4 TABLE II: Discretized final-state probability distribution P ( E i ) for He following the β decay of a T − anion. The mean excitation energies E i are given relative to the ground state of $^{3}$He . 30 40 50 60 70 Energy [eV] 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Probability Density [eV -1 ] FIG. 1: (Color online) Final-state continuum probability den- sity of He after β decay of T − for θ = 24 ◦ (red), 30 ◦ (blue), and 36 ◦ (black). (The energy scale is given relative to the He ground state.) differences. The deviation is most remarkably for the first excited state that according to the present work and [17] should be populated with about 47 % probability and thus should clearly dominate the final-state distribution. However, in the MCDF results in [18] its probability is found to be about 21 %. For the other states, except n = 3, the results in [18] are always smaller than the present ones. The deviation increases rather uniformly from about 17 to 28 % for n varying between 1 and 10. Since relativistic effects are expected to be small for light nuclei like T − and $^{3}$He , it appears very likely that the main reason for the difference of the results in [18] to the present ones (as well as the ones in [17]) is due to the small number of configurations used in the MCDF method compared with the present full CI method. Un- fortunately, no details (like energies) of the MCDF cal- culation in [18] are available to further clarify this issue, but any realistic estimate of the size of relativistic effects excludes their responsibility for the large discrepancy be- tween the results in [18] compared to the non-relativistic calculations of this work or the one in [17]. The calculated transition-probability density into the electronic continuum of $^{3}$He is presented for three dif- a For energies above 904 eV the model tail in Eq. (13) was used. E i (eV) P ( E i )(%) E i (eV) P ( E i )(%) E i (eV) P ( E i )(%) E i (eV) P ( E i )(%) 25.084 0.36869 50.096 0.07054 75.086 0.09926 186.05 0.00960 26.081 0.32908 51.097 0.07403 76.085 0.09172 191.06 0.00873 27.081 0.28924 52.100 0.08005 77.085 0.08480 196.06 0.00796 28.081 0.25425 53.104 0.09041 78.086 0.07863 201.06 0.00727 29.082 0.22462 54.112 0.10943 80.950 0.31969 206.07 0.00666 30.082 0.19976 55.125 0.14982 85.967 0.23208 211.08 0.00612 31.083 0.17887 56.158 0.26863 90.980 0.17471 232.06 0.03471 32.084 0.16126 57.305 1.44117 95.991 0.13529 272.24 0.01998 33.084 0.14632 57.863 16.80345 101.00 0.10714 313.03 0.01250 34.085 0.13358 58.911 0.15914 106.01 0.08644 352.94 0.00832 35.085 0.12267 59.972 0.02281 111.01 0.07084 392.90 0.00581 36.085 0.11328 61.109 0.00924 116.02 0.05883 433.04 0.00421 37.086 0.10517 62.095 3.16161 121.02 0.04942 472.98 0.00314 38.086 0.09816 63.026 0.13662 126.03 0.04194 513.67 0.00239 39.087 0.09209 64.113 0.13095 131.03 0.03590 553.22 0.00186 40.087 0.08684 65.091 0.09512 136.03 0.03098 591.30 0.00148 41.088 0.08233 66.100 0.11217 141.03 0.02692 630.58 0.00119 42.088 0.07847 67.099 0.12245 146.04 0.02355 654.79 0.00101 43.089 0.07523 68.105 0.13639 151.04 0.02071 664.12 0.00089 44.089 0.07256 69.171 0.26130 156.04 0.01832 663.99 0.00081 45.089 0.07046 70.210 0.20446 161.04 0.01629 666.03 0.00073 46.085 0.06892 71.109 0.10126 166.05 0.01454 688.91 0.00063 47.084 0.06803 72.101 0.12307 171.05 0.01303 776.21 0.00048 48.090 0.06792 73.077 0.12211 176.05 0.01173 1550.1 a 0.00358 a 49.098 0.06870 74.083 0.10784 181.05 0.01059 ∑ P ( E i ) 29.65399