The document describes energy levels, radiative rates, and collision strengths for electron impact excitation of hydrogen-like, helium-like, and lithium-like ions with atomic numbers Z ≤ 30. It provides tables of calculated energy levels from various structure codes and compares them to experimental values from NIST. It also lists applications of these data to astrophysical, solar, lasing, and fusion plasmas and describes common structure and scattering codes used to perform the calculations.
Electron impact excitation of H-like, He-like and Li-like ions with Z ≤ 30
1. ELECTRON IMPACT EXCITATION OF H-LIKE,
He-LIKE and Li-LIKE IONS WITH Z ≤ 30
KANTI M. AGGARWAL
Astrophysics Research Centre
Queen’s University Belfast
BELFAST BT7 1NN
Northern Ireland, UK
15 December 2011
2. ATOMIC PARAMETERS
• ENERGY LEVELS
Ej − Ei = hνij = hc/λij
• RADIATIVE RATES (A, s−1 ),
OSCILLATOR STRENGTHS (f, dimensionless),
LINE STRENGTHS (S, a.u.)
mc 2 ωj
fi,j = 8π 2 e2 λji ωi Aji = 1.49 × 10−16 λ2 (ωj /ωi )Aji
ij
2.0261×1018 303.75
E1: Aji = ωj λ3 S and fij = λji ωi S,
ji
1.1199×1018
E2: Aji = ωj λ5 S and fij = 167.89 S,
λ3 ω i
ji ji
2.6974×1013 4.044×10−3
M1: Aji = ωj λ3 S and fij = λji ωi S,
ji
1.4910×1013
fij = 2.236×10
−3
M2: Aji = ωj λ5 S and 3 ω
λji i S.
ji
λ is in ˚.
A
• LIFE-TIME
τj = 1Aji
i
• COLLISION STRENGTHS (CROSS SECTIONS)
Ωij (E) = ki 2 ωi σij (πa0 2 )
3. • EFFECTIVE COLLISION STRENGTHS (RATE COEFFICIENTS)
−Ej /kTe
Υ(Te ) = 0 Ωe
∞
d(Ej /kTe )
8.63×10−6 −Eij /kTe
qij = ωi Te 1/2
e Υij cm3 /s
qji = 8.63×10 Υij cm3 /s
−6
ω T 1/2
j e
• LINE INTENSITY RATIO
n L
Iji =Aji Nj NA,Z NA hνji 1+NHe 4π ergs cm−2 s−1 sr−1
I(λij ) Aji λmn Nj
R= I(λmn ) = Anm λij Nn
10. fig.3
(a)
100
3p3/2 – 3d5/2
Ω
50
5g7/2 – 5f7/2
0
0 200 400 600
Ej (Ryd)
10
(b)
3p3/2 – 3d5/2
Ω
5
5g7/2 – 5f7/2
0
0 2000 4000 6000
Ej (Ryd)
Figure 3: Comparison of collision strengths (Ω) with scattered energy (E j ) for the 3p3/2 - 3d5/2 and 5g7/2 - 5f7/2 transitions of
(a) O VIII and (b) Ni XXVIII. Continuous and broken curves are from CB and circles and stars are from FAC.
13
11. fig. 4
(a)
100
3p3/2 – 3d5/2
50
Effective collision strength
5g7/2 – 5f7/2
0
104 105 106 107 108
Te (K)
6
(b)
4 3p3/2 – 3d5/2
2
5g7/2 – 5f7/2
0
104 105 106 107 108
Te (K)
Figure 4: Comparison of effective collision strengths (Υ) for the 3p3/2 - 3d5/2 and 5g7/2 - 5f7/2 transitions of (a) O VIII and (b)
Ni XXVIII. Continuous and broken curves are from CB and FAC, respectively.
14
12. Figure 2: Comparison of collision strengths from our calculations from darc (continuous curves) and
fac (broken curves) for the 2–6 (circles: 1s2s 3 S1 - 1s2p 3 Po ), 4–14 (triangles: 1s2p 3 Po - 1s3d 3 D2 ),
2 1
and 10–24 (stars: 1s3p 3 Po - 1s4d 3 D2 ) allowed transitions of Cl XVI.
1
Figure 3: Comparison of collision strengths from our calculations from darc (continuous curves) and
fac (broken curves) for the 2–8 (circles: 1s2s 3 S1 - 1s3s 3 S1 ), 2–15 (triangles: 1s2s 3 S1 - 1s3d 3 D3 ), and
4–10 (stars: 1s2p 3 Po - 1s3p 3 Po ) forbidden transitions of Cl XVI.
1 1
12
13. Figure 6: Comparison of collision strengths from our calculations from darc (continuous curves) and fac
(broken curves) for the 23–35 (circles: 4d 3 D1 – 5p 3 Po ), 25–33 (triangles: 4d 3 D3 – 5p 3 Po ), and 25–34 (stars:
2 0
4d 3 D3 – 5p 3 Po ) transitions of Mg XI.
1
18
14. Figure 7: Collision strengths for the 1s2 1 S0 - 1s2s 3 S1 (1–2) transition of Mg XI.
19
15. Figure 11: Comparison of effective collision strengths for the 13–14 (circles: 1s3d 3 D1 – 1s3d 3 D2 ), 14–15
(triangles: 1s3d 3 D2 – 1s3d 3 D3 ), and 15–16 (stars: 1s3d 3 D3 – 1s3d 1 D2 ) transitions of S XV. Continuous
and dotted curves are from the present darc and earlier R- matrix codes [20], respectively.
23
16. Figure 12: Comparison of effective collision strengths for the 19–46 (circles: 1s4p 3 Po – 1s5g 3 G4 ), 26–36
0
(triangles: 1s4f 3 Fo – 1s5p 3 Po ), and 29–34 (stars: 1s4f 3 Fo – 1s5p 3 P1 ) transitions of S XV. Continuous and
2 2 4
o
dotted curves are from the present darc and earlier R- matrix codes [20], respectively.
24
17. Figure 10: Comparison of effective collision strengths for the 7–8 (circles: 3d 2 D3/2 – 3d 2 D5/2 ), 12–13 (triangles: 4d 2 D3/2 –
4d 2 D5/2 ), and 14–15 (stars: 4f 2 Fo – 4f 2 Fo ) transitions of Fe XXIV. Continuous and broken curves are from the present
5/2 7/2
DARC and earlier BPRM codes [25], respectively.
22
18. SUMMARY
H-like ions
Calculations have been reported for many H-like ions, but results are
particularly required for ions of 19 ≤ Z ≤ 23 and Z ≥ 29.
He-like ions
Calculations have been reported for He-like ions up to Z = 21, but
work is in progress for ions of Z ≥ 22.
Li-like ions
Calculations have been reported for Li-like ions up to Z = 28. Results
from BPRM calculations are also available for ions up to Z = 36, but
calculations from DARC will be helpful for assessing accuracy and
establishing reliability.