Bound and continuum state $\beta^-$ decay of bare atoms: enhancement of decay rate and changes in $\beta^{-}$ decay branching

We have calculated rates of $\beta^{-}$ decay to both continuum and bound states separately for some fully ionized (bare) atoms in the mass range A $\approx$ 60-240. One of the motivations of this work is that the previous theoretical calculations were very old and/or informatically incomplete. Probably no theoretical study on this subject has been done in the last three decades. For the calculation, we have derived a framework from the usual $\beta^{-}$ decay theory used by previous authors. Dependence of the calculated rates on the nuclear radius and neutral atom Q-value have been examined. We have used the latest experimental data for nuclear and atomic observables, such as $\beta^{-}$ decay Q-value, ionization energy, neutral atom $\beta^{-}$ decay branchings, neutral atom half-lives etc. Results of $\beta^{-}$ decay rates for decay to continuum and bound states and the enhancement factor due to the bound state decay for a number of nuclei have been tabulated and compared with the previously calculated values, if available. The effective rate or half-life calculated for bare atom might be helpful to set a limit for the maximum enhancement due to bound state decay. Finally, $\beta^{-}$ decay branching for bare atom has been calculated. The changes in branching in bare atom compared to that in the neutral atom and for the first time branching flip for a few cases have been obtained. Reason for this branching change has been understood in terms of Q-values of the transitions in the neutral and bare atoms. Verification of this branching change / flip phenomenon in bare atom decay might be of interest for future experiments.