Regge, T.; Bound States, Shadow States and Mandelstam Representation
Nuovo Cim. 18 (1960) 947;
In a previous paper a technique involving complex angular momenta was used in order to prove the Mandelstam representation for potential scattering. One of the results was that the number of subtractions in the transmitted momentum depends critically on the location of the poles (shadow states) of the scattering matrix as a function of the complex orbital momentum. In this paper the study of the position of the shadow states is carried out in much greater detail. We give also related inequalities
concerning bound states and resonances. The physical interpretation of the shadow states is then discussed.
Related references See also T. Regge, Nuovo Cim. 14 (1959) 951;
A. Klein, Jour. Math. Phys. 1 (1960) 41;
R. Blankenbecler, M. L. Goldberger, M. N. Khuri, and S. B. Treiman, Ann.Phys. 10 (1960) 62;