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BOUNDS ON SCATTERING PHASE SHIFTS: STATIC CENTRAL POTENTIALS

Journal Article · · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D
;
It was recently shown that rigorous upper bounds on scattering lengths ran be obtained by adding to the Kohn variational expression certain integrals involving approximate wave functions for each of the negative-energy states. For potentials which vanish identically beyond a certain point, it is possible to extend the methed to positive-energy scattering; one obtains upper bounds on (-k cot?)/sup -1/, where ? is the phase shift. In addition to the negative-energy states one must consider a finite number of states with positive energies lying below the scattering energy. The states in this associated energy eigenvalue problem are defined by the imposition of certain boundary conditions on the wave functions. A second approach, involving an associated potential-strength eigenvalue problem, is used. The second method includes the first as a special case and, more significantly, can be extended to scattering by compound systems. If some states are not accounted for, a bound on cot? is not obtained; nevertheless it is still possible to obtain a rigorous lower bound on ?. Upper bounds on ? may also be obtained, but in a way which is probably not very useful for many-bedy scattering problems. (auth)
Research Organization:
New York Univ., New York
NSA Number:
NSA-15-003581
OSTI ID:
4119411
Report Number(s):
CX-49; 0031-899X
Journal Information:
Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 120; ISSN PHRVA
Country of Publication:
Country unknown/Code not available
Language:
English

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Related Subjects

EIGENVALUES
ENERGY
PHYSICS
SCATTERING