Papers by Muhammad Bhatti
Physical Review A, 1986
Evaluations of parity-violating and charge-parityviolating effects in heavy one-valence-electron ... more Evaluations of parity-violating and charge-parityviolating effects in heavy one-valence-electron atoms, employing the Hartree-Fock potential and several model potentials, are extended to include first-order electron-electron Coulomb corrections using many-body perturbation theory. Parity- conserving quantities, including valence energies, hyperfine splittings, and oscillator strengths, are also calculated and compared with experiment to determine the reliability of the weak-interaction calculations. It is found that the spread between calculations carried out in first-order perturbation theory starting from different potentials is of the same order of magnitude as the spread between the corresponding lowest-order evaluations. It is concluded that second-order many-body perturbation theory must give significant contributions. Some technical problems associated with going to second order are discussed. Presumably, this spread will vanish as higher-and-higher- order perturbations are included. For this purpose we em- ploy three model potentials (described in the Appendix) together with the Hartree-Fock potential. The principal result of our first-order calculations is that there is a great deal of sensitivity to core polarization, so that the spread in values between quantities calculated in first order start- ing from different potentials ranges up to 20%, compar- able to the spread found in lowest order. While somewhat better results were obtained for excited-state properties, due to the diminished effect of core polarization, it is clear that predictions of ground-state atomic properties at a level well under 10% will require the use of second- order perturbation theory and perhaps some form of in- finite summation. During the past decade, various many-body calculations of parity violation in heavy atoms have appeared, several of which go beyond the present calculations and include second-order correlation corrections. Closest to the present approach is the calculation of Martensson- Pendrill, which is a complete first-order calculation of the parity violation in Cs starting from a Hartree-Fock potential. The first-order parity-violating matrix element in Cs based on the Hartree-Pock potential in the present paper agrees very well with the result of Ref. 7. Indeed, such agreement is expected since the principal difference between the present calculation and that of Martensson- Pendrill concerns the way in which perturbation theory is implemented. %e also mention the elegant work of Dzu- ba et aI. on Cs which also starts with a Hartree-Fock po- tential and includes both firstand second-order correla- 34 1043 Qc1986 The American Physical Society -0.162 99 -0.095 57 -0.00644 -0.10200 -O.Q93 98 -0.007 12 -0.101 11 -0.06140 -0.002 29 -0.063 70 -0.04505 -0.002 12 -0.047 16 -0.044 56 -0.002 30 -0.046 86 -0.033 45 -0.00092 -0.034 37 -0.143 43 0.003 16 -0.14027 -0.09247 0.001 71 -0.09077 -0.088 92 -0.000 13 -0.08905 -0.058 27 O.OQ046 -0.057 81 -0.043 79 0.00026 -0.043 53 -0.042 70 -0.000 19 -0.042 89 -0.032 13 0.000 16 -0.031 97 -0.15348 0.022 58 -0.13090 -0.096 15 0.009 70 -0.08645 -0.094 80 0.008 98 -0.085 82 -0.062 15 0.005 31 -0.056 84 -0,045 70 0.003 20 -0.042 51 -0.045 26 0.003 00 -0.042 26 -0.033 82 0.002 11 -0.031 72 -0.14309 0.02608 -0.11701 -0.092 23 0.012 14 -0.08009 -0.089 15 0.01025 -0.07890 -0.05901 0.00607 -0.052 95 -0.04424 0,003 91 -0.040 33 -0.043 23 0,003 43 -0.039 80 -0.032 51 0.00243 -0.03007 Norcross -0.15345 0.011 96 -0.141 49 -0.096 31 0.005 27 -0.091 04 -0.09494 0.004 64 -0.090 31 -0.061 97 0.002 79 -0.059 18 -0.045 56 0.001 58 -0.043 98 -0.045 12 0.001 42 -0.043 70 -0.033 72 0.001 09 -0.032 63 -0.143 01 0.017 63 -0.125 38 -0.092 50 0.00924 -0.083 26 -0.089 28 0.007 42 -0.081 86 -0.058 83 0.004 19 -0.054 63 -0.044 10 0.002 78 -0.041 32 -0.043 07 0.002 33 -0.040 74 -0.032 40 0.001 67 -0.030 73 HF -0.13929 -0.090 82 -0.089 99 -0.58 70 -0.043 89 -0.043 60 -0.03244 -0.127 37 -0.085 62 -0.083 79 -0.055 19 -0.04202 -0.041 37 -0.03095 Expt. ' -0.153 51 -0.096 19 -0.095 11 -0.061 77 -0.045 45 -0.045 10 -O.Q33 62 -0.143 10 -0.092 17 -0.089 64 -0.058 65 -0.043 93 -0.043 10 -0.032 30 0th 1st Sum 0th 1st Sum 0th 1st Sum 0th 1st Sum 0th 1st Sum -0.370 79 -0.01442 -0.385 20 -0.18707 0.001 22 -0.185 86 -0.15907 0.00024 -0.158 83 -0.093 83 0.001 98 -0.091 85 -0.06441 0.000 67 -0.063 74 -0.369 75 0.088 79 -0.28096 -0.171 33 0.040 32 -0.13100 -0.144 23 0.023 20 -0.121 03 -0.092 67 0.007 54 -0.085 13 -0.063 13 0.005 76 -0.057 37 -0.377 98 0.10506 -0.272 92 -0.17626 0.049 22 -0.12704 -0.148 52 0.030 32 -0.11820 -0.095 24 0.01122 -0.08402 -0.06426 0.007 77 -0.05649 -0.274 61 -0.13379 -0.121 62 -0.083 22 -0.05644 -0.33904 -0.16882 -0.15143 -0.09079 -0.065 51 'M. A.
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Papers by Muhammad Bhatti