A Binomial Congruence by Mike Swarbrick Jones

By Mike Swarbrick Jones

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J the outgoing partial wave of total spin j+: 2i A. o! (E) J {e J = e 2i o ~(E) J { + 1 i r . (E) J EC -E-ll. (E) -1/2 if . (E) J J EC 1 -E-ll. (E) +1/2 if. (E) EC 1 -E-ll. (E) -1/2 i J r. J } (63a) } (E) with ll j (E) r. J (E) (63b) ~The relation between the scattering amplitude J. and A. is given as well known by Jj 1 2i (Aj-1) J J 35 2i oj(E) where e is the phasefactor of the outgoing asymptotic wave w 0' 0 ~t(E) t without resonance scattering, ,J asymp . e. that phasefactor which near to the considered resonance belongs to potential, or background scattering.

_,. _,. v5 (3 7) 1 5

Because if one takes this repulsive core properly into account one has to include strong nuclear correlations+ for small distances (~lo- 14 em) . In atomic and molecular physics the situation is just opposite. Here the atoms and molecules can be polarized over relatively large distances because of the long range character of the Coulomb forces. This complicates the numerical calculations very much. On the other hand no extremely strong two-particle-correlatio ns exist now for small particle distances.

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