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

AbstraktAbstract

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

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