Addition theorems for spin spherical harmonics. I Preliminaries

We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II

Addition theorems for spin spherical harmonics. II Results

Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and $|s'-s|=0$, 1. We obtain also a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics

The event generator DECAY4 for simulation of double beta processes and decay of radioactive nuclei

The computer code DECAY4 is developed to generate initial energy, time and angular distributions of particles emitted in radioactive decays of nuclides and nuclear (atomic) deexcitations. Data for description of nuclear and atomic decay schemes are taken from the ENSDF and EADL database libraries. The examples of use of the DECAY4 code in several underground experiments are described.Comment: 8 pages, 1 fi