o l a r i z a t i o n a n d a n g u l a r d i s t r i b u t i o n f r o m the 4°Ca(d, p)llCag.s, reaction at 5 M e V . T h e indicated errors are statistical only. T h e n u m b e r s refer to the potentials o f table 2. F o r the sake of clarity, the a n g u l a r d i s t r i b u t i o n s c o r r e s p o n d i n g to sets 1 a n d 4 have been omitted.



elastically scattered from carbon at 45 ° as determined by Moss and Haeberli 1 5 ) . The analysing power was found to be -0.68_+ 0.04 at the scattered proton energy of 5.87 MeV. It was also found that the analysing power was not particularly energy sensitive over a proton energy range from 5.39 to 6.00 MeV, the measured analysing power always being within the limits - 0 . 6 1 to - 0 . 6 8 . For a polarization measurement, the protons were degraded in energy so as to enter the polarimeter within the calibrated range. Each experimental point was the result of two measurements, the polarimeter being rotated by 180 ° between the first and second. Tests with a tantalum second scatterer indicated that instrumental asymmetries were less than 2 ~. The target was a 5 mg/cm 2 rolled calcium foil t. The target angle was adjusted to minimize as much as possible the energy spread of the protons entering the magnet, the typical effective thickness being ~ 500 keV. The deuteron energy was adjusted so that the energy at the center of the target was 5.00 MeV. Consequently, the emergent protons resulted from deuteron interactions in the approximate energy range of 4.75 to 5.25 MeV. TABLE 1 4°Ca(d, p)41Cag.s, polarization Eo = 5 MeV

0¢.m.(deg.) 25.6 35.8 46.0 56.1 66.2

0. . . . (deg.)

P~AP -0.057~0.046 -0.062 ±0.049 -0.049~0.047 -0.135±0.049 -0.087±0.047

76.3 86.3 96.3 106.3 116.2

P~zAP -0.110±0.051 -0.084 ± 0.049 -0.062 :L0.037 -0.201 ±0.051 -0.147±0.054

The polarization angular distribution is given in table 1 and plotted in fig. 1. The error bars indicate statistical errors only and do not take into account the uncertainty in the analysing power of the polarimeter which is estimated to be _+ 4 / o/ , o• The general features of the distribution are consistent with the results 4,16-1s) at 5.8, I0.0, 10.9 and 14.3 MeV, namely small negative polarizations in the forward direction with some evidence of a negative peak in the vicinity of ~ 100 ', though not as pronounced as at the higher energies.

3. Analysis DWBA calculations were carried out by means of the computer code D W U C K ~9). The optical potentials were of the form

U(r) = Uc(r ) - Vf(r, r0, a ) + 4 ia' W d~ If(r, r~, a')] dr

+ ~


[f(r, ro, a)],

Oak Ridge National Laboratory, Nuclear Division, Oak Ridge, Tennessee.

a°Ca(d, p)41Ca REACTION

11 I

where Uc(r ) is the C o u l o m b potential of a sphere of radius Saxon form f a c t o r f ( r , r o, a) is

rocA ~, and the W o o d s -

f(r, to, a) = {1 + e x p [(r-roA~)/a]} -1 The radius roc was taken to be 1.25 fm for protons and 1.30 fm for deuterons. The potential parameters used were the 5 MeV parameters of ref. 2) that were found to fit the elastic scattering and (d, p) and (d, n) distributions except that in the present analysis the spin-orbit potentials were not set equal to zero. The proton parameters were V = 4 9 . 5 M e V , W = 10.6MeV, r 0 = r6 = 1.25fm, a = 0 . 6 5 f m , a' = 0.47 fm, V~ = 8 MeV and W~ = 0 MeV. The captured neutron was assumed bound in a well of radius 1.25 fm and diffuseness 0.65 fm and a spin-orbit strength o f 25 times the T h o m a s term was included in the potential. Various combinations of Vs and W, were tried for the deuteron potential as indicated in table 2. All calculations were carried out with finite-range corrections. Except for the largest values of V~ and W~, the deuteron elastic scattering predictions were not changed significantly by the inclusion of the spin-orbit term in the deuteron potential. F o r Vs = 10 MeV, the change TABLE 2

Deuteron optical-model parameters Set No. 1 2 3 4

V (MeV)

r0 (fro)

a (fm)

W (MeV)

r0' (fro)

a' (fm)

Vs (MeV)

Ws (MeV)


