Analytical approach for the Quartet Condensation Model

Abstract

Within the Quartet Condensation Model (QCM), the isovector pairing correlations for $N=Z$ nuclei are described with a very high accuracy by a condensate of $\alpha$-like quartets. The usual approach involves cumbersome recurrence relations in order to compute numerically the relevant quantities of the model: the norm of the quartet states and the mean value of the isovector pairing Hamiltonian as functions of the pair mixing amplitudes. We present the final analytical expressions for the above mentioned quantities, for all cases up to four quartets in the valence shell. The analytical QCM expressions were obtained by a straightforward implementation of the SO(5) algebra in the symbolic computer algebra system Cadabra2. The norm of the quartet states and the mean value of the Hamiltonian are polynomial functions of the mixing amplitudes. The numerical implementation of the QCM model is thus made trivial as matter of copying and pasting the presented formulas. We introduce in this work the method of computer aided analytical calculus for a many body setting. In particular, we provide precise and easy to use tools for the description of isovector pairing correlations.

5 pages

References in corpus (12)

• Four-particle condensate in strongly coupled fermion systems
• Concepts of alpha-particle condensation
• Giant Dipole Resonance as a Fingerprint of $\alpha$ Clustering Configurations in ${}^{12}$C and ${}^{16}$O
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Alpha-like quartet condensation and isovector pairing correlations in N=Z nuclei
• Isoscalar dipole transition as a probe for asymmetric clustering
• Four-nucleon alpha-type correlations and proton-neutron pairing away of N=Z line
• Isovector proton-neutron pairing and Wigner energy in Hartree-Fock mean field calculations
• Structure of the number projected BCS wave function
• Quartet correlations in N=Z nuclei induced by realistic two-body interactions
• Isovector and isoscalar proton-neutron pairing in $N>Z$ nuclei
• Localization of pairing correlations in nuclei within relativistic mean field models

Cited by in corpus (6)

• A quartet BCS-like theory
• Bridging the quartet and pair pictures of isovector proton-neutron pairing
• Disentangling the pair and quartet condensates
• Unified description of pairing and quarteting correlations within the particle-hole-boson approach
• Proton-neutron pairing and binding energies of nuclei close to N=Z line
• Structure of the quartetting ground state of $N=Z$ nuclei