Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

Abstract

Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the (π, K) one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of 12 Λ C are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the most noteworthy difference is that the ratio Γn/Γp is appreciably higher and closer to the experimental value in the relativistic calculation. Large discrepancies between ours and previous relativistic calculations are found, for which we do not encounter any fully satisfactory explanation. The most recent experimental data is well reproduced by our results. In summary, we have achieved our purpose to develop a reliable model for the relativistic calculation of the nonmesonic weak decay of Λ-hypernuclei, which can now be extended to evaluate similar processes in charmed nuclei.

Nonmesonic weak decay of charmed hypernuclei

“…The first of these relations can be easily verified, while the second one is shown in Appendix A of Ref. [58]. Now we introduce the angular momentum couplings J = j Λ + c + j n and J = j Λ + j p in M π , and J = j Λ + c + j n and J = j p + j Λ in M K .…”

“…[69] -they are collected in the Appendix B of Ref. [58]. Presently, not much is known about the effect of SU(4) flavor symmetry breaking on these effective couplings; recent studies of related couplings (e.g.…”

“…The numerical values for the cutoffs are the same as those used in Ref. [58], namely, Λ π = 1.3 GeV and Λ K = 1.2 GeV.…”

“…From previous works of Refs. [54,55,58,65,75,76], we know that to describe the NMWD in Λ hypernuclei with open-shell cores within the IPSM it is enough to make the replacementĴ 2 /ĵ 2 Λ → F j N J in the decay-rate expression with the DCSC, where F j N J is a spectroscopic factor. Making the same replacements here, i.e.Ĵ 2 /ĵ 2…”

“…In the present work we use the relativistic formalism developed in Ref. [58] for the NMWD of Λ hypernuclei to investigate the similar decay process in Λ + c hypernuclei. The formalism is based on an independent-particle shell model.…”