Off-Energy-Shell Partial-Wave Amplitudes
- 25 August 1969
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 184 (5), 1888-1893
- https://doi.org/10.1103/physrev.184.1888
Abstract
We present dispersion relations which give the full off-energy-shell -matrix elements for all values of the parametric energy in terms of bound-state form factors, a subtraction constant, and the half-off-shell -matrix elements in the scattering () region. Study of the half-off-shell matrix for shows that it can be written as the product of a real matrix and the on-shell matrix. We combine these results to obtain a representation of the full off-energy-shell -matrix elements in terms of experimental on-shell -matrix elements, the real half-off-shell factors , a subtraction constant and bound-state form factors. Our results are based only on assumptions of time-reversal invariance, off-energy-shell unitarity, analyticity, and asymptotic behavior. The results are independent of any specific dynamical assumptions. We conclude with a discussion of the special case of uncoupled partial waves and the advantages of a separable representation of the half-off-shell factors.
Keywords
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