Abstract
The three-body wave function built on the basis of the Gaussian function, calculated using the three-body Hamiltonian with the Pauli blocking operator is studied. As an example, the wave function of the ground state of the 9 Be was taken. Analytical expressions are presented for the overlap matrix elements of the basis function for both basic and alternative set of relative Jacobi coordinates. The correlation densities of the wave function are calculated and illustrated depending on the set of orbital quantum numbers.
Highlights
The three decades have passed since the significant large root mean square radii of the 6 He, 6 Li, 8 He, 8 Li, 9 Li, 9 Be exotic nuclei were revealed by Tanihata I. and co-workers [1]
Analytical expressions are presented for the overlap matrix elements of the basis function for both basic and alternative set of relative Jacobi coordinates
The solution of the Schrödinger equation for the few body problem is consisted in finding the factor, i.e. weight, of the matrix elements of the Hamiltonian calculated with the Gaussian functions, and, in varying the parameters of the arguments of the exponential function
Summary
The three decades have passed since the significant large root mean square radii of the 6 He, 6 Li, 8 He, 8 Li, 9 Li, 9 Be exotic nuclei were revealed by Tanihata I. and co-workers [1]. Suggesting a large deformation or a long tail in the matter distribution. These discoveries have allowed the existing science to look from a new perspective at the interaction of nucleons in atomic nuclei, and challenged already known theoretical methods. The solution of the Schrödinger equation for the few body problem is consisted in finding the factor, i.e. weight, of the matrix elements of the Hamiltonian calculated with the Gaussian functions, and, in varying the parameters of the arguments of the exponential function. It should be noted that in this method the parameters of the wave function are varied in order to obtain the minimum eigenvalue of the Hamiltonian matrix. The approach is called as Stochastic Variational Method (SVM)
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