Test of bound-state approximations in a three-body model of rearrangement collisions

Journal Article · Wed Aug 01 00:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.437· OSTI ID:6089381

Greben, J M; Levin, F S

A common approximation in atomic, molecular, and nuclear rearrangement processes is to neglect n-body breakup contributions (n > or = 3) by replacing the full wave function by (sums of) product wave functions, each of which is related to a specific asymptotic arrangement channel. We test this bound-state approximation in a simple three-body model of nuclear stripping by comparing bound-state approximation calculations with exact and distorted-wave Born-approximation-type calculations. Calculated are the stripping and elastic amplitudes and cross sections for deuteron energies E/sub d/ = 1.78, 6.7, 11.2, and 15.12 MeV. The bound-state approximation is best below the breakup threshold (E/sub BU/ = 2.225 MeV), where it provides an excellent fit in the forward direction and a qualitative fit over the whole angular range. For E/sub d/ = 6.7 MeV the breakup cross section is still very small; however, the intermediate continuum states already play an important role and the bound-state approximation becomes quite poor. At this energy the distorted-wave Born approximation-type calculation, which is based on exact elastic wave functions and therefore accounts partly for the continuum, is still quite good. For the two higher energies both continuum and multistep effects appear to be very important, rendering both distorted-wave Born approximation and bound-state approximation poor approximations outside the forward region. The qualitative features of the elastic cross sections are explained in terms of the momentum dependence of the bound-state wave functions and two-body T matrices.

• Research Organization: TRIUMF and University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada
• OSTI ID: 6089381
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 20:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653001 -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AMPLITUDES
BORN APPROXIMATION
BOUND STATE
CHARGED-PARTICLE REACTIONS
CROSS SECTIONS
DEUTERON REACTIONS
DIRECT REACTIONS
DWBA
ELASTIC SCATTERING
ENERGY RANGE
FUNCTIONS
IMPULSE APPROXIMATION
MANY-BODY PROBLEM
MATRICES
MEV RANGE
MEV RANGE 01-10
MEV RANGE 10-100
NUCLEAR REACTIONS
S MATRIX
SCATTERING
SCATTERING AMPLITUDES
STRIPPING
THREE-BODY PROBLEM
TRANSFER REACTIONS
TWO-BODY PROBLEM
WAVE FUNCTIONS