Atomic effects of beta decay in astrophysics and in elementary particle physics

The thesis consists mainly of two parts. The first part is a study of the bound-state {dollar}beta{dollar} decay of {dollar}sp{lcub}187{rcub}{dollar}Re and its application in Astrophysics. There existed an uncertainty in the ratio {dollar}rhosb{lcub}b{rcub}{dollar} of bound-state to continuum {dollar}beta{dollar} decay of {dollar}sp{lcub}187{rcub}{dollar}Re in both theory and experiment. A more definite theoretical result of {dollar}rhosb{lcub}b{rcub}{dollar} {dollar}approx{dollar} 1% is obtained by using single-configuration and multi-configuration Hartree-Fock-Dirac approximations. The results obtained are close to those obtained by Williams, Fowler, and Koonin by a modified Thomas-Fermi model. The bound-state {dollar}beta{dollar} decay of {dollar}sp{lcub}187{rcub}{dollar}Re at high temperatures is also studied. The second part of the thesis is a generalization of the Thomas-Fermi results of various energy contributions to the ground-state energy of a neutral atom. An analytical expression for the ratio of the electron-electron to electron-nuclear interaction is obtained by the corrected Thomas-Fermi result, the ratio obtained gives a better agreement with the Hartree-Fock numerical results.