Analyzing power measurements for the 13C(p ,d)12C reaction at 200 and 400 MeV

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26 February 1981

ANALYZING POWER MEASUREMENTS FOR THE 13C(p, d)12C REACTION AT 200 AND 400 MeV R.P. LILJESTRAND, J.M. CAMERON, D.A. ttUTCHEON, R. MACDONALD, W.J. McDONALD, C.A. MILLER and W.C. OLSEN University of Alberta 1, Edmonton, Alberta, Canada T6G 2N5

J.J. K R A U S H A A R and J.R. SHEPARD Nuelear Physics Laboratory z, University of Colorado, Boulder, CO 80309, USA J.G. ROGERS TRIUMF 1, Vancouver, B.C, Canada V6T 2A3 J.T. TINSLEY University of Oregon, Eugene, OR 97403, USA and C.E. STRONACH Virginia State University, Petersburg, VA 23803, USA Received 30 June 1980

Cross sections and analyzing powers for the 13C(p, d) reaction have been measured at 200 and 400 MeV to the 0÷, ground state and 2÷, 4.44 MeV state of 12C. While the cross sections are rather structureless, DWBA calculations in exact finite range account well for both the magnitude and shape of the angular distributions. On the other hand, the measured analyzing powers are in serlous disagreement with the DWBA calculations.

Stripping and pickup reactions have been among the chief tools used to study nuclear single-hole states. At low projectile energies the cross sections for the reaction are well described by distorted wave Born approximation (DWBA) calculations and may be used to identify the appropriate angular m o m e n t u m transfer (l) for the transition. It has also been found that the analyzing powers for these reactions, measured with polarized beams, display strong/'-dependence. The DWBA calculations, however, are rather limited in their ability to reproduce the general features o f the analyzing i Work supported in part by the National Research Council, Canada. 2 Work supported in part by the USDOE.

powers [ 1 - 7 ] . Recent extension of (19, d) cross section measurements to energies in the 1 5 0 - 8 0 0 MeV range, potentially allowing examination o f deep hole states, have been made [ 8 - 1 5 ] . The DWBA remains moderately successful in reproducing the shapes o f the angular distributions and the strengths of the transitions to known single-hole states. However, the shapes of the angular distributions become nearly independent of /-transfer as the energy increases [13,16,17], generally following an exponential decrease with scattering angle. This effect clearly limits the usefulness of (p, d) reactions in identifying the structure o f the new states excited at these higller energies. Asymmetry measurements are likely to depend more sensitively on the reaction amplitudes and might 311

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be expected to contain more information than cross sections. To examine this proposition we have made the first asymmetry measurements of the (~, d) reaction at medium energies. Specifically, we have examined the 1 3 C ~ , d)12C reaction leading to the ground state (0 +) and 4.44 MeV state (2 +) using 200 and 400 MeV protons. These transitions correspond to Pl/2 and P3/2 pickup, respectively. The measurements were performed using the polarized proton beam and 1.4 GeV/c magnetic spectrometer at TRIUMF. Energy loss and timeof-flight information permitted rejection of the tritons which formed a significant background at large angles. The energy resolution of about 1.2 MeV FWHM was

26 February 1981

sufficient to clearly resolve the 12C ground and first excited states. The target used was 37.3 mg/cm 2 carbon enriched to 99% 13 C. Beam charge and polarization were monitored using a polarimeter situated upstream from the target. The cross sections for both the ground (0 +) and first excited (2 +) states shown in figs. 1 and 2 demonstrate a smooth and rather featureless decrease with scattering angle at both 200 and 400 MeV. Furthermore, there is little difference between the 200 and 400 MeV cross sections when data at equal momentum transfer are compared. In contrast, the analyzing powers exhibit very pronounced structure at both energies. At forward

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Fig. 1. Cross sections and analyzing powers for the 13C(p, d)lZc reaction at 200 MeV. The dashed curves are the results of a zero range DWBA calculation using the potentials shown in table 1. The solid curves are the results of EFR calculations using the same potentials. 312

