Test of the DWBA in (3He, α) reactions leading to configuration and analogue states

doi:10.1016/0375-9474(67)90761-0

Nuclear Physics A

Volume 104, Issue 1, 13 November 1967, Pages 136-176

https://doi.org/10.1016/0375-9474(67)90761-0 Get rights and content

Abstract

The DWBA methods are re-examined to analyse the reactions ^{50, 52, 54}Cr(³He, α) at E_He = 18 MeV. The use of the (³He, α) reaction as a spectroscopic tool is limited by the angular momentum mismatch which causes the nuclear interior to contribute significantly to the reaction. As a consequence, some of the usual approximations become critical. The “measured” elastic scattering parameters do not sufficiently determine the cross sections. In addition, the degenerate sets of parameters for composite particle scattering in both channels cannot be combined arbitrarily. However, the exact matrix element of the distorted wave theory indicates that the α potential should be roughly equal to the sum of the ³He and neutron potentials. This prescription was found to be valid by calculations of mismatch transitions using all the possible combinations of measured parameters in both channels. The effects of nonlocality and finite range are discussed. It is shown that a sharp radial cutoff is not permissible. The effects of spin-orbit coupling on the angular distributions and absolute cross sections are investigated; the J-effects of the data are partially overestimated by the calculations. The absolute normalization factor of the DWBA cross section, derived from the present analysis, agrees with theoretical predictions. The accuracy of the extracted spectroscopic factors is discussed. The bound state wave functions for the analogue state transitions are obtained by solving the coupled Lane equations. This leads to agreement of the derived spectroscopic factors with the sum rule predictions.

