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Register a new userOn the binding energy of double Lambda hypernuclei in the relativistic mean field theory
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S. Marcos Univ. of Cantabria
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We calculate the binding energy of two $Lambda$ hyperons bound to a nuclear core within the relativistic mean field theory. The starting point is a two-body relativistic equation of the Breit type suggested by the RMFT, and corrected for the two-particle interaction. We evaluate the 2 $Lambda$ correlation energy and estimate the contribution of the $sigma^*$ and $Phi$ mesons, acting solely between hyperons, to the bond energy $Delta{B_{LambdaLambda}}$ of $^6_{LambdaLambda}He$, $^{10}_{LambdaLambda}Be$ and $^{13}_{LambdaLambda}B$. Predictions of the $Delta{B_{LambdaLambda}}$ A dependence are made for heavier $Lambda$-hypernuclei.
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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 Physical origin of the nuclear symmetry energy is studied within the relativistic mean field (RMF) theory. Based on the nuclear binding energies calculated with and without mean isovector potential for several isobaric chains we conform earlier Skyrme-Hartree-Fock result that the nuclear symmetry energy strength depends on the mean level spacing $epsilon (A)$ and an effective mean isovector potential strength $kappa (A)$. A detaied analysis of isospin dependence of the two components contributing to the nuclear symmetry energy reveals a quadratic dependence due to the mean-isoscalar potential, $simepsilon T^2$, and, completely unexpectedly, the presence of a strong linear component $simkappa T(T+1+epsilon/kappa)$ in the isovector potential. The latter generates a nuclear symmetry energy in RMF theory that is proportional to $E_{sym}sim T(T+1)$ at variance to the non-relativistic calculation. The origin of the linear term in RMF theory needs to be further explored.
We calculate the $Lambda Lambda to YN$ transition rate of ${^{phantom{Lambda}6}_{Lambda Lambda}}$He by the hybrid picture, the $pi$ and $K$ exchanges plus the direct quark processes. It is found that the hyperon-induced decay is weaker than the nucleon-induced decay, but the former may reveal the short-range mechanism of the weak transition and also give a clear signal of the strong $Delta I=3/2$ transition. The $Lambda Lambda to Y N$ transition in double-$Lambda$ hypernucleus is complement to the $Lambda N to NN$ transition as it occurs only in the J=0 channel, while the J=1 transition is dominant in the $Lambda N to NN$ case.
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