The Two Center Oscillator Potential with Finite Depth

Abstract

It is suggested to diagonalize the Hamilton operator of a two-or more center shell model in terms of oscillator functions concentrated around the individual centers. The method is applied to the case of a two center oscillator with finite depth.

New and efficient method for solving the eigenvalue problem for the two-center shell model with finite-depth potentials

“…( 26) the effect of finite surface diffuseness by evaluating the volume integral of the potential. We find that this is important in order to keep the depth parameter in a Woods-Saxon potential similarly to each other between 16 O and 32 S. Notice also that we interpolate the inverse of the radius parameter, 1/R, rather than the radius parameter itself. We find that this scheme is more convenient for our purpose, as, at large distances z, the interpolation with R with the volume conservation of Eq.…”

“…where V 0 ( 32 S) and R( 32 S) are the depth and the radius parameters for the 32 S nucleus, respectively, while V 0 ( 16 O) and R( 16 O) are those for the 16 O nucleus. The value of x is determined by imposing the volume conservation condition given by,…”

“…FIG. 2: (a) Neutron single-particle energies for the 16 O+ 16 O system as a function of the separation distance between the two 16 O nuclei. The solid and the dashed lines indicate the energies for the positive and the negative parity states, respectively.…”

“…The first approach is to expand singleparticle wave functions on some basis and then to obtain eigen-functions by diagonalizing the Hamiltonian matrix. For this purpose, the two-center harmonic oscillator basis [11], a deformed harmonic oscillator basis with singlecenter [6,12,13], and a non-orthogonal two-center basis [14][15][16][17] have been used. The second approach, on the other hand, is to expand each potential in a two-center potential on some basis and then to shift it with a quantum mechanical shift operator [18,19].…”

“…We apply the method in Sec. III to a system with two 16 O nuclei. To this end, we use a two-center single-particle potential with two shifted spherical Woods-Saxon potentials.…”