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Register a new userA particle-hole model approach for hypernuclei
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M. Martini
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A particle-hole model is developed to describe the excitation spectrum of single lambda hypernuclei and the possible presence of collective effects is explored by making a comparison with the mean-field calculations. Results for the spectra of 12C, 16O, 40Ca, 90Zr and 208Pb single lambda hypernuclei are shown. The comparison with the available experimental data is satisfactory. We find that collective phenomena are much less important in hypernuclei than in ordinary nuclei.
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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.
We develop both relativistic mean field and beyond approaches for hypernuclei with possible quadrupole-octupole deformation or pear-like shapes based on relativistic point-coupling energy density functionals. The symmetries broken in the mean-field states are recovered with parity, particle-number, and angular momentum projections. We take $^{21}_Lambda$Ne as an example to illustrate the method, where the $Lambda$ hyperon is put on one of the two lowest-energy orbits (labeled as $Lambda_s, Lambda_p$), respectively. We find that the $Lambda$ hyperon in both cases disfavors the formation of a reflection-asymmetric molecular-like $^{16}$O$+alpha$ structure in $^{20}$Ne, which is consistent with the Nilsson diagram for the hyperon in $(beta_2, beta_3)$ deformation plane. In particular, we show that the negative-parity states with the configuration $^{20}$Ne($K^pi=0^-)otimes Lambda_s$ are close in energy to those with the configuration $^{20}$Ne($K^pi=0^+)otimes Lambda_p$, even though they have very different structures. The $Lambda_s$ ($Lambda_p$) becomes more and more concentrated around the bottom (top) of the pear with the increase of octupole deformation.
We extend the recently developed Jacobi no-core shell model to hypernuclei. Based on the coefficients of fractional parentage for ordinary nuclei, we define a basis where the hyperon is the spectator particle. We then formulate transition coefficients to states that single out a hyperon-nucleon pair which allow us to implement a hypernuclear many-baryon Hamiltonian for $p$-shell hypernuclei. As a first application, we use the basis states and the transition coefficients to calculate the ground states of $^{4}_{Lambda}$He, $^{4}_{Lambda}$H, $^{5}_{Lambda}$He, $^{6}_{Lambda}$He, $^{6}_{Lambda}$Li, and $^{7}_{Lambda}$Li and, additionally, the first excited states of $^{4}_{Lambda}$He, $^{4}_{Lambda}$H, and $^{7}_{Lambda}$Li. In order to obtain converged results, we employ the similarity renormalization group (SRG) to soften the nucleon-nucleon and hyperon-nucleon interactions. Although the dependence on this evolution of the Hamiltonian is significant, we show that a strong correlation of the results can be used to identify preferred SRG parameters. This allows for meaningful predictions of hypernuclear binding and excitation energies. The transition coefficients will be made publicly available as HDF5 data files.
Applying the sum rule approach, we investigate the energy of a soft dipole motion in $Lambda$ hypernuclei, which results from a dipole oscillation of a $Lambda$ hyperon against the core nucleus. To this end, we systematically study single-$Lambda$ hypernuclei, from $^{16}_{;,Lambda}$O to $^{208}_{;;;Lambda}$Pb, for which the ground state wave function is obtained in the framework of Hartree-Fock method with several Skyrme-type $Lambda N$ interactions. Our results indicate that the excitation energy of the soft dipole $Lambda$ mode, $E_{sdLambda}$, decreases as the mass number increases. We find that the excitation energy is well parametrized as $E_{sdLambda}=26.6A^{-1/3}+11.2A^{-2/3}$ MeV as a function of mass number $A$.
The non--mesonic weak decay of double--$Lambda$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $Lambda Nto nN$, widely studied in single--$Lambda$ hypernuclei, additional hyperon--induced mechanisms, $Lambda Lambdato Lambda n$, $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^-p$, are accessible in double--$Lambda$ hypernuclei and are investigated here. As in previous works on single--$Lambda$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one--meson exchange weak transition potential (including the ground state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two--pion--exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei $^{10}_{LambdaLambda}$Be and $^{13}_{LambdaLambda}$B. Our predictions are compared with a few previous evaluations. The rate for the $Lambda Lambdato Lambda n$ decay is dominated by $K$--, $K^*$-- and $eta$--exchange and turns out to be about 2.5% of the free $Lambda$ decay rate, $Gamma_{Lambda}^{rm free}$, while the total rate for the $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^- p$ decays, dominated by $pi$--exchange, amounts to about 0.25% of $Gamma_{Lambda}^{rm free}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the non--mesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$--dibaryon.
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