c ******************* 786 **************************** c Ref: "Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. IX. Ni XXVI and Ni XXVII for UV and X-ray modeling", Sultana N. Nahar, Astrophys. J. Suppl. 158, 80 (2005) c **************************************************** c Ni XXVIII : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: Ni XXVIII + h\nu <-> Ni XXVIII* Contents of the file (contains both LS and fine structure transitions): --------------------- i) Table 1 - Ion Information and Configuration Set: ii) LS Term Energies (Relative to the ground) iii) Transitions in pure LS coupling - Oscillator Strengths: iv) Fine Structure energies: relativistic(BP): v-a) Same Spin-Multiplicity Dipole allowed E1 (E1d) fine structure transitions v-b) Fine structure intercombination (E1i) transitions vi) Forbidden Electric Octupole E3 & Magnetic Quadrupole M2 transitions: vii) Forbidden Electric Quadrupole E2 & Magnetic Dipole M1 transitions: --------------------------------------------------------------------------- i) Table 1 - Ion Information and Configuration Set: --------------------------------------------------- Ion: nz = 28, nelc = 1 Total Number of LS terms= 10 Configuration set: 10 configurations: first 10 spectroscopic, rest 0 correlation 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f NOTE: Available observed energies are implemented Number of orbitals = 10 Scaling parameters of the orbitals: 1.00000(1s) 1.00000(2s) 1.00000(2p) 1.00000(3s) 0.00000(3p) 1.00000(3d) 1.00000(4s) 1.00000(4p) 1.00000(4d) 1.00000(4f) -------------------------------------------------------------------------- ii) LS Term Energies (Relative to the ground) ---------------------------------------------- Note: Configuration numbers are as in Table 1. LS energies: i SLP E(Rel,Ry) cfg# 1 2Se 0.000000 1 2 2Po 588.001099 3 3 2Se 588.002991 2 4 2De 696.889893 6 5 2Po 696.889954 5 6 2Se 696.889954 4 7 2Fo 735.001038 10 8 2Po 735.001038 8 9 2Se 735.001099 7 10 2De 735.002991 9 Number of first LS terms optimized = 10 -------------------------------------------------------------------------- iii) Transitions in pure LS coupling - Oscillator Strengths: ------------------------------------------------------------ Table Explanation: ------------------ LSi:CFi -> Initial LS term & configuration number as in Table 1 LSf:CFf -> Final LS term & configuration number as in Table 1 fL, fV -> oscillator strengths in length and velocity forms -------------------- Ni LSi:CFi Nf LSf:CFf