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. 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 ion-ion elastic interactions are accounted for by a distortion coefficient. Since the ion-ion interactions are dominated by the imaginary part of the optical potentials, the distortion coefficients can be evaluated in the strong absorption limit. For a Gaussian potential form factor, the distortion coefficient is evaluated in closed form, revealing the relation to the total reaction cross section. It is shown that at small momentum transfer distortion effects reduce to a simple scaling factor, allowing us to define a reduced forward-angle cross section which is given by nuclear matrix elements of $\beta$ decay type. Thus we introduce new unit cross sections, as those traditionally used with light projectiles for spectroscopic purposes, for heavy-ion charge-exchange reactions. Results are discussed for ${\tau }_{\pm }$ excitations of ${}^{18}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$, respectively. Spectral distributions of nuclear-charge-changing transitions are obtained by self-consistent Hartree-Fock-Bogolubov (HFB) and quasiparticle random phase approximation (QRPA) theory and compared to spectroscopic data. The interplay of nuclear structure and reaction dynamics is illustrated for the single-charge exchange (SCE) reaction ${}^{18}\mathrm{O}+{}^{40}\mathrm{Ca}\to {}^{18}\mathrm{F}+{}^{40}\mathrm{K}$ at $T_{\mathrm{lab}}=270$ MeV, by performing full-scale numerical calculations of the SCE cross section. We also show that the latter compare rather well with the results obtained within the strong absorption limit, thus confirming the possibility to factorize the forward-angle cross section into intrinsic nuclear transition dynamics and reaction dynamics.

• Received 16 February 2018
• Revised 27 August 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044620