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Electron-impact excitation cross sections for O IV
Volume 74A, number 5
PHYSICS LETTERS
26 November 1979
ELECTRON-IMPACT EXCITATION CROSS SECTIONS FOR 0 IV P.S. GANAS California State University at Los AnEeles, Los Angeles, CA 90032, USA Received 1 August 1979
Generalized oscillator strengths and integrated cross sections from threshold to 1 keY are calculated in the Born approximation for the electron impact excitation of 0 IV.
The purpose of this note is to present the results of calculations of generalized oscillator strengths (GOS) and integrated cross sections for the electron-impact excitation of 0 IV in the Born approximation. We discuss transitions in which the valence electron is promoted from the 2s22p(2P) ground state into various s, p, d excited states. Lines of 0 IV have been identifled in the solar spectrum. These lines permit the direct determination of the chemical abundance of this substance in the upper chromosphere and in the corona. Despite the importance of the 0 IV ion in astrophysica! observations, there is very little experimental or theoretical information available on electron-impact excitation cross sections at high energy. The potential for an electron in the 0 IV ion is, in atomic units: V(r) = _(2/r){4[H(er/d 1) + 11_i + 4} (1) —
where r is the electron—nucleus distance, and d, H are adjustable parameters. This pote~itia1is a particular case of a more general form which has been used to characterize electron—atom interactions [1]. The potential is inserted into the radial Schrodinger equation which is solved numerically to obtain the single-particle wavefunctions. In a previous article [2] it was shown that if the are chosen d= 0.5063, H potential = 1.7686, parameters then the potential (1) as reproduces the observed energy levels of 0 IV and gives optical oscillator strengths (OOS) which are in reasonable agreement with experiment and other theories. The OOS are generally within 15% of other theoretical values and experiment,
The general formulas which are used to compute the GOS are based on the first Born approximation and the Russell—Saunders LS-coupling scheme, and may be found in an earlier article [3]. The following notation is introduced for use in subsequent discussions. We define x = K2a~,where K is the momentum transfer and a 0 is the Bohr radius. Also x~= W/R where W is the excitation energy in eV, and R is the Rydberg energy. We also define ~ = x/x~. The computed GOS for various excitations from the 2p ground state and for a range of ~from 10—2 to 10~are displayed in fig. 1. As ~ 0, the GOS for the optically allowed transitions 2p—ns and 2p—nd approach the OOS values, while the GOS for the optically forbidden transitions 2p—np approach zero. As ~ increases from zero, the GOS for 2p—ns decrease and pass through a series of oscillations, while the GOS for 2p—nd decrease monotonically without oscillations. For 2p—np the GOS at first increase, attaining a maximum value, and then decrease monotonically thereafter. To facilitate use of the GOS in applications, we have parametrized all the GOS with simple analytic forms. For optically allowed transitions the GOS, f(s), is parametrized using the form 2 ~‘~‘ + ~eit~ / ‘~‘ =A’e°~ “ and for optically forbidden transitions: f(~\ ~ + ‘~e7~~ (3 -~
‘
~‘ ‘~‘
~
~
/
The values of the adjustable parameters A, c~f3, ‘I’ which reproduce all the GOS in the region in which 307
Volume 74A, number S
PHYSICS LETTERS
10°
26 November 1979
iO—’~ 3d
\\
\~3s
~~~~‘0~,
-
~
3d
~
4d\\~
4d~~
\~1~\\\ \\ \~\
l0-°
17
\\~\
f /
\~\\\
\\ \\\ \~ \ \\ \\\
7
\\~\3P
\~\\
\~\\
I
111111111
IlIlilli
I0_2
I0’
liii,
100
I
10’
~~5d 3s~
\\~~\\\
\\\
\~‘ III~r
4$
III,,,,
102
5s Fig. 1. GOS for 2p—ns, 2p—np and 2p—nd excitations of the valence electron in 0 IV. The curves are the results of this work. The solid dots and open circles give representative fits using eqs. (2) and (3). Values off(x) below iø-~are multiplied by iO~.
