0νββ and 2νββ nuclear matrix elements evaluated in closure approximation, neutrino potentials and SU(4) symmetry

The intimate relation between the Gamow-Teller part of the matrix element M^(0ν)_(GT) and the 2νββ closure matrix element M^(2ν)_(cl) is explained and explored. If the corresponding radial dependence C^(2ν)_(cl)(r) would be known, M^(0ν) corresponding to any mechanism responsible for the 0νββ decay can be obtained as a simple integral. However, the M^(2ν)_(cl) values, and therefore also the functions C^(2ν)_(cl)(r), sensitively depend not only on the properties of the first few 1^+ states but also of higher-lying 1^+ states in the intermediate odd-odd nuclei. We show that the β^− and β^+ amplitudes of such states typically have opposite relative signs, and their contributions reduce severally the M^(2ν)_(cl) values. We suggest that demanding that M^(2ν)_(cl) = 0 is a sensible alternative way, within the QRPA method, of determining the amount of renormalization of isoscalar particle-particle interaction strength g^(T=0)_(pp). Using such prescription, the matrix elements M^(0ν) are evaluated; their values are not very different (≤ 20%) from the usual QRPA values when g^(T=0)_(pp) is related to the known 2νββ half-lives. We note that vanishing values of M^(2ν)_(cl) are signs of a partial restoration of the spin-isospin SU(4) symmetry