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PHYSICS LETTERS

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26 February 1981

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Fig. 2. Cross sections and analyzing powers for the 13C(~, d)lzC reaction at 400 MeV. The solid curves are the results of EFR calculations using the potentials shown in table 1. The dashed curves are also the results of EFR calculations using the same potentials except the spin-orbit potentials in both the proton and deuteron channels were set equal to zero. angles for 200 MeV there is also a distinct difference between the / = 1/2 (g.s.) and / = 3/2 (4.44 MeV) analyzing powers. Again comparison of the 200 and 400 MeV analyzing power data also shows rough agreement at equal m o m e n t u m transfer. Distorted wave Born approximation calculations have been performed in zero-range (ZR) using the code DWUCK4 [18] and in exact finite range (EFR) using DWUCK5 [18]. The EFR calculations were performed as in ref. [19] except that S- and D-wave deuteron contributions were combined coherently. The geometry of the bound state well was determined as discussed in ref. [20]. The proton distorting potential for the 400 MeV

measurements was generated using the leading term of the optical potential in the KMT multiple scattering theory [21 ]. The deuteron potential was obtained by doubling the potential strengths of the KMT proton 1 potential at 7Tp. The geometry was altered to account for the finite size of the deuteron. The strengths of the spin-orbit potentials are simple estimates based on low energy p + nucleus results. For the 200 MeV calculations, the empirical p + 12C potentials of Comfort and Karp [22] were used; their 183 MeV potential was adopted for the proton distortion while the strengths of the 96 MeV potential were appropriately adjusted to give the deuteron potential. All potentials are shown 313

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PHYSICS LETI'ERS

Table 1 Optical potential parameters used in DWBA calculations. Tp (MeV) 200 200 400 400

p+13C d+12C p+13C d+12C n+12C

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a

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12.5 -46.0 9.98 -44.1 _ b)

1.20 1.20 0.948 0.896 1.44

0.63 0.635 0.472 0.725 0.36

-13.1 18.0 -41.76 -49.3 _

1.20 1.35 0.948 0.896 _

0.61 0.655 0.472 0.725 _

4.1 5.83 3.75 3.75 c)

0.47 0.50 0.472 0.725

1.25 1.30 1.25 1.30

0.90 0.90 0.948 0.896

a) Assuming spin-orbit potential of the form (h/mTrc)2(Vso/r) (dr/dr) L • o, where f is the usual Woods Saxon form. b) Well depth adjusted to give correct neutron separation energy. c) Spin-orbit potential of Thomas-Fermi form tied to central potential, proportionality factor ~ = 25. in table 1. The DWBA calculations were normalized using spectroscopic factors computed with the A = 12 and 13 wave functions o f Norton and Goldhammer [23 ]. The values are C2S -- 0.67 for the transition to the ground state ( l P l / 2 pickup) and C2S = 1.1 to the 4.44 MeV 2 + level (1 P3/2) pickup. The calculations are also presented in figs. 1 and 2. At 200 MeV, fig. 1 indicates the D-state contributions (treated via E F R calculations) to the differential cross sections are small, their principal effect being to introduce somewhat more structure into the ground state angular distribution. Comparing the E F R and Z R results gives an effective ZR normalization o f D 0 ~ 85 MeV fm 3/2, compared to the low energy value o f ~ 125 MeV fm 3/2. The 200 MeV analyzing powers are not strongly influenced by D-state contributions for ~<30 ° although big effects are seen at larger angles. Contributions from the D state account for roughly one-half o f the differential cross section at 400 MeV and consequently must be treated explicitly. The sensitivity of the 200 MeV calculations to uncertainties in the distorting potentials was explored in some detail and found to be appreciable, particularly for the deuteron channel. Several phenomenologicat proton potentials were employed as well as one based on the KMT. Since no 200 MeV deuteron elastic scattering data exists, potentials were obtained either by extrapolating global potentials or by constructing them from phenomenological proton potentials for Tp ~ 100 MeV. The extrapolated potentials were found to give very poor agreement with the cross-section data. This may very well have been a consequence o f unreliable extrapolation over a large range. The constructed potentials were o f b o t h the Watanabe (folded over q~d) 314