the GOS is significantly large, are given in table 1. The formulas which are used to obtain the integrated cross sections from the GUS may be found in earlier work [4]. The computed integrated cross sections for the various excitations in 0 IV, for incident electron energies ranging from threshold to I keV, are displayed in fig. 2. In the absence of any experimental cross sections at high energy, it is not possible to make a direct comparison of the present results with experiment. However, an indication of the accuracy of our results within the framework of the Born approximaTable 1 Values of the unitless parameters A, a, 8, ‘y in eqs. (2)
and
2pto
A
/3
7
3s 4s 5s
0.0303 1.8357 0.0059 0.7300 0.0022 0.7000 0.3212 0.4635 0.4385 1.4737 0.1159 0.9535 0.04860.8169
—0.5491 —1.3000 —1.3000 —0.62 15 0.2266 0.0642 0.0322
0.5133 0. 7000 0.7000 0.7929 0.6159 0.3605 0.2777
a
(3~
10-2
I
10
I
I 102
jQ3
E(eV) Fig. 2. The curves are the computed integrated cross sections for 2p—ns, 2p—np and 2p—nd excitations of the valence electron in 0 IV.
tion may be obtained by checking the accuracy of the OOS derived from the present model, since the GOS reduce to the OOS in the limit of zero momentum transfer. In a previous article [2] we compared the OOS derived from the present model with experimental and other theoretical values, and it was found that the agreement was generally within 15%. This indicates that the cross sections obtained in this work have an accuracy of 15% or better, and they are realistic except at low energies near threshold. These cross sections may be useful as input data for such applied calculations as electron-energy deposition problems. References
3d 4d Sd
308
[1] A.E.S. Green, D.L. Sellin and A.S. Zachor, Phys. Rev. 184 (1969) 1. [2] P.S. Ganas, Phys. Lett. 73A (1979) 161. [31 PA. Kazaks, P.S. Ganas and A.E.S. Green, Phys. Rev. A6 (1972) 2169. [41 P.S. Ganas and A.E.S. Green, Phys. Rev. A4 (1971) 182.
PHYSICS LETTERS
26 November 1979
ELECTRON-IMPACT EXCITATION CROSS SECTIONS FOR 0 IV P.S. GANAS California State University at Los AnEeles, Los Angeles, CA 90032, USA Received 1 August 1979
Generalized oscillator strengths and integrated cross sections from threshold to 1 keY are calculated in the Born approximation for the electron impact excitation of 0 IV.
The purpose of this note is to present the results of calculations of generalized oscillator strengths (GOS) and integrated cross sections for the electron-impact excitation of 0 IV in the Born approximation. We discuss transitions in which the valence electron is promoted from the 2s22p(2P) ground state into various s, p, d excited states. Lines of 0 IV have been identifled in the solar spectrum. These lines permit the direct determination of the chemical abundance of this substance in the upper chromosphere and in the corona. Despite the importance of the 0 IV ion in astrophysica! observations, there is very little experimental or theoretical information available on electron-impact excitation cross sections at high energy. The potential for an electron in the 0 IV ion is, in atomic units: V(r) = _(2/r){4[H(er/d 1) + 11_i + 4} (1) —
where r is the electron—nucleus distance, and d, H are adjustable parameters. This pote~itia1is a particular case of a more general form which has been used to characterize electron—atom interactions [1]. The potential is inserted into the radial Schrodinger equation which is solved numerically to obtain the single-particle wavefunctions. In a previous article [2] it was shown that if the are chosen d= 0.5063, H potential = 1.7686, parameters then the potential (1) as reproduces the observed energy levels of 0 IV and gives optical oscillator strengths (OOS) which are in reasonable agreement with experiment and other theories. The OOS are generally within 15% of other theoretical values and experiment,
