IMPROVED MINIMUM PRINCIPLE FOR SINGLE-CHANNEL SCATTERING,
Abstract
The minimum principle for single-channel scatter ing obtained previously required the introduction of channel radii for an incident relative kinetic energy E greater than zero. The channel radii, which greatly complicate the numerical calcula tions, no longer appear in recent formal theories of reations and they need not appear in the mini mum principle formulation. By projecting out all of the open-channel components from the full wave function, it is possible to eliminate the continuum states of the total Hamiltonian H originally present below E. The closed-channel Hamiltonian has only a discete spectrum below the inelastic threshold. By appropriately substract ing the contributions from the discrete portion of the spectrum, the closed-channel Hamiltonian can be used to obtain a minimum principle for k cot eta where eta is the phase shift. This min imum principle provides a rigorous criterion for determining the parameters in a trial function and for choosing among the numerical results ob tained with different trial functions. The meth od requires that one solve exactly the static approximation equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 26, 1962
- Accession Number
- AD0412535
Entities
People
- Larry Spruch
- Thomas F. O'malley
- Yukap Hahn