Abstract
Two types of potentials are given in the present paper. The two potentials have Gaussian radial dependences. Such shapes of radial functions are suitable for using in the unitary scheme model. The first potential is given in the form of an attractive force and the second is given in the form of a superposition of repulsive and attractive forces. The two potentials are used to calculate the binding energy of the carbon nucleus 12C. For this purpose, we expand the ground-state wave function of carbon in a series of the bases of the unitary scheme model and apply the variational method. To calculate the necessary matrix elements required to obtain the binding energy of carbon, we factorized the unitary scheme model bases in the form of products of two wave functions: the first function represents the set of the A-4 nucleons and the second function represents the set of the last four nucleons by using the well-known four-body fractional parentage coefficients. Good results are obtained for the binding energy of 12C by using the two potentials.
Highlights
The ground states of nuclei with Z = N = magic number: 4He, 16C, etc. have spherical shapes with total angular momentum equals zero, spin angular momentum zero, and isotopic spin equals zero
The unitary scheme model, which is formulated by a precise application of the group theoretical methods, achieved great success in describing the ground and excited states of light nuclei by using nucleon-nucleon interactions and three-body interactions
It is of interest to investigate the behavior of the ground state of nuclei by using four-body interactions in the form of α −α interactions
Summary
Have spherical shapes with total angular momentum equals zero, spin angular momentum zero, and isotopic spin equals zero. In such nuclei, the nucleons are clustered into groups with similar features. The nucleons are clustered into groups with similar features This can be recognized from some phenomena of nuclear behavior. The fact that two protons and two neutrons in the α-particle could strongly interact played an important role in calculating the binding energy of this nucleus. The nuclear ground states would be expected to favor such quasi-α particle configurations and, exhibit large spatial symmetry
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