The general formulas which are used to compute the GOS are based on the first Born approximation and the Russell—Saunders LS-coupling scheme, and may be found in an earlier article [3]. The following notation is introduced for use in subsequent discussions. We define x = K2a~,where K is the momentum transfer and a 0 is the Bohr radius. Also x~= W/R where W is the excitation energy in eV, and R is the Rydberg energy. We also define ~ = x/x~. The computed GOS for various excitations from the 2p ground state and for a range of ~from 10—2 to 10~are displayed in fig. 1. As ~ 0, the GOS for the optically allowed transitions 2p—ns and 2p—nd approach the OOS values, while the GOS for the optically forbidden transitions 2p—np approach zero. As ~ increases from zero, the GOS for 2p—ns decrease and pass through a series of oscillations, while the GOS for 2p—nd decrease monotonically without oscillations. For 2p—np the GOS at first increase, attaining a maximum value, and then decrease monotonically thereafter. To facilitate use of the GOS in applications, we have parametrized all the GOS with simple analytic forms. For optically allowed transitions the GOS, f(s), is parametrized using the form 2 ~‘~‘ + ~eit~ / ‘~‘ =A’e°~ “ and for optically forbidden transitions: f(~\ ~ + ‘~e7~~ (3 -~
‘
~‘ ‘~‘
~
~
/
The values of the adjustable parameters A, c~f3, ‘I’ which reproduce all the GOS in the region in which 307
Volume 74A, number S
PHYSICS LETTERS
10°
26 November 1979
iO—’~ 3d
\\
\~3s
~~~~‘0~,
-
~
3d
~
4d\\~
4d~~
\~1~\\\ \\ \~\
l0-°
17
\\~\
f /
\~\\\
\\ \\\ \~ \ \\ \\\
7
\\~\3P
\~\\
\~\\
I
111111111
IlIlilli
I0_2
I0’
liii,
100
I
10’
~~5d 3s~
\\~~\\\
\\\
\~‘ III~r
4$
III,,,,
102
5s Fig. 1. GOS for 2p—ns, 2p—np and 2p—nd excitations of the valence electron in 0 IV. The curves are the results of this work. The solid dots and open circles give representative fits using eqs. (2) and (3). Values off(x) below iø-~are multiplied by iO~.
the GOS is significantly large, are given in table 1. The formulas which are used to obtain the integrated cross sections from the GUS may be found in earlier work [4]. The computed integrated cross sections for the various excitations in 0 IV, for incident electron energies ranging from threshold to I keV, are displayed in fig. 2. In the absence of any experimental cross sections at high energy, it is not possible to make a direct comparison of the present results with experiment. However, an indication of the accuracy of our results within the framework of the Born approximaTable 1 Values of the unitless parameters A, a, 8, ‘y in eqs. (2)
and
2pto
A
/3
7
3s 4s 5s
0.0303 1.8357 0.0059 0.7300 0.0022 0.7000 0.3212 0.4635 0.4385 1.4737 0.1159 0.9535 0.04860.8169
—0.5491 —1.3000 —1.3000 —0.62 15 0.2266 0.0642 0.0322
0.5133 0. 7000 0.7000 0.7929 0.6159 0.3605 0.2777
a
(3~
10-2
I
10
I
I 102
jQ3
E(eV) Fig. 2. The curves are the computed integrated cross sections for 2p—ns, 2p—np and 2p—nd excitations of the valence electron in 0 IV.
tion may be obtained by checking the accuracy of the OOS derived from the present model, since the GOS reduce to the OOS in the limit of zero momentum transfer. In a previous article [2] we compared the OOS derived from the present model with experimental and other theoretical values, and it was found that the agreement was generally within 15%. This indicates that the cross sections obtained in this work have an accuracy of 15% or better, and they are realistic except at low energies near threshold. These cross sections may be useful as input data for such applied calculations as electron-energy deposition problems. References
3d 4d Sd
308
[1] A.E.S. Green, D.L. Sellin and A.S. Zachor, Phys. Rev. 184 (1969) 1. [2] P.S. Ganas, Phys. Lett. 73A (1979) 161. [31 PA. Kazaks, P.S. Ganas and A.E.S. Green, Phys. Rev. A6 (1972) 2169. [41 P.S. Ganas and A.E.S. Green, Phys. Rev. A4 (1971) 182.