Relativistic Hartree approach with exact treatment of vacuum polarization for finite nuclei

Abstract

We study the relativistic Hartree approach with an exact treatment of the vacuum polarization in the Walecka ͑-͒ model. The contribution from the vacuum polarization of the nucleon-antinucleon field to the source term of the meson fields is evaluated by performing the energy integrals of the Dirac Green function along the imaginary axis. With the present method of calculating the vacuum polarization in finite system, the total binding energies and charge radii of 16 O and 40 Ca can be reproduced. On the other hand, the level splittings in the single-particle level, in particular the spin-orbit splittings, are not described well because the inclusion of vacuum effect provides a large effective mass with small meson fields. We also show that the derivative expansion of the effective action is fairly useful for the estimation of the vacuum effect.

Spontaneous chiral symmetry breaking in the massless linear sigma model by fermion and boson loop corrections

“…In order to keep the boson masses massless in the renormalization procedure, we take a renormalization condition for mass (3). Here, we keep only the lowest order derivative term, since the derivative expansion [26] is known to converge rapidly in the finite density [15,27].…”

“…Through this effective potential and spontaneous chiral symmetry breaking, all of the particles have the massive propagators so that some long-range interactions do not appear due to the massless model. Up to this stage one-loop corrections are usually included in the renormalized potential and renormalized densities [14,15,27]. It means that the effect of the renormalization is included in the potential and densities from the Fermi sea with the no sea approximation and the self consistency.…”

Self-consistent relativistic random-phase approximation with vacuum polarization

“…Here, we may need to use a standard technique of the renormalization to obtain explicit forms of V F (σ), Z σ F (σ), and Z ω F (σ). The method of calculating them has been discussed by many authors [18,19,20] and it has also been verified that the convergence of the expansion is quite rapid within a mean-field approximation [15,16,21]. In the present calculation, we employ only the first three terms in the right-hand side of Eq.…”

“…al. [15] wherein the density variation has been found to be substantially large. The use of the effective action developed in Ref.…”

“…The renormalization procedure in a finite nuclear system requires considerable effort even at the mean-field level [15,16]. The explicit calculation of the vacuum polarization for finite system has been performed recently by Haga et.…”