Final-state spectrum of ${}^3\mathrm{He}$ after ${\beta }^{-}$ decay of tritium anions ${\mathrm{T}}^{-}$

The final-state spectrum of $\beta$ decaying tritium anions ${\mathrm{T}}^{-}$ was calculated. The wave functions describing the initial ${\mathrm{T}}^{-}$ ground state and the final ${}^3\mathrm{He}$ states were obtained by the full configuration-interaction method. The transition probability was calculated within the sudden approximation. The transition probability into the electronic continuum was extracted from the complex-scaled resolvent and shown to converge for very high energies to an approximate analytical model probability distribution.

Figure 1

Final-state continuum probability density of $\mathrm{He}$ after $\beta$ decay of ${\mathrm{T}}^{-}$ for $\theta ={24}^{°}$(red), ${30}^{°}$(blue), and ${36}^{°}$(black). (The energy scale is given relative to the $\mathrm{He}$ ground state.)

Figure 2

Final-state continuum probability density of He after $\beta$ decay of ${\mathrm{T}}^{-}$ (solid) and a model tail with $Z_e=1.3074$ (dashed). The inset shows the probability density on a linear scale.