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Register a new userCollective excitations of $Lambda$ hypernuclei
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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.
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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...
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.
The non-mesonic weak decay of polarized Lambda-hypernuclei is studied for the first time by taking into account, with a Monte Carlo intranuclear cascade code, the nucleon final state interactions. A one-meson-exchange model is employed to describe the Lambda N-> n N processes in a finite nucleus framework. The relationship between the intrinsic Lambda asymmetry parameter a_Lambda and the asymmetry a^M_Lambda accessible in experiments is discussed. A strong dependence of a^M_Lambda on nucleon final state interactions and detection threshold is obtained. Our results for a^M_Lambda are consistent with ^{11}_Lambda B and ^{12}_Lambda C data but disagree with observations in ^5_Lambda He.
$Lambda^+_c$- and $Lambda_b$-hypernuclei are studied in the quark-meson coupling (QMC) model. Comparisons are made with the results for $Lambda$-hypernuclei studied in the same model previously. Although the scalar and vector potentials felt by the $Lambda$, $Lambda_c^+$ and $Lambda_b$ in the corresponding hypernuclei multiplet which has the same baryon numbers are quite similar, the wave functions obtained, e.g., for $1s_{1/2}$ state, are very different. The $Lambda^+_c$ baryon density distribution in $^{209}_{Lambda^+_c}$Pb is much more pushed away from the center than that for the $Lambda$ in $^{209}_Lambda$Pb due to the Coulomb force. On the contrary, the $Lambda_b$ baryon density distributions in $Lambda_b$-hypernuclei are much larger near the origin than those for the $Lambda$ in the corresponding $Lambda$-hypernuclei due to its heavy mass. It is also found that level spacing for the $Lambda_b$ single-particle energies is much smaller than that for the $Lambda$ and $Lambda^+_c$.
Using the Hartree-Fock plus random-phase-approximation (HF+RPA), we study the impurity effect of $Lambda$ hyperon on the collective vibrational excitations of double-$Lambda$ hypernuclei. To this end, we employ a Skyrme-type $Lambda N$ and $LambdaLambda$ interactions for the HF calculations, and the residual interactions for RPA derived with the same interactions. We find that inclusion of two $Lambda$ hyperons in $^{16}$O shifts the energy of the collective states towards higher energies. In particular, the energy of the giant monopole resonance of $^{,,18}_{LambdaLambda}$O, as well as that of $^{210}_{LambdaLambda}$Pb, becomes larger. This implies that the effective incompressibility modulus increases due to the impurity effect of $Lambda$ particle, if the $beta$-stability condition is not imposed.
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