耦合通道光学势方法研究电子碰撞氧原子2p～4～3P-2p～33s～3S～0跃迁过程
摘要
电子与氧原子的碰撞有重要的意义。电子与氧原子的碰撞广泛应用在天体物理、激光物理、等离子体物理中，在这些领域中需要大量的散射数据。氧原子的真空紫外辐射引发与电子的碰撞是以大气辉光和极光为特点的，而这种情况与火星和金星非常类似。对于太阳和恒星来说中性氧原子的真空紫外辐射射线是研究天体周围区域的跃迁和色球情况的重要判定来源。由于这些诸多原因电子与氧原子的碰撞就显得尤其重要。
由于电子与氧原子碰撞的重要性，引起了人们探究电子与氧原子碰撞的兴趣。人们很早就开始了电子与氧原子碰撞的研究。电子与氧原子碰撞的实验方面的工作是有限的。最初实验的跃迁的散射截面的结果是由Doering和Vaughan(1986),Vaughan和Doering (1986,1987), Gulcicek和Doering (1988)给出的。在理论研究方面，Smith(1976)使用了R-矩阵理论方法2个靶态密耦展开近似，Tayal和Henry (1988, 1989, 1990)分别使用了R-矩阵理论方法的12个，7个，3个靶态密耦展开近似分别计算了电子与氧原子的碰撞激发散射截面。Zatsarinny 和 Tayal(2002)用R-矩阵理论方法的26个靶态密耦展开近似计算了和等跃迁的截面。Kanik et al(2001)运用R-矩阵理论方法
的22个靶态密耦展开近似计算了30eV, 50eV, 100eV时跃迁的散射截面。Tayal(2002)用伪态模拟连续态，改进了R-矩阵理论方法。Johnson et al (2003)应用改进的R-矩阵理论方法计算了15, 17.5 ,20, 22.5, 27.5 eV 时跃迁的散射截面，结果有了很大的改进。 尽管目前理论工作的不断努力，但是明显的偏差不仅在理论和实验存在,不同的实验, 不同的理论考虑之间也有显著的不同.原因是氧原子的复杂的开壳层结构,具有大的电子关联效应和通道之间很强的耦合, 特别是连续态在碰撞中起着重要的作用，使电子同氧原子碰撞理论研究非常困难.
动量空间耦合通道光学势方法（CCO）使用了Feshbach算符P 和Q，在动量空间求解一组耦合的积分方程，靶的连续态是通过一个从头算的复的光学势包括在这个耦合的积分方程中。这个方法在处理具有一个和两个价电子的原子碰撞问题上取得了很大的成功。在现在的工作中我们首次把CCO方法应用到电子与开壳层氧原子碰撞理论研究中。我们计算了电子与氧原子碰撞的直接电离截面，入射能量为15eV、17.5eV、20eV、22.5eV、25eV、27.5eV、30eV、50eV、100eV 时跃迁的微分截面、积分截面和总的散射截面。在现在的计算中靶的波函数是应用了单组态HF波函数表示的。计算中，在P空间包括了
, ,，,,七个能量最低物理通道，Q空间连续态包括在，，， ，， 通道的光学势中。我们把计算结果与相应的实验结果和R-矩阵理论结果进行了比较。
现在计算的电子与氧原子的碰撞电离截面是不包括自电离的直接的电离截面。没有关于直接电离截面的实验数据，我们只与Yong-Ki Kim(2002)R-矩阵理论计算结果进行了比较。由于R-矩阵理论计算的结果包括自电离的总的电离截面，因此我们的结果比R-矩阵理论计算结果略微小些。
现在的入射能量为15eV、17.5eV、20eV、22.5eV、25eV、27.5eV时的跃迁微分截面与实验结果和Johnson(2003)的用伪态来模拟连续态的R-矩阵理论（RMPS）计算结果进行了比较。在入射能量15eV、17.5eV、20eV时，现在的计算结果与实验结果符合得较好，要比Johnson(2003)的R-矩阵理论结果更符合实验结果。在入射能量为22.5eV、25eV、27.5eV时，现在的计算结果与实验结果和Johnson(2003)的R-矩阵理论计算结果比较有一定的差别，比实验值和R-矩阵理论结果略大。入射能量为30eV、50eV、100eV时的跃迁微分截面
与实验结果和Kanik et al(2001)的R-矩阵理论结果进行了比较。Kanik et al(2001)运用R-矩阵理论方法的22个靶态密耦展开近似计算了碰撞散射截面。入射能量为30eV时，现在的结果也比实验结果和Kanik et al (2001)的R-矩阵理论结果略大。我们考虑主要原因是由于没有加入自电离的效应。入射能量为50eV、100eV时，我们的结果与实验值符合得较好，比R-矩阵理论结果更接近实验结果。
现在计算的积分截面的结果要比Tayal(2002)R-矩阵理论计算的结果更平滑，而且更接近实验结果。现在计算总的散射截面没有任何理论计算和实验结果报告，是我们首次得到的。
从我们的计算中可以证明，CCO方法能够处理开壳层的复杂原子的碰撞问题。现在的结果与实验结果比较，还有一定的误差，主要是由于我们忽略了自电离态在碰撞通道的耦合作用。我们相信，随着一个更多通道的，能够包括自电离态的和使用组态相互作用CCO方法的出现，理论计算的结果一定会得到改进，这是我们下一步工作的目标。
Electron-impact excitation of atomic oxygen is of great interest in aeronomy and astrophysics. For example, electron- impact-
