Pair condensation and bound states in fermionic systems

Abstract

We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature Tc2 for the superfluid phase transition and the limiting temperature Tc3 for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature Tc3 > Tc2.

Composition of Nuclear Matter with Light Clusters and Bose–Einstein Condensation of $$\alpha $$ α Particles

“…In the following we will also neglect the medium modifications of the binding energies of clusters, i.e., their dependence on the temperature and density of the ambient matter, which is justified at densities below n sat /3. These modifications are discussed elsewhere [13,14,24,33,40]. The numerical values of the binding energies of light clusters used in our computations are B d = 2.225 (deuteron), B t = 8.482 (triton), B h = 7.718 (helion) and B α =28.3 MeV (α particle).…”

“…Another aspect of the problem is the effects of light clusters in intermediate energy heavy ion collisions [22,23,24,25,26,27] which were extensively studied using various methods, see for example [28,29,30]. Furthermore, the general many-body problem of bound state formation in nuclear medium is an outstanding problem on its own right [31,32,33,34,35,36,37,38,39,40,41,42].…”

Nuclear Superconductivity in Compact Stars: BCS Theory and Beyond

“…In isospin-symmetric nuclear matter, neutron-proton (np) pairing undergoes a smooth transition leading from an assembly of np Cooper pairs at higher densities to a gas of Bose-condensed deuterons as the nucleon density is reduced to extremely low values. 86,87,88,89,90 This transition may be relevant -and could then yield valuable information on np correlations -in low-density nuclear sys- tems (especially the nuclear surface), in expanding nuclear matter from heavyion collisions, and in supernova matter. The underlying equations of the theory are (13) and (14) with E A = 0; we shall address the effects of asymmetry at a later point.…”

“…Deviations from the original BCS theory are understandable in that (i) the system is in the strong-coupling regime, and (ii) the pairing is in a spin-triplet rather than a spin-singlet state. 90 One measure of coupling strength is the ratio ∆(0)/|µ| of the zero-temperature energy gap to the magnitude of the chemical potential. It is seen from Fig.…”

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

“…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 .…”