The Coulomb barrier transmission coefficient in nuclear reactions
Abstract
This thesis mainly deals with the Coulomb wavefunctions and their applications in a nuclear fusion theory. When two charged particles come close they interact through a Coulomb potential. As solutions of a Schrodinger equation with the Coulomb potential, we construct the regular and irregular Coulomb wavefunctions. These are used to construct the exterior wavefunctions outside a nucleus that satisfy the boundary conditions at the nuclear surface. We also derive their recurrence relations and asymptotic forms. Some forms of the Coulomb wavefunctions are useful in analytic calculations but are cumbersome in most numerical calculations. A computer code is developed to calculate the values of the Coulomb wavefunctions using power series expansions. The Coulomb wavefunctions are used to calculate the transmission coefficient which plays a crucial role in the calculation of cross sections. Several methods are used to calculate the transmission coefficient in an attempt to fit experimental data both including and excluding a resonance peak. The conventional formula for the transmission coefficient, which is widely used, will be compared with our new formulae which include a realistic nuclear potential inside a nucleus. They provide information both at the nuclear surface and in the inside of the nucleus. Our new methods may be applied to the low energy nuclear fusion reactions involved in the magnetic confinement and inertial fusions and also in astrophysical problems. The results for the nuclear reactions, $D(D, p)\sp3 He, D(D, n)T,\sp3 He(D, p)\sp4 He,T(D, n)\sp4 He,$ and $\sp7 Be(p, \gamma)\sp8 B$ are presented. All the results are consistent with the conventional results within 10%. However, our newly formulated coefficient improve the nuclear reaction data analyses by producing good fits with less physical assumptions without an arbitrary fitting parameter. In this work we confine ourselves to S-waves assuming that the energies interested are low enough to insure our confinement. Finally, it is recommended to include several more angular momentum waves. By including higher angular momentum terms, more plausible fits for the experimental data are expected.
Degree
Ph.D.
Advisors
Kim, Purdue University.
Subject Area
Nuclear physics
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