Ei Ef aji(s-1) fL fV %diff 1 2Se: 1 2 2Po: 3 0.0000 588.0011 3.853E+14 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 5 2Po: 5 0.0000 696.8900 1.029E+14 7.91E-02 7.91E-02 0.0E+00 1 2Se: 1 8 2Po: 8 0.0000 735.0010 4.193E+13 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 3 2Se: 2 588.0011 588.0030 6.552E-01 1.00E-05 0.00E+00 1.0E+02 2 2Po: 3 4 2De: 6 588.0011 696.8899 3.976E+13 6.96E-01 6.96E-01 4.8E-04 2 2Po: 3 6 2Se: 4 588.0011 696.8900 3.883E+12 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 9 2Se: 7 588.0011 735.0011 1.585E+12 3.04E-03 3.05E-03 1.6E-01 2 2Po: 3 10 2De: 9 588.0011 735.0030 1.269E+13 1.22E-01 1.22E-01 1.4E-03 3 2Se: 2 5 2Po: 5 588.0030 696.8900 1.380E+13 4.35E-01 4.35E-01 0.0E+00 3 2Se: 2 8 2Po: 8 588.0030 735.0010 5.945E+12 1.03E-01 1.03E-01 4.9E-03 4 2De: 6 7 2Fo:10 696.8899 735.0010 8.479E+12 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 8 2Po: 8 696.8899 735.0010 2.137E+11 1.10E-02 1.10E-02 2.5E-06 5 2Po: 5 9 2Se: 7 696.8900 735.0011 1.129E+12 3.22E-02 3.22E-02 1.9E-06 5 2Po: 5 10 2De: 9 696.8900 735.0030 4.329E+12 6.18E-01 6.18E-01 1.6E-03 6 2Se: 4 8 2Po: 8 696.8900 735.0010 1.885E+12 4.85E-01 4.85E-01 1.0E-03 7 2Fo:10 10 2De: 9 735.0010 735.0030 4.097E+00 9.00E-05 7.14E-06 8.5E+01 8 2Po: 8 10 2De: 9 735.0010 735.0030 4.428E+00 2.40E-04 2.50E-04 2.0E+00 LS transitions: Number of oscillator strengths = 17 ----------------------------------------------------------------------------- iv) Fine Structure energies: relativistic(BP): ----------------------------------------------- Theory Expt(+Theo with 0% diff) ie SLp(cf#) 2J k*cm E(Ry) cfg SLP E(Ry) %df 1 2Se( 1) 1 0.0 0.0000E+00 1s 2000 0.0000E+00 0.0 2 2Po( 3) 1 65146016.0 5.9365E+02 2p 2011 5.9336E+02 0.0 3 2Se( 2) 1 65150172.0 5.9369E+02 2s 2000 5.9342E+02 0.0 4 2Po( 3) 3 65373044.0 5.9572E+02 2p 2011 5.9547E+02 0.0 5 2Po( 5) 1 77279888.0 7.0423E+02 3p 2011 7.0394E+02 0.0 6 2Se( 4) 1 77281192.0 7.0424E+02 3s 2000 7.0395E+02 0.0 7 2De( 6) 3 77345184.0 7.0482E+02 3d 2020 7.0456E+02 0.0 8 2Po( 5) 3 77345336.0 7.0482E+02 3p 2011 7.0456E+02 0.0 9 2De( 6) 5 77367448.0 7.0502E+02 3d 2020 7.0477E+02 0.0 10 2Po( 8) 1 81516848.0 7.4284E+02 4p 2011 7.4255E+02 0.0 11 2Se( 7) 1 81517392.0 7.4284E+02 4s 2000 7.4256E+02 0.0 12 2Po( 8) 3 81543424.0 7.4308E+02 4p 2011 7.4282E+02 0.0 13 2De( 9) 3 81543560.0 7.4308E+02 4d 2020 7.4282E+02 0.0 14 2Fo(10) 5 81552584.0 7.4316E+02 4f 2031 7.4290E+02 0.0 15 2De( 9) 5 81552816.0 7.4316E+02 4d 2020 7.4290E+02 0.0 16 2Fo(10) 7 81557256.0 