Induced vacuum ultraviolet (VUV) emissions of atomic oxygen are prominent features in the spectra of Earth’s airglow and aurora as well as the atmospheres of other planets such as Mars and Venus. VUV emission lines of neutral atomic oxygen so appear in solar and stellar spectra and provide one of the primary diagnostics of physical conditions in the chromospheres and tra- nsition regions of these objects.Consequently the collision of el- ectron and atomic oxygen has a great significance especially.
The significance of electron atomic oxygen collision arouses
a great number of people to study it .The previous experimental work on atomic oxygen collision had been limited. The original experiment date of 2p43P-2p33s3S0 transition cross section was obtained by Doering and Vaughan (1986,1987), Gulcicek and Doering(1988). Doering and Gulcicek(1989) , Doering 和 Yang (2001), Doering ,Gulcicek and Vaughan（1985）,Kanik et al (2001)，Johnson et al (2003) have also maken much work with the experiments of electron atomic oxygen collision. On the theoretical side, Smith(1976) used a two states close-coupling approximation to calculate the sections. Tayal
and Henry (1988, 1989, 1990) calculate electron-impact excitation cross sectionsusing twelve, seven, three states close-coupling R-matrix approximation .Zatsarinny and Tayal (2002)calculated transition cross section of 2p43P-2p33s3S0 and 2p43P-2p33d0D0 et al with coupling expanded of twenty-six target states by R-matrix method. Kanik et al (2001) applied R-matrix method to calculate transition cross section of 2p43P-2p33s3S0 with coupling expanded of twenty-two target state in energies of 30, 50 and 100eV . The obvious deviation exists between theory and experiment as well as distinct differences are produced in different calculation and experiments .A possible reason is these calculation omit continuous states, that play an very important role in electron-oxygen collisions, Later, Tayal (2002) adopted pseudo-states to simulate continuous state and mended the R-matrix method. Johnson et al (2003) applied the method to calculate the transition cross section of 2p43P-2p33s3S0 in energies of 15 , 17.5, 20eV and got an improved result.
