boundary

Asmptotically, for inelastic scattering, the wavefunction becomes

exp [ -i (k R -l ¼/2) ] - S exp [ i (k R - l ¼/2) ]

and, in the case of photodissociation,

exp [ -i (k R -l ¼/2) ] S - exp [ i (k R - l ¼/2) ]

This is equivalent to, in the case of inelastic scattering, to

- y_l (1 - S_r ) + j_l S_i + i [ - j_l (1 + S_r ) + y_l S_i ]

and, in the case of photodissociation, to

y_l (1 - S_r ) + j_l S_i + i [ - j_l (1 + S_r ) - y_l S_i ]

Here, j_l and y_l designate the usual Ricatti-Bessel functions [1] and S_r and S_i designate the real and imaginary parts of the S matrix.

[1] M. Abramowitz and I. Stegun, Natl. Bur. Stand. Appl. Math. Ser. 55 (1965), p. 445.