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Register a new userNew effective interactions in RMF theory with non-linear terms and density-dependent meson-nucleon coupling
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New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1 with nonlinear sigma- and omega-meson self-coupling, PK1R with nonlinear sigma-, omega- and rho-meson self-coupling and PKDD with the density-dependent meson-nucleon coupling, are proposed. They are able to provide an excellent description not only for the properties of nuclear matter but also for the nuclei in and far from the valley of beta-stability. For the first time in the parametrization of the RMF Lagrangian density, the center-of-mass correction is treated by a microscopic way, which is essential to unify the description of nuclei from light to heavy regions with one effective interaction.
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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.
We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.
We demonstrate the calculation of the coupling constants and form factors required by effective hadron lagrangians using the quark model. These relations follow from equating expressions for strong transition amplitudes in the two approaches. As examples we derive the NNm nucleon-meson coupling constants and form factors for m = pi, eta, eta, sigma, a_0, omega and rho, using harmonic oscillator quark model meson and baryon wavefunctions and the 3P0 decay model; this is a first step towards deriving a quark-based model of the NN force at all separations. This technique should be useful in the application of effective lagrangians to processes in which the lack of data precludes the direct determination of coupling constants and form factors from experiment.
Changes in the meson-nucleon coupling constant and the vertex form factor in nuclear matter are studied in a modified Skyrme Lagrangian including the sigma-meson field that satisfies the scale invariance. Renormalization of the axial-vector coupling constant, and the nucleon mass are studied in a consistent model. The results are consistent with the empirical evidence. A calculation of pi N commutator, sigma-term, indicates that the medium changes its magnitude considerably.
An improved quark mass density- dependent model with the non-linear scalar sigma field and the $omega$-meson field is presented. We show that the present model can describe saturation properties, the equation of state, the compressibility and the effective nuclear mass of nuclear matter under mean field approximation successfully. The comparison of the present model and the quark-meson coupling model is addressed.
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