Theory of Single Charge Exchange Heavy Ion Reactions

TL;DR

This paper reformulates the theory of heavy ion single charge exchange reactions, connecting nuclear structure and reaction dynamics, and provides analytical and computational tools for analyzing such reactions, including their relation to beta decay.

Contribution

The paper introduces a new formulation of the reaction amplitude in momentum space, incorporating optical potential effects and detailed multipole structure analysis, linking reaction theory with nuclear beta decay.

Findings

Reaction amplitude factorizes into form factors and interaction terms.

Distortion effects at small momentum transfer simplify to a scaling factor.

Spectral distributions for specific isotopes are computed and compared to data.

Abstract

The theory of heavy ion single charge exchange reactions is reformulated. In momentum space the reaction amplitude factorizes into a product of projectile and target transition form factors, folded with the nucleon-nucleon isovector interaction and a distortion coefficient which accounts for initial and final state ion-ion elastic interactions. The multipole structure of the transition form factors is studied in detail for Fermi-type non-spin flip and Gamow-Teller-type spin flip transitions, also serving to establish the connection to nuclear beta decay. The reaction kernel is evaluated for central and rank-2 tensor interactions. Initial and final state elastic ion-ion interaction are shown to be dominated by the imaginary part of the optical potential allowing to evaluate the reaction coefficients in the strong absorption limit, realized by the black disk approximation. In that limit the distortion coefficient is evaluated in closed form, revealing the relation to the total reaction cross section and the geometry of the transition form factors. It is shown that at small momentum transfer distortion effects reduce to a simple scaling factor, allowing to define reduced forward-angle cross section which is given by nuclear matrix elements of beta decay-type. The response function formalism is used to describe nuclear charge changing transitions. Spectral distributions obtained by a self-consistent HFB and QRPA approach are discussed for $\tau_\pm$ excitations of $^{18}O$ and $^{40}Ca$, respectively, and compared to spectroscopic data. The interplay of nuclear structure and reaction dynamics is illustrated for the single charge exchange reaction $^{18}O+^{40}Ca \to ^{18}F+^{40}K$ at $T_{lab}=270$ MeV.