1Laboratoire de Spectrométrie lonique et Moléculaire, Centre National de la Recherche Scientifique, Laboratoire 171, Université Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cédex, France
2Laboratoire Aimé Cotton, Bât. 505, Centre National de la Recherche Scientifique, II Campus, 91405 Orsay, France
P. Ceyzeriat and M. Aymar, "Improvements to second-order lifetime calculations within the parametric potential model: application to the Al iv case," J. Opt. Soc. Am. 72, 116-125 (1982)
Dipolar electric radiative lifetimes are calculated for Al iv. The semiempirical method that associates the parametric procedure, the optimization of a central parametric potential, and a second-order calculation of the radial matrix elements of the transition operator is shown to be related in a natural way to the effective-operator formalism and to perturbation theory. In contrast to previous applications of this method, all second-order contributions are taken into account. Two types of improvement are introduced, namely, the contributions arising from the inner shells and p5 shell excitations and the contributions of the continuum. They are shown to lead to a significant decrease in the discrepancies between the dipole-length and dipole-velocity results. Furthermore, their sizes in the second-order corrections are far from negligible in most cases and can even contribute in an essential way.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
See text, Section 3.B.
Deviation Δτ/τ between the length and velocity results expressed in percentages.
Complete second-order correction.
Table 2
Relative Length–Velocity Discrepancy Mean Value and Standard Deviation over Subsets of Results and Over the Whole Set of Results within the Different Levels of Approximation in Columns a–e
Mean-Value Standard Deviation
First-Order Result
Second-Order Results with No Improvement
Second-Order Results with One Improvement
Final Results
a
b
c
d
e
10.22
6.93
0.635
1.335
2.575
σ(3s)
0.51
0.5
0.505
0.535
0.505
7.369
4.515
4.258
2.435
2.861
σ(3p)
9.661
5.765
1.494
0.430
3.864
4.008
2.853
2.07
3.805
1.114
σ(3d)
1.900
0.603
1.322
5.484
0.619
2.337
5.96
1.98
1.385
0.355
σ(4s)
1.916
5.603
1.025
0.281
0.305
2.388
6.548
6.244
1.901
0.8959
σ(4p)
2.373
2.463
6.842
0.655
0.567
3.319
2.316
0.5875
3.982
0.786
σ(4d)
1.929
0.789
0.463
5.573
0.389
3.217
1.772
1.706
1.6425
1.499
σ(4f)
1.428
0.513
1.030
0.417
0.504
1.8
7.737
3.162
1.460
0.225
σ(5s)
1.676
7.445
2.275
0.075
0.102
whole set of results
3.956
3.978
2.715
2.584
1.300
σ
4.587
3.933
3.445
3.511
1.760
Table 3
Probabilities (in nanoseconds) of Resonance Transitions from Low-Lying Excited States Calculated Using Different Methodsa
L, length; V, velocity.
a, b, and e are at the levels of approximation as noted in a, b, and e columns in Tables 1 and 2. DHF, RRPA, RPA (Ref. 27) (oscillator strength results have been converted into transition probabilities, HF (Ref. 26), and HF + second order (Ref. 28) are defined in Section 3.C.
Tables (3)
Table 1
Lifetime Results (in nanoseconds) in Five Cases Corresponding to Different Degrees of Approximation
See text, Section 3.B.
Deviation Δτ/τ between the length and velocity results expressed in percentages.
Complete second-order correction.
Table 2
Relative Length–Velocity Discrepancy Mean Value and Standard Deviation over Subsets of Results and Over the Whole Set of Results within the Different Levels of Approximation in Columns a–e
Mean-Value Standard Deviation
First-Order Result
Second-Order Results with No Improvement
Second-Order Results with One Improvement
Final Results
a
b
c
d
e
10.22
6.93
0.635
1.335
2.575
σ(3s)
0.51
0.5
0.505
0.535
0.505
7.369
4.515
4.258
2.435
2.861
σ(3p)
9.661
5.765
1.494
0.430
3.864
4.008
2.853
2.07
3.805
1.114
σ(3d)
1.900
0.603
1.322
5.484
0.619
2.337
5.96
1.98
1.385
0.355
σ(4s)
1.916
5.603
1.025
0.281
0.305
2.388
6.548
6.244
1.901
0.8959
σ(4p)
2.373
2.463
6.842
0.655
0.567
3.319
2.316
0.5875
3.982
0.786
σ(4d)
1.929
0.789
0.463
5.573
0.389
3.217
1.772
1.706
1.6425
1.499
σ(4f)
1.428
0.513
1.030
0.417
0.504
1.8
7.737
3.162
1.460
0.225
σ(5s)
1.676
7.445
2.275
0.075
0.102
whole set of results
3.956
3.978
2.715
2.584
1.300
σ
4.587
3.933
3.445
3.511
1.760
Table 3
Probabilities (in nanoseconds) of Resonance Transitions from Low-Lying Excited States Calculated Using Different Methodsa
L, length; V, velocity.
a, b, and e are at the levels of approximation as noted in a, b, and e columns in Tables 1 and 2. DHF, RRPA, RPA (Ref. 27) (oscillator strength results have been converted into transition probabilities, HF (Ref. 26), and HF + second order (Ref. 28) are defined in Section 3.C.