DESCRIPTION OF LOW-ENERGY STATES OF NUCLEAR ISOTOPES IN TERMS OF THE S-MATRIX POLE TRAJECTORY IN THE COMPLEX REDUCED-MASS PLANE

The analytic properties of the S matrix in the complex plane of the re duced mass mu are studied for the case of a superposition of Coulomb r epulsive and short-range attractive potentials. A physical interpretat ion of its poles for real values of the energy E is given. The thresho ld behavior of the pole mu (E) for E --> 0+ is used to obtain an appro ximate expression relating the parameters of the low-energy states of nuclear isotopes with the same spin and parity J(pi). In the case of a lpha decay this relation is the well known Geiger-Nuttall law for isot opes with fixed characteristics J(pi).