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Register a new userDescription of single-Lambda hypernuclei with relativistic point coupling model
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We extend the relativistic point coupling model to single-$Lambda$ hypernuclei. For this purpose, we add $N$-$Lambda$ effective contact couplings to the model Lagrangian, and determine the parameters by fitting to the experimental data for $Lambda$ binding energies. Our model well reproduces the data over a wide range of mass region although some of our interactions yield the reverse ordering of the spin-orbit partners from that of nucleons for heavy hypernuclei. The consistency of the interaction with the quark model predictions is also discussed.
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The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Lambda$Li. Many more data on low-lying states of $Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Lambda$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $Lambda$ hyperon is injected into the lowest positive-parity ($Lambda_s$) and negative-parity ($Lambda_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(beta, gamma)$ deformation plane. We also calculate the PESs for the $Lambda$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_{Lambda}$Mg and $^{31}_{Lambda}$Si as examples, we analyse the impurity effects of $Lambda_s$ and $Lambda_p$ on the low-lying states of the core nuclei...
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.
We discuss low-lying collective excitations of $Lambda$ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of $Lambda$ hypernuclei in the $sd$-shell region. Based on the relativistic mean-field (RMF) approach, we show that the oblate deformation for $^{28}$Si nucleus may disappear when a $Lambda$ particle is added to this nucleus. We then discuss the rotational excitations of $^{25}_{Lambda}$Mg nucleus using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of $^{25}_{Lambda}$Mg nucleus is predicted to be slightly reduced due to an addition of $Lambda$ particle. We demonstrate that this leads to a reduction of electromagnetic transition probability, $B(E2)$, in the ground state rotational band. We also present an application of random phase approximation (RPA) to hypernuclei, and show that a new dipole mode, which we call a soft dipole $Lambda$ mode, appears in hypernuclei, which can be interpreted as an oscillation of $Lambda$ particle against the core nucleus.
A model is proposed for the spectrum of $Lambda$ hypernuclei based on the $u(3)times u(2)$ Lie algebra, in which the internal degrees of freedom of the spin-1/2 $Lambda$ particle are treated in the Fermionic $u(2)$ scheme, while the motion of the hyperon inside a nucleus is described in the Bosonic $u(3)$ harmonic oscillator scheme. Within this model, a simple formula for single-particle energies of the $Lambda$ particle is obtained from the natural dynamical symmetry. The formula is applied to the experimental data on the reaction spectroscopy for the $^{89}_Lambda$Y and $^{51}_Lambda$V hypernuclei, providing a clear theoretical interpretation of the observed structures.
Spin-isospin transitions in nuclei away from the valley of stability are essential for the description of astrophysically relevant weak interaction processes. While they remain mainly beyond the reach of experiment, theoretical modeling provides important insight into their properties. In order to describe the spin-isospin response,vcthe proton-neutron relativistic quasiparticle random phase approximation (PN-RQRPA) is formulated using the relativistic density-dependent point coupling interaction, and separable pairing interaction in both the $T=1$ and $T=0$ pairing channels. By implementing recently established DD-PCX interaction with improved isovector properties relevant for the description of nuclei with neutron-to-proton number asymmetry, the isobaric analog resonances (IAR) and Gamow-Teller resonances (GTR) have been investigated. In contrast to other models that usually underestimate the IAR excitation energies in Sn isotope chain, the present model accurately reproduces the experimental data, while the GTR properties depend on the isoscalar pairing interaction strength. This framework provides not only an improved description of the spin-isospin response in nuclei, but it also allows future large scale calculations of charge-exchange excitations and weak interaction processes in stellar environment.
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