^{1}

^{ 2}

^{1}

^{2}

The conserving

The linear and nonlinear hadronic mean-field approximations have been extensively applied to finite nuclei, nuclear matter,
and neutron stars
[

The current nonlinear mean-field approximation is
constructed with

The density-dependent correlations among properties of
nuclear matter and neutron stars have been discussed in terms of effective
masses and coupling constants of mesons and baryons, which are defined
self-consistently to maintain conditions of conserving approximations
[

The Lagrangian of nonlinear

The nonlinear model is motivated by preserving the
structure of Serot and Walecka's linear

The properties at saturation of symmetric nuclear
matter and neutron stars are taken so as to fix nonlinear coupling constants.
The binding energy at saturation is fixed as

It can be checked numerically that the baryons and an
electron,

The self-consistency required by thermodynamic
consistency restricts values of nonlinear coefficients. The suppressions of
nonlinear coefficients and nonlinear interactions are directly observed in
self-consistent effective masses and self-energies of mesons and baryons, which
are discussed as

The density-dependent, effective coupling constants are assumed to be induced by

The introduction of nonlinear

The scalar sources of nucleons (

The scalar sources of baryons are, respectively, given
by

The energy density, pressure of isospin-asymmetric,
and charge-neutral nuclear matter are calculated by way of the energy-momentum
tensor as

Properties of nuclear matter and (

9.326 | 10.421 | 4.765 | 10.0 | 20.0 | 20.0 | 4.00 | 18.0 | ||

0.013 | 0.048 | 9.063 | 10.800 | 7.567 | |||||

0.70 | 1.02 | 1.01 | 329 | 30.0 |

The maximum
masses,

( | ||
---|---|---|

1.00 | 2.22 | 2.14 |

2/3 | 2.08 | 2.24 |

1/3 | 1.93 | 1.21 |

( | ||
---|---|---|

1.00 | 2.22 | 2.15 |

2/3 | 1.67 | 1.00 |

1/3 | 1.56 | 1.02 |

The binding energies of (

The binding energies of (

The equations of motion, self-energies (

The effective masses of

The effective masses of

The hyperon-onset densities at phase transition are given by chemical potentials as

The hyperon-onset densities are determined by chemical
potentials which are equal to the single particle energy. The single particle
energies of baryons,

The hyperon coupling constants,

With a given ratio

The equation of state for (

The equation of state for

The equation of state (EOS) given by (

The incompressibility,

Incompressibilities of (

Nucleon symmetry energies
of

The lowest binding energies of

The current conserving mean-field approximation and renormalized nonlinear interactions have exhibited interesting density-dependent correlations among observables of nuclear and high-density hyperonic matter.

(1) The hyperon-onset densities are fairly fixed, respectively, although density-dependent interactions prominently affect the EOS and properties of nuclear and neutron matter. Therefore, the hyperon-onset density could be one of the important constraints on theoretical and experimental models of high density, exotic nuclear matter. The signals of hyperon production and onset density should be investigated further in heavy-ion collision experiments, and the results obtained in the current investigation should be examined carefully for nonlinear interactions including all other hyperons.

(2) The onset density of

(3) The softening of EOS and discontinuity of
incompressibility are interrelated to the strength of the hyperon coupling
constants and effective masses of mesons and hyperons; hence, theoretical and
experimental analyses of incompressibility and EOS in high densities are
essential to determine physical quantities. The discontinuous change is also
obtained for the symmetry energy for (

(4) The binding energies, effective masses, and
coupling constants of hyperons generate strong density correlations among
properties of nuclear matter and neutron stars. Therefore, the binding energies
and coupling ratios of hyperons, the hyperon-onset densities and signals of
phase transition of (

(5) The values of hyperon coupling ratios, (

The densities of hyperon onset and phase transitions,
(

The authors would like to acknowledge Professor T. Muto of Chiba Institute of Technology for his valuable comments on binding energies of hyperons. The work is supported by Osaka Gakuin Junior College research grant for the 2008 Academic Year.