The momentum space coupled channels optical (CCO) methd uses the Feshbach operator P and Q to solve a set of coupled integral equations in momentum space. And the continuum states of target are included in the coupled integral equation with an ab intito complex optical potential. The method makes a great success in applying to the atom targets with one or two valent electrons.It′s the first time we apply CCO method to investigate el- ectron scattering by atomic oxygen which has an openshell
structure .We calculate the direct ionization cross section of electron -oxygen, differential and integral cross sections of 2p43P- 2p3 3s3 S0 at 15, 17.5, 20, 22.5, 25, 27.5, 30, 50, 100eV. Target wave function is expressed with single configuration HF wave function in present calculation. In the present calculations, P space contains 2p43P, 3s3S0, 3p4P, 3d3D0, 4s3S0, 4p3P, 5s3S0,which are physical channels with lowest energy and the continuum states (Q space) are included in the optical potential of channels as following channel couplings: ，，， ，， .
Transition cross sections of 2p4 3P-2p33s3S0 with input energy at15, 17.5, 20, 22.5, 25, 27.5eV are compared with experimental data and calculation result obtained by Johnson et al(2003) with the R-matrix theory using pseudo-states to simulate the continuum states.At 15,17.5,20eV,the present results agree with experimental date much better than R-matrix theory. And at 22.5, 25, 27.5eV, there are some differences between the results.Our results are a litlle larger than experimental data and R-matrix theory. Differential cross sections of 2p43P-2p33s3S0 are compared with the results of experiment and the R-matrix theory (Kanik et al 2001) whit
由于电子与氧原子碰撞的重要性，引起了人们探究电子与氧原子碰撞的兴趣。人们很早就开始了电子与氧原子碰撞的研究。电子与氧原子碰撞的实验方面的工作是有限的。最初实验的跃迁的散射截面的结果是由Doering和Vaughan(1986),Vaughan和Doering (1986,1987), Gulcicek和Doering (1988)给出的。在理论研究方面，Smith(1976)使用了R-矩阵理论方法2个靶态密耦展开近似，Tayal和Henry (1988, 1989, 1990)分别使用了R-矩阵理论方法的12个，7个，3个靶态密耦展开近似分别计算了电子与氧原子的碰撞激发散射截面。Zatsarinny 和 Tayal(2002)用R-矩阵理论方法的26个靶态密耦展开近似计算了和等跃迁的截面。Kanik et al(2001)运用R-矩阵理论方法
的22个靶态密耦展开近似计算了30eV, 50eV, 100eV时跃迁的散射截面。Tayal(2002)用伪态模拟连续态，改进了R-矩阵理论方法。Johnson et al (2003)应用改进的R-矩阵理论方法计算了15, 17.5 ,20, 22.5, 27.5 eV 时跃迁的散射截面，结果有了很大的改进。 尽管目前理论工作的不断努力，但是明显的偏差不仅在理论和实验存在,不同的实验, 不同的理论考虑之间也有显著的不同.原因是氧原子的复杂的开壳层结构,具有大的电子关联效应和通道之间很强的耦合, 特别是连续态在碰撞中起着重要的作用，使电子同氧原子碰撞理论研究非常困难.
