Quantum gravity corrections to the mean field theory of nucleons

In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schrödinger’s equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods–Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schrödinger’s equation for the Woods–Saxon potential. We will also construct the wave function for the deformed Schrödinger’s equation.

Comparative Analysis of Woods-Saxon and Yukawa Model Nuclear Potentials

In this paper, we model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons. The single particle energy states are obtained by solving the time independent Schrodinger wave equation using matrix diagonalization method with infinite spherical well wave-functions as the basis. The best fit model parameters are obtained by using variational Monte-Carlo algorithm wherein the relative mean-squared error, christened as chi-squared value, is minimized. The universal parameters obtained using Woods-Saxon potential are found to be matched with literature reported data resulting a chi-square value of 0.066 for neutron states and 0.069 for proton states whereas the chi-square value comes out to be 1.98 and 1.57 for neutron and proton states respectively by considering Yukawa potential. To further assess the performance of both the interaction potentials, the model parameters have been optimized for three different groups, light nuclei up to 16O - 56Ni, heavy nuclei 100Sn - 208Pb and all nuclei 16O - 208Pb. It is observed that Yukawa model performed reasonably well for light nuclei but did not give satisfactory results for the other two groups while Woods-Saxon potential gives satisfactory results for all magic nuclei across the periodic table.

An investigation of alpha-transfer reaction 28Si(20Ne,16O)32S

The alpha-transfer reaction 28Si(20Ne,16O)32S at 52.3 and 70 MeV is examined by using the double-folding (DF) based on the optical model. The real part is obtained for ten different density distributions of 20Ne projectile. For the imaginary part, the Woods-Saxon potential is used. The obtained results are compared with the experimental data of alpha-transfer reaction as well as the literature results. It is seen that the results are in good agreement with the data, and are better than the literature results.

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.