Theory of Double Charge Exchange Reaction as Probes for Double Beta Decay*

Single charge exchange reactions and single beta decay have established an interesting and
fruitful relationship serving for the advantage of both fields. I'll address the question whether there exists a
similar connection between nuclear double charge exchange (DCE) reactions and nuclear double beta decay (DBD). After early, disappointing attempts, DCE reactions with nuclear beams were neglected. However, recent experiments have changed the situation
by indicating the possible dominance of mesonic DCE processes. A DCE reaction
theory focused on mesonic processes is presented. Leaving aside the higher order mean-field multi-particle
transfer contributions, the competition of two interfering reaction mechanisms is essential for understanding a DCE reaction. They given by second
order sequential Double Single Charge Exchange (DSCE) and Meson-Nucleon Majorana DCE (MDCE), formally a
first order process by virtual two–meson exchange.
The DSCE mechanism is a conventional distorted wave (DW) two-step reaction. The DSCE
reaction amplitude is transformed by suitable recoupling techniques into a form corresponding in structure to the
nuclear matrix elements (NME) of 2ν2β decay, albeit with a transition operator defined by meson exchange. The second order DSCE response functions are described by higher rank polarization tensors, in practice conveniently constructed
in Quasiparticle Random Phase Approximation (QRPA).
The MDCE mode is formally a one—step DW reaction but monitored by the coherent exchange of pairs of charged
mesons between projectile and target. Each of these mesons undergoes a single charge exchange reaction, thereby
initiating short—range correlations through the intranuclear exchange of neutral mesons. The MDCE reaction corre-
sponds to a combination of an off-shell (π+, π−) reaction in one of the ions and a complementary (π−, π+) reaction
in the other ion. Altogether, the MDCE process proceeds by a dynamically generated effective rank-2 isotensor
interaction.
The elementary MDCE vertices differ significantly from the conventional SCE and DSCE charge exchange vertices.
While the latter are given by NN isovector interactions, e.g. by the exchange of virtual charged pions, described ba
a ladder diagram [3-5]. The MDCE process, however, is driven by the (off-shell) isovector pion-nucleon T-matrix,
governed by excitations of nucleon resonances as e.g. ∆33(1232) [3,6]. The MDCE interaction is a dynamically
generated rank–2 isotensor interaction described by box diagrams, extending over the two colliding nuclei. From
a nuclear structure point of view, the MDCE operator induces two–particle-two–hole DCE
transitions in the one and the other nucleus.
The DCE formalism will be introduced with main focus on the MDCE theory. In closure approximation nuclear
matrix elements are obtained which are of a striking similarity to the NMEs of 0ν2β DBD, where the neutral pions
replace the Majorana neutrinos. Physics aspects of DSCE and MDCE processes will be illustrated on examples of
QRPA response functions and cross sections and compared to data.