动量空间耦合通道光学势方法（CCO）使用了Feshbach算符P 和Q，在动量空间求解一组耦合的积分方程，靶的连续态是通过一个从头算的复的光学势包括在这个耦合的积分方程中。这个方法在处理具有一个和两个价电子的原子碰撞问题上取得了很大的成功。在现在的工作中我们首次把CCO方法应用到电子与开壳层氧原子碰撞理论研究中。我们计算了电子与氧原子碰撞的直接电离截面，入射能量为15eV、17.5eV、20eV、22.5eV、25eV、27.5eV、30eV、50eV、100eV 时跃迁的微分截面、积分截面和总的散射截面。在现在的计算中靶的波函数是应用了单组态HF波函数表示的。计算中，在P空间包括了
, ,，,,七个能量最低物理通道，Q空间连续态包括在，，， ，， 通道的光学势中。我们把计算结果与相应的实验结果和R-矩阵理论结果进行了比较。
现在计算的电子与氧原子的碰撞电离截面是不包括自电离的直接的电离截面。没有关于直接电离截面的实验数据，我们只与Yong-Ki Kim(2002)R-矩阵理论计算结果进行了比较。由于R-矩阵理论计算的结果包括自电离的总的电离截面，因此我们的结果比R-矩阵理论计算结果略微小些。
现在的入射能量为15eV、17.5eV、20eV、22.5eV、25eV、27.5eV时的跃迁微分截面与实验结果和Johnson(2003)的用伪态来模拟连续态的R-矩阵理论（RMPS）计算结果进行了比较。在入射能量15eV、17.5eV、20eV时，现在的计算结果与实验结果符合得较好，要比Johnson(2003)的R-矩阵理论结果更符合实验结果。在入射能量为22.5eV、25eV、27.5eV时，现在的计算结果与实验结果和Johnson(2003)的R-矩阵理论计算结果比较有一定的差别，比实验值和R-矩阵理论结果略大。入射能量为30eV、50eV、100eV时的跃迁微分截面
与实验结果和Kanik et al(2001)的R-矩阵理论结果进行了比较。Kanik et al(2001)运用R-矩阵理论方法的22个靶态密耦展开近似计算了碰撞散射截面。入射能量为30eV时，现在的结果也比实验结果和Kanik et al (2001)的R-矩阵理论结果略大。我们考虑主要原因是由于没有加入自电离的效应。入射能量为50eV、100eV时，我们的结果与实验值符合得较好，比R-矩阵理论结果更接近实验结果。
现在计算的积分截面的结果要比Tayal(2002)R-矩阵理论计算的结果更平滑，而且更接近实验结果。现在计算总的散射截面没有任何理论计算和实验结果报告，是我们首次得到的。
从我们的计算中可以证明，CCO方法能够处理开壳层的复杂原子的碰撞问题。现在的结果与实验结果比较，还有一定的误差，主要是由于我们忽略了自电离态在碰撞通道的耦合作用。我们相信，随着一个更多通道的，能够包括自电离态的和使用组态相互作用CCO方法的出现，理论计算的结果一定会得到改进，这是我们下一步工作的目标。
Electron-impact excitation of atomic oxygen is of great interest in aeronomy and astrophysics. For example, electron- impact-
Induced vacuum ultraviolet (VUV) emissions of atomic oxygen are prominent features in the spectra of Earth’s airglow and aurora as well as the atmospheres of other planets such as Mars and Venus. VUV emission lines of neutral atomic oxygen so appear in solar and stellar spectra and provide one of the primary diagnostics of physical conditions in the chromospheres and tra- nsition regions of these objects.Consequently the collision of el- ectron and atomic oxygen has a great significance especially.
The significance of electron atomic oxygen collision arouses
a great number of people to study it .The previous experimental work on atomic oxygen collision had been limited. The original experiment date of 2p43P-2p33s3S0 transition cross section was obtained by Doering and Vaughan (1986,1987), Gulcicek and Doering(1988). Doering and Gulcicek(1989) , Doering 和 Yang (2001), Doering ,Gulcicek and Vaughan（1985）,Kanik et al (2001)，Johnson et al (2003) have also maken much work with the experiments of electron atomic oxygen collision. On the theoretical side, Smith(1976) used a two states close-coupling approximation to calculate the sections. Tayal
and Henry (1988, 1989, 1990) calculate electron-impact excitation cross sectionsusing twelve, seven, three states close-coupling R-matrix approximation .Zatsarinny and Tayal (2002)calculated transition cross section of 2p43P-2p33s3S0 and 2p43P-2p33d0D0 et al with coupling expanded of twenty-six target states by R-matrix method. Kanik et al (2001) applied R-matrix method to calculate transition cross section of 2p43P-2p33s3S0 with coupling expanded of twenty-two target state in energies of 30, 50 and 100eV . The obvious deviation exists between theory and experiment as well as distinct differences are produced in different calculation and experiments .A possible reason is these calculation omit continuous states, that play an very important role in electron-oxygen collisions, Later, Tayal (2002) adopted pseudo-states to simulate continuous state and mended the R-matrix method. Johnson et al (2003) applied the method to calculate the transition cross section of 2p43P-2p33s3S0 in energies of 15 , 17.5, 20eV and got an improved result.
