Effect of deformation on two-neutrino double beta decay matrix elements

Abstract

We study the effect of deformation on the two-neutrino double beta decay for ground state to ground state transitions in all the nuclei whose half-lives have been measured. Our theoretical framework is a deformed QRPA based in Woods-Saxon or Hartree-Fock mean fields. We are able to reproduce at the same time the main characteristics of the two single beta branches, as well as the double beta matrix elements. We find a suppression of the double beta matrix element with respect to the spherical case when the parent and daughter nuclei have different deformations.It has been observed that the matrix elements M 2ν in all the measured 2ν ββ cases for the 0 + → 0 + transition are quenched with respect to those predicted from pure quasiparticle transitions. The physical mechanisms responsible for this reduction have been a subject of great interest. In this work, we study the effect of the parent and daughter deformations on the M 2ν matrix elements.We use a deformaed quasiparticle random phase approximation (pnQRPA) to describe simultaneously the energy distributions of the single β Gamow-Teller (GT) strength and the matrix element M 2ν of all the double beta emitters whose half-lives have been measured: 48 Ca, 76 Ge, 82 Se, 96 Zr, 100 Mo, 116 Cd, 128 Te, 130 Te, 136 Xe, and 150 Nd. The formalism includes a deformed quasiparticle basis and residual spin-isospin separable interactions in both particle-hole (ph) and particle-particle (pp) channels. We consider two different deformed mean fields: a phenomenological Woods-Saxon (WS) potential and a selfconsistent Hartree-Fock (HF) with Skyrme interactions [1]. While the deformation in the HF calculation is obtained selfconsistently, in the WS case it is an input parameter taken to reproduce the experimental quadrupole moments.We describe the 2ν ββ process as two successive GT transitions via intermediate 1 + states,1

Nuclear deformation and neutrinoless double-$β$ decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd nuclei in mass mechanism

“…It is clear that when the deformations of parent and daughter nuclei are similar the NTMEs have a well defined maximum, and when the absolute value of the difference in deformation increases the NTMEs are strongly reduced, in full agreement with the results reported in [71]. In the case of 150 Nd→ 150 Sm transition, the large difference in the observed deformation parameters β 2 of parent and daughter isotopes suggests that the reduction of NTMEs is substantial.…”

“…Hence, it is clear that the deformation effects are important in case of (β − β − ) 2ν as well as (β − β − ) 0ν decay so far as the nuclear structure aspect of β − β − decay is concerned. A suppression of the double beta matrix element with respect to the spherical case has been reported when the parent and daughter nuclei have different deformations [71]. To investigate this effect we present in Fig.…”

Nuclear deformation and neutrinoless double-βdecay ofZr94,96,Chaturvedi1, Chandra2, Rath3 et al. 2008Phys. Rev. C611870View full textAdd to dashboardCite

“…It is clear that when the deformations of parent and daughter nuclei are similar the NTMEs have a well-defined maximum, and when the absolute value of the difference in deformation increases the NTMEs are strongly reduced, in full agreement with the results reported in [71]. In the case of the 150 Nd → 150 Sm transition, the large difference in the observed deformation parameters β 2 of parent and daughter isotopes suggests that the reduction of NTMEs is substantial.…”

“…Hence, it is clear that the deformation effects are important in cases of (β − β − ) 2ν as well as (β − β − ) 0ν decay so far as the nuclear structure aspect of β − β − decay is concerned. A suppression of the double beta matrix element with respect to the spherical case has been reported when the parent and daughter nuclei have different deformations [71]. To investigate this effect we present in Fig.…”

Double Beta Decay, Majorana Neutrinos, and Neutrino Mass

“…76 Ge, that they are not. Some preliminary work on ββ(2ν) with a "deformed QRPA" exists (Alvarez-Rodriguez et al, 2006;Šimkovic et al, 2003), but ββ(0ν) remains uninvestigated. With today's computers, however, there is no reason not to use a deformed QRPA.…”