Narrow Results

We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The hyperfine splittings for the 2S charmonium and 1S bottomonium are calculated. The pseudoscalar and vector decay constants of the B_c meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar^-β+κr^β+V₀, with β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector parts in the form V_V(r) = -Ar^-β+(1-∊)κr^β and V_S(r) = ∊κr^β+V₀; where 0≤∊≤1. The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.

A simple phenomenological potential model is suggested to describe the interaction between the constituent quarks of meson systems. Taking the spin-dependence terms in consideration modifies some previous potential models. The resonance masses and the leptonic decay widths of , , , , and mesons are calculated using the nonrelativistic wave equation. A comparison between the present calculations and the available experimental results are given.

We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the 2S charmonium and 1S bottomonium are also calculated. Further, the pseudoscalar and vector decay constants of the B_c meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar^-β + κr^β + V₀, with β = 1, 1/2, 3/4 decomposed into scalar and vector parts in the form V_V(r) = -Ar^-β + (1-∊)κr^β and V_S(r) = ∊κr^β + V₀; where 0≤∊≤1. We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar (∊ = 1), equal mixture of scalar-vector (∊ = 1/2), and vector (∊ = 0) confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.

Masses and decay width for some heavy baryons are studied within Isgur–Wise formalism. The extended Cornell potential is employed. The hyper-radial Schrödinger equation with extended Cornell potential is solved to obtain eigenvalues of energy and baryonic wave function by using the extended iteration method. Masses and the rate of decay width for some heavy baryons are calculated. The present results are improved in comparison with other recent works and are in a good agreement with experimental data.

The half-lives of the $\alpha$ decay for even–even nuclei having $Z=62–118$ (164 nuclei) have been calculated by using the Wentzel–Kramers–Brillouin (WKB) method together Bohr–Sommerfeld (BS) quantization condition for cosh potential in two-different forms with and without the isospin effects for six different parameter sets. By comparing the obtained results with the experimental values, the rms deviations have been computed. It is obtained that when the cosh potential is used in 2 different type forms, the rms values are also changed and the better one for obtaining the half-lives is cosh-2 form. Even if the isospin-dependent potential does not have so much effect on rms values in this sort of WKB with BS calculations with cosh potential forms, considering the isospin effect together the isospin-dependent nuclear diffuseness parameter have a strong influence on the rms values. New hindrance factor formula based on liquid drop model was used in order to show the influence of hindrance factor on the $\alpha$ decay half-lives. It is pointed out that this new function of the hindrance factor does not depend on the magic numbers, it contains fewer free parameters and using of this improves the calculations positively. New estimates by using present model have also been made for even–even nuclei having with $Z=118–120$ which do not have the measured $\alpha$ decay half-lives yet and they have been compared the results of the ImSahu model. The present results would provide useful information and knowledge for the explanation of half-lives of $\alpha$ decay of nuclei and future possible experimental studies.

The reaction rates of the direct astrophysical capture processes ${}^3\mathrm{\text{He}}{(\alpha ,\gamma )}^7\mathrm{\text{Be}}$ and ${}^3\mathrm{\text{H}}{(\alpha ,\gamma )}^7\mathrm{\text{Li}}$, as well as the abundance of the ${}^7\mathrm{\text{Li}}$ element are estimated in the framework of a two-body potential model. The estimated ${}^7\mathrm{\text{Li/H}}$ abundance ratio of ${}^7\mathrm{\text{Li/H}}=(5.07\pm 0.14)\times 10^{-10}$ is in a very good agreement with the recent measurement ${}^7\mathrm{\text{Li/H}}=(5.0\pm 0.3)\times 10^{-10}$ of the LUNA collaboration.