Two neutrino double beta decay within the ξ-approximation

We examine the contributions of odd-parity nuclear operators to the two-neutrino double beta decay 0 → 0 amplitude, which come from the P -wave Coulomb corrections to the electron wave functions and the recoil corrections to the nuclear currents. Although they are formally of higher order in αZ/2 or v/c of the nucleon than the usual Fermi and GamowTeller matrix elements, explicit calculations performed within the QRPA show that they are significant when confronted with the experimental data. Fellow of the Fundación Antorchas and of the Universidad Nacional de La Plata. Fellow of the CONICET from Argentina. The two neutrino double beta decay (2νββ) 0 → 0 is the rarest process observed so far in nature. As such, it offers a unique opportunity for testing the nuclear physics techniques for half-lives T 2ν 1/2 ∼ (10 − 10) years [1, 2, 3, 4, 5, 6]. But, before resorting to a particular nuclear model, the expression for the 2νββ decay rate has to be figured out from the weak Hamiltonian. 1 Except for the work of Williams and Haxton [8], the allowed approximation (AA) has been universally adopted in all previous theoretical studies. This approximation is obtained in the long-wavelenth limit for the outgoing electrons and neutrinos by retaining only the Fermi (F) and Gamow-Teller (GT) operators in the nonrelativistic impulse approximation for the hadronic current J(r) = ∑