Nucleon effective masses in neutron-rich matter

Abstract

Various kinds of isovector nucleon effective masses are used in the literature to characterize the momentum/energy dependence of the nucleon symmetry potential or self-energy due to the space/time non-locality of the underlying isovector strong interaction in neutron-rich nucleonic matter. The multifaceted studies on nucleon isovector effective masses are multi-disciplinary in nature. Besides structures, masses and low-lying excited states of nuclei as well as nuclear reactions, studies of the isospin dependence of short-range correlations in nuclei from scatterings of high-energy electrons and protons on heavy nuclei also help understand nucleon effective masses especially the so-called E-mass in neutron-rich matter. A thorough understanding of all kinds of nucleon effective masses has multiple impacts on many interesting issues in both nuclear physics and astrophysics. Indeed, essentially all microscopic many-body theories and phenomenological models with various nuclear forces available in the literature have been used to calculate single-nucleon potentials and the associated nucleon effective masses in neutron-rich matter. There are also fundamental principles connecting different aspects and impacts of isovector strong interactions. In particular, the Hugenholtz-Van Hove theorem connects analytically nuclear symmetry energy with both isoscalar and isovector nucleon effective masses as well as their own momentum dependences. It also reveals how the isospin-quartic term in the equation of state of neutron-rich matter depends on the high-order momentum-derivatives of both isoscalar and isovector nucleon potentials. The Migdal-Luttinger theorem facilitates the extraction of nucleon E-mass and its isospin dependence from experimentally constrained single-nucleon momentum distributions. The momentum/energy dependence of the symmetry potential and the corresponding neutron-proton effective mass splitting also affect transport properties and the liquid-gas phase transition in neutron-rich matter. Moreover, they influence the dynamics and isospin-sensitive observables of heavy-ion collisions through both the Vlasov term and the collision integrals of the Boltzmann-Uehling-Uhlenbeck transport equation. We review here some of the significant progresses made in recent years by the nuclear physics community in resolving some of the hotly debated and longstanding issues regarding nucleon effective masses especially in dense neutron-rich matter. We also point out some of the remaining key issues requiring further investigations in the era of high precision experiments using advanced rare isotope beams. Nucleon effective masses in non-relativistic modelsWe focus on non-relativistic nucleon effective masses or the ones derived from the Schrödinger equivalent singleparticle potential in relativistic models. The k-mass M * ,k J and E-mass M * ,E J of a nucleon J = n/p can be obtained from the momentum and energy dependence of the single-nucleon potential U J (ρ, δ, k, E) in nucleonic matter of density ρ and isospin asymmetry δ...

Skewness of nuclear matter and three-particle correlations

“…The second derivative of Eq. (22) and its relation to the incompressibility (K) of nuclear matter is given by [7,10]…”

“…The properties of infinite nuclear matter have been the subject of intensive investigations for many decades, mainly because of the wide range of applications, including the properties of heavy nuclei and their excitation modes [1,2], heavy ion collisions [3], the physics of supernova explosions [4,5], and neutron stars [6]. Besides the binding energy per nucleon and the saturation density, other basic properties of nuclear matter like the effective mass of nucleons and its momentum dependence [7], the incompressibility [8], the symmetry energy and its density dependence [9], and recently the skewness [10], provide basic information on the effective interaction between nucleons in the medium. Theoretical descriptions of those and other important properties of nuclear matter have been based on Brückner's G-matrix approach [11][12][13], relativistic theories based on meson exchange [14][15][16], effective interactions of the Skyrme [17] and Landau-Migdal type [18], and effective field theories [19][20][21][22][23].…”

Constraints on Skyrme equations of state from doubly magic nuclei, ab initio calculations of low-density neutron matter, and neutron stars

“…Some parameters of the EOS that are crucial for neutron star properties are not well constrained by nuclear reaction or structure experiment. In particular, the value of neutron effective mass remains very uncertain [2,3]. In this paper, we focus on the role of the neutron effective mass on the high density EOS, and show that it can be tightly constrained using properties of doubly-magic nuclei, ab-initio calculations of low-density neutron matter in conjunction with astrophysical and gravitational wave observations.…”

Transport approaches for the description of intermediate-energy heavy-ion collisions

“…There are different definitions of the in-medium nucleon effective mass (see, e.g., Ref. [177] for a recent review), and I mostly concentrate on the non-relativistic 'k-mass' m * n/p = m 1 +…”

“…So far, most studies favor a larger neutron effective mass than proton in a neutron-rich medium (see Table 2 of Ref. [177]), and this leads to the increasing trend of the symmetry potential with decreasing nucleon momentum [178]. However, the possibility for a larger proton effective mass than neutron in neutron-rich matter can not be completely ruled out yet.…”