Effect of the δ\delta-meson on the instabilities of nuclear matter under strong magnetic fields

We study the influence of the isovector-scalar meson on the spinodal instabilities and the distillation effect in asymmetric non-homogenous nuclear matter under strong magnetic fields, of the order of $10^{18}-10^{19}$ G. Relativistic nuclear models both with constant couplings (NLW) and with density dependent parameters (DDRH) are considered. A strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. It is shown that for neutron rich matter the inclusion of the $\delta$ meson increases the size of the instability region for NLW models and decreases it for the DDRH models. The effect of the $\delta$ meson on the transition density to homogeneous $\beta$-equilibrium matter is discussed. The DDRH$\delta$ model predicts the smallest transition pressures, about half the values obtained for NL$\delta$.Comment: 6 pages, 5 figues, 3 tables, accepted for publication in Phys. Rev.

A new description of motion of the Fermionic SO(2N+2) top in the classical limit under the quasi-anticommutation relation approximation

The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidian space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anti-commutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation, due to the unpaired-mode effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi anti-commutation-relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters k and l in the Lagrange multipliers can be determined withuout any inconcistency.Comment: 36 pages, no figures, typos corrected, published versio

An inverse indefinite numerical range problem

https://thekeep.eiu.edu/den_1997_feb/1008/thumbnail.jp

Color symmetrical superconductivity in a schematic nuclear quark model

In this note, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. The physical properties of the BCS vacuum (average numbers of quarks of different colors) remain unchanged under an arbitrary color rotation. In the usual approach to color superconductivity, the pairing correlations affect only the quasi-particle states of two colors, the single particle states of the third color remaining unaffected by the pairing correlations. In the theory of color symmetrical superconductivity here proposed, the pairing correlations affect symmetrically the quasi-particle states of the three colors and vanishing net color-charge is automatically insured. It is found that the groundstate energy of the color symmetrical sector of the Bonn model is well approximated by the average energy of the color symmetrical superconducting state proposed here

Electron--phonon coupling and anharmonic effects in metal clusters

The periods of the harmonic oscillations of the ion core of charged sodium clusters around the equilibrium shapes are considered. It is found that these periods are of the order of magnitude of the experimentally measured relaxation times of the plasmons, which suggests the importance of the electron-ion coupling and stresses the role played by the electron-phonon interaction in the dissipation of the plasmon energy. The relation of the process to fission is briefly discussed.Comment: 6 pages, no figures, to appear in EPLetter

Aspects of short range correlations in a relativistic model

In the present work short range correlations are introduced for the first time in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation using an effective Hamiltonian derived from the $\sigma-\omega$ Walecka model. The unitary correlation method is used to introduce short range correlations. The effect of the correlations in the ground state properties of the nuclear matter is discussed.Comment: 7 pages, 3 figure

On the Courant-Fischer theory for Krein spaces

http://www.sciencedirect.com/science/article/B6V0R-4V462G8-2/2/25c16be9e99d2fbaa89b7c1a6a47e95

Short range correlations in relativistic nuclear matter models

Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. It is shown that the correlations give rise to an extra node in the ground-state wave-function in the nucleons, contrary to what happens in non-relativistic calculations with a hard core. The effect of the correlations in the ground state properties of the nuclear matter and neutron matter is studied. The nucleon effective mass and equation of state (EOS) are very sensitive to short range correlations. In particular, if the pion contact term is neglected a softening of the EOS is predicted. Correlations have also an important effect on the neutron matter EOS which presents no binding but only a very shallow minimum contrary to the Walecka model.Comment: 8pages, 4 figure

Analogs of Cauchy–Poincaré and Fan–Pall interlacing theorems for J-Hermitian and J-normal matrices

AbstractThe interlacing theorem of Cauchy–Poincaré states that the eigenvalues of a principal submatrix A0 of a Hermitian matrix A interlace the eigenvalues of A. Fan and Pall obtained an analog of this theorem for normal matrices. In this note we investigate analogs of Cauchy–Poincaré and Fan–Pall interlacing theorems for J-Hermitian and J-normal matrices. The corresponding inverse spectral problems are also considered