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arXiv:0901.0675 · Physical Review C

Critical temperature for α -particle condensation within a momentum-projected mean-field approach

Takaaki Sogo, Rimantas Lazauskas, GERD RÖPKE, Peter Schuck

Published May 12, 2009• 42 citations
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Abstract

\ensuremath{\alpha}-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum-projected mean-field ansatz for the quartet. The self-consistent single-particle wave functions are shown and discussed for various values of the density at the critical temperature. Excellent agreement of the critical temperature with a numerical solution of the Faddeev-Yakubovsky equation is obtained.

DOI
10.1103/physrevc.79.051301

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\ensuremath{\alpha}-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum-projected mean-field ansatz for the quartet. The self-consistent single-particle wave functions are shown and discussed for various values of the density at the critical temperature. Excellent agreement of the critical temperature with a numerical solution of the Faddeev-Yakubovsky equation is obtained.
We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)--type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an $\ensuremath{\alpha}$-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and $\ensuremath{\alpha}$ condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be modified by the pair and quartet correlations and show a hierarchical structure of in-medium cluster formations in infinite nuclear matter. The present results may also contribute to the interdisciplinary understanding of fermionic condensations beyond the BCS paradigm in many-body systems.
Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.
When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterized states, e.g., $\ensuremath{\alpha}$ clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional calculations with with the relativistic and the Gogny approaches on the diluted 16O^{16}\mathrm{O}16O nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. A complementary study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter.
The properties of symmetric nuclear matter are investigated within Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The in-medium scattering equation is solved for a realistic (nonseparable) nucleon-nucleon interaction including both particle-particle and hole-hole propagation. The corresponding two-particle propagator is constructed explicitly from the single-particle spectral functions. Results are obtained for finite temperatures and an extrapolation to T=0T=0T=0 is presented.
We derive three-body equations valid at finite densities and temperatures. The equations are based on the cluster mean field approach consistently including proper self-energy corrections and Pauli blocking. As an application we investigate the binding energies of triton and determine the Mott densities and momenta relevant for a many particle description of nuclear matter in a generalized Beth-Uhlenbeck approach. The method, however, is not restricted to nuclear physics problems but may also be relevant, e.g., to treat three-particle correlations in weakly doped semiconductors or strongly coupled dense plasmas.