Light nuclei quasiparticle energy shifts in hot and dense nuclear matter

Abstract

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schrödinger equation for the A-particle cluster is obtained accounting for the effects of the correlated medium such as self-energy, Pauli blocking, and Bose enhancement. Similar to the single-baryon states (free neutrons and protons), the light elements (2 A 4, internal quantum state ν) are treated as quasiparticles with energies E A,ν (P; T , n n , n p ). These energies depend on the center-of-mass momentum P, as well as temperature T and the total densities n n , n p of neutrons and protons, respectively. No β equilibrium is considered so that n n , n p (or the corresponding chemical potentials µ n , µ p ) are fixed independently. For the single-nucleon quasiparticle energy shift, different approximate expressions such as Skyrme or relativistic mean-field approaches are well known. Treating the A-particle problem in appropriate approximations, results for the cluster quasiparticle shifts are given. Properties of dense nuclear matter at moderate temperatures in the subsaturation density region considered here are influenced by the composition. This in turn is determined by the cluster quasiparticle energies, in particular the formation of clusters at low densities when the temperature decreases and their dissolution due to Pauli blocking as the density increases. Our finite-temperature Green function approach covers different limiting cases: the low-density region where the model of nuclear statistical equilibrium and virial expansions can be applied and the saturation-density region where a mean-field approach is possible.

Parametrization of light nuclei quasiparticle energy shifts and composition of warm and dense nuclear matter

“…The effective mass correction is also easily calculated for given wave functions, see [13,15]. The influence of the self-energy shifts on the binding energy is small and will be considered below in Sec.…”

“…[15]. We consider only bound states and include A in the quantum state ν, dropping the spin quantum number.…”

“…In warm nuclear matter, significant contributions to the spectral function are due to the imaginary part of the self-energy. Within a cluster decomposition, see [15], the A-nucleon propagators arise. The corresponding A-nucleon spectral function describes also the formation of bound states, that appear as peaks at E A,ν ( P) = E A,ν + P 2 /(2Am) in the low-density limit.…”

“…The solution of the few nucleon problem in the low-density limit can be found from variational, Faddeev [21,22], Green's-function Monte Carlo [20], etc., approaches. We use a variational approach with the Jastrow ansatz [15] for ψ νP (1 . .…”

“…The aim of the present work is to provide the medium modification of the energies of light elements (A ≤ 4) in dense nuclear matter in a compact form, that can be easily used in further calculations. We generalize and improve previous parametrizations of the quasiparticle energies of light elements [15] as a function of P, T, n, and Y p . Our goal is to achieve an accuracy of better than 1% in a wide region of parameter values.…”