Some analytic investigations of two-nucleon S matrices and wave functions

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1988

OSTI ID:6827731

Yidana, P V.A.

Models of the two-nucleon interaction have been investigated in s wave using new analytic methods. They are central interactions expressible as sums of Yukawas. The results can be related to separable expansion of potentials and to inverse scattering theory. Some rational functions methods are presented which give solutions of the homogeneous Lippmann-Schwinger equation either at bound state or antibound state energies. These solutions are used to construct an analytic unitary pole expansion of rank N for both cases. A new result is the convergence of the phase shifts and wave functions at intermediate energies, up to k = 5fm{sup {minus}1}, as the rank N approaches 13. Accurately computed phase shifts have been used to construct (i) rational S matrices and (ii) S matrices with a rational factor and an essential singularity at infinity. A powerful statistical Pade method is presented and employed in these constructions. S matrices such as these, characterized by their zeros and poles, are in a convenient form for inverse scattering theory. A new result, falling into case (ii), is that Gamow (i.e., resonance) states, identified as poles in the fourth quadrant of the momentum plane for the S matrix, occur in such large numbers for Re(k) {le} 5 fm{sup {minus}1} that Gamow separable expansions would be expected to converge slowly at intermediate energies.

• Research Organization: Rhode Island Univ., Kingston, RI (USA)
• OSTI ID: 6827731
• Country of Publication: United States
• Language: English

Related Subjects

653000* -- Nuclear Theory
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
BARYON-BARYON INTERACTIONS
CALCULATION METHODS
DATA
FUNCTIONS
HADRON-HADRON INTERACTIONS
INFORMATION
INTERACTIONS
MATHEMATICAL MODELS
NUCLEON-NUCLEON INTERACTIONS
NUMERICAL DATA
PADE APPROXIMATION
PARTIAL WAVES
PARTICLE INTERACTIONS
PHASE SHIFT
S WAVES
SCATTERING
THEORETICAL DATA
WAVE FUNCTIONS