Investigation of the excitation of the internal states of hydrogen atom
Keywords:
scattering cross section, excitation cross section, nonideal semiclassical plasma, equation Calogero, effective interaction potentialAbstract
In this paper, the processes of the excitation of electron levels of hydrogen atom in an electron impact are presented. Excitation cross sections for different values of plasma dimensionless parameters are calculated that determine the state of the system. The method of quantum mechanics was used to theoretically study the processes of excitation of electron states of atom. To find the phase shifts, the Calogero equation was solved with an effective interaction potential between electron and atom in partially ionized hydrogen plasma. This effective potential takes into account the quantum-mechanical diffraction effect at small distances, the screening effect at large distances, has a finite value at distances close to zero. The excitation cross section was determined by integrating the differential scattering cross section over the scattering angles, the minimum scattering angle corresponding to this collision with the energy transfer equal to the excitation energy. The obtained results showed good agreement with the experimental data.
References
1 Walters H.R.J. Positron scatteringby atomic hydrogen at intermediate energies: 1s–1s–2s and 1s–2p transitions // J. Phys. B. – 1988. – Vol. 21. – P. 1893–1906.
2 Kernoghan A.A., Robinson D.J.R., McAlinden M.T., Walters H.R.J. Positron scatteringby atomic hydrogen // J. Phys. B. – 1996. – Vol. 29. – P. 2089–2102.
3 Zhou S., Li H., Kaupilla W.E., Kwan C.K., Stein T.S. Measurements of total and positronium formation cross section for positrons and electrons scattered by hydrogen atoms and molecules // Phys. Rev. A. – 1997. – Vol. 55. – P. 361–368.
4 Jones G.O., Charlton M., Slevin J., Laricchia G., Koever A., Poulsen M.R., Nic Chormaic S. Positron impact ionization of atomic hydrogen // J. Phys. B. – 1993. – Vol. 26. – P. 483–488.
5 Lugosi L., Paripas B., Gyemant I.K., Tokesi K. Differential cross sections for positron impact excitation of hydrogen // Radiation Physics and Chemistry – 2003. – Vol. 68. – P. 199–203.
6 Olson R.E. n 1 distributions inAq++H electroncapture collisions // Phys. Rev. A. – 1981. – Vol. 24. – P. 1726–1733.
7 Shultz D.R., Reinhold C.O., Olson R.E. Large-angle scatteringin positron-helium and positron-krypton collisions // Phys. Rev. A. – 1989. – Vol. 40. – P. 4947–4958.
8 Tokesi K., Koever A. Electron capture to the continuum at 54.4 eV positron-argon collisions // J. Phys. B. – 1996. – Vol. 33. – P. 3067–3077.
9 Morgan T.G., Geddes J. and Gilbody H.B. Formation of H(2p) and H(2s) atoms in collisions of 2-26 kev protons with hydrogen atoms // J. Phys. B. – 1973. – Vol. 6. – P. 2118.
10 Chang Y.P. and Fite W.L. Cross section for production of the metastable H(2s) state in proton collision with atomic hydrogen // Phys. Rev. A. – 1977. – Vol. 16. – P. 933.
11 Kimura M.and Thorson W.R. Molecular-state studies of charge transfer in Li3+-H, Be4+-H and B5+-H collisions // J. Phys. B: At. Mol. Phys. – 1983. – Vol. 16. – P. 1471.
12 Winter T.G. and Lin C.D. Triple-center treatment of electron transfer and excitation in p-H collisions // Phys. Rev. A. – 1984. – Vol. 29. – P. 567.
13 Janev R.K. and Krstic P.S. Excitation and ionization processes in slow collisions of ground-state and excited hydrogen atoms with protons // Phys. Rev. A. – 1992. – Vol. 46. – P. 5554.
14 Luedde H.J. and Dreizler R.M. Direct and capture processes in proton hydrogen scattering. II Total cross sections for bombarding energies of 1 to 50 keV// J. Phys. B. – 1982. – Vol. 15. – P. 2703.
15 Fritsch W. and Lin C.D. Coupled-state calculations for excitation, charge transfer, and ionization in 1-75-keV proton-hydrogen-atom collisions // Phys. Rev. A. – 1983. – Vol. 27. – P. 3361.
16 Shakesshaft R. Coupled-state calculations of proton—hydrogen-atom scattering using a scaled hydrogenic basis set // Phys. Rev. A. – 1978. – Vol. 18. – P. 1930.
17 Fitchard E., Ford A.L. and Reading J.F. Hydrogen-atom excitation and ionization by proton impact in the 50- to 200-keV energy region // Phys. Rev. A. – 1977. – Vol. 16. – P. 1325.
18 Freeman E.L. and Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: I // UKAEA Rept. No. CLM-R137 (Culham Laboratory, Abingdon, England, 1974); and: Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: II // UKAEA Rept. No. CLM-R175 (Culham Laboratory, Abingdon, England, 1977).
19 Celiberto R., Janev R.K., Laricchimta A., Capitelli M., Wadehra J.M. and Atems D.E. Cross section data for electron-impact inelastic processes of vibