Theory for Quartet Condensation in Fermi Systems with Applications to Nuclei and Nuclear Matter

Abstract

The theory of quartet condensation is further developed. The onset of quartet- ting in homogeneous fermionic matter is studied with the help of an in-medium modified four fermion equation. It is found that at very low density quartetting wins over pairing. At zero temperature, in analogy to pairing, a set of equations for the quartet order parameter is given. Contrary to pairing, quartetting only exists for strong coupling and breaks down for weak coupling. Reasons for this finding are detailed. In an application to nuclear matter, the critical temperature for α particle condensation can reach values up to around 8 MeV. The disappearance of α-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0₂⁺ of ¹²C is identified as an 'α-particle condensate' state. It is conjectured that such states also exist in heavier na-nuclei, like ¹⁶O, ²⁰Ne, etc. The sixth 0⁺ state in ¹⁶O is proposed as an analogue to the Hoyle state. The Gross-Pitaevski equation is employed to make an estimate of the maximum number of a particles a condensate state can contain. Possible quartet condensation in other systems is discussed briefly.