Physical Interpretation of Anomalous Absorption of Partial Waves by Nuclear Optical Potentials

Abstract

A formula for semi-classical elastic S-matrix element has been derived by Brink and Takigawa for a potential having three turning points with a potential barrier (see [1] ) . If S, 1 denotes the S-matrix element corresponding to angular momentum l and total angular momentum j, S1 J is given, in the usual notation, by . s: {1 + N(iE;)exp(2iS32 )} Su =exp(2zu1) N(z'c) exp( 2z.8 ) , 32 (l) where N(z) is defined by N(z) = f rxp(zln(~)) and E = -i S21 . r 1 +z n If k = ~2:~£ is the wave number corresponding to a zero of semi-classical S-matrix element, it can be shown that 1 + 1 + exp(2nc) exp (2 1· s 31 ) -_ 0 N(ic) and one obtains s31 = (2n +I) H + __!__ ln(--N_(_ic_)_J 2 2i I + exp(2nc) (2) which is a necessary and sufficient condition for the semi-classical S-matrix element to be zero. Now, S U = 0 means the absence of an outgoing wave. Since the asymptotic wave boundary condition for the corresponding partial wave U U (k,r) is given by U lJ (k,r) ~ U1H (k,r)- SuUt) (k,r), (3) where U 1(- l and U j + l stand for the incoming and outgoing Coulomb wave functions respectively. A new phenomenon was discovered by M. Kawai and Y. Iresi (See[2]) in case of elastic scattering of nucleons on composite nuclei. They found that elastic S-matrix element becomes very small for special combinations of energy (E), orbital angular momentum (!), total angular momentum (j) and target nucleus. It has been found that this phenomenon is universal for light ion elastic scattering (see[3 ]). To the zero S-matrix element corresponding to this phenomenon, we have found that 2_ ln __!!ii~) __ ~ 0 both in case of deuterons scattering on nuclei and 2i 1 + exp(27r£) 4 He scattering on 40 Ni ,which means Su = (2n + 1) 7l'. It can be shown [1] that th~ S- 2 2i.~ 2iS1 matrix element can be put into the form Su :::::: _e_ + -=---z = 178 + 171 assuming that N N I e ZiS32 I :-:; I N 12 , where 17 B and 171 stand for the amplitude of the reflected wave at the external turning point and the amplitude of the reflected wave at the innermost turning point, respectively. Then it is clear that Su = 0 is due to the fact that the destructive interference of these waves in the asymptotic region.