ABSTRACT
Goeppert-Mayer [133] was the first in 1935, following the suggestion of Wigner, to predict that two neutrino double beta decay (2νDBD) half-lives could be > 1020 yr. This process corresponds to (Z,A) −→ (Z+2,A) + e−1 +e
− 2 +νe1 +νe2 . Soon after this, in 1937 following the fundamental sugges-
tion of Majorana [134], Racah [135] pointed out the possibility of neutrinoless double beta decay, hereafter called 0νββ or 0ν DBD or NDBD. This process corresponds to (Z,A) −→ (Z+2,A) + e−1 + e−2 . Furry [136] in 1939, for the first time studied 0ν DBD half-lives. The neutrinoless double beta decay which involves emission of two electrons without the accompanying neutrinos and which violates lepton number conservation has obvious fundamental significance, and it is a challenging problem both for the experimentalists and theoreticians. Recent neutrino oscillation experiments have demonstrated that neutrinos have mass, leading to the Nobel prize in 2015 [137, 138]. The observation of 0νββ decay is expected to provide information regarding the absolute neutrino mass which is not known. To extract neutrino mass, the nuclear transition matrix elements (NTME) must be known from a reliable nuclear model and hence the main goal of nuclear theorists is to calculate the needed NTME as reliably as possible. On the other hand experimental programs have been initiated at different laboratories across the globe to observe this decay and the experiments are already in advanced stages of development. The most recent experimental results for 0νββ decay of 136Xe have been reported by KamLAND-Zen collaboration [139] and EXO 200 collaboration [140] and they give a lower limit of 3.4× 1025 yr for the half-life. On the other hand, phase I results from GERDA experiment [141] for 76Ge gave a lower limit of 3.0×1025 yr for the half-life. Thus, till today NDBD is still not observed.