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One-nucleon pickup reactions on 32S: Experimental results and shell-model calculations
1999, Nuclear Physics A
The ³²S(d,³He)³¹P and $^{32} S (^{3} He,α)^{31} S$ reactions have been investigated at incident energies of E_d = 27 MeV and E_{3_He} = 25 MeV. The experimental values of excitation energies (0 ⩽ E_x(MeV) ⩽ 8) have been compared with the predictions of a complete sd-shell space, shell-model calculation. Spectroscopic factors obtained for 22 levels of ³¹S through the DWBA analysis of the experimental angular distributions have also been compared with the shell-model predictions. In order to reconcile the experimental and shell-model predicted values of the spectroscopic factors, the geometrical parameters of the spin-orbit part of the transferred nucleon potential are required to be smaller than those of the central part as it was previously observed in studies of the one-proton (³He,d) stripping reaction. The experimental fragmentation of the $1d_{52}$ and $2s_{12}$ strengths is correctly reproduced by the shell-model calculations. Twenty pairs of levels were identified as mirror states in the ³¹S and ³¹P nuclei and the ambiguities concerning the J^π-values of eleven ³¹S levels could be removed.
Spectroscopic factors from one-proton stripping reactions on sd-shell nuclei: experimental measurements and shell-model calculations
1994, Nuclear Physics, Section A
The (³He,d) reaction has been investigated at 25 MeV on the target nuclei ¹⁶O, ¹⁸O, ¹⁹F, ²³Na, ²⁴Mg, ²⁵Mg, ²⁶Mg, ²⁷Al, ²⁸Si, ²⁹Si, ³⁰Si, ³¹P, ³²S, ³⁴S, ³⁵Cl, ³⁷Cl and ³⁹K. Attention is restricted to the few even-parity levels in each final nucleus which are strongly populated. Values of the single-nucleon Spectroscopic factors C²S are obtained from the differential cross sections measured for these levels by analyzing them in the framework of the DWBA theory of nuclear reactions. The DWBA calculations use sets of ³He and deuteron optical-potential parameters which are experimentally validated and internally consistent. The absolute values of C²S thus extracted are rather insensitive to which sets of equivalent optical-model parameters are used in the DWBA analyses (variations of the order of ±15%) and the variations in the relative values for the different transitions are very insensitive to these choices. Most of the sensitivity which does exist can be traced to the specification of the absorptive part of the deuteron potential. The values of C²S are not sensitive to the presence of spin-orbit terms in either the deuteron or the ³He potential. Contrary to the case for optical-model potentials, however, absolute values of C²S are very sensitive to the radius parameter r₀ chosen for the potential which binds the transferred proton, although relative values are almost completely insensitive to this choice. The effects of the spin-orbit part of this bound-state potential on $j = l + 12 and j = l − 12$ transitions have also been carefully investigated. Evidence is developed that the radius parameter r_s.o. of the spin-orbit part of the bound-state potential should be smaller than that of the central part. The values of C²S extracted from the present data both with standard DWBA analyses (r₀ = r_s.o. and a₀ = a_s.o.) and with analyses which incorporate a modified treatment of the spin-orbit term of the bound-state potential (r₀ ≠ r_s.o. and a₀ ≠ a_s.o.) are compared with the predictions of the USD shell-model hamiltonian. The ratios between the experimentally based spectroscopic factors and the model predictions exhibit a marked difference between transitions into the $1 d_{32}$ orbit and transitions into the $1 d_{52}$ orbit when the standard DWBA analysis is used. However, this difference between $1d_{32}$ and $1d_{52}$ transitions is greatly reduced if, while the conventional values r₀ = 1.25 fm and a₀= 0.65 fm continue to be used for the central component of the bound-state potential, values of r_s.o. = 1.00 fm and a_s.o. = 0.52 fm are used for the spin-orbit part.
Consistent description of the (t, 3He) reaction for A = 12-89
1991, Nuclear Physics, Section A
New differential cross section data for seven target nuclei were analysed using a microscopic model. Particular care was taken to ensure that the absolute magnitude of the cross sections was correctly measured. The predicted direct or one-step (t, ³He) reaction did not account for the magnitude of the data except for forward angles and A⩾40. The calculations were estended to include the contributions from two-step or sequential single-nucleon transfers. Calculations were made using the second-order DWBA and zero-range or full finite-range forms. In the latter the non-orthogonality between the basis states in the two-step transfers was included. The transfer amplitudes were deduced from comparisons of predicted angular distributions with data obtained from the (t, α) and (t, d) reactions, and from amplitudes determined by repeating previously reported shell-model calculations. The full finite-range DWBA calculations which included non-orthogonality terms, accounted for both the shape and magnitude of the data within a factor of 3 in the worst case. The (t, α) reaction angular distributions are, however, poorly predicted.
γ-decay of the deeply-bound hole states in 101Pd, 105Pd, 107Pd, 111Sn, 117Sn observed in the (3He, αγ) reaction at 70 MeV
1985, Nuclear Physics, Section A
The γ-decay of deep-hole states in ^{101, 105, 107}Pd was studied via the (³He, αγ) reaction at E_³he = 70 MeV and supplemented by data from ^{112, 118}Sn targets to investigate the deep-hole spreading mechanism. The γ-decay pattern for the $g_{92}$ deep-hole state shows a strong dependence on the spreading width: if the deep-hole state is observed as a sharp peak, it mainly decays to the low-lying $72^{+}$ state by a spin-flip M1 transition with a large M1-E2 mixing ratio; if the deep-hole state is observed as a broad bump, it decays statistically indicating the complete spreading of the hole strength over the underlying states; if the deep-hole state is observed with a structure intermediate between a sharp peak and broad bump, its γ-decay shows both decay patterns.
A sharp peak at E_x = 2.396 MeV in ¹⁰¹Pd which carries a large fraction of the $g_{92}$ hole strength (C²S = 2.0) was found to be a single state having a width of less than 2.5 keV.
For the spin-flip M1 transition the destructive interference between the $g_{92}$ component and the coupled components of the deep-hole state was found in heavily spread states.
A quasiparticle-plus-rotor (QPR) model was applied to calculate the fragmentation in the doorway stage for the $g_{92}$ neutron deep-hole state in the Pd isotopes. A reasonable agreement between the calculation and the experimental results was obtained for the strength fragmentation, for the nucleus ¹⁰¹Pd. However, the large M1-E2 mixing ratio experimentally observed was not reproduced.
Inelastic scattering and reaction data analysis for the 3He+44,48Ca systems
1985, Nuclear Physics, Section A
Analysing-power and cross-section distributions for the inelastic and single-nucleon transfer reactions involving the scattering of 33 MeV polarised helions from ^44,48Ca targets have been measured, and analysed with the DWBA framework. The inelastic scattering distributions are found to be insensitive to the ambiguities in the spin-orbit component of the distorting optical-model potential — which are shown to exist when fitting the elastic data. The deformation length is found to be a better representative of the nuclear shape than the deformation parameter. For the (³ $He$ , d) and (³ $He$ , α) reactions, both the zero-range and finite-range (within the local-energy approximation) calculations have been carried out and several effects such as the inclusion of non-locality correction, the j-dependence of the distributions, and the sensitivity of the predictions to the entrance- and exit-channel distorting potentials are discussed. The deduced spectroscopic factors are consistently lower than the values reported in the literature by other investigators, although the relative spectroscopic factors are shown to be in good agreement with those of others. The data measured for the charge-exchange reactions, ⁴⁸Ca(³ $He$ , t), populating a number of levels in ⁴⁸Sc are also presented.
The (3He, p) reaction induced by polarized 3He on 7Li, 9Be and 12C
1983, Nuclear Physics, Section A
Differential cross sections and analysing powers have been measured for the reactions $^{12} C (^{3} He, p)^{14} N_{g.s.}$ , 2.31, 3.95 Me V, $^{9} Be(^{3} He, p)^{11} B_{g.s.}$ , 2.125, 4 $^{7} Li (^{3} He, p)^{9} B_{g.s.}$ at an incident energy of 33 MeV and for the reactions $^{9} Be (^{3} He, p)^{11} B_{g.s.}$ , 2.125 MeV, and $^{7} Li (^{3} He, p)^{9} Be_{g.s.}$ at an incident energy of 14 MeV. The data have been analysed in terms of a deuteron cluster transfer and full microscopic calculations within the DWBA framework. Special attention was paid to the sensitivity of the calculations to the choice of optical potentials, form factor and binding energy description. The ¹²C(³He, p)¹⁴N reaction was also analysed in terms. of the coupled-channels Born approximation.

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^†: On leave from the Institut für Strahlen- und Kernphysik der Universität Bonn.

^††: Present address: Lawrence Radiation Laboratory, University of California, Berkeley.

^†††: Research sponsored by the U.S. Atomic Energy Commission under cotract with the Union Carbide Corporation.

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Nuclear Physics A

Abstract

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Consistent description of the (t, <sup>3</sup>He) reaction for A = 12-89

γ-decay of the deeply-bound hole states in <sup>101</sup>Pd, <sup>105</sup>Pd, <sup>107</sup>Pd, <sup>111</sup>Sn, <sup>117</sup>Sn observed in the (<sup>3</sup>He, αγ) reaction at 70 MeV

Inelastic scattering and reaction data analysis for the <sup>3</sup>He+<sup>44,48</sup>Ca systems

The (<sup>3</sup>He, p) reaction induced by polarized <sup>3</sup>He on <sup>7</sup>Li, <sup>9</sup>Be and <sup>12</sup>C