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Register a new userBeyond mean-field approach for pear-shaped hypernuclei
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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.
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We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $Lambda$ hyperon with orbital angular momentum $ell=0$ (or $ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) otimes Lambda p_{1/2}]^J$ and $[^{A-1}Z (Ipm2 ^+) otimes Lambda p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as the collective correlation of nuclear core becomes stronger. Finally, we show how the energies of hypernuclear low-lying states are sensitive to parameters in the effective $N Lambda $ interaction, the uncertainty of which has a large impact on the predicted maximal mass of neutron stars.
The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A semiclassical extension of this approach to quantum many-body systems was suggested by Uehling and Uhlenbeck in 1933 for both Fermi and Bose statistics, and many further generalization of this approach are known as the Boltzmann-Uehling-Uhlenbeck (BUU) equations. Here I suggest a pure quantum version of the BUU type of equations, which is mathematically equivalent to a generalized Time-Dependent Density Functional Theory extended to superfluid systems.
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.
New effective $Lambda N$ interactions are proposed for the density dependent relativistic mean field model. The multidimensionally constrained relativistic mean field model is used to calculate ground state properties of eleven known $Lambda$ hypernuclei with $Age 12$ and the corresponding core nuclei. Based on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_sigma$ and $R_omega$ of scalar and vector coupling constants between $Lambda N$ and $NN$ interactions are determined by fitting calculated $Lambda$ separation energies to experimental values. We propose six new effective interactions for $Lambda$ hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2 and PKDD-Y3 with three ways of grouping and including these eleven hypernuclei in the fitting. It is found that the two ratios $R_sigma$ and $R_omega$ are correlated well and there holds a good linear relation between them. The statistical errors of the ratio parameters in these effective interactions are analyzed. These new effective interactions are used to study the equation of state of hypernuclear matter and neutron star properties with hyperons.
Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a Generator Coordinate Method based on angular-momentum and particle-number projected triaxially deformed Hatree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the Generator Coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to 25Mg illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-A nuclei throughout the nuclear chart.
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