7.4320E+02 4f 2031 7.4294E+02 0.0 level 2 = 2Po(J2= 1), cnf = 3 has the largest % diff= ------------------------------------------------------------------------ v-a) Same Spin-Multiplicity Dipole allowed E1 (E1d) fine structure transitions -------------------------------------------------------- Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 fij, S, aji -> Oscillator strength fij, line strengh S & transition probability aji for electic dipole E1 same-spin transition ------------------------ Nj Ni SLpCj SLpCi gj gi wl(A) Ej(Ry) Ei(Ry) fij S aji(s-1) 2 1 2Po 3 2Se 1 2 2 1.54 593.36 0.00 1.34E-01 1.354E-03 3.79E+14 3 2 2Se 2 2Po 3 2 2 15188 593.42 593.36 2.26E-04 2.255E-02 6.52E+03 4 1 2Po 3 2Se 1 4 2 1.53 595.47 0.00 2.66E-01 2.683E-03 3.79E+14 4 3 2Po 3 2Se 2 4 2 444 595.47 593.42 1.56E-02 4.559E-02 2.63E+08 5 1 2Po 5 2Se 1 2 2 1.29 703.94 0.00 2.34E-02 1.997E-04 9.32E+13 5 3 2Po 5 2Se 2 2 2 8.25 703.94 593.42 1.40E-01 7.611E-03 1.38E+13 6 2 2Se 4 2Po 3 2 2 8.24 703.95 593.36 1.20E-02 6.507E-04 1.18E+12 6 4 2Se 4 2Po 3 2 4 8.40 703.95 595.47 1.45E-02 1.608E-03 2.75E+12 6 5 2Se 4 2Po 5 2 2 91037 703.95 703.94 2.27E-04 1.358E-01 1.82E+02 7 2 2De 6 2Po 3 4 2 8.19 704.56 593.36 6.76E-01 3.649E-02 3.36E+13 7 4 2De 6 2Po 3 4 4 8.35 704.56 595.47 6.89E-02 7.584E-03 6.59E+12 7 5 2De 6 2Po 5 4 2 1469 704.56 703.94 1.78E-02 1.723E-01 2.75E+07 8 1 2Po 5 2Se 1 4 2 1.29 704.56 0.00 4.87E-02 4.150E-04 9.71E+13 8 3 2Po 5 2Se 2 4 2 8.20 704.56 593.42 2.71E-01 1.461E-02 1.34E+13 8 6 2Po 5 2Se 4 4 2 1493 704.56 703.95 2.79E-02 2.746E-01 4.17E+07 8 7 2Po 5 2De 6 4 4 671880 704.56 704.56 3.95E-06 3.529E-02 5.72E-02 9 4 2De 6 2Po 3 6 4 8.34 704.77 595.47 6.20E-01 6.812E-02 3.97E+13 9 8 2De 6 2Po 5 6 4 4338 704.77 704.56 5.42E-03 3.096E-01 1.28E+06 10 1 2Po 8 2Se 1 2 2 1.23 742.55 0.00 7.29E-03 5.892E-05 3.23E+13 10 3 2Po 8 2Se 2 2 2 6.11 742.55 593.42 2.97E-02 1.195E-03 5.31E+12 10 6 2Po 8 2Se 4 2 2 23.61 742.55 703.95 1.53E-01 2.373E-02 1.83E+12 10 7 2Po 8 2De 6 2 4 23.99 742.55 704.56 9.36E-03 2.956E-03 2.17E+11 11 2 2Se 7 2Po 3 2 2 6.11 742.56 593.36 1.69E-03 6.806E-05 3.03E+11 11 4 2Se 7 2Po 3 2 4 6.20 742.56 595.47 2.76E-03 2.249E-04 9.58E+11 11 5 2Se 7 2Po 5 2 2 23.60 742.56 703.94 2.78E-02 4.321E-03 3.33E+11 11 8 2Se 7 2Po 5 2 4 23.98 742.56 704.56 3.32E-02 1.050E-02 7.71E+11 11 10 2Se 7 2Po 8 2 2 91037 742.56 742.55 7.70E-04 4.616E-01 6.20E+02 12 1 2Po 8 2Se 1 4 2 1.23 742.82 0.00 1.58E-02 1.273E-04 3.49E+13 12 3 2Po 8 2Se 2 4 2 6.10 742.82 593.42 6.01E-02 2.415E-03 