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

We calculated rates of ${\beta }^{-}$ decay to both continuum and bound states separately for some fully ionized (bare) atoms in the mass range $\mathrm{A}\approx 60–240$. 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 $Q$ values have been examined. We have used the latest experimental data for nuclear and atomic observables, such as ${\beta }^{-}$ decay $Q$ values, ionization energy, neutral atom ${\beta }^{-}$ decay branchings, and neutral atom half-lives. 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 a bare atom might be helpful to set a limit on the maximum enhancement due to bound state decay. Finally, ${\beta }^{-}$ decay branching for a bare atom has been calculated. The changes in branching in a bare atom compared with that in a neutral atom and for the first time branching flip for a few cases have been obtained. The 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 or flip phenomenon in bare-atom decay might be of interest for future experiments.

Figure 1

Ratio of ${\lambda }_B/{\lambda }_C$ vs the neutral atom $Q$ value $Q_n$ (in keV) for various ${\beta }^{-}$ transitions (for the radius $R_1$). The dotted curves are obtained from fitting to Eq. (16). See text for details.

Figure 2

Ratio of ${\lambda }_{\mathrm{Bare}}/{\lambda }_{\mathrm{Neutral}}$ vs the neutral-atom $Q$ value $Q_n$ (in keV) for various ${\beta }^{-}$ transitions (for the radius $R_1$). See text for details.

Figure 3

Comparison of the ${\beta }^{-}$-decay branchings for neutral and bare ${}^{136}\mathrm{Cs}$ isotopes (for the radius $R_1$).

Figure 4

Decay rates (${\mathrm{s}}^{-1}$) for neutral (${\lambda }_{\mathrm{Neutral}}$) and bare (${\lambda }_{\mathrm{Bare}}$) atoms along with all the decay components (${\lambda }_B$ and ${\lambda }_C$) of the bare atom (for the radius $R_1$) with the neutral atom $Q$-value $Q_n$ (in keV). See text for details.

Figure 5

Comparison of level branchings on neutral and bare ${}^{228}\mathrm{Ra}$ isotope (for the radius $R_1$). Left panel shows neutral atom, right panel shows bare atom.

Figure 6

${\beta }^{-}$ decay transition (${}^{95}\mathrm{Nb}, {}^{110}\mathrm{Ag}, {}^{115}\mathrm{Cd}, {}^{123}\mathrm{Sn}, {}^{134}\mathrm{Cs}$) with neutral atom branchings given [10]. Here, $T_{1/2}$ is the total half-life of the parent level (including all possible decay channels, viz. $\beta , \alpha$, IT, etc.). However, only allowed (a), first-forbidden nonunique (nu), and first-forbidden unique (u) ${\beta }^{-}$ decay transitions are shown in these figures.

Figure 7

${\beta }^{-}$ decay transition (${}^{136}\mathrm{Cs}, {}^{148}\mathrm{Pm}, {}^{152}\mathrm{Eu}, {}^{155}\mathrm{Eu}$) with neutral-atom branchings [10]. Here, $T_{1/2}$ is the total half-life of the parent level (including all possible decay channels, viz. $\beta , \alpha$, IT, etc.). However, only allowed (a), first-forbidden nonunique (nu), and first-forbidden unique (u) ${\beta }^{-}$ decay transitions are shown in these figures.

Figure 8

${\beta }^{-}$ decay transition (${}^{207}\mathrm{Tl}, {}^{228}\mathrm{Ra}, {}^{227}\mathrm{Ac}$) with neutral atom branchings [10]. Here, $T_{1/2}$ is the total half-life of the parent level (including all possible decay channels, viz. $\beta , \alpha$, IT, etc.). However, only allowed (a), first-forbidden nonunique (nu), and first-forbidden unique (u) ${\beta }^{-}$ decay transitions are shown in these figures.