Study of various discretization methods of the neutron-proton breakup continuum in deuteron nucleus collisions

Thesis/Dissertation · Thu Dec 31 23:00:00 EST 1981

OSTI ID:5004657

Rasoanaivo, R Y

The effect of the type of discretization of the n-p breakup continuum on the elastic deuteron nucleus scattering is studied in the absence of stripping channels. First, the diagonalization method is considered. The Hamiltonian of the n-p pair H/sub np/(r vector) is discretized by constructing its eigenstates (I = 0) in terms of a finite number N of L/sup 2/- functions generated by the operator H/sub np/(r) + w(r), where w(r) is equal to ..cap alpha..(r-r/sub 0/)/sup 2/ for r>r/sub 0/ and to zero elsewhere (r/sub 0/ and ..cap alpha.. are variable parameters). Second, the k X k method/sup 10/ is performed for three different bin sizes, K = 0.48 fm/sup -1/, 0.24 fm/sup -1/ and 0.12 f/sup -1/. Both techniques yield a finite discrete set of coupled differential equations which couple the elastic wavefunction with N-1 discretized n-p breakup c.m. wavefunction. Numerical analysis is presented in the case of deuteron incident on a /sup 58/Ni at three energies, E/sub d/ = 21.6 MeV, 45 MeV and 80 MeV. The convergence of the reflection coefficient absolute value S(L) with respect to the number of breakup channels is particularly examined. The two discretization procedures are found to give consistent results despite the slight difference in terms of speed of convergence. Also, it appears that the discretization technique is more critical for the low energy scattering than for the high energy ones. Furthermore, the effect of the long range part of the breakup coupling potentials on the elastic T-matrix is examined on both numerical and theoretical grounds. In the case of one breakup channel coupled to the elastic channel, the contribution of the tail of the potential V/sub 22/(R) to the elastic T-matrix is analytically evaluated by means of the Green's formalism. It was found that this contribution is small especially for the low partial waves. This finding is supported by numerical results. The generalization to the case of many channel coupling is also formally given.

• Research Organization: Connecticut Univ., Storrs (USA)
• OSTI ID: 5004657
• Country of Publication: United States
• Language: English

Related Subjects

651515* -- Nuclear Properties & Reactions
A=39-58
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BARYON-BARYON INTERACTIONS
BREAKUP REACTIONS
CHARGED-PARTICLE REACTIONS
DATA
DEUTERON REACTIONS
ELASTIC SCATTERING
ENERGY RANGE
HADRON-HADRON INTERACTIONS
INFORMATION
INTERACTIONS
MATRICES
MEV RANGE
MEV RANGE 10-100
NICKEL 58 TARGET
NUCLEAR REACTIONS
NUCLEON-DEUTERON INTERACTIONS
NUMERICAL DATA
NUMERICAL SOLUTION
PARTIAL WAVES
PARTICLE INTERACTIONS
PROTON-DEUTERON INTERACTIONS
SCATTERING
TARGETS
THEORETICAL DATA