5.39E+12 12 6 2Po 8 2Se 4 4 2 23.44 742.82 703.95 2.94E-01 4.536E-02 1.78E+12 12 7 2Po 8 2De 6 4 4 23.82 742.82 704.56 1.67E-03 5.243E-04 1.97E+10 12 9 2Po 8 2De 6 4 6 23.95 742.82 704.77 1.10E-02 5.203E-03 1.92E+11 12 11 2Po 8 2Se 7 4 2 3504 742.82 742.56 4.02E-02 9.265E-01 1.09E+07 13 2 2De 9 2Po 3 4 2 6.10 742.82 593.36 1.16E-01 4.639E-03 1.04E+13 13 4 2De 9 2Po 3 4 4 6.18 742.82 595.47 1.17E-02 9.530E-04 2.04E+12 13 5 2De 9 2Po 5 4 2 23.44 742.82 703.94 5.83E-01 9.005E-02 3.54E+12 13 8 2De 9 2Po 5 4 4 23.82 742.82 704.56 6.09E-02 1.910E-02 7.16E+11 13 10 2De 9 2Po 8 4 2 3374 742.82 742.55 3.35E-02 7.440E-01 9.80E+06 13 12 2De 9 2Po 8 4 4 761313 742.82 742.82 1.57E-05 1.624E-01 1.69E-01 14 7 2Fo10 2De 6 6 4 23.77 742.90 704.56 1.01E+00 3.152E-01 7.93E+12 14 9 2Fo10 2De 6 6 6 23.90 742.90 704.77 4.81E-02 2.273E-02 5.62E+11 14 13 2Fo10 2De 9 6 4 11388 742.90 742.82 5.17E-03 7.754E-01 1.77E+05 15 4 2De 9 2Po 3 6 4 6.18 742.90 595.47 1.07E-01 8.719E-03 1.25E+13 15 8 2De 9 2Po 5 6 4 23.77 742.90 704.56 5.45E-01 1.706E-01 4.29E+12 15 12 2De 9 2Po 8 6 4 11388 742.90 742.82 8.87E-03 1.330E+00 3.04E+05 15 14 2De 9 2Fo10 6 6 421279 742.90 742.90 6.81E-06 5.738E-02 2.50E-01 16 9 2Fo10 2De 6 8 6 23.87 742.94 704.77 9.64E-01 4.545E-01 8.46E+12 16 15 2Fo10 2De 9 8 6 22794 742.94 742.90 2.45E-03 1.104E+00 2.36E+04 Number of non-zero E1 transitions = 48 (I1 = 48) Number of E1 transitions including (SD=0)= 48 Number of lines in the table = 71 v-b) Fine structure intercombination (E1i) transitions ------------------------------------------------------ Fine structure E1i intercombination transitions in Breit-Pauli approx: Ni Nj SLpCi SLpCj gi gj wl(A) Ei(Ry) Ej(Ry) fij S aji(s-1) Number of intercombination transitions, E1i = 0 ------------------------------------------------------------------------------ vi) Forbidden Electric Octupole E3 & Magnetic Quadrupole M2 transitions: ------------------------------------------------------ Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SE3, AE3 -> line strengh S & transition probability A for electic octupole E3 transition SM2, AM2 -> line strengh S & transition probability A for magnetic quadrupole M2 transition ------------------------ Ni Nj SLpCi SLpCj gi gj wl(A) SE3 AE3 SM2 AM2 s-1 s-1 9 2 2De 6 2Po 3 6 2 8.18 1.85E-04 7.92E+06 9.32E-01 6.33E+07 9 5 2De 6 2Po 5 6 2 1097 6.01E-03 3.28E-07 4.43E+00 6.90E-03 10 9 2Po 8 2De 6 2 6 24.12 3.91E-03 2.59E+05 8.30E-02 7.58E+04 14 1 2Fo10 2Se 1 6 2 1.23 5.48E-08 1.38E+09 