Multiple scattering of short waves at a system of interacting particles

Abstract

where a is the l inear s ize of the par t ic les , whose m e a n d i s t a n c e apar t is d; K = 27r/X; and X is wavelength. The f i r s t condition impl ies shor t wavelengths, which gives us a kinet ic equation for the quadrat ic field par a m e t e r s . The condition d >> a r e s t r i c t s the d i scuss ion to s y s t e m s of low densi ty (gases), e . g . , the t r a n s m i s sion of Xor T rays by mat te r , l ight sca t t e r ing in the a tmosphere , and an approximat ion to the quantummechan ica l t r e a t m e n t of mult iple sca t t e r ing [1]. Pa r t i c l e in te rac t ion has been cons idered in re la t ion to the der iva t ion of mo lecu la r in te rac t ions f r o m X r a y and neut ron sca t t e r ing data [2,3], in which the s inglesca t t e r ing approximat ion was used. Here the effects a r e d i scussed for mult iple sca t t e r ing . Here the mean field is cons ide red ; a subsequent communica t ion will ,deal with m e a n s q u a r e field quant i t ies . 1. A s y s t e m of ident ical spher ica l ly s y m m e t r i c a l pa r t i c l e s fi l ls a volume V of l inear d imens ions L (V cc Ls). The posi t ion of a pa r t i c l e is defined by that of i ts cen te r rn ; then rij = I r] -r~ l, r~ = 1 r -r~ l, Oo = Ir ~u = (rj -rl)/r m l (r) is the length of the pa r t of a r a y r x Q o ( x > / O ) , within V. A plane wave r is inc i dent on pa r t i c l e rn, and the sca t t e red field at point r is defined by the sca t t e r ing ope ra to r T(rn), so the field a t ' r for an isola ted pa r t i c l e is