5 nent is then obtained by fitting the model spectrum to the ab initio spectrum of the full two-electron calculation in the energy range between 500 eV and 10,000 eV. The initial T − ground-state wavefunction (omitting the spin part for better readability) is then approximated as ferent complex-scaling angles ( θ = 24 $^{◦}$, 30 $^{◦}$, and 36 $^{◦}$) in Fig. 1. The overall spectrum is practically independent of θ . This indicates the high quality of the adopted ba- sis set also for describing the electronic continuum. As is usually the case, (higher lying) resonances are most sensitive to the choice of θ . This is due to the fact that it is difficult to find a single value of θ that is equally appropriate for describing a certain resonance and the underlying background continuum. where 〈 r | 1 s $^{Z$_{e}$}$〉 is an STO with ( n, l, m ) = (1 , 0 , 0), i. e. an atomic hydrogen 1s orbital with effective charge Z$_{e}$ . In the spirit of the sudden approximation the spectator electron remains in its orbital and the final state of the He + ion is modeled as The continuum probability density is dominated by a peak corresponding to the first doubly excited singlet state 2s $^{2}$. About 19% of the T − decays ends up in the energy interval between 54 . 5 eV and 60 eV. Above the 65 . 4 eV threshold the higher-lying doubly excited states 2s n s and in the regime up to 79 eV (with diminishing im- portance) the 3s n s peaks can be identified. The complex- scaling method provides the probability density P ( E ) at any value of E and thus as a continuous function. In view of the sharp resonant structures and in accordance with the experimental needs, the final-state distribution is given in a discretized form as in [14]. For this pur- pose, the probability distribution P ( E ) has been divided into small bins covering an energy range of 1 . 0 eV (up to a transition energy of 78 . 59 eV), 5 . 0 eV (from 78 . 59 to 214 eV), and 40 . 0 eV (from 214 to 904 eV). For each bin the average excitation energy E$_{i}$ and the integrated tran- sition probability P ( E$_{i}$ ) were calculated and are given in Table II. | ˜ Ψ T − i 〉 = | 1 s $^{Z$_{e}$}$1 s $^{Z$_{e}$}$〉 (11) | ˜ Ψ $^{He}$( E ) 〉 = 2 $_{−}$1 2 ( | 1 s $^{Z$_{e}$}$φ$_{c}$ ( E ) 〉 + | φ$_{c}$ ( E )1 s $^{Z$_{e}$}$〉 ) (12) | φ$_{c}$ ( E ) 〉 is the Coulombic continuum wavefunction where | φ$_{c}$ ( E ) 〉 is the Coulombic continuum wavefunction for energy E and charge Z = +1. Using these model wavefunctions the analytic expression ˜ P ( Z$_{e}$, E ) = 2 ( 8(1 − Z$_{e}$ ) Z 3 / 2 e e − 2 arctan( κ/Z e ) κ √ 1 − e $_{−}$2 π κ ( κ 2 + Z 2 $_{e}$) 2 ) 2 dE Ry (13) with κ = √ ( E + 2) / Ry and 1Ry = 13 . 60585972 eV is obtained for the probability density, i. e. for the model tail for the high-energy continuum states. A fit to the ab initio spectrum yielded Z$_{e}$ = 1 . 3074. As is evident from (13) the probability density decays exponentially for high energies which is the most essential property. (In fact, it has been verified that all subsequent conclu- sions are unchanged, if a different model tail is used in which the initial-state charge is fixed to the one of the tritium nucleus ( Z = 1) and the effective charge of the final Coulomb wave is used as fit parameter.) For the high-energy continuum states (above 904 eV) an approximate model tail is introduced, similar to the case of T$_{2}$ [11, 14]. However, the situation is more com- plicated for T $^{−}$. In T$_{2}$ β decay the high-energy tail was derived based on the idea that for sufficiently large ener- gies of the escaping (formerly bound) electron the effec- tive potential of the remaining $^{3}$HeT2+ ion can be well approximated by a point charge Z = 2. In fact, the remaining electron and tritium nucleus may be viewed as pure spectators and thus the transition probability should approach for high energies the one obtained for a β -decaying tritium atom for which an analytical result is known. Due to the existence of two equivalent electrons, the atomic result is simply multiplied by a factor of two [11]. Fig. 2 compares the calculated final-state probability density with the analytical model tail and confirms the applicability of the latter for high energies, in fact already starting from about 200 to 250 eV, similarly as for T$_{2}$. The integrated probability density (including the model tail for energies above 904 eV) yields a total probability of 29 . 65% for ionization of He following β decay of T $^{−}$. The mean excitation energy E relative to the electronic ground-state energy of T − can be obtained from While for T$_{2}$ a hydrogenic wavefunction is a reason- able first-order approximation for the initial state, this is not the case for T $^{−}$. In fact, within independent- particle models T − is unstable. As a consequence, the fast electron in the final state may be well represented by a Coulomb wavefunction for a point charge Z = 1 (formed by the remaining He + ion), but the modeling of the initial state is less obvious within an independent particle model. This is also evident from the alternative point of view that a description of the remaining T nu- cleus and bound electron as a spectator would correspond for the active electron to an initial state with Z = 0 and thus no bound state. In order to obtain an atomic-like high-energy tail the initial state is thus modeled as a hydrogen-like state with variable exponent. This expo- Insertion of the final-state probability distribution cal- culated in this work in (14) yields E = 27 . 487eV for the mean excitation energy of the decay product. This result may be compared to the one obtained by the alternative relation E = ∑ n E$_{n}$P$_{n}$ + ∫ 904eV 24 . 59eV EP ( E ) dE + ∫ ∞ 904eV E ˜ P ( E ) dE. (14) E = 〈 Ψ T − i | ˆ H(He ) | Ψ T − i 〉 = E$_{0}$ (T $^{−}$) − 2 〈 Ψ T − i | 1 r | Ψ T − i 〉 . (15)