[24] and J o h n s o n - S o p e r (no folding) [25] type. Differences arising from the two methods o f combining the n u c l e o n - n u c l e u s potentials were found to be smaller than differences arising from ambiguities in the potentials themselves. Special attention was paid to the s p i n - o r b i t potentials in the optical potentials. Their importance is obvious when one notes that the 0+(191/2) and 2+(P3/2) analyzing powers are essentially in phase beyond 0 ~ 15 °. If no s p i n - o r b i t distortions were present the Pl/2 analyzing powers would be twice as large as those for the P3/2 and o f the opposite sign, even in the presence of D-state contributions (see ref. [7]). Such is clearly not the case. Zero range DWBA calculations indicated that, while neither appreciably affects the cross sections, both the proton and deuteron s p i n - o r b i t interactions have a strong influence on the calculated analyzing powers, with the proton having a somewhat larger effect. Of interest at a phenomenological level is that agreement with both the Pl/2 and P3/2 analyzing powers was substantially improved when the deuteron s p i n - o r b i t potential was set to zero. Treatment o f the deuteron Sstate in E F R had little effect on the calculated analyzing powers. As can be seen in fig. 1, treatment of the deuteron D state in E F R calculations tended to wash out the structure in the calculated analyzing powers for 0 > 30 °, worsening agreement with the data. This effect is likely due to averaging over the increased number o f spin orientations possible when the D state is treated explicitly. The various potential combinations caused variations both in the overall magnitude o f the cross sections (results varied by factors as large as four) and in the shapes (rate of fall-off and location of inflection points) of the angular

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distributions. The calculated analyzing powers did not vary significantly for 0 ~< 25 ° and at the larger angles variations were simple shifts in a positive or negative direction of otherwise invariant oscillatory patterns. These sensitivities coupled with the lack of reliable published analyses of the relevant elastic scattering data, especially for deuterons, introduce many ambiguities into the calculations. The curves shown in fig. 1 represent the best overall agreement between calculations and the data. The 400 MeV calculations in fig. 2 were done using KMT potentials for both channels. Again, differences arising from the use of either the Watanabe or J o h n s o n Soper folding prescriptions for the deuteron potential were seen to be quite small. Substituting a deuteron potential based on the 200 MeV p + C potential in table 1 also had little effect on the calculated cross sections and did not result in improved agreement for the analyzing powers. Since no appropriate phenomenological potentials were available, low energy proton and deuteron spin-orbit potentials were used at Tp = 400 MeV. Since there is evidence that the proton spin-orbit potential strength drops slowly with increasing energy, [26] the two sets of curves in fig. 2 can be considered to reflect the extremes of spin-orbit strength. Calculations using the (unknown) appropriate phenomenological potentials might be expected to "fall between" these two sets of results. The E F R - D W B A is seen to give a reasonable account of the measured cross sections. However, it should be noted that the differences between the shapes calculated tbr the two transitions are markedly greater than those observed experimentally indicating that the DWBA overestimates the j-dependence of the cross section. In contrast, the calculated analyzing powers bear only a vague resemblance to the data. While the calculations do correctly predict a much larger negative analyzing power for the j = 1 - 1/2 state than for the / = l + I/2 state at forward angles, the overall agreement is very poor at the higher energy. At both energies calculations were insensitive to variations (e.g., 1.2 ~< r 0 < 1.5 fm) of the binding well geometry which in turn give rise to changes (in configuration and momentum space) in the bound state wave function. This is particularly surprising at 400 MeV where the distorting potentials are relatively small and one might expect to see changes in the predicted oscil-

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latory pattern corresponding to changes in the position of the node in the momentum space bound state wave function, as predicted by the plane wave Born approximation (PWBA). It can then be inferred that the PWBA is quite unreliable at these energies, even qualitatively, and that information about high momentum components of the nuclear wave function is not readily accessible even assuming that distortion effects are correctly treated using the DWBA. In conclusion, we have presented the first analyzing power measurements for the medium energy (p, d) reaction. The angular distributions of these quantities for the transitions to the ground and first excited states in the 13C(p,d) 12C reaction show a great deal of structure in contrast to the nearly featureless cross sections. These two transitions represent Pl/2 and P3/2 pickup, respectively, and distinctive j-dependence is observed at forward angles for the lower bombarding energies. At larger angles or higher momentum transfers, the analyzing powers are seen to be roughly independent of bombarding energy and j-transfer for fixed momentum transfer. The highly structured analyzing power data does prc.vlde, as anticipated, a demanding test of the DWBA. Although it reproduces the measured cross sections quite well, the DWBA unambiguously fails this test, reproducing crudely only tl~e most general features of the analyzing powers for Tp = 200 MeV. The failure is spectacular at 400 MeV. While sensitivity to poorly known deuteron optical potentials is appreciable, it does not seem likely that reasonable variation of the optical model parameters can bring about acceptable agreement. Similar severe disagreement - which cannot be remedied by reasonable variation of input parameters - has been reported for the 24Mg(p, d) reactions at Tp ~ 100 MeV [27]. The apparent failure of the DWBA, even at 200 MeV where the standard low energy reaction model should still be appropriate, is disconcerting and is being studied further. Such studies are likely to be greatly facilitated by recent analyzing power measurements on 13C at 65 [28] and 123 [29] MeV and on other targets at 200 MeV [30] which will serve to establish the systematics of the reaction. Identification of the causes of the failure is likely to result in both a greater understanding of the DWBA and a greatly increased utility of the (p, d) reaction as a spectroscopic tool to be used, for example, in the identification of deep-hole states in nuclei.

