2-NEUTRINO DOUBLE-BETA DECAY - CRITICAL ANALYSIS

A critical analysis of various approximate schemes for calculating the matrix elements for two-neutrino double-beta decay (2 beta 2 nu decay ) is performed. The time integral representation of the 2 beta 2 nu-de cay matrix element is used for this purpose. It is shown that, within the single-particle approximation of the nuclear Hamiltonian, the 2 be ta 2 nu-decay matrix element is equal to zero because of the mutual ca ncellation of the direct and cross terms. The quasiboson approximation (QBA) and renormalized QBA (RQBA) schemes imply that the 2 beta 2 nu- decay transition operator is constant if the initial and final quasipa rticle-random-phase-approximation (QRPA) and renormalized-QRPA (RQRPA) Hamiltonians are required to be equivalent. This means that 2 beta 2 nu-decay is a higher order process in the boson expansion of the nucle ar Hamiltonian and that its higher order boson approximations are impo rtant. The equivalence of the initial and final QRPA and RQRPA Hamilto nians is discussed within the QBA and the RQBA, respectively. It is fo und that the mismatch of the two Hamiltonians becomes worse with incre asing strength of particle-particle interaction, especially in the cas e of QRPA Hamiltonians. It is assumed to be one of the factors respons ible for extreme sensitivity of the 2 beta 2 nu-decay matrix element t o the residual interaction appearing in explicit calculations involvin g an intermediate nucleus. Further, the operator expansion method (OEM ) is reconsidered, and new 2 beta 2 nu-decay transition operators are rederived in a consistent way. The validity of the OEM approximation i s discussed in respect to the other approximation schemes. The OEM, co mbined with QRPA or RQRPA ground-state wave functions, reflects sensit ively instabilities incorporated in the ground states being considered . Therefore, the predictive power of the OEM must be studied with aid of the other ground-state wave functions-for example, shell-model ones .