Two-neutrino double beta decay with operator expansion method

Matrix elements for 0??? decay calculated with the operator expansion method and QRPA wave functions

“…The OEM expression for 2vflfl decay, on the other hand, contains no comparable terms. If we reconsider the differences between the derivation of the 2v and the 0v expressions, we find that for the 2v mode there is an additional commutator in the "starting" expression (8) here, to be compared with (6) of [25]): a function of gpp always crosses zero for a specific choice of gep" From these considerations it would seem that at least the "crossing zero" of M 2v is artifical. The dear pendence of the OEM 0v results on gpp would then be caused by the use of QRPA wave functions in our numerical calculation.…”

“…The idea is to calculate 2v1313 decay half lives and compare them to experimental data. From the degree of agreement between theory and experiment one can get then some hint on the reliability of the underlying nuclear structure This is an interesting finding, since in the work of [25] it has been found that in OEM 2vfl,# decay matrix elements are only weakly dependent on the choice of gpp.…”

“…The results of this work [25], using the proton-neutron quasiparticle RPA model of [16,20] for the calculation of the nuclear wave functions, were rather surprising: matrix elements of this model seemed to be only weakly dependent on a special model parameter, the strength of the particle-particle interaction gpp, which played a crucial role in all earlier studies -using QRPA -of 2vBfl…”

“…Thus, many calculations have been restricted to the so-called closure approximation [2] In the present work we follow a radically different idea, the operator expansion method (OEM) [22][23][24]. OEM has been proposed in order to avoid the direct calculation of the intermediate states and has lately been applied to the calculation of 2v B fl decay matrix elements [25] with rather promising results. Since in the original version of OEM [22,24] (hereafter OEM 1) the derivation is rather lengthy, in the following we will rederive the OEM 1 expression for the mass mechanism in 0 v tiff decay in a more elegent way.…”

“…On the other hand, recently a novel method has been proposed for the calculation of tiff decay matrix elements which avoids both, the closure approximation as well as a direct calculation of the intermediate spectrum, the operator expansion method (OEM) [22][23][24]. OEM has also recently been combined with a state of the art calculation for the nuclear ground state wave functions for 2vflfl decay [25].…”