Theoretical wavelengths and transition probabilities for the 3S –3P and 3S –4P transitions of Na-like ions are presented. The theoretical data are computed from relativistic Hartree-Fock wave functions. Similar data for additional transitions between low-lying states (n = 3 and 4) of the Fe15+, Mo31+, W63+, and Au68+ ions are also reported. Relativistic effects in the oscillator strengths for the resonance transitions are qualitatively similar to those already observed in the Li sequence. Comparison with available experimental data on wavelengths for Fe15+ and Mo31+ ions shows excellent agreement (1% or better).
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Spectroscopic data for the sodium sequence. Dipole oscillator strengths (f), line strengths (S), and transition probabilities (A) are defined by Eqs. (5), (9), and (11), and upper and lower states are denoted by |k〉 and |i〉, respectively.
Present work based on the Hartree-Fock wave functions.
Reference 21.
Reference 20.
Reference 25.
Reference 26.
The relativistic values of the ionization potential were obtained by taking differences between the total energies of the parent and daughter ions. The nonrelativistic values were calculated from the 3s orbital energy of the parent ion.
Reference 27.
TABLE III
Spectroscopic data for Fe15+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
2.508(+02)
3.282(+02)
2.94(−01)
1.56(+10)
3P(1/2)
4S(1/2)
6.304(+01)
1.746(+01)
6.22(−02)
1.04(+11)
3P(1/2)
4D(3/2)
5.424(+01)
7.233(+01)
3.00(−01)
3.40(+11)
3P(3/2)
3D(3/2)
2.646(+02)
6.571(+01)
2.79(−02)
2.66(+09)
3P(3/2)
3D(5/2)
2.627(+02)
5.930(+02)
2.54(−01)
1.63(+10)
3P(3/2)
4S(1/2)
6.387(+01)
3.759(+01)
6.61(−02)
2.16(+11)
3P(3/2)
4D(3/2)
5.486(+01)
1.531(+01)
3.14(−02)
6.95(+10)
3P(3/2)
4D(5/2)
5.482(+01)
1.367(+02)
2.80(−01)
4.15(+11)
3D(3/2)
4P(1/2)
7.703(+01)
2.334(+01)
3.40(−02)
7.65(+10)
3D(3/2)
4P(3/2)
7.655(+01)
4.393
6.45(−03)
7.34(+09)
3D(3/2)
4F(5/2)
6.648(+01)
5.470(+02)
9.24(−01)
9.30(+11)
3D(5/2)
4P(3/2)
7.671(+01)
4.004(+01)
3.91(−02)
6.65(+10)
3D(5/2)
4F(5/2)
6.660(+01)
3.920(+01)
4.41(−02)
6.63(+10)
3D(5/2)
4F(7/2)
6.658(+01)
7.845(+02)
8.82(−01)
9.96(+11)
4S(1/2)
4P(1/2)
9.046(+02)
7.334(+02)
1.82(−01)
1.48(+09)
4S(1/2)
4P(3/2)
8.427(+02)
1.473(+03)
3.93(−01)
1.84(+09)
4P(1/2)
4D(3/2)
6.812(+02)
1.414(+03)
4.66(−01)
3.35(+09)
4P(3/2)
4D(3/2)
7.211(+02)
2.834(+02)
4.41(−02)
5.66(+08)
4P(3/2)
4D(5/2)
7.145(+02)
2.554(+03)
4.02(−01)
3.50(+09)
4D(3/2)
4F(5/2)
1.686(+03)
1.665(+03)
1.11(−01)
1.74(+08)
4D(5/2)