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 6.10 1.59E-04 5.34E+07 0.00E+00 0.00E+00 14 6 2Fo10 2Se 4 6 2 23.40 1.69E-02 4.60E+05 0.00E+00 0.00E+00 14 11 2Fo10 2Se 7 6 2 2679 8.90E-02 9.39E-09 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 6.09 3.12E-06 1.05E+06 1.21E-01 3.57E+07 15 5 2De 9 2Po 5 6 2 23.39 1.54E-02 4.22E+05 2.29E+00 8.11E+05 15 10 2De 9 2Po 8 6 2 2603 2.95E-01 3.82E-08 1.90E+01 3.96E-04 16 1 2Fo10 2Se 1 8 2 1.23 7.31E-08 1.38E+09 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 6.09 2.13E-04 5.35E+07 0.00E+00 0.00E+00 16 6 2Fo10 2Se 4 8 2 23.37 2.25E-02 4.64E+05 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 23.74 6.27E-03 1.16E+05 7.69E+00 1.90E+06 16 11 2Fo10 2Se 7 8 2 2398 1.19E-01 2.05E-08 0.00E+00 0.00E+00 16 13 2Fo10 2De 9 8 4 7594 8.08E-02 4.36E-12 1.89E+01 1.40E-06 Number of transitions: E3 = 16, M2 = 8, Total E3+M2 = 24 Total number of lines of M2/E3 transitions = 16 ---------------------------------------------------------------------------- vii) Forbidden Electric Quadrupole E2 & Magnetic Dipole M1 transitions: ----------------------------------------------------- Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SE2, AE2 -> line strengh S & transition probability A for electric quadrupole E2 transition SM1, AM1 -> line strengh S & transition probability A for magnetic dipole M1 transition ------------------------ Ni Nj SLpCi SLpCj gi gj wl SE2 AE2 SM1 AM1 A s-1 s-1 3 1 2Se 2 2Se 1 2 2 1.54 0.00E+00 0.00E+00 2.12E-04 7.90E+08 4 2 2Po 3 2Po 3 4 2 431 7.56E-04 2.11E+01 1.32E+00 1.11E+05 5 2 2Po 5 2Po 3 2 2 8.24 0.00E+00 0.00E+00 6.09E-06 1.47E+05 5 4 2Po 5 2Po 3 2 4 8.40 5.66E-04 1.14E+10 1.79E-04 4.08E+06 6 1 2Se 4 2Se 1 2 2 1.29 0.00E+00 0.00E+00 6.58E-05 4.09E+08 6 3 2Se 4 2Se 2 2 2 8.24 0.00E+00 0.00E+00 2.31E-05 5.56E+05 7 1 2De 6 2Se 1 4 2 1.29 2.71E-06 3.15E+11 1.66E-06 5.17E+06 7 3 2De 6 2Se 2 4 2 8.20 2.26E-03 2.56E+10 5.27E-06 6.44E+04 7 6 2De 6 2Se 4 4 2 1493 1.73E-02 9.78E-01 2.04E-07 4.12E-04 8 2 2Po 5 2Po 3 4 2 8.19 4.99E-04 5.67E+09 7.25E-05 8.89E+05 8 4 2Po 5 2Po 3 4 4 8.35 5.50E-04 5.68E+09 9.17E-05 1.06E+06 8 5 2Po 5 2Po 5 4 2 1469 2.75E-02 1.68E+00 1.33E+00 2.82E+03 9 1 2De 6 2Se 1 6 2 1.29 4.05E-06 3.14E+11 0.00E+00 0.00E+00 9 3 2De 6 2Se 2 6 2 8.18 3.39E-03 2.59E+10 0.00E+00 0.00E+00 9 6 2De 6 2Se 4 6 2 1111 2.62E-02 4.33E+00 0.00E+00 0.00E+00 9 7 2De 6 2De 6 6 4 4338 5.84E-03 1.06E-03 2.39E+00 1.32E+02 10 2 2Po 8 2Po 3 2 2 6.11 0.00E+00 0.00E+00 1.67E-06 9.86E+04 10 4 2Po 8 2Po 3 2 4 6.20 