Ghost-Eliminating Modifications in Multipion Amplitudes: Factorization on Leading Trajectories

Abstract

The modification of B , to eliminate the ghost at alp = 0 i s investigated, The J1JZJ3 leading three-particle vertex in B , i s calculated. Using this form, it i s shown that no finite number of t e r m modification of B, without trajectory depression satisfies consistent factorization in all multipion anlplitudes. Allowing trajectory depression, although daughter levels still presumably do not factorize, a solution i s found in which (a) all leading trajectories factorize, (b) a r e nondegenerate, and (c) the ppp vertex need not be zero. We believe this to be the suitable generalization of the Lovelace 4 -r amplitude. For Voi: the double sum degenerates to a single term with b, =J,, B= J, + J, -a, and we obtain J t J +J3-ol-B-y J J J (-1/21 "' ; '= n!g!y!(J,ay)!(J,a -p)!(J3py)! 'Factorizing this form into contributions from each of the four vertices of Fig. 3, we obtain Eq. (2).

Accurate calculation of phase shifts for electron He collisions

“…Norcross's calculation is for P-wave phase shifts only. Other calculations for triplet P-wave phase shifts include the one by Jacobs (1971) using the (1s, 2s, 2p) close coupling method, the one by Oppenheimer et al (1975) using the bound-state method and the one by McGreevy and Steward (1977) using the perturbation theory. Only Khan et al (1982) and Oza (1986) did the calculation for the D-wave phase shifts, beside the S-and P-wave ones.…”