4F(5/2)
1.723(+03)
1.188(+02)
5.16(−03)
1.16(+07)
4D(5/2)
4F(7/2)
1.709(+03)
2.379(+03)
1.04(−01)
1.79(+08)
TABLE IV
Spectroscopic data for Mo31+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
1.042(+02)
2.200(+02)
1.82(−01)
5.58(+10)
3P(1/2)
4S(1/2)
1.651(+01)
9.237
4.82(−02)
1.18(+12)
3P(1/2)
4D(3/2)
1.502(+01)
7.042(+01)
4.04(−01)
5.97(+12)
3P(3/2)
3D(3/2)
1.344(+02)
4.387(+01)
1.40(−02)
5.19(+09)
3P(3/2)
3D(5/2)
1.269(+02)
3.989(+02)
1.35(−01)
3.73(+10)
3P(3/2)
4S(1/2)
1.712(+01)
2.309(+01)
5.81(−02)
2.64(+12)
3P(3/2)
4D(3/2)
1.552(+01)
1.615(+01)
4.48(−02)
1.24(+12)
3P(3/2)
4D(5/2)
1.547(+01)
1.420(+02)
3.95(−01)
7.34(+12)
3D(3/2)
4P(1/2)
1.875(+01)
1.018(+01)
2.34(−02)
8.87(+11)
3D(3/2)
4P(3/2)
1.845(+01)
1.655
3.86(−03)
7.57(+10)
3D(3/2)
4F(5/2)
1.706(+01)
3.773(+02)
9.52(−01)
1.45(+13)
3D(5/2)
4P(3/2)
1.860(+01)
1.575(+01)
2.43(−02)
7.03(+11)
3D(5/2)
4F(5/2)
1.719(+01)
2.725(+01)
4.55(−02)
1.03(+12)
3D(5/2)
4F(7/2)
1.717(+01)
5.464(+02)
9.14(−01)
1.55(+13)
4S(1/2)
4P(1/2)
4.256(+02)
5.244(+02)
1.06(−01)
3.91(+09)
4S(1/2)
4P(3/2)
3.108(+02)
1.065(+03)
2.95(−01)
1.02(+10)
4P(1/2)
4D(3/2)
2.731(+02)
9.480(+02)
2.99(−01)
1.34(+10)
4P(3/2)
4D(3/2)
3.579(+02)
1.896(+02)
2.28(−02)
1.19(+09)
4P(3/2)
4D(5/2)
3.347(+02)
1.718(+03)
2.21(−01)
8.77(+09)
4D(3/2)
4F(5/2)
6.172(+02)
1.067(+03)
7.44(−02)
8.69(+08)
4D(5/2)
4F(5/2)
7.008(+02)
7.591(+01)
3.11(−03)
4.22(+07)
4D(5/2)
4F(7/2)
6.639(+02)
1.525(+03)
6.59(−02)
7.48(+08)
TABLE V
Spectroscopic data for W63+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
2.211(+01)
1.681(+02)
2.11(−01)
1.44(+12)
3P(1/2)
4S(1/2)
4.013
5.801
4.01(−02)
1.66(+13)
3P(1/2)
4D(3/2)
3.666
4.863(+01)
3.68(−01)
9.13(+13)
3P(3/2)
3D(3/2)
6.619(+01)
3.318(+01)
6.95(−03)
1.06(+10)
3P(3/2)
3D(5/2)
4.563(+01)
3.108(+02)
9.44(−02)
2.02(+11)
3P(3/2)
4S(1/2)
4.565
2.484(+01)
7.55(−02)
4.83(+13)
3P(3/2)
4D(3/2)
4.121
1.551(+01)
5.22(−02)
2.05(+13)
3P(3/2)
4D(5/2)
4.072
1.294(+02)
4.41(−01)
1.18(+14)
3D(3/2)
4P(1/2)
4.773
9.679
2.81(−02)
1.65(+13)
3D(3/2)
4P(3/2)
4.508
9.206(−01)
2.83(−03)
9.29(+11)
3D(3/2)
4F(5/2)
4.283
2.938(+02)
9.51(−01)
2.31(+14)
3D(5/2)
4P(3/2)
4.651
1.042(+01)
2.07(−02)
9.58(+12)
3D(5/2)
4F(5/2)
4.412
2.182(+01)
4.57(−02)
1.57(+13)
3D(5/2)
4F(7/2)
4.386
4.411(+02)
9.30(−01)
2.42(+14)
4S(1/2)
4P(1/2)
1.806(+02)
3.943(+02)
6.06(−02)
1.24(+10)
4S(1/2)
4P(3/2)
5.596(+01)
8.305(+02)
4.12(−01)
4.38(+11)
4P(1/2)
4D(3/2)
5.544(+01)
7.230(+02)
3.62(−01)
3.93(+11)
4P(3/2)
4D(3/2)
1.752(+02)
1.444(+02)
1.14(−02)
2.48(+09)
4P(3/2)
4D(5/2)
