Method of expansion in resonance functions in nuclear physics

A problem of applying the method of expansion in resonance functions to nuclear physics tasks is discussed. The Mittag-Leffler expansion is considered for S matrix, for the Green function and for wave functions at positive energies. General view of these expansions for potentials of a finite interaction radius has been obtained. A task of using the resonance functions during investigations into one-particle resonance states of deformed nuclei and in structural calculations when continuum impurity plays a considerable role. Existing methods of accountancy of contribution of one-particle continuum states to shell corrections is described in short. It is concluded that the method of the Mittag-Leffler expansion can be used for the calculation of simple analytical expressions for S matrix, energy states in tasks of scattering and the Green functions of the one-particle task for potentials including usual nuclear potentials (spherically-symmetrical and deformed) and the Coulomb potential of repulsion