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Register a new userLambda hypernuclei and neutron star matter in a chiral SU(3) relativistic mean field model with a logarithmic potential
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We develop a chiral SU(3) symmetric relativistic mean field (RMF) model with a logarithmic potential of scalar condensates. Experimental and empirical data of symmetric nuclear matter saturation properties, bulk properties of normal nuclei, and separation energies of single- and double-$Lambda$ hypernuclei are well explained. The nuclear matter equation of state (EOS) is found to be softened by $sigmazeta$ mixing which comes from determinant interaction. The neutron star matter EOS is further softened by $Lambda$ hyperons.
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Based on relativistic mean field (RMF) models, we study finite $Lambda$-hypernuclei and massive neutron stars. The effective $N$-$N$ interactions PK1 and TM1 are adopted, while the $N$-$Lambda$ interactions are constrained by reproducing the binding energy of $Lambda$-hyperon at $1s$ orbit of $^{40}_{Lambda}$Ca. It is found that the $Lambda$-meson couplings follow a simple relation, indicating a fixed $Lambda$ potential well for symmetric nuclear matter at saturation densities, i.e., around $V_{Lambda} = -29.786$ MeV. With those interactions, a large mass range of $Lambda$-hypernuclei can be well described. Furthermore, the masses of PSR J1614-2230 and PSR J0348+0432 can be attained adopting the $Lambda$-meson couplings $g_{sigmaLambda}/g_{sigma N}gtrsim 0.73$, $g_{omegaLambda}/g_{omega N}gtrsim 0.80$ for PK1 and $g_{sigmaLambda}/g_{sigma N}gtrsim 0.81$, $g_{omegaLambda}/g_{omega N}gtrsim 0.90$ for TM1, respectively. This resolves the Hyperon Puzzle without introducing any additional degrees of freedom.
Deformed multi-$Lambda$ hypernuclei are studied within a relativistic mean-field model. In this paper, we take some $N=Z$ hyper isotope chains, i.e., $^{8+n}_{ nLambda}{rm Be}$, $^{20+n}_{ nLambda}{rm Ne}$, and $^{28+n}_{ nLambda}{rm Si}$ systems where $n = 2$, $4$ for Be, and $n = 2$, $8$ for Ne and Si. A sign of two-$^6_{2Lambda}$He cluster structure is observed in the two-body correlation in $^{12}_{4Lambda}$Be. In the Ne hyper isotopes, the deformation is slightly reduced by addition of $Lambda$ hyperons whereas it is significantly reduced or even disappears in the Si hyper isotopes.
This research article is a follow up of earlier work by M. Ikram et al., reported in International Journal of Modern Physics E {bf{25}}, 1650103 (2016) wherein we searched for $Lambda$ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (ie.$^{16}O - ^{208}Pb$) by injecting $Lambda$s into them. In present manuscript, working within the state-of-art relativistic mean field theory with inclusion of $Lambda N$ and $LambdaLambda$ interaction in hypernuclei using the predicted doubly magic nucleonic cores ie. $^{292}$120, $^{304}$120, $^{360}$132, $^{370}$132, $^{336}$138, $^{396}$138 of elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicity are made on the basis of one-, two-$Lambda$ separation energy ($S_Lambda, S_{2Lambda}$) and two lambda shell gaps ($delta_{2Lambda}$) in multi-$Lambda$ hypernuclei. The calculations suggest that the $Lambda$ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the $Lambda$ shell closures after introducing the $Lambda$s in elusive superheavy nucleonic cores. Moreover, in support of $Lambda$ shell closure the investigation of $Lambda$ pairing energy and effective $Lambda$ pairing gap has also been made. The appearance of new lambda shell closures other than the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of spin-orbit coupling in hypernuclei compared to normal nuclei.
The equations of state for neutron matter, strange and non-strange hadronic matter in a chiral SU(3) quark mean field model are applied in the study of slowly rotating neutron stars and hadronic stars. The radius, mass, moment of inertia, and other physical quantities are carefully examined. The effect of nucleon crust for the strange hadronic star is exhibited. Our results show the rotation can increase the maximum mass of compact stars significantly. For big enough mass of pulsar which can not be explained as strange hadronic star, the theoretical approaches to increase the maximum mass are addressed.
The effect of strange interactions in neutron star matter and the role of the strange meson-hyperon couplings are studied in a relativistic quark model where the confining interaction for quarks inside a baryon is represented by a phenomenological average potential in an equally mixed scalar-vector harmonic form. The hadron-hadron interaction in nuclear matter is then realized by introducing additional quark couplings to $sigma$, $omega$, $rho$, $sigma^*$ and $phi$ mesons through mean-field approximations. The meson-baryon couplings are fixed through the SU(6) spin-flavor symmetry and the SU(3) flavor symmetry to determine the hadronic equation of state (EoS). We find that the SU(3) coupling set gives the potential depth between $Lambda$s around $-5$ MeV and favours a stiffer EoS.The radius for the canonical neutron star lies within a range of $12.7$ to $13.1$ km.
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