1.155(+02)
1.335(+03)
1.60(−01)
5.34(+10)
4D(3/2)
4F(5/2)
1.679(+02)
8.092(+02)
6.68(−02)
1.05(+10)
4D(5/2)
4F(5/2)
3.326(+02)
5.693(+01)
1.58(−03)
9.54(+07)
4D(5/2)
4F(7/2)
2.325(+02)
1.159(+03)
4.61(−02)
4.27(+09)
TABLE VI
Spectroscopic data for Au68+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
1.739(+01)
1.635(+02)
2.29(−01)
2.53(+12)
3P(1/2)
4S(1/2)
3.410
5.521
3.94(−02)
2.26(+13)
3P(1/2)
4D(3/2)
3.101
4.445(+01)
3.49(−01)
1.21(+14)
3P(3/2)
3D(3/2)
6.105(+01)
3.226(+01)
6.43(−03)
1.15(+10)
3P(3/2)
3D(5/2)
3.909(+01)
3.041(+02)
9.46(−02)
2.75(+11)
3P(3/2)
4S(1/2)
3.967
2.649(+01)
8.13(−02)
6.89(+13)
3P(3/2)
4D(3/2)
3.555
1.539(+01)
5.27(−02)
2.78(+13)
3P(3/2)
4D(5/2)
3.505
1.269(+02)
4.41(−01)
1.59(+14)
3D(3/2)
4P(1/2)
4.134
1.033(+01)
3.04(−02)
2.37(+13)
3D(3/2)
4P(3/2)
3.865
8.797(−01)
2.77(−03)
1.24(+12)
3D(3/2)
4F(5/2)
3.675
2.862(+02)
9.48(−01)
3.12(+14)
3D(5/2)
4P(3/2)
4.007
1.033(+01)
2.09(−02)
1.30(+13)
3D(5/2)
4F(5/2)
3.803
2.139(+01)
4.56(−02)
2.10(+13)
3D(5/2)
4F(7/2)
3.778
4.330(+02)
9.30(−01)
3.26(+14)
4S(1/2)
4P(1/2)
1.620(+02)
3.800(+02)
5.71(−02)
1.45(+10)
4S(1/2)
4P(3/2)
4.343(+01)
8.060(+02)
4.52(−01)
7.99(+11)
4P(1/2)
4D(3/2)
4.342(+01)
7.032(+02)
3.94(−01)
6.97(+11)
4P(3/2)
4D(3/2)
1.619(+02)
1.406(+02)
1.06(−02)
2.69(+09)
4P(3/2)
4D(5/2)
9.842(+01)
1.306(+03)
1.61(−01)
7.41(+10)
4D(3/2)
4F(5/2)
1.387(+02)
7.907(+02)
6.93(−02)
1.60(+10)
4D(5/2)
4F(5/2)
3.101(+02)
5.549(+01)
1.45(−03)
1.01(+08)
4D(5/2)
4F(7/2)
2.008(+02)
1.134(+03)
4.58(−02)
5.68(+09)
TABLE VII
Comparison of wavelengths for additional lines of Fe15+.
Spectroscopic data for the sodium sequence. Dipole oscillator strengths (f), line strengths (S), and transition probabilities (A) are defined by Eqs. (5), (9), and (11), and upper and lower states are denoted by |k〉 and |i〉, respectively.
Present work based on the Hartree-Fock wave functions.
Reference 21.
Reference 20.
Reference 25.
Reference 26.
The relativistic values of the ionization potential were obtained by taking differences between the total energies of the parent and daughter ions. The nonrelativistic values were calculated from the 3s orbital energy of the parent ion.
Reference 27.
TABLE III
Spectroscopic data for Fe15+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
2.508(+02)
3.282(+02)
2.94(−01)
1.56(+10)
3P(1/2)
4S(1/2)
6.304(+01)
1.746(+01)
6.22(−02)
1.04(+11)
3P(1/2)
4D(3/2)
5.424(+01)
7.233(+01)
3.00(−01)
3.40(+11)
3P(3/2)
3D(3/2)
2.646(+02)
6.571(+01)
2.79(−02)
2.66(+09)
3P(3/2)
3D(5/2)
2.627(+02)
5.930(+02)
