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Elastic and inelastic differential and integral cross sections for low-energy vibrational excitation of H2 by electron impact are studied with exact exchange. The resulting coupled integrodifferential equations are solved using a combination of linear-algebraic and R-matrix-propagator techniques. The converged (0→0,0→1,0→2) differential and integral cross sections are obtained. The calculated results are in good agreement with experimental resalts and other calculations, showing that the exact exchange based on equations of vibrational close coupling plays an important role in low-energy electron scattering from H2 molecule.
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Keywords:
- exact exchange /
- H2 molecular vibrational excitation /
- differential cross section /
- integral cross sections
[1] Massey H S 1969 Electronic and Inoic Impact Phenomena, Vo1.II: Electron Collision with Molecules and Photoionization (Oxford University, London)
[2] Capitelli M, Celiberto R, Esposito F, Laricchiuta A, Hassouni K, Longo S 2002 Plasma Sources Sci. Technol. 11 A7-A25
[3] Lieberman M A, Lichtenberg A J 1994 Principles of Plasma Discharges, Materials Processing ed Wiley(New York)
[4] Lane N F 1980 Rev. Mod. Phys. 52 29
[5] White R D, Robson R E, Morrison M A, Li B, Ness K F 2007 J. Phys. Conf. 71 012004
[6] Crompton R W, Morrison M A 1993 Aust. J. Phys. 46 203
[7] Brunger M J, Buckman S J, Newman D S, Alle D T 1991 J. Phys. B 24 1435
[8] Shyn T W, Sharp W E 1981 Phys. Rev. A 24 1734
[9] Jones R K 1985 Phys. Rev. A 31 2898
[10] Ferch J, Raith W, Schröder K 1980 J. Phys. B 13 1481
[11] Subramanian, Kumar V 1989 J. Phys. B 22 2387
[12] Nickel J C, Kanik I, Trajmar S, Imre K 1992 J. Phys. B 25 2427
[13] Schneider B I, Collins L A 1983 Phys. Rev. A 27 2847
[14] Horá Acˇ ek J, í Azˇ ek M, Houfek K, Koloren Acˇ P 2006 Phys. Rev. A 73 022701
[15] Wang B, Feng H, Sun W G, Zeng Y Y, Dai W 2009 Acta Phys. Sin. 58 6932(in Chinese)[王 斌、冯 灏、孙卫国、曾阳阳、戴维 2009 58 6932]
[16] Morrison M A, Saha B C 1986 Phys. Rev. A 34 2796
[17] Sun W G, Morrison M A, Isaacs W A, Trail W K, Alle D T, Gulley R J, Brennan M J, Buckman S J 1995 Phys. Rev. A 52 1229
[18] Morrison M A, Sun W 1995 Computational Methods for Electron-Molecule Collisions ed Huo W, Gianturco F A (New York: Plenum) chapter 6, pp 131—90
[19] Chandra N, Temkin A 1976 Phys. Rev. A 13 188
[20] Morrison M A, Feldt A N, Austin D 1984 Phys. Rev. A 30 2811
[21] Mazon K T, Fujiwara R, Lee M T 2001 Phys. Rev. A 64 042705
[22] Morrison M A, Crompton R W, Saha B C, Petrovic Z L 1987 Aust. J .Phys. 40 239
[23] Zeng Y Y, Feng H, Sun W G, Wang B 2009 Chin. Phys. Lett. 26 023402
[24] Wang X L, Feng H, Sun W G, Fan Q C, Zeng Y Y, Wang B 2010 Acta Phys. Sin. 59 0937(in Chinese)[王小炼、冯 灏、孙卫国、樊群超、曾阳阳、王 斌 2010 59 0937]
[25] Morrison M A, Trail W K 1993 Phys. Rev. A 48 2874
[26] Feng H, Sun W, Morrison M A, Feldt A N 2009 J. Phys. B 42 175201
[27] Zare R N 1988 Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York)
[28] Rose M E 1957 Elementary Theory of Angular Momentum (Wiley, New York)
[29] Edmonds A R 1968 Angular Momentum in Quantum Mechanics (Princeton Univer. Press, Jersey N)
[30] Collins L A, Schneider B I 1981 Phys. Rev. A 24 2387
[31] Schneider B I, Collins L A 1982 J. Phys. B 15 L335
[32] Schneider B I, Collins L A 1983 Phys. Rev. A 27 2847
[33] Schneider B I, Collins L A 1984 Phys. Rev. A 30 95
[34] Schneider B I, Walker R B 1978 J. Chem. Phys. 70 2466
[35] Schneider B I, Taylor H S 1982 J. Chem .Phys. 77 379
[36] Simons G, Parr R G, Finlan M J 1973 J. Chem. Phys. 59 3229
[37] Trail W K, Morrison M A, Isaacs W A, Saha B 1990 Phys. Rev. A 41 4868
[38] Dai W, Feng H, Sun W G, Tang Y J, Shen L, Yu J Z 2008 Acta Phys. Sin. 57 144 (in Chinese)[戴 伟、冯 灏、孙卫国、唐永健、申 立、于江周 2008 57 144]
[39] Linder F, Schmidt H 1971 Z. Naturforsch. 26A 1603
[40] Wong S F, Schulz G J 1974 Phys. Rev. Lett. 32 1089
