Abstract
It is shown that the Schrödinger equation for the sum of the potential of a square well and the Coulomb potential of a uniformly charged sphere admits an analytical solution for arbitrary values of the orbital angular momentum. An explicit form of this solution has been found. Using the obtained solution, the influence of the Coulomb interaction for both point and distributed nuclear charges on the values of asymptotic normalization coefficients for various nuclear systems is investigated. It is shown that taking into account the non-point distribution of the nuclear charge has little effect on the calculated values of the asymptotic normalization coefficients, provided that the binding energy of the system is assumed to be fixed.
A new technique towards finding asymptotic normalization coefficients
in the complex-ranged Gaussian basis is presented. It is shown that a
diagonalisation procedure for the total Hamiltonian matrix in the given
basis results in approximation for a radial part of the bound state wave
function from the origin up to the far asymptotic distances, which
allows to extract ANCs rather accurately. The method is illustrated by
calculations of single-particle ANCs for nuclei bound states in cases of
non-local nucleon-nucleus interactions, in particular, phenomenological
global potentials with the Perey-Buck’s non-locality.
In my presentation, I will discuss the use of transfer reactions as an indirect method of determining information important for nuclear astrophysics. Specifically, I will focus on peripheral reactions and their analysis with the Asymptotic Normalization Coefficients (ANC) method. I will present results from related experiments that have been conducted at the Cyclotron Institute, Texas A&M University with focus on the 0ptical Model Parameters obtained and the need for reliable calculations. Additionally, I will describe the im- provements in the measured data that we obtained after upgrading the detection system used.
Study of the Influence of Different Methods of Taking into Account the Coulomb Interaction on Determining Asymptotic Normalization Coefficients within the Framework of Exactly Solvable Model