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R efere n ces [ 1 [ L.M. Reber and J.X. Saladin, Phys. Rev. 133 (1964) B1155. [2] N.S. Chant et al., Nucl. Phys. A99 (1967) 669; N.S. Chant and J.M. Nelson, Nucl. Phys. A117 (1968) 385; B. Mayer, J. Gosset, J.L. Escudie and H. Kamitsubo, Nucl. Phys. A177 (1971) 205. [ 3 ] D.C. Kocher and W. Haeberli, Nucl. Phys. A196 (1972) 225. [4] M. Pignanelli et al., Phys. Rev. C8 (1973) 2120. [5] S.E. Vigdor, R.D. Rathmell, H.S. Liers and W. Haeberli, Nucl. Phys. A210 (1973) 70. [6] R.F. Casten et al., Nucl. Phys. A202 (1973) 161. [7] R.C. Johnson et al., Nucl. Phys. A208 (1973) 221. [ 8 ] D. Bachelier, M. Bernas, I. Brissaud, P. Radvani and M. Roy, Nucl. Phys. 88 (1966) 307. [9] J. K/illne and E. Hagberg, Phys. Scripta 4 (1971) 151 ; J. K/illne and B. Fagerstrom, Proc. 5th Intern. Conf. High-energy phys. nucl. struct. (1974) p. 369. [10] S.D. Baker et al., Phys. Lett. 52B (1974) 57. [11] T. Bauer et al., Phys. Lett. 67B (1977) 265. [121 J. Berger et al., Lett. Nuovo Cimento 19 (1977) 287. [13] T. Bauer et al., Phys. Rev. C21 (1980) 757. [14] J. Kgllne et al., Phys. Rev. Lett. 41 (1978) 1638. [15] J. K/illne et al., Phys. Rev. C, to be published. [16] E. Rost and J.R. Shepard, Phys. Lett. 59B (1975) 413.

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[17] J.R. Shepard, E. Rost and G.R. Smith, Phys. Lett. 89B (1979) 13. [18] P.D. Kunz, Univ. of Colorado, unpublished. [19] E. Rost, J.R. Shepard and D.A. Sparrow, Phys. Rev. C17 (1978) 1513. [20] J.R. Shepard and P. Kaczkowski, Univ. of Colorado, Tech. Prog. Rept. (1977)p. 160. [21] H. Feshbach, A. Gal and G. Hufner, Ann. Phys. 66 (1971) 20, and references therein. [22] J.R. Comfort and B.C. Karp, Univ. of Pittsburgh, to be published. [23] J.L. Norton and P. Goldhammer, Nucl. Phys. A165 (1971) 33; J.L. Norton, Ph.D. Thesis, Univ. of Kansas, unpublished. [24] S. Watanabe, Nucl. Phys. 8 (1958) 484. [25] R.C. Johnson and P.J.R. Soper, Phys. Rev. C1 (1970) 976. [ 26 ] A. Nadasen et al., Indiana Univ. Cyclotron Facility, preprint. [27] J.R. Shepard, E. Rost and P.D. Kunz, invited contribution to the Fifth Intern. Symp. on Polarization phenomena in nuclear physics (Santa Fe, NM, August 1980), and to be published. [28] K. Hosono et al., RCNP (Osaka) Annual Rept. (1978) p. 7. [29] D.A. Miller et al., Indiana Univ., Cyclotron Facility, to be published. [30] R.P. Liljestrand et al., to be published.