Correlated model forΛhypernuclei

Abstract

We study the properties of hypernuclei containing one Λ hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of Λ-hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the Λ particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani Λ-nucleon potential are adopted. The effect of many-body forces are considered by means either of a three body Λ-nucleon-nucleon potential of the Argonne type or of a density dependent modification of the Λ-nucleon interaction, fitted to reproduce the Λ binding energy in nuclear matter. While Jastrow correlations underestimate the attractive contribution of the three body Λ interaction, the density dependent potential provides a good description of the Λ binding energies over all the nuclear masses range, in spite of the relative simplicity of the model.

Hypernuclear single particle spectra based on in-medium chiral dynamics

“…Experimental energies [1] are shown in comparison with the results of the present calculations, using the input parameters of Table 1 and ζ = 0.5 (column FKVW). Also listed are results of five different models: Quark Meson Coupling (QMC) [12,13], Fermi Hypernetted Chain (FHNC) [18], Skyrme (SK) [16], Brueckner-Hartree-Fock (BHF) [19] with the Njimegen SC97F potential [50], and RMF models with a tensor coupling [11] (RMFI with f Λ ω /g Λ ω = −1) and density-dependent couplings [14] Tables 2 and 3), calculated with the FKVW density functional using the three parameter sets for the ΛN couplings (cf. Table 1).…”

Quantifying short-range correlations in nuclei

“…[28], the "CBF" one is for 16 O and from Ref. [29], and the "cluster" one is for 16 O and from Ref. [31], ΨD (k12) is the l = 2 component of the non-relativistic deuteron wave function generated with the Paris potential [32,33] (not to scale).…”

“…(28,29,30). This can also be done for any other basis |nljm of non-relativistic single-particle states.…”

“…We have opted to display the results relative to the sum rule values of the Eqs. (28) and (29), which allows one to interpret the results in terms of probabilities: given an arbitrary pair wave function, what is the chance that it has zero orbital relative momentum and a specific spin quantum number. In a naive IPM picture for 4 He, the pp pair is in a |l 12 = 0, S = 0, T = 1 state.…”

A particle–hole model approach for hypernuclei

“…The Table 9 Renormalized energy differences Eq. (36). We have also indicated the maximum value of the angular momentum of the multipole excitation …”