On two-sided estimates of the particle scattering amplitude by a potential and the amplitudes of multichannel processes

Functions permitting two-sided estimates to be obtained for the real and imaginary parts of the particle scattering amplitude by a nonspherical potential and for the amplitudes of multichannel processes are considered. To diminish the interval between the two estimates it is proposed to use Schwinger iteration of the test functions, whose multiparticle generalization permits estimation of the error in the approximation of P-coupled channels and the approximate assignment of the wave functions and the energy of the internal motion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 78–83, July, 1973.The author is deeply grateful to his colleagues m the Theoretical Physics Laboratory of the Joint Institute of Nuclear Research, Lkhagva Oido-Vyn' and Doctor B. N. Zakhar'ev, for formulating the problem and for useful comments which made this research realizable.