Equation of state of neutron-rich matter in [formula omitted]-dimensions

Abstract

Nuclear systems under constraints, with high degrees of symmetries and/or collectivities may be considered as moving effectively in spaces with reduced spatial dimensions. We first derive analytical expressions for the nucleon specific energy E0(ρ), pressure P0(ρ), incompressibility coefficient K0(ρ) and skewness coefficient J0(ρ) of symmetric nucleonic matter (SNM), the quadratic symmetry energy Esym(ρ), its slope parameter L(ρ) and curvature coefficient Ksym(ρ) as well as the fourth-order symmetry energy Esym,4(ρ) of neutron-rich matter in general d spatial dimensions (abbreviated as “dD”) in terms of the isoscalar and isovector parts of the isospin-dependent single-nucleon potential according to the generalized Hugenholtz–Van Hove (HVH) theorem. The equation of state (EOS) of nuclear matter in dD can be linked to that in the conventional 3-dimensional (3D) space by the ϵ-expansion which is a perturbative approach successfully used previously in treating second-order phase transitions and related critical phenomena in solid state physics and more recently in studying the EOS of cold atoms. The ϵ-expansion of nuclear EOS in dD based on a reference dimension df=d−ϵ is shown to be effective with −1≲ϵ≲1 starting from 1≲df≲3 in comparison with the exact expressions derived using the HVH theorem. Moreover, the EOS of SNM (with/without considering its potential part) is found to be reduced (enhanced) in lower (higher) dimensions, indicating in particular that the many-nucleon system tends to be more bounded but saturate at higher densities in spaces with lower dimensions. The symmetry energy perturbed from its counterpart in 3D is found to strongly depend on the momentum-dependence of the nucleon isovector potential. Moreover, the specific structure of the fourth-order symmetry energy in dD is also analyzed generally, and it is found to be naturally small, confirming the parabolic approximation for the EOS of neutron-rich matter from an even wider viewpoint. The links between the EOSs in 3D and dD spaces from the ϵ-expansion provide new perspectives to the EOS of neutron-rich matter. Further studies and potential applications of these links in nuclear physics and/or astrophysics are discussed.