Post-prior equivalence for transfer reactions with complex potentials

TL;DR

This paper investigates the post-prior equivalence in transfer reaction calculations involving complex potentials, extending existing models to include bound state transfer and analyzing the impact of complex potentials on cross section formulas.

Contribution

It generalizes the Ichimura-Austern-Vincent model to include transfer to bound states with complex potentials, revealing additional terms in the prior cross section formula.

Findings

Additional term in prior cross section due to complex potential

Numerical validation of post-prior equivalence for deuteron-induced reactions

Extension of the model to account for bound state transfer with complex potentials

Abstract

In this paper, we address the problem of the post-prior equivalence in the calculation of inclusive breakup and transfer cross sections. For that, we employ the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)], conveniently generalized to include the part of the cross section corresponding the transfer to bound states. We pay particular attention to the case in which the unobserved particle is left in a bound state of the residual nucleus, in which case the theory prescribes the use of a complex potential, responsible for the spreading width of the populated single-particle states. We see that the introduction of this complex potential gives rise to an additional term in the prior cross section formula, not present in the usual case of real binding potentials. The equivalence is numerically tested for reaction induced by deuterons.