Low-momentum interactions with Brown-Rho-Ericson scalings, and the density dependence of the nuclear symmetry energy

Abstract

We have calculated the nuclear symmetry energy Esym(ρ) up to densities of 4 ∼ 5ρ0 with the effects from the Brown-Rho (BR) and Ericson scalings for the in-medium mesons included. Using the V low−k low-momentum interaction with and without such scalings, the equations of state (EOS) of symmetric and asymmetric nuclear matter have been calculated using a ring-diagarm formalism where the particle-particle-hole-hole ring diagrams are included to all orders. The EOS for symmetric nuclear matter and neutron matter obtained with linear BR scaling are both overly stiff compared with the empirical constraints of Danielewicz et al. [9]. In contrast, satisfactory results are obtained by either using the non-linear Ericson scaling or by adding a Skyrme-type three-nucleon force (TNF) to the unscaled V low−k interaction. Our results for Esym(ρ) obtained with the non-linear Ericson scaling are in good agreement with the empirical values of Tsang et al. [7] and Li et al. [10], while those with TNF are slightly below these values. For densities below the nuclear saturation density ρ0, the results of the above calculations are nearly equivalent to each other and all in satisfactory agreement with the empirical values.

Half-Skyrmions and the equation of state for compact-star matter

“…The above V low−k ring-diagram framework has been applied to symmetric and asymmetric nuclear matter [22,23] and to the nuclear symmetry energy [8]. This framework has also been tested by applying it to dilute cold neutron matter in the limit that the 1 S 0 scattering length of the underlying interaction approaches infinity [24,25].…”

“…P denotes principal-value integration and the intermediate state momentum q is integrated from 0 to ∞ for the whole-space T and from 0 to Λ for T low−k . Because we shall calculate the nuclear symmetry energy E sym (n) up to n ∼ 5n 0 , we shall use Λ = 3 fm −1 [8]. The above V low−k preserves the low-energy phase shifts in the vacuum (up to energy Λ 2 ) and the deuteron binding energy of V N N .…”

“…The choice for the parameters in Region II will be addressed later. We shall calculate n 0 and E 0 /A using a low-momentum ring-diagram approach [8,[22][23][24][25], where the pphh ring diagrams are summed to all orders within a model space of decimation scale Λ. Few loworder (1st-, fourth-and eighth-order) such diagrams are displayed in Fig.…”

“…In this note, we confront our predictions with nature by translating the (semi-)classical results of [6] into the parameters of an effective Lagrangian having chiral symmetry and conformal symmetry, and then do a quantum-EFT calculation for nuclear matter and compact-star matter using a renormalization-group (RG) based formalism [8]. For the range n 1/2 = (1.5 − 2.0)n 0 considered in [6], we have applied our formalism to neutron star calculations and a comparison of our results with the recently discovered two-solar-mass neutron star [9] will be discussed.…”

Nucleon–anti-nucleon intruder state of Dirac equation for nucleon in deep scalar potential well

“…A desirable feature is its large energy gap between major shells. For example, the large energy gap between the 1s0d and 0p shells allows us to treat the nucleus 18 O using a small 2p0h model space, namely treating it simply as two 0s1d valence nucleons outside a closed 16 O core. Pioneered by Gerry, a large number of shell-model studies of nuclei using realistic nucleon-nucleon interactions have been carried out.…”