Abstract: | One considers the total scattering cross section on the potential gV(x), x![epsi](/content/n0ht0ut48g74k575/xxlarge949.gif) m, m 3, for large values of the coupling constant g and of the wave number k. One assumes that V(x)![sim](/content/n0ht0ut48g74k575/xxlarge8764.gif) (x/|1x|)|x|– , 2 >m+1, as ¦x¦![rarr](/content/n0ht0ut48g74k575/xxlarge8594.gif) . It is shown that for gk–1 , g3–ak2(a–2) the scattering cross section is equal asymptotically to a(gk–1) , x=(m–1)( –1)–1. Here the coefficient a is determined only by the function and the number . Under the additional conditions >0, V>0, the indicated asymptotic behavior holds in the large domain gk–1 , gka–z c(gk–1) , >0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 105–136, 1986. |