Break-up channels in muon capture onHe3

Abstract

The µ − + 2 H → ν µ +n+n, µ − + 3 He → ν µ + 3 H, µ − + 3 He → ν µ +n+d and µ − + 3 He → ν µ +n+n+p capture reactions are studied with various realistic potentials under full inclusion of final state interactions. Our results for the two-and three-body break-up of 3 He are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana IX three-nucleon potential. Most of our results are based on the single nucleon weak current operator. As a first step, we have tested our calculation in the case of the µ − + 2 H → ν µ + n + n and µ − + 3 He → ν µ + 3 H reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3 He in the break-up channels: 544 s −1 and 154 s −1 for the n + d and n + n + p channels, respectively. Our results have also been compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.

Radiative pion capture in H2 , He3 , and Golak1, Skibiński2, Topolnicki3 et al. 2018Phys. Rev. CSelf Cite

“…Thus the comparisons of various results computed from the nonrelativistic and relativistic nuclear kinematics performed in Refs. [65,66] for muon capture had to be repeated with a new mass of the absorbed particle.…”

“…Note that the same choice is also made for radiative pion capture in 3 He and 3 H. It provides the simplest relations between the total angular momentum projections of the initial and final nuclear systems. We generate the nuclear matrix elements N nn,±1 (m 1 , m 2 , m d ) in momentum space [65], as summarized briefly in Appendix A. Although the three-dimensional formalism of Ref.…”

“…where j A is the single-nucleon axial current from Refs. [65,69]. This step is justified by the fact that for low momentum transfers the term g A 1 σ absolutely dominates momentum space matrix elements of j A , which contain additionally (p/m) 2 relativistic corrections and read…”

“…Many elements of our calculations for all the listed reactions are essentially the same as those performed for the corresponding muon capture reactions in Refs. [65,66]. In particular the formulas concerning kinematics can be directly used, if the muon mass is replaced by the negative pion mass.…”

“…Recently we have established a theoretical framework for the A 3 muon capture reactions [65,66]. Important building blocks of this framework were cross-checked with the results from Ref.…”