4.22E-05 3.89E+09 4.15E-05 2.36E+06 10 5 2Po 8 2Po 5 2 2 23.60 0.00E+00 0.00E+00 1.76E-06 1.80E+03 10 8 2Po 8 2Po 5 2 4 23.99 1.13E-02 1.19E+09 1.54E-04 1.51E+05 11 1 2Se 7 2Se 1 2 2 1.23 0.00E+00 0.00E+00 7.06E-05 5.15E+08 11 3 2Se 7 2Se 2 2 2 6.11 0.00E+00 0.00E+00 9.56E-06 5.65E+05 11 6 2Se 7 2Se 4 2 2 23.60 0.00E+00 0.00E+00 5.45E-06 5.59E+03 11 7 2Se 7 2De 6 2 4 23.98 1.77E-03 1.87E+08 1.13E-09 1.10E+00 11 9 2Se 7 2De 6 2 6 24.11 2.84E-03 2.93E+08 0.00E+00 0.00E+00 12 2 2Po 8 2Po 3 4 2 6.10 2.60E-05 1.29E+09 1.29E-05 3.85E+05 12 4 2Po 8 2Po 3 4 4 6.18 4.37E-05 2.03E+09 3.04E-05 8.66E+05 12 5 2Po 8 2Po 5 4 2 23.44 9.83E-03 5.84E+08 9.94E-05 5.21E+04 12 8 2Po 8 2Po 5 4 4 23.82 1.10E-02 6.00E+08 2.72E-05 1.36E+04 12 10 2Po 8 2Po 8 4 2 3374 3.15E-01 3.02E-01 1.33E+00 2.33E+02 13 1 2De 9 2Se 1 4 2 1.23 2.24E-06 3.39E+11 1.90E-07 6.96E+05 13 3 2De 9 2Se 2 4 2 6.10 3.91E-05 1.95E+09 1.50E-06 4.47E+04 13 6 2De 9 2Se 4 4 2 23.44 3.12E-02 1.85E+09 4.96E-07 2.59E+02 13 7 2De 9 2De 6 4 4 23.82 7.16E-03 3.92E+08 1.08E-05 5.40E+03 13 9 2De 9 2De 6 4 6 23.95 3.17E-03 1.69E+08 3.54E-05 1.74E+04 13 11 2De 9 2Se 7 4 2 3504 2.53E-01 2.01E-01 1.31E-07 2.05E-05 14 2 2Fo10 2Po 3 6 2 6.09 7.27E-04 2.42E+10 0.00E+00 0.00E+00 14 4 2Fo10 2Po 3 6 4 6.18 2.15E-04 6.66E+09 1.41E-06 2.69E+04 14 5 2Fo10 2Po 5 6 2 23.39 5.76E-02 2.30E+09 0.00E+00 0.00E+00 14 8 2Fo10 2Po 5 6 4 23.77 1.70E-02 6.27E+08 2.18E-06 7.30E+02 14 10 2Fo10 2Po 8 6 2 2603 1.78E-01 4.16E-01 0.00E+00 0.00E+00 14 12 2Fo10 2Po 8 6 4 11388 5.03E-02 7.35E-05 5.23E-08 1.59E-07 15 1 2De 9 2Se 1 6 2 1.23 3.38E-06 3.41E+11 0.00E+00 0.00E+00 15 3 2De 9 2Se 2 6 2 6.10 6.14E-05 2.04E+09 0.00E+00 0.00E+00 15 6 2De 9 2Se 4 6 2 23.40 4.66E-02 1.86E+09 0.00E+00 0.00E+00 15 7 2De 9 2De 6 6 4 23.77 3.04E-03 1.12E+08 1.09E-05 3.64E+03 15 9 2De 9 2De 6 6 6 23.90 1.26E-02 4.52E+08 5.47E-05 1.80E+04 15 11 2De 9 2Se 7 6 2 2679 3.79E-01 7.68E-01 0.00E+00 0.00E+00 15 13 2De 9 2De 9 6 4 11388 9.46E-02 1.38E-04 2.40E+00 7.29E+00 16 4 2Fo10 2Po 3 8 4 6.18 1.29E-03 3.00E+10 0.00E+00 0.00E+00 16 8 2Fo10 2Po 5 8 4 23.74 1.02E-01 2.84E+09 0.00E+00 0.00E+00 16 12 2Fo10 2Po 8 8 4 7594 3.02E-01 2.51E-03 0.00E+00 0.00E+00 16 14 2Fo10 2Fo10 8 6 22794 3.22E-02 1.10E-06 3.43E+00 9.75E-01 Number of transitions: E2 = 44, M1 = 39, Total E2+M1 = 83 Total number of transitions lines (including non-spectroscopic) = 53 NT= total number of forbidden (E2,M1,E3,M2) transitions = 83 + 24 = 107 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 48 + 107 = 155