The breathing-mode giant monopole resonance and the surface compressibility in the relativistic mean-field theory

Abstract

The breathing-mode isoscalar giant monopole resonance (GMR) is investigated using the generator coordinate method within the relativistic mean-field (RMF) theory. Employing the Lagrangian models of the nonlinear-σ model (NLσ), the scalarvector interaction model (SVI) and the σ-ω coupling model (SIGO), we show that each Lagrangian model exhibits a distinctly different GMR response. Consequently, Lagrangian models yield a different value of the GMR energy for a given value of the nuclear matter incompressibility K ∞ . It is shown that this effect arises largely from a different value of the surface incompressibility K surf inherent to each Lagrangian model, thus giving rise to the ratio K surf /K ∞ which depends upon the Lagrangian model used. This is attributed to a difference in the density dependence of the meson masses and hence to the density dependence of the nuclear interaction amongst various Lagrangian models. The sensitivity of the GMR energy to the Lagrangian model used and thus emergence of a multitude of GMR energies for a given value of K ∞ renders the method of extracting K ∞ on the basis of interpolation amongst forces as inappropriate. As a remedy, the need to 'calibrate' the density dependence of the nuclear interaction in the RMF theory is proposed.Key words: Relativistic mean-field theory, nonlinear-σ model, scalar-vector interaction model SVI, σ-ω coupling model SIGO, density dependence of meson masses, generator coordinate method, breathing-mode giant monopole resonance, incompressibility of nuclear matter, surface incompressibility.

Equations of state for supernovae and compact stars

“…Interestingly, the former values are fully compatible with the final results of Lattimer and Lim (2013) Constraints for the nuclear incompressibility K can be deduced from fitting results of theoretical models to experimental data on the isoscalar giant monopole resonance (ISGMR), also called the breathing mode. However, it is perceived in the literature that the extraction of K from ISGMR data is not unambiguous as it relates to the density dependence of the symmetry energy in the models Shlomo, Kolomietz, and Colò, 2006;Sharma, 2009). For example, RMF models often obtain larger values for K in the range of 250-270 MeV ) than nonrelativistic models.…”

A statistical model for a complete supernova equation of state

“…The nuclear compressibility is rather high compared to the value of K = 240±20 MeV [55] or K = 248±8 MeV [56] deduced with theoretical models from experimental data on isoscalar giant monopole resonances (ISGMR) which probe nuclear matter slightly below saturation density. However, it is perceived in the literature that the extractation of K from ISGMR data is not unambiguous as it is dependent on the density dependence of the symmetry energy of the nuclear interactions which are taken for the analysis of the data [55,56,57]. For RMF models without further constraints on the density dependence of the symmetry energy usually higher values for K in the range of 250 to 270 MeV are obtained [56].…”

Breathing mode in an improved transport approach

“…The densities are obtained as the selfconsistent solution of Eqs. (8)(9)(10)(11)(18)(19)(20), with p F i = (3π 2 ρ i ) 1/3 (i = p, n) according to the local density approximation. This method then yields a consistent description of the groundstate.…”