Configuration mixing effects in direct reactions

Abstract

The “direct” transfer of a nucleon in stripping and pick-up reactions is a more complicated process than suggested by the picture of insertion of the nucleon into a single-particle well; for an accurate evaluation of the form factors one should take into account configuration mixing in the target and residual nuclei. Form-factor equations, previously derived by Pinkston and Satchler and by Berggren, are rederived by an alternative variational method. A general method for practical calculations of form factors by solving these equations is given. The method can be regarded as a one-step iteration of the form factor equations in which the inhomogeneous term is approximated from the usual shell-model calculation. Such “structure-stripping” calculations are performed for 58Ni, 57Ni and the resulting form factors are used to study ( p, d) and ( d, t) reactions on 58Ni. In the ( p, d) calculations a somewhat improved fit is obtained for the angular distribution for the f 5 2 pick-up to the 0.78- MeV( 5 2− ) state of 57Ni. The remaining discrepancy between theory and experiment shows that effects other than those relating to the form factor must also be examined to explain the observed angular distribution. The 58Ni( d, t) 57Ni calculation for the f 5 2 pick-up indicates that the spectroscopic factor obtained by using the conventional “well-depth” (or “separation-energy”) prescription for the form factor can be in error by as much as 50 %. A simpler phenomenological method to generate form factors is also given. This method uses the same Saxon-Woods parameters ( V 0, R 0, a, V s0 ) for calculating all form factors for transitions between two given nuclei, and, at the same time, insures a correct tail (governed by the actual separation energy) for each form factor. This method is of restricted applicability.