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negligible mass dependence. Hence a large mass depen- dence is also not expected in the case of tritium anions. The non-relativistic Hamiltonian for the two-electron sys- tem has the form (atomic units with m$_{e}$ = 1, e = 1, ℏ = 1 are used throughout, if not specified otherwise): 

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where Z is the charge of the nucleus and r i the posi- tion vector of the i th electron. Due to the fact that the only bound state of T − is a singlet state with angular momentum L = M = 0 [19], only symmetric spatial con- figuration state functions (CSF) are important, 

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To determine the eigenstates and corresponding energy eigenvalues a simple expansion in Slater-type orbitals (STO) is used, 

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The n, l, m are integer parameters with limitations anal- ogously to the ones for the hydrogen quantum numbers and the Y m l represent the spherical harmonics. The ζ$_{i}$ are positive real parameters. An appropriate choice of these parameters allows for the achievement of an in principle complete coverage of the Hilbert space of the one-particle part of Hamiltonian (3). In the full configuration- interaction (CI) method the eigenstates are expressed as a linear superposition of all possible symmetry-adapted CSFs 

that can be formed with the aid of the chosen STO basis. The expansion coefficients c$_{jk}$ are determined by solving the generalized eigenvalue problem obtained from insert- ing the wavefunction ansatz of Eq. (6) into the eigenvalue equation of the Hamiltonian (3). 

The final-state spectrum of He is calculated within the sudden approximation [20] that is based on the fact that the escaping β electron has a much higher veloc- ity than the bound electrons. In the analysis of tritium neutrino-mass experiments like KATRIN only the β elec- trons with an energy near the endpoint of the β spectrum at 18 . 6 keV are used. Their velocity is clearly much larger than the average speed of the bound electrons in T $^{−}$. In fact, the validity of the sudden approximation has been demonstrated for T$_{2}$ in [10, 11, 21] where the first-order correction terms were derived and explicitly calculated. From those results it is apparent that also for T − the sudden approximation is expected to be valid within the accuracy required for the analysis of an experiment like 

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KATRIN. Nevertheless a brief discussion of possible ef- fects beyond the sudden approximation on the final-state spectrum is given at the end of this work. 

A basis set of 555 STOs yielding 3481 CSFs in the full CI calculation was used to obtain the final results shown in this work. This STO basis set contains all pos- sible kinds of orbitals (with restrictions on l and m as mentioned above) up to the angular quantum number l = 7 , − 7 ≤ m ≤ 7. For the optimization of the pa- rameters ζ$_{i}$ a genetic and several other algorithms [22] were tested . However, none of those algorithms lead to completely convincing results. Therefore, the parame- ters were finally optimized by hand. The difficulty of the parameter optimization is due to the requirement to con- struct a basis set with high coverage of the Hilbert space while avoiding inaccuracies due to numerically caused lin- ear dependencies. With the aim to achieve a uniform de- scription of the possible He final states it is favorable to obtain a homogeneous and a high density of states in the continuum as well as a large number of bound states. If a large number of CFSs is used, the optimization of the individual ζ$_{i}$ values becomes less important, since the full CI method leads to a sufficient mixing of the Hilbert space covered by the various STOs. Therefore, the pa- rameters ζ$_{i}$ were chosen to start in an interval between 2 and 3 and to decrease in value for increasing n (for a given l ). This procedure avoids numerical problems and allows the construction of a huge, but linearly independent ba- sis set. This basis set is used for both the ground state of T − and all final states of He . The chosen basis leads for T − to the ground-state energy E T − 0 = − 14 . 3602 eV that is only 0 . 8 meV above the very accurate values in [23, 24]. In the case of He the adopted basis set yields 16 states below the ionization continuum. Out of those 16 states 15 are identified as true physical states, while the 16th state is a pseudo state that resembles the remaining in- finite number of Rydberg states as a consequence that a finite basis set is adopted. 

Within the sudden approximation the transition prob- ability for T − decays into bound states of He is simply given by the squared overlap 

n To calculate the transition-probability density into continuum states the complex scaling method is used. It is based on the mathematical development by Aguilar, Balslev, and Combes [26, 27] as well as Simon [28]. The application of this method leads in practice to a sim- ple but powerful modification of the Hamiltonian ˆ H in Eq. (3), 

In Eq. (8) ˆ T and ˆ V are the usual kinetic and potential en- ergy operators of He, respectively. The complex-scaling 

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