2.54(−01)
1.63(+10)
3P(3/2)
4S(1/2)
6.387(+01)
3.759(+01)
6.61(−02)
2.16(+11)
3P(3/2)
4D(3/2)
5.486(+01)
1.531(+01)
3.14(−02)
6.95(+10)
3P(3/2)
4D(5/2)
5.482(+01)
1.367(+02)
2.80(−01)
4.15(+11)
3D(3/2)
4P(1/2)
7.703(+01)
2.334(+01)
3.40(−02)
7.65(+10)
3D(3/2)
4P(3/2)
7.655(+01)
4.393
6.45(−03)
7.34(+09)
3D(3/2)
4F(5/2)
6.648(+01)
5.470(+02)
9.24(−01)
9.30(+11)
3D(5/2)
4P(3/2)
7.671(+01)
4.004(+01)
3.91(−02)
6.65(+10)
3D(5/2)
4F(5/2)
6.660(+01)
3.920(+01)
4.41(−02)
6.63(+10)
3D(5/2)
4F(7/2)
6.658(+01)
7.845(+02)
8.82(−01)
9.96(+11)
4S(1/2)
4P(1/2)
9.046(+02)
7.334(+02)
1.82(−01)
1.48(+09)
4S(1/2)
4P(3/2)
8.427(+02)
1.473(+03)
3.93(−01)
1.84(+09)
4P(1/2)
4D(3/2)
6.812(+02)
1.414(+03)
4.66(−01)
3.35(+09)
4P(3/2)
4D(3/2)
7.211(+02)
2.834(+02)
4.41(−02)
5.66(+08)
4P(3/2)
4D(5/2)
7.145(+02)
2.554(+03)
4.02(−01)
3.50(+09)
4D(3/2)
4F(5/2)
1.686(+03)
1.665(+03)
1.11(−01)
1.74(+08)
4D(5/2)
4F(5/2)
1.723(+03)
1.188(+02)
5.16(−03)
1.16(+07)
4D(5/2)
4F(7/2)
1.709(+03)
2.379(+03)
1.04(−01)
1.79(+08)
TABLE IV
Spectroscopic data for Mo31+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
1.042(+02)
2.200(+02)
1.82(−01)
5.58(+10)
3P(1/2)
4S(1/2)
1.651(+01)
9.237
4.82(−02)
1.18(+12)
3P(1/2)
4D(3/2)
1.502(+01)
7.042(+01)
4.04(−01)
5.97(+12)
3P(3/2)
3D(3/2)
1.344(+02)
4.387(+01)
1.40(−02)
5.19(+09)
3P(3/2)
3D(5/2)
1.269(+02)
3.989(+02)
1.35(−01)
3.73(+10)
3P(3/2)
4S(1/2)
1.712(+01)
2.309(+01)
5.81(−02)
2.64(+12)
3P(3/2)
4D(3/2)
1.552(+01)
1.615(+01)
4.48(−02)
1.24(+12)
3P(3/2)
4D(5/2)
1.547(+01)
1.420(+02)
3.95(−01)
7.34(+12)
3D(3/2)
4P(1/2)
1.875(+01)
1.018(+01)
2.34(−02)
8.87(+11)
3D(3/2)
4P(3/2)
1.845(+01)
1.655
3.86(−03)
7.57(+10)
3D(3/2)
4F(5/2)
1.706(+01)
3.773(+02)
9.52(−01)
1.45(+13)
3D(5/2)
4P(3/2)
1.860(+01)
1.575(+01)
2.43(−02)
7.03(+11)
3D(5/2)
4F(5/2)
1.719(+01)
2.725(+01)
4.55(−02)
1.03(+12)
3D(5/2)
4F(7/2)
1.717(+01)
5.464(+02)
9.14(−01)
1.55(+13)
4S(1/2)
4P(1/2)
4.256(+02)
5.244(+02)
1.06(−01)
3.91(+09)
4S(1/2)
4P(3/2)
3.108(+02)
1.065(+03)
2.95(−01)
1.02(+10)
4P(1/2)
4D(3/2)
2.731(+02)
9.480(+02)
2.99(−01)
1.34(+10)
4P(3/2)
4D(3/2)
3.579(+02)
1.896(+02)
2.28(−02)
1.19(+09)
4P(3/2)
4D(5/2)
3.347(+02)
1.718(+03)
2.21(−01)
8.77(+09)
4D(3/2)
4F(5/2)
6.172(+02)
1.067(+03)
7.44(−02)
8.69(+08)
4D(5/2)
4F(5/2)
7.008(+02)
7.591(+01)
3.11(−03)
4.22(+07)
4D(5/2)
4F(7/2)
6.639(+02)
1.525(+03)
6.59(−02)
7.48(+08)
TABLE V
Spectroscopic data for W63+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
2.211(+01)
1.681(+02)
2.11(−01)
1.44(+12)
3P(1/2)
4S(1/2)
4.013
5.801
4.01(−02)
