Nuclear form factors and closure approximation in the study of the (μ-,e-) conversion in nuclei

The methods of studying the exotic (μ-,e-) conversion in nuclei are discussed. For the coherent process the dependence of the rate on the nuclear parameters is obtained by using shell model nuclear form factors. For the noncoher­ent processes the relevant matrix elements are calculated in the framework of the closure approximation. Finally the fraction of the transition rate of the coherent process throughout the periodic table is calculated.

Double beta decay without invoking closure

The nuclear matrix elements of PU operators entering in the 0v ßß-decay of 76Ge-->76Se have been calculated explicitly in the context of QRPA within the model space 0f7/2 - 0h11/2. T h e validity of the closure approximation has been tested and seems to be quite satisfactory for those matrix elements which are not usually suppressed. Our results indicate that they are dominated by multipoles other than 0+ and 1+ and that the matrix elements are comparable to those of shell model calculations.

Analysis of the Closure Approximation for a Class of Stochastic Differential Equations

Motivated by the numerical study of spin-boson dynamics in quantum open systems, we present a convergence analysis of the closure approximation for a class of stochastic differential equations. We show that the naive Monte Carlo simulation of the system by direct temporal discretization is not feasible through variance analysis and numerical experiments. We also show that the Wiener chaos expansion exhibits very slow convergence and high computational cost. Though efficient and accurate, the rationale of the moment closure approach remains mysterious. We rigorously prove that the low moments in the moment closure approximation of the considered model are of exponential convergence to the exact result. It is further extended to more general nonlinear problems and applied to the original spin-boson model with similar structure.