VARIATIONAL METHOD FOR SCATTERING LENGTH

Journal Article · Sun Oct 01 04:00:00 EDT 1961 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.124.130· OSTI ID:4824161

Ohmura, T

The properties of the scattering length obtained by Kohn's method, which is one of Hulthen's variational methods, arc studied by assuming a linear trial function with n adjustable parameters. The scattering length A/sup (n)/ decreases monotoiiically as the number of adjustable parameters n increases, if there is no bound state in the system. This conclusion essentially comes from the upper bound theorem of Spruch and Rosenberg. When the system has m bound states, the scattering length increases in value only m times, and otherwise decreases monotonically. Therefore, after one verifies the presence of m increases, the calculated value is certain to give an upper bound on the scattering length. The connection between the result above and the condition of Rosenberg, Spruch, and O'Malley is considered. In the Appendix comparison is made of the scattering length A/sup (n)/ obtained by Hulthen's original method and Kohn's method when m bound states exist in general. (auth)

• Research Organization: Washington Univ., St. Louis
• NSA Number: NSA-15-032643
• OSTI ID: 4824161
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 124; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BINDING ENERGY
BOUND STATE
EQUATIONS
NUMERICALS
PHYSICS
SCATTERING
VARIATIONS