Comparative analysis of muon-capture and 0νββ -decay matrix elements

Abstract

Average matrix elements of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta (0νββ) decays of current experimental interest are computed and compared with the corresponding energy and multipole decompositions of 0νββ-decay nuclear matrix elements (NMEs). The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The 0νββ NMEs include the appropriate short-range correlations, nuclear form factors, and higher-order nucleonic weak currents. The nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of the proton-neutron quasiparticle random-phase approximation with twonucleon interactions based on the Bonn one-boson-exchange G matrix. Both the OMC and 0νββ processes involve 100-MeV-range momentum exchanges and hence similarities could be expected for both processes in the feeding of the 0νββ intermediate states. These similarities may help improve the accuracy of the 0νββ NME calculations by using the data from the currently planned OMC experiments.

Comparative Analysis of Nuclear Matrix Elements of 0νβ+β+ Decay and Muon Capture in 106Cd

“…In Figure 2, we compare the large component, G −1 , of the bound-muon wave function, computed using this method (blue line), with the approximate wave function (black line) of Equation (13). For the sake of comparison, we have also plotted the exact solution of the Dirac equation corresponding to pointlike nucleus (red line).…”

“…As mentioned in section 4.1, the OMC matrix elements have usually been computed by approximating the bound-muon wave function by a point-like-nucleus approximation. In our previous works [13,41,42] we used the Bethe-Salpeter pointlike-nucleus approximation formula for the muon wave function. Here we study the effect of the exact muon wave function, solved from the Dirac equation by taking into account the finite size of the nucleus with uniform charge distribution, on the OMC matrix elements.…”

“…In [14], double beta decays of 106 Cd were studied in the pnQRPA framework using 40 Ca as the inert core. Here we extend those studies, for the ground-state-to-ground-state transition, by making a comparative analysis of the 0νβ + β + -decay and OMC NMEs of 106 Cd in the pnQRPA formalism with large no-core single-particle bases, in a manner pursued in [13]. The OMC on 106 Cd leads to excited states of 106 Ag which, on the other hand, act as virtual intermediate states of the β + β + decay of 106 Cd (see Figure 1).…”

“…It was found that there was a clear correlation between the energy-distributed OMC rates to 1 + states and the energy-based decomposition of the NMEs for the 2νβ − β − decays of the sd-shell nuclei 36 Ar, 46 Ca, and 48 Ca. In [13], we extended these studies to 0νβ − β − decays of medium-heavy and heavy nuclei by computing the average matrix elements corresponding to the OMC transitions to the intermediate nuclei of 0νβ − β − decays up to some 50 MeV using the pnQRPA formalism. We then compared these matrix elements with the energy-multipole decompositions of the NMEs of 0νβ − β − decays computed using the same formalism and model spaces.…”

Role of Single-Particle Energies in Microscopic Interacting Boson Model Double Beta Decay Calculations

“…Since 0νββ decay is a unique, not yet observed process, it is a challenge also for theoretical models. Thus, information from other studies such as nucleon transfer reactions [14][15][16][17][18][19][20], the photonuclear reactions [21][22][23], the nuclear muon capture process [24][25][26], the study of single β [27][28][29], and 2νββ decays [29][30][31][32][33][34][35], as well as, single-charge-exchange [36][37][38][39][40][41][42][43], and pion double-charge-exchange [44][45][46] reactions are highly valuable in view of estimating the uncertainties of 0νββ decay calculations.…”