Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--

Abstract

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume delta-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.

17 pages, 15 figures, full paper following arXiv:1205.5354 and Phys. Rev. C 86 (2012) 021301(R)

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• Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double-$\beta$ and $\beta$ decays
• Examinations of the consistency of the quasiparticle random-phase approximation approach to double-$\beta$ decay of ${}^{48}$Ca
• Estimation of nuclear matrix elements of double-$\beta$ decay from shell model and quasiparticle random-phase approximation
• Two decay paths for calculation of nuclear matrix element of neutrinoless double-beta decay using quasiparticle random-phase approximation
• Effects of perturbation for transition operator of double-$\beta$ decay on nuclear matrix element, effective axial-vector current coupling, and half-life