Nuclear Matrix Elements for Heavy Ion Sequential Double Charge Exchange Reactions

TL;DR

This paper develops a theoretical framework for heavy ion double charge exchange reactions, focusing on nuclear matrix elements and their calculation using QRPA, with implications for understanding nuclear structure and reactions.

Contribution

It introduces a comprehensive formal theory for DSCE reactions, including nuclear response functions and explicit NME expressions using QRPA, advancing the modeling of such processes.

Findings

Derived explicit expressions for nuclear matrix elements using QRPA.

Analyzed differences between first and second interaction vertices in DSCE.

Presented reduction schemes for transition form factors and cross section calculations.

Abstract

The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuclear DSCE response functions on the basis of polarization propagator theory. The nuclear response tensors resemble the nuclear matrix elements of $2\nu\beta\beta$ decay in structure but contain in general a considerable more complex multipole and spin structure. The QRPA theory is used to derive explicit expressions for nuclear matrix elements (NMEs). The differences between the NME of the first and the second interaction vertexes in a DSCE reaction is elucidated. Reduction schemes for the transition form factors are discussed by investigating the closure approximation and the momentum structure of form factors. DSCE unit strength cross sections are derived.