1.66(+13)
3P(1/2)
4D(3/2)
3.666
4.863(+01)
3.68(−01)
9.13(+13)
3P(3/2)
3D(3/2)
6.619(+01)
3.318(+01)
6.95(−03)
1.06(+10)
3P(3/2)
3D(5/2)
4.563(+01)
3.108(+02)
9.44(−02)
2.02(+11)
3P(3/2)
4S(1/2)
4.565
2.484(+01)
7.55(−02)
4.83(+13)
3P(3/2)
4D(3/2)
4.121
1.551(+01)
5.22(−02)
2.05(+13)
3P(3/2)
4D(5/2)
4.072
1.294(+02)
4.41(−01)
1.18(+14)
3D(3/2)
4P(1/2)
4.773
9.679
2.81(−02)
1.65(+13)
3D(3/2)
4P(3/2)
4.508
9.206(−01)
2.83(−03)
9.29(+11)
3D(3/2)
4F(5/2)
4.283
2.938(+02)
9.51(−01)
2.31(+14)
3D(5/2)
4P(3/2)
4.651
1.042(+01)
2.07(−02)
9.58(+12)
3D(5/2)
4F(5/2)
4.412
2.182(+01)
4.57(−02)
1.57(+13)
3D(5/2)
4F(7/2)
4.386
4.411(+02)
9.30(−01)
2.42(+14)
4S(1/2)
4P(1/2)
1.806(+02)
3.943(+02)
6.06(−02)
1.24(+10)
4S(1/2)
4P(3/2)
5.596(+01)
8.305(+02)
4.12(−01)
4.38(+11)
4P(1/2)
4D(3/2)
5.544(+01)
7.230(+02)
3.62(−01)
3.93(+11)
4P(3/2)
4D(3/2)
1.752(+02)
1.444(+02)
1.14(−02)
2.48(+09)
4P(3/2)
4D(5/2)
1.155(+02)
1.335(+03)
1.60(−01)
5.34(+10)
4D(3/2)
4F(5/2)
1.679(+02)
8.092(+02)
6.68(−02)
1.05(+10)
4D(5/2)
4F(5/2)
3.326(+02)
5.693(+01)
1.58(−03)
9.54(+07)
4D(5/2)
4F(7/2)
2.325(+02)
1.159(+03)
4.61(−02)
4.27(+09)
TABLE VI
Spectroscopic data for Au68+. See Table I for legends.
Transition
Wavelength (Å)
Z2S (a.u.)
f
A (1/s)
|i〉
|k〉
3P(1/2)
3D(3/2)
1.739(+01)
1.635(+02)
2.29(−01)
2.53(+12)
3P(1/2)
4S(1/2)
3.410
5.521
3.94(−02)
2.26(+13)
3P(1/2)
4D(3/2)
3.101
4.445(+01)
3.49(−01)
1.21(+14)
3P(3/2)
3D(3/2)
6.105(+01)
3.226(+01)
6.43(−03)
1.15(+10)
3P(3/2)
3D(5/2)
3.909(+01)
3.041(+02)
9.46(−02)
2.75(+11)
3P(3/2)
4S(1/2)
3.967
2.649(+01)
8.13(−02)
6.89(+13)
3P(3/2)
4D(3/2)
3.555
1.539(+01)
5.27(−02)
2.78(+13)
3P(3/2)
4D(5/2)
3.505
1.269(+02)
4.41(−01)
1.59(+14)
3D(3/2)
4P(1/2)
4.134
1.033(+01)
3.04(−02)
2.37(+13)
3D(3/2)
4P(3/2)
3.865
8.797(−01)
2.77(−03)
1.24(+12)
3D(3/2)
4F(5/2)
3.675
2.862(+02)
9.48(−01)
3.12(+14)
3D(5/2)
4P(3/2)
4.007
1.033(+01)
2.09(−02)
1.30(+13)
3D(5/2)
4F(5/2)
3.803
2.139(+01)
4.56(−02)
2.10(+13)
3D(5/2)
4F(7/2)
3.778
4.330(+02)
9.30(−01)
3.26(+14)
4S(1/2)
4P(1/2)
1.620(+02)
3.800(+02)
5.71(−02)
1.45(+10)
4S(1/2)
4P(3/2)
4.343(+01)
8.060(+02)
4.52(−01)
7.99(+11)
4P(1/2)
4D(3/2)
4.342(+01)
7.032(+02)
3.94(−01)
6.97(+11)
4P(3/2)
4D(3/2)
1.619(+02)
1.406(+02)
1.06(−02)
2.69(+09)
4P(3/2)
4D(5/2)
9.842(+01)
1.306(+03)
1.61(−01)
7.41(+10)
4D(3/2)
4F(5/2)
1.387(+02)
7.907(+02)
6.93(−02)
1.60(+10)
4D(5/2)
4F(5/2)
3.101(+02)
5.549(+01)
1.45(−03)
1.01(+08)
4D(5/2)
4F(7/2)
2.008(+02)
1.134(+03)
4.58(−02)
5.68(+09)
TABLE VII
Comparison of wavelengths for additional lines of Fe15+.