Density dependent hadron field theory for hypernuclei

Abstract

The Density Dependent Relativistic Hadron Field (DDRH) theory, previously introduced and applied to isospin nuclei, is extended to hypernuclei by including the octet hyperons. Infinite matter Dirac-Brueckner theory for octet baryons and the derivation of in-medium DDRH baryon-meson vertices is discussed. From the properties of Dirac-Brueckner interactions it is found that hyperon and nucleon self-energies and vertices are related by the ratios of free space coupling constants. This leads to simple scaling laws for the in-medium hyperon and nucleon vertices. The model is applied in relativistic DDRH mean-field calculations to singl$\Lambda nuclei. Free space N-Lambda T-matrix results are used for the scalar vertex. As the only free parameter the hyperon vector vertex scaling factor is adjusted to a selected set of hypernuclear data. Spectroscopic data of single Lambda hypernuclei over the full mass range are well described. The reduced Lambda spin-orbit splitting is reproduced and found to be related closely the medium dependence of scalar and vector interactions.Comment: 38 pages, 9 figure

Application of the density dependent hadron field theory to neutron star matter

“…This so called vector density dependence (VDD) leads to quite satisfactory results for finite nuclei [25] and hypernuclei [29] and is a natural choice for the parameterization of the DB self-energies as was discussed in [28]. A straightforward extension to meson-hyperon vertices is the ansatz [29] …”

“…In this work the extension to hypernuclei as introduced in [29] is used. The 1/2 + baryon octet is taken into account including the S = −1 (Λ, Σ) and S = −2 (Ξ) hyperons.…”

“…The mapping of the DBHF self-energies to infinite nuclear matter DDRH vertices is done in the local density approximation (LDA), e.g. [23,31,32], and has been thoroughly discussed in [28,29]. In [28] a momentum correction of the self-energies was introduced to improve the applicability of DB calculations to the relativistic Hartree approximation.…”

“…Since such calculations are not available we extrapolate the density dependence and the strength of the vertices from DB calculations of nuclear matter and from hypernuclear data. As discussed in [29] this provides at least qualitative information about DB results of strange matter. This approach is discussed in Sec.…”

“…In the DDRH model they can be treated in almost the same manner as in standard RMF theory, allowing an easy extension of the model to the SU(3) f octet baryons as was shown in [29]. Since we assume in general density dependent hyperon-meson vertices we should in principle derive their parameterization from DB calculations that include hyperons.…”