Double-β-decay matrix elements

Abstract

The validity of the commonly assumed closure approximation has been tested by explicit calculations of the Ov PP-decay matrix elements of Ge Se performed in the context of quasiparticle random-phase approximation with a realistic model space. The closure approximation seems to work well for those matrix elements not very suppressed. Our results indicate that unlike the 2v decay, the Ov PP-decay matrix elements are not greatly suppressed but are comparable to those of shell model calculations. They are dominated by multipoles other than 0+ and 1+.Although at present there exist no data which contradict the standard model of the electroweak [SU (2) xU(1)] and the strong SU3(3), interactions there is a general belief that the standard model with its 23 unspecified parameters cannot be the ultimate fundamental theory of nature. Therefore during the last years various extensions of the standard model have been considered. Among them the most popular have been various unification schemes of the electroweak and strong forces, including the grand unified theories (GUT's) with their supersymmetric extensions and, more recently, superstring and superstring-inspired models.An interesting feature of such extensions of the standard model is that the neutrino turns out quite naturally to be a massive majorana particle, i.e. , loosely speaking identical with its own antiparticle. In such a situation the neutrinoless double P decay' (Ov PP decay) becomes possible. Thus if such a process is eventually detected it would indicate physics beyond the standard model. ' ' But, even if one is not able to observe the neutrinoless double P decay, an upper limit on its transition probability or a lower bound on its lifetime can provide rather stringent restrictions on the parameters of these models.For the extraction of these constraints from the data a reliable calculation of the nuclear matrix elements involved is quite crucial. Since the natural final states of Ov PP decay, i.e. , the double isobaric analog (DIA) and the double Gamow-Teller (DGT) states, cannot be reached due to the limited available energy, the populated states (ground state or low-lying excited states ) are very weak. Thus the transition probability depends on fine details of nuclear structure. Thus one may have to worry about problems which are normally assumed not be be critical." In this class of problems one may include the validity of closure approximation, the short-range correlations between the nucleons, and the role of the weak magnetism term of the weak hadronic current.The closure approximation in the usual two neutrino double P decay has to be circumvented. It has, however, been assumed to be good in Ov PP decay since in this case the propagator is expected to be dominated by the virtual neutrino momentum.Nevertheless, some groups ' have not used closure in the sense that they explicitly used the intermediate nuclear states. They did not, however, use the exact energy-dependent transition operator.In this Rapid Communication we are going to employ a method...

Double-beta decay in gauge theories

“…In Quasiparticle Random Phase Approximation (QRPA) one must construct the intermediate states anyway. In any case it was explicitly shown, taking advantage of the momentum space formalism developed by Vergados [25], that this approximation is very good [26,27]. The same conclusion was reached independently by others [28].…”

Overlap of quasiparticle random-phase approximation states based on ground states of different nuclei: Mathematical properties and test calculations

“…First, we use the like-particle quasiparticle random-phase approximation (QRPA) [17] (formulation of the QRPA) [18] (application to the 0νββ decay suggested) for axially deformed nuclei, which can be applied after the closure approximation is used. This approximation has been proven to be good in the 0νββ decay by the analytical argument [11] and several realistic calculations [13,[19][20][21][22].…”

0νββ decays and shell model wave functions ofGe76andSeWu1, Cl2, Song3 1993Phys. Rev. C2050View full textAdd to dashboardCite

“…that of the 2vP/3 decay matrix elements [16]. References [7] and [10] point out that unlike the 2vPP decay, the OvPP decay matrix elements calculated by the QRPA approach are not greatly suppressed but are comparable to those of the shell model calculations.…”