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

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-$\Lambda$ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the $(\pi,K)$ one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of ${}^{12}_{\Lambda}\textrm{C}$ 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 $\Gamma_{n}/\Gamma_{p}$ 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 $\Lambda$-hypernuclei, which can now be extended to evaluate similar processes in charmed nuclei

One-nucleon-induced nonmesonic hypernuclear decay in laboratory coordinates

We present a formalism for the computation of one-nucleon-induced nonmesonic weak hypernuclear decay rates in laboratory coordinates, within an independent-particle shell model framework, with a view to its generalization to the case of two-nucleon-induced transitions.Instituto de Física La Plat

One-nucleon-induced nonmesonic hypernuclear decay in laboratory coordinates

We present a formalism for the computation of one-nucleon-induced nonmesonic weak hypernuclear decay rates in laboratory coordinates, within an independent-particle shell model framework, with a view to its generalization to the case of two-nucleon-induced transitions.Fil: Galeão, A. P.. Universidade Estadual Paulista Julio de Mesquita Filho. Instituto de Física Teórica; BrasilFil: Barbero, Cesar Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Física La Plata; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Exactas; ArgentinaFil: de Conti, C.. Universidade Estadual Paulista Julio de Mesquita Filho. Campus Experimental de Itapeva; BrasilFil: Krmpotic, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Física La Plata; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) \Lambda N\go nN of $\Lambda$ hypernuclei $^{4}_\Lambda$He, $^{5}_\Lambda$He, $^{12}_\Lambda$C, $^{16}_\Lambda$O, and $^{28}_\Lambda$Si, as a function of the sum of kinetic energies $E_{nN}=E_n+E_N$ for $N=n,p$. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parameterization. Two versions of the Independent-Particle Shell Model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account, and (b) IPSM-b, where the highly excited hole states are considered to be quasi-stationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All $np$ and $nn$ spectra exhibit a series of peaks in the energy interval 110 MeV $<E_{nN}<170$ MeV, one for each occupied shell-model state. The IPSM-a could be a pretty fair approximation for the light $^{4}_\Lambda$He and $^{5}_\Lambda$He hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to take into account the spreading in strength of the deep-hole states, and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final state interactions and of the two-nucleon-induced decay mode.Comment: v1: 20 pages, 3 figures, 1 table, submitted for publication; v2: minor corrections, improved figures, published versio

Rho-nucleon tensor coupling and charge-exchange resonances

The Gamow–Teller resonance in ²⁰⁸Pb is discussed in the context of a self-consistent RPA, based on the relativistic mean field theory. We inquire on the possibility of substituting the phenomenological Landau–Migdal force by a microscopic nucleon–nucleon interaction, generated from the rho-nucleon tensor coupling. The effect of this coupling turns out to be very small when the short range correlations are not taken into account, but too large when these correlations are simulated by the simple extraction of the contact terms from the resulting nucleon–nucleon interaction.Facultad de Ciencias Exacta

Kinematical and nonlocality effects on the nonmesonic weak hypernuclear decay

We make a careful study about the nonrelativistic reduction of one-meson-exchange models for the nonmesonic weak hypernuclear decay. Starting from a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*), the strangeness-changing weak ΛN → NN transition potential is derived, including two effects that have been systematically omitted in the literature, or, at best, only partly considered. These are the kinematical effects due to the difference between the lambda and nucleon masses, and the first-order nonlocality corrections, i.e., those involving up to first-order differential operators. Our analysis clearly shows that the main kinematical effect on the local contributions is the reduction of the effective pion mass. The kinematical effect on the nonlocal contributions is more complicated, since it activates several new terms that would otherwise remain dormant. Numerical results for ¹²ΛC and ⁵ΛHe are presented and they show that the combined kinematical plus nonlocal corrections have an appreciable influence on the partial decay rates. However, this is somewhat diminished in the main decay observables: the total nonmesonic rate, Γnm, the neutron-to-proton branching ratio, Γn/ Γp, and the asymmetry parameter, aΛ. The latter two still cannot be reconciled with the available experimental data. The existing theoretical predictions for the sign of aΛ in ⁵ΛHe are confirmed.Facultad de Ciencias Exacta

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

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 Λ¹²C 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.Facultad de Ciencias ExactasInstituto de Física La Plat