[41] Yoon J S, Song M Y, Han M J, Hwang S H, Chang W S, Lee B J, Itikawa Y 2008 J. Phys. Chem. Ref. Data 37 913
[42] Ehrhardt H, Langhans L, Linder F, Taylor H S 1968 Phys. Rev. 173 222
[43] England J P, Elford M T, Crompton R W 1988 Aust. J. Phys. 41 573
[44] Buckman S J, Brunger M J 1997 Aust. J. Phys. 50 483
[45] Crompton R W, Morrison M A 1993 Aust. J. Phys. 46 203
[46] Allan M 1985 J. Phys. B 18 L451
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[1] Massey H S 1969 Electronic and Inoic Impact Phenomena, Vo1.II: Electron Collision with Molecules and Photoionization (Oxford University, London)
[2] Capitelli M, Celiberto R, Esposito F, Laricchiuta A, Hassouni K, Longo S 2002 Plasma Sources Sci. Technol. 11 A7-A25
[3] Lieberman M A, Lichtenberg A J 1994 Principles of Plasma Discharges, Materials Processing ed Wiley(New York)
[4] Lane N F 1980 Rev. Mod. Phys. 52 29
[5] White R D, Robson R E, Morrison M A, Li B, Ness K F 2007 J. Phys. Conf. 71 012004
[6] Crompton R W, Morrison M A 1993 Aust. J. Phys. 46 203
[7] Brunger M J, Buckman S J, Newman D S, Alle D T 1991 J. Phys. B 24 1435
[8] Shyn T W, Sharp W E 1981 Phys. Rev. A 24 1734
[9] Jones R K 1985 Phys. Rev. A 31 2898
[10] Ferch J, Raith W, Schröder K 1980 J. Phys. B 13 1481
[11] Subramanian, Kumar V 1989 J. Phys. B 22 2387
[12] Nickel J C, Kanik I, Trajmar S, Imre K 1992 J. Phys. B 25 2427
[13] Schneider B I, Collins L A 1983 Phys. Rev. A 27 2847
[14] Horá Acˇ ek J, í Azˇ ek M, Houfek K, Koloren Acˇ P 2006 Phys. Rev. A 73 022701
[15] Wang B, Feng H, Sun W G, Zeng Y Y, Dai W 2009 Acta Phys. Sin. 58 6932(in Chinese)[王 斌、冯 灏、孙卫国、曾阳阳、戴维 2009 58 6932]
[16] Morrison M A, Saha B C 1986 Phys. Rev. A 34 2796
[17] Sun W G, Morrison M A, Isaacs W A, Trail W K, Alle D T, Gulley R J, Brennan M J, Buckman S J 1995 Phys. Rev. A 52 1229
[18] Morrison M A, Sun W 1995 Computational Methods for Electron-Molecule Collisions ed Huo W, Gianturco F A (New York: Plenum) chapter 6, pp 131—90
[19] Chandra N, Temkin A 1976 Phys. Rev. A 13 188
[20] Morrison M A, Feldt A N, Austin D 1984 Phys. Rev. A 30 2811
[21] Mazon K T, Fujiwara R, Lee M T 2001 Phys. Rev. A 64 042705
[22] Morrison M A, Crompton R W, Saha B C, Petrovic Z L 1987 Aust. J .Phys. 40 239
[23] Zeng Y Y, Feng H, Sun W G, Wang B 2009 Chin. Phys. Lett. 26 023402
[24] Wang X L, Feng H, Sun W G, Fan Q C, Zeng Y Y, Wang B 2010 Acta Phys. Sin. 59 0937(in Chinese)[王小炼、冯 灏、孙卫国、樊群超、曾阳阳、王 斌 2010 59 0937]
[25] Morrison M A, Trail W K 1993 Phys. Rev. A 48 2874
[26] Feng H, Sun W, Morrison M A, Feldt A N 2009 J. Phys. B 42 175201
[27] Zare R N 1988 Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York)
[28] Rose M E 1957 Elementary Theory of Angular Momentum (Wiley, New York)
[29] Edmonds A R 1968 Angular Momentum in Quantum Mechanics (Princeton Univer. Press, Jersey N)
[30] Collins L A, Schneider B I 1981 Phys. Rev. A 24 2387
[31] Schneider B I, Collins L A 1982 J. Phys. B 15 L335
[32] Schneider B I, Collins L A 1983 Phys. Rev. A 27 2847
[33] Schneider B I, Collins L A 1984 Phys. Rev. A 30 95
[34] Schneider B I, Walker R B 1978 J. Chem. Phys. 70 2466
[35] Schneider B I, Taylor H S 1982 J. Chem .Phys. 77 379
[36] Simons G, Parr R G, Finlan M J 1973 J. Chem. Phys. 59 3229
[37] Trail W K, Morrison M A, Isaacs W A, Saha B 1990 Phys. Rev. A 41 4868
[38] Dai W, Feng H, Sun W G, Tang Y J, Shen L, Yu J Z 2008 Acta Phys. Sin. 57 144 (in Chinese)[戴 伟、冯 灏、孙卫国、唐永健、申 立、于江周 2008 57 144]
[39] Linder F, Schmidt H 1971 Z. Naturforsch. 26A 1603
[40] Wong S F, Schulz G J 1974 Phys. Rev. Lett. 32 1089
[41] Yoon J S, Song M Y, Han M J, Hwang S H, Chang W S, Lee B J, Itikawa Y 2008 J. Phys. Chem. Ref. Data 37 913
[42] Ehrhardt H, Langhans L, Linder F, Taylor H S 1968 Phys. Rev. 173 222
[43] England J P, Elford M T, Crompton R W 1988 Aust. J. Phys. 41 573
[44] Buckman S J, Brunger M J 1997 Aust. J. Phys. 50 483
[45] Crompton R W, Morrison M A 1993 Aust. J. Phys. 46 203
[46] Allan M 1985 J. Phys. B 18 L451
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