Table A.1
The calculated E1 matrix elements (in a.u.) at different levels of approximation in the FSMRCC method using the length-gauge expression.
| Transition | DHF | RCCSD | RCCSDT | Breit | Final | MCDHF/RCI |
|---|---|---|---|---|---|---|
| 6s1/2 → 5p1/2 | 3.403 | 2.876 | 2.786 | 0.005 | 2.791(50) | 2.736 |
| 6s1/2 → 5p3/2 | 5.073 | 4.343 | 4.212 | 0.004 | 4.216(75) | 4.132 |
| 7s1/2 → 5p1/2 | 0.704 | 0.684 | 0.688 | ∼ 0.0 | 0.688(5) | 0.679 |
| 7s1/2 → 5p3/2 | 0.988 | 0.967 | 0.967 | ∼ 0.0 | 0.967(5) | 0.962 |
| 7s1/2 → 6p1/2 | 8.215 | 7.468 | 7.329 | 0.008 | 7.337(76) | 7.260 |
| 7s1/2 → 6p3/2 | 12.121 | 11.100 | 10.892 | 0.006 | 10.90(10) | 10.77 |
| 8s1/2 → 5p1/2 | 0.366 | 0.366 | 0.370 | ∼ 0.0 | 0.370(4) | 0.363 |
| 8s1/2 → 5p3/2 | 0.509 | 0.512 | 0.519 | ∼ 0.0 | 0.519(5) | 0.509 |
| 8s1/2 → 6p1/2 | 1.475 | 1.445 | 1.450 | ∼ 0.0 | 1.450(6) | 1.477 |
| 8s1/2 → 6p3/2 | 2.029 | 1.997 | 2.011 | 0.001 | 2.012(10) | 2.037 |
| 8s1/2 → 7p1/2 | 14.864 | 13.833 | 13.615 | 0.013 | 13.63(12) | 13.68 |
| 8s1/2 → 7p3/2 | 21.836 | 20.453 | 20.133 | 0.006 | 20.139(25) | 20.130 |
| 5p1/2 → 5s1/2 | 3.059 | 2.403 | 2.318 | 0.003 | 2.321(50) | 2.188 |
| 5p3/2 → 5s1/2 | 4.302 | 3.395 | 3.271 | 0.004 | 3.275(80) | 3.098 |
| 6p1/2 → 5s1/2 | 0.400 | 0.183 | 0.135 | 0.001 | 0.133(25) | 0.0816∗ |
| 6p3/2 → 5s1/2 | 0.643 | 0.342 | 0.282 | 0.001 | 0.283(23) | 0.195∗ |
| 6p1/2 → 6s1/2 | 7.673 | 7.227 | 7.202 | 0.001 | 7.203(20) | 7.127 |
| 6p3/2 → 6s1/2 | 10.691 | 10.067 | 10.040 | 0.004 | 10.044(52) | 9.945 |
| 7p1/2 → 5s1/2 | 0.174 | 0.056 | 0.031 | 0.001 | 0.032(10) | 0.0102∗ |
| 7p3/2 → 5s1/2 | 0.293 | 0.128 | 0.086 | 0.001 | 0.087(17) | 0.0305∗ |
| 7p1/2 → 6s1/2 | 1.036 | 0.865 | 0.825 | 0.003 | 0.828(30) | 0.779 |
| 7p3/2 → 6s1/2 | 1.616 | 1.395 | 1.341 | 0.001 | 1.342(21) | 1.269 |
| 7p1/2 → 7s1/2 | 13.980 | 13.522 | 13.523 | ∼ 0.0 | 13.52(12) | 13.42 |
| 7p3/2 → 7s1/2 | 19.405 | 18.747 | 18.762 | 0.003 | 18.76(15) | 18.65 |
| 5d3/2 → 5p1/2 | 5.700 | 4.540 | 4.399 | 0.009 | 4.408(43) | 4.261 |
| 5d3/2 → 5p3/2 | 2.654 | 2.145 | 2.075 | 0.002 | 2.077(53) | 2.016 |
| 5d3/2 → 6p1/2 | 11.980 | 11.773 | 11.722 | −0.001 | 11.72(10) | 11.62 |
| 5d3/2 → 6p3/2 | 5.318 | 5.240 | 5.219 | ∼ 0.0 | 5.219(86) | 5.176 |
| 5d3/2 → 7p1/2 | 1.214 | 1.799 | 1.861 | −0.008 | 1.853(25) | 1.870 |
| 5d3/2 → 7p3/2 | 0.447 | 0.689 | 0.719 | −0.002 | 0.717(12) | 0.730 |
| 5d5/2 → 5p3/2 | 7.945 | 6.416 | 6.219 | 0.009 | 6.228(16) | 6.030 |
| 5d5/2 → 6p3/2 | 16.000 | 15.769 | 15.728 | −0.002 | 15.73(12) | 15.57 |
| 5d5/2 → 7p3/2 | 1.370 | 2.108 | 2.220 | 0.008 | 2.228(20) | 2.226 |
| 6d3/2 → 5p1/2 | 2.051 | 1.805 | 1.791 | 0.002 | 1.793(51) | 1.700 |
| 6d3/2 → 5p3/2 | 0.923 | 0.824 | 0.808 | ∼ 0.0 | 0.808(28) | 0.778 |
| 6d3/2 → 6p1/2 | 9.332 | 7.657 | 7.418 | 0.018 | 7.436(69) | 7.310 |
| 6d3/2 → 6p3/2 | 4.406 | 3.671 | 3.554 | 0.005 | 3.559(47) | 3.502 |
| 6d3/2 → 7p1/2 | 24.483 | 24.176 | 24.135 | −0.001 | 24.135(67) | 24.122 |
| 6d3/2 → 7p3/2 | 10.886 | 10.777 | 10.766 | ∼ 0.0 | 10.766(41) | 11.75 |
| 6d5/2 → 5p3/2 | 2.773 | 2.474 | 2.406 | ∼ 0.0 | 2.406(22) | 2.333 |
| 6d5/2 → 6p3/2 | 13.156 | 10.936 | 10.616 | 0.018 | 10.63(11) | 10.44 |
| 6d5/2 → 7p3/2 | 32.723 | 32.407 | 32.340 | 0.003 | 32.343(22) | 32.322 |
| 4f5/2 → 5d3/2 | 16.563 | 15.704 | 15.556 | 0.002 | 15.558(30) | 15.321 |
| 4f5/2 → 6d3/2 | 23.873 | 24.109 | 24.130 | −0.001 | 24.129(38) | 24.510 |
| 4f5/2 → 5d5/2 | 4.440 | 4.213 | 4.283 | ∼ 0.0 | 4.283(46) | 4.109 |
| 4f7/2 → 5d5/2 | 19.855 | 18.842 | 18.706 | ∼ 0.0 | 18.706(45) | 18.375 |
| 4f5/2 → 6d5/2 | 6.372 | 6.434 | 6.444 | ∼ 0.0 | 6.444(55) | 6.544 |
| 4f7/2 → 6d5/2 | 28.495 | 28.772 | 28.808 | 0.001 | 28.809(86) | 29.263 |
Notes. The final results from the FSMRCC method are listed along with the estimated uncertainties and they are compared with the MCDHF/RCI calculations. The transitions with the largest relative difference for the matrix elements are marked with asterisks ∗, see text.
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