Role of the supersymmetric semiclassical approach in barrier penetration and heavy-ion fusion

Journal Article · Tue Nov 01 04:00:00 EST 1994 · Physical Review, C (Nuclear Physics); (United States)

DOI:https://doi.org/10.1103/PhysRevC.50.2458· OSTI ID:6947605

Sil, T; Dutt, R ^[1]; Varshni, Y P ^[2]

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1. Department of Physics, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2. Department of Physics, University of Ottawa, Ottawa, Ontario, K1N 6N5 (Canada)

The problem of heavy-ion fusion reactions in the one-dimensional barrier penetration model (BPM) has been reexamined in light of supersymmetry-inspired WKB (SWKB) method. Motivated by our recent work [Phys. Lett. A 184, 209 (1994)] describing the SWKB method for the computation of the transmission coefficient [ital T]([ital E]), we have performed similar calculations for a potential barrier that mimics the proximity potential obtained by fitting experimentally measured fusion cross section [sigma][sub [ital F]]([ital E]) for the light-light and light-heavy systems. For illustration, we have first dealt with an analytically solvable potential which interpolates between two well-known nuclear barriers such as the Morse and the Eckart for two limiting values of the free parameter of the potential. Comparison of the predicted [ital T]([ital E]) with the exact analytic ones reveals that the present scheme yields consistently better results than those obtained from the WKB approximation. Furthermore, in contrast to the WKB method, analytic continuation of our SWKB transmission coefficient for the corresponding potential well (obtained through the inversion procedure) leads to exact energy eigenvalues. We have further studied the energy dependence of the total fusion cross section for different processes such as [sup 16]O+[sup 12]C,[sup 19]F+ [sup 12]C,[sup 16]O+[sup 208]Pb, and [sup 16]O with even isotopes of Sm, using a parametrized potential barrier suggested by Ahmed. The predicted cross sections are in agreement with values obtained from the WKB method and with direct experimental measurements for the beam energy near and above the Coulomb barrier. In the case of sub-barrier fusion, our results are substantially better than those given by the Hill-Wheeler parabolic approximation which overestimates [sigma][sub [ital F]]([ital E]), especially for the light-ion systems.

• OSTI ID: 6947605
• Journal Information: Physical Review, C (Nuclear Physics); (United States), Journal Name: Physical Review, C (Nuclear Physics); (United States) Vol. 50:5; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

663300 -- Nuclear Reactions & Scattering
General-- (1992-)
663450* -- Heavy-Ion-Induced Reactions & Scattering-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CARBON 12 TARGET
CHARGED-PARTICLE REACTIONS
CROSS SECTIONS
ENERGY DEPENDENCE
FLUORINE 19 REACTIONS
HEAVY ION FUSION REACTIONS
HEAVY ION REACTIONS
ISOTOPES
LEAD 208 TARGET
MORSE POTENTIAL
NUCLEAR REACTIONS
ONE-DIMENSIONAL CALCULATIONS
OXYGEN 16 REACTIONS
POTENTIALS
RARE EARTH ISOTOPES
SAMARIUM ISOTOPES
SUPERSYMMETRY
SYMMETRY
TARGETS
TRANSMISSION
WKB APPROXIMATION