110 110 110 110

1.03 1.03 1.03 1.03

0.92 0.92 0.92 0.92

9.8 9.8 9.3 9.8

1.64 1.64 1.64 1.64

0.53 0.53 0.53 0.53

0.0 5.0 10.0 8.36

0.0 0.0 0.0 3.59

0.62 0.64 0.64 0.73

in the elastic scattering could be compensated by reducing W by 0.5 MeV. This small change in W has little effect on the polarization predictions. The inclusion of the spin-orbit term in potential No. 4 produced a larger discrepancy with the elastic scattering. N o attempt was made to compensate this by adjusting the other parameters. The fits to the polarization data and to the 5 MeV (d, p) distribution of ref. 2) for the various spin-orbit potentials of table 2 are also shown in fig. 1. The corresponding spec~roscopic factors for the (d, p) distribution are included in table 2. Calculations were also performed with the potential of ref. 2) in which V = 78 MeV but with Vs = 5 MeV and again the polarization was similar to the other calculations. Finally, an average potential that was found to fit the elastic scattering data 2,12) from 5 to 14.3 MeV was tried. It was found that r 0 = 1.00 fin, a = 0.88 fm, r~ = 1.55 fm and a' = 0.50 fm gave the best overall agreement when V and W were allowed to vary to minimize ;~2 for each distribution. As in all the optical-model searches, Vs and W~ were set equal to zero. At 5 MeV, V and W were found to be 118 and 10.6 MeV, respectively. Then Vs was set equal to 5 MeV and W s to zero. In this case also, the predictions were largely unchanged.




4. Conclusions The p o l a r i z a t i o n shows the same trends as the higher energy m e a s u r e m e n t s but with decreased m a g n i t u d e and is also quite similar to the c o r r e s p o n d i n g (d, n) polarization distribution 2o). It is clear that simply adding a spin-orbit potential of the a bo v e f o r m to the particular potentials f o u n d to fit the elastic scattering does not impr o v e the a g r e e m e n t to the polarization. It also appears that the calculations are quite insensitive to the spin-orbit potential and also to the exact f o r m o f the rest o f the optical p o t e n t i a l at this lower energy. Thus, we are faced with a serious discrepancy between the calculations and e x p e r i m e n t a l results. Th er e is also the disturbing feature that the spectroscopic factors are considerably below the expected value o f unity. It would be interesting as a result o f the relative success o f the B H M M theory 2 ~) and W B P m o d e l 22) in predicting the p o l a r i z a t i o n at higher energies to see these calculations extended to the 5-6 MeV region. We are indebted to J. J. W. Bogaards and R. G. H u m p h r i e s for their help in the course o f these often long experiments. We are also grateful to Dr. P. D. K u n z for m a k i n g his D W B A code available to us. O n e o f us ( D . P . G . ) wishes to t h an k the N a t i o n a l R e s e a r c h C o u n c i l for financial assistance.

References 1) J. C. Legg, H. D. Scott and M. K. Mehta, Nucl. Phys. 84 (1966) 398 2) H. G. Leighton, G. Roy, D. P. Gurd and T. B. Grandy, Nucl. Phys. A109 (1968) 218 3) L. L. Lee, Jr., J. P. Schiffer, B. Zeidman, G. R. Satchler, R. M. Drisko and R. H. Bassel, Phys. Rev. 136 (1964) B971 4) Sven A. Hjorth, J. X. Saladin and G. R. Satchler, Phys. Rev. 138 (1965) B1425 5) M. A. A, Toosi and Eugene V. Ivash, to be published 6) R. C. Johnson and F. D. Santos, Phys. Rev. Lett. 19 (1967) 364 7) C. A. Pearson and M. C6z, Nucl. Phys. 82 (1966) 533 8) C. A. Pearson and M. C6z, Nucl. Phys. 82 (1966) 545 9) C. A. Pearson and M. C6z, Ann. of Phys. 39 (1966) 199 10) S. T. Butler, R. G. Hewitt, B. H. J. McKellar and R. M. May, Ann. of Phys. 43 (1967) 282 11) J. L. Alty, L. L. Green, G. D. Jones and J. F. Sharpey-Schafer, Nucl. Phys. 86 (1966) 65 12) R. H. Bassel, R. M. Drisko, G. R. Satchler, L. L. Lee, Jr., J. P. Schiffer and B. Zeidman, Phys. Rev. 136 (1964) B960 13) G. Roy, D. Gedcke, H. G. Leighton, S. T. Lam and D. P. Gurd, Bull. Am. Phys. Soc. 12 (1967) 1183 14) D. P. Gurd, G. Roy and H. G. Leighton, Nucl. Instr. 61 (1968) 72 15) S. J. Moss and W. Haeberli, Nucl. Phys. 72 (1965) 417 16) K. A. Kuenhold, P. L. Beach, G. A. Bokowski and T. R. Donoghue, Bull. Am. Phys. Soc. 13 (1968) 116 17) R. W. Bercaw and F. B. Shull, Phys. Rev. 133 (1964) B632 18) S. Kato, N. Takahashi, M. Takeda, T. Yamazaki and S. Yakusawa, Nucl. Phys. 64 (1965) 24l 19) P. D. Kunz, private communication 20) D. A. Gedcke, S. T. Lain, S. M. Tang, G. M. Stinson and J, T. Sample, to be published 21) R. M. May and J. Truelove, Ann. of Phys. 43 (1967) 322 22) J. M. Bang, C. A. Pearson and L. P6cs, Nucl. Phys. A100 (1967) 24