The momentum space coupled channels optical (CCO) methd uses the Feshbach operator P and Q to solve a set of coupled integral equations in momentum space. And the continuum states of target are included in the coupled integral equation with an ab intito complex optical potential. The method makes a great success in applying to the atom targets with one or two valent electrons.It′s the first time we apply CCO method to investigate el- ectron scattering by atomic oxygen which has an openshell
structure .We calculate the direct ionization cross section of electron -oxygen, differential and integral cross sections of 2p43P- 2p3 3s3 S0 at 15, 17.5, 20, 22.5, 25, 27.5, 30, 50, 100eV. Target wave function is expressed with single configuration HF wave function in present calculation. In the present calculations, P space contains 2p43P, 3s3S0, 3p4P, 3d3D0, 4s3S0, 4p3P, 5s3S0,which are physical channels with lowest energy and the continuum states (Q space) are included in the optical potential of channels as following channel couplings: ，，， ，， .
Transition cross sections of 2p4 3P-2p33s3S0 with input energy at15, 17.5, 20, 22.5, 25, 27.5eV are compared with experimental data and calculation result obtained by Johnson et al(2003) with the R-matrix theory using pseudo-states to simulate the continuum states.At 15,17.5,20eV,the present results agree with experimental date much better than R-matrix theory. And at 22.5, 25, 27.5eV, there are some differences between the results.Our results are a litlle larger than experimental data and R-matrix theory. Differential cross sections of 2p43P-2p33s3S0 are compared with the results of experiment and the R-matrix theory (Kanik et al 2001) whit
引文
[1] Feldman P D,Burgh E C,Durrance S T and Davidsen A F 2000 Astrophys.J.538 395
[2] I Kanik,P V Johnson,M B Das,M A Khakoo and S S Tayal
Electron-impact studies of atomic oxygen: I. Differential and
integral cross sections; experiment and theory
J.Phys.B:At.Mol.Opt.Phys 34(2001)2647-2665
[3]Doering J P and Vaughan S O ,Absolute experimental differential
and integral electron excitation cross sections for atomic oxygen
1. The (3P3S0) transition (1304 ?) at 100 eV
1986 J. Geophys. Res. 91 3279-3286
[4]Vaughan S O and Doering J PAbsolute experimental differential and
integral electron excitation cross sections for atomic oxygen, 2, The (3P3S°) transition (1304 ?) from 16.5 to 200 eV with comparison to atomic hydrogen
1986 J.Geophys.Res.91 13755-13760
[5]Vaughan S O and Doering J P Absolute experimental differential and integral electron excitation cross sections for atomic oxygen 3. The (3P3D°) transitions (989 ?) from 20 to 200 eV with improved values for the (3P3S°) transition (1304 ?)
1987 J.Geophys.Res.92 7749-7753
[6]Gulcicek E E and Doering J P 1988 Absolute differential and integral electron excitation cross sections for atomic oxygen. VI. The /sup 3/P to /sup 3/P and /sup 3/P to /sup 5/P transitions from 13.87 to 100 eV J. Geophys. Res. 93 5885-5889
[7] Doering, J., and E. Gulcicek , Absolute differential and integral electron excitation cross sections for atomic oxygen 8. The 3P→5S° transition (1356 ?) from 13.9 to 30 eV, J. Geophys. Res.,
94(A3), 2733–2736, 1989.
[8] Doering J P and Yang J Atomic oxygen 3P→3S0 (λ1304?) transition revisited: Cross section near threshold
2001 J. Geophys. Res. 106 203
[9] Doering J P, Gulcicek E E and Vaughan S O 1985 J. Geophys. Res. Space Phys. 90 5279
[10]P V Johnson1, IKanik1, M AKhakoo2, JWMcConkey3 and
S. S.Tayal4
Low energy differential and integral electron-impact cross sections for the 2s22p4 3P → 2p33s 3So excitation in atomic oxygen
J.Phys.B:At.Mol.Opt.Phys. 36 (2003) 4289–4299
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[12] Tayal S S and Henry R J W 1988 Electron-impact excitation of atomic oxygen Phys.Rev.A 38 5945-5948
[13] Tayal S S and Henry R J W Oscillator strengths and electron collisional excitational excitation cross sections for atomic oxygen 1989 Phys.Rev.A 39 4531-4536
[14] Tayal S S and Henry R J W Angular distributions for electron-impact excitation of atomic oxygen 1990Phys.Rev.A 42 320-323
[15] O Zatsarinny and S S Tayal R-matrix calculation with non-orthogonal orbitals for electron-impact excitation of atomic oxygen J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 241–253
[16] Noren C,Kanik I,Johnson P V,McCartney P,James G K and Ajello J M 2001 J.phys.B:At.Mol.Opt.Phys.34 2667
[17] S.S.Tayal PHYSICAL REVIEW A, Angular distributions for electron-impact excitation of atomic oxygen 42, VOLUME 320-323(1990)
[18] S. S. Tayal PHYSICAL REVIEW A, Importance of coupling to the continuum for electron-impact excitation of atomic oxygen
66, 030701R （2002）
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Ann. Phys.(N.Y.), 5,357-5390(1958)
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－1983 Phys.Rev. A 28 2693-2707
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[23] I.E.McCarthy,K.Ratnavelu and A.M.Weigold, Continuum effects in electron-helium total cross sections J. Phys. B: At. Mol. Opt. Phys. 21 No 23 (14 December 1988) 3999-4005
[24] Bray I, McCarthy I E, Mitroy J and Ratnavelu K,1989 Phys. Rev. A Coupled channel in the distorted-wave representation 39,4998-5009
[25] Yong-Ki Kim Physical Review AIonization of carbon, nitrogen, and oxygen by electron impact
66 012708 (2002)
[2] I Kanik,P V Johnson,M B Das,M A Khakoo and S S Tayal
Electron-impact studies of atomic oxygen: I. Differential and
integral cross sections; experiment and theory
J.Phys.B:At.Mol.Opt.Phys 34(2001)2647-2665
[3]Doering J P and Vaughan S O ,Absolute experimental differential
and integral electron excitation cross sections for atomic oxygen
1. The (3P3S0) transition (1304 ?) at 100 eV
1986 J. Geophys. Res. 91 3279-3286
[4]Vaughan S O and Doering J PAbsolute experimental differential and
integral electron excitation cross sections for atomic oxygen, 2, The (3P3S°) transition (1304 ?) from 16.5 to 200 eV with comparison to atomic hydrogen
1986 J.Geophys.Res.91 13755-13760
[5]Vaughan S O and Doering J P Absolute experimental differential and integral electron excitation cross sections for atomic oxygen 3. The (3P3D°) transitions (989 ?) from 20 to 200 eV with improved values for the (3P3S°) transition (1304 ?)
1987 J.Geophys.Res.92 7749-7753
[6]Gulcicek E E and Doering J P 1988 Absolute differential and integral electron excitation cross sections for atomic oxygen. VI. The /sup 3/P to /sup 3/P and /sup 3/P to /sup 5/P transitions from 13.87 to 100 eV J. Geophys. Res. 93 5885-5889
[7] Doering, J., and E. Gulcicek , Absolute differential and integral electron excitation cross sections for atomic oxygen 8. The 3P→5S° transition (1356 ?) from 13.9 to 30 eV, J. Geophys. Res.,
94(A3), 2733–2736, 1989.
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