Overlap of quasiparticle random-phase approximation 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 to simulate the overlap of the intermediate nuclear states of the double-β 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 δ-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.

Two decay paths for calculating the nuclear matrix element of neutrinoless double-βdecay using quasiparticle random-phase approximation

“…In Ref. [14], the author obtained a value of 0.06, which is very close to the semi-experimental result, via a simple hybrid estimation combining the M (2ν) of Ref. [24] and the product of the normalization factors of the lpQRPA ground states.…”

“…Remarkable progress has been made recently, in that a few groups have independently performed QRPA calculations ( [13] and references therein), with the converged results with respect to the dimension of the wave-function space, and relatively similar 0νββ NMEs were obtained within a range significantly smaller than the abovementioned factor of 2-3. Recently, the author has made additional progress by modifying the QRPA approach for calculation of the NME of 0νββ decay in terms of the overlap calculation of the intermediate states of the decay [14]. In the QRPA approach, the intermediate states obtained on the basis of the initial and final states are not identical; therefore, this overlap calculation is not trivial.…”

“…Another new aspect of the modified QRPA approach is the use of a virtual decay path, e.g., a two-neutron removal followed by a two-proton addition, in order to calculate the NME of 0νββ decay under the closure approximation [14,17,18]. The like-particle (lp)QRPA is the main method for obtaining intermediate states on this virtual path.…”

Many-body correlations of quasiparticle random-phase approximation in nuclear matrix elements of neutrinolessdouble−βdecay

“…1 in Ref. [13]. The spaces of the intermediate states should be such that they cover the space obtained by the first (inverse second) step of 0νββ decay from the initial (final) state, e.g., {c † p c n |I (A,Z) }.…”

“…[13], we investigated how to calculate the overlap of two QRPA states based on different nuclei by calculating up to negligible-order terms in the expansion of the overlap with respect to the backward amplitudes of the QRPA solutions. 1 Here we note the equations of the overlap that include only the relevant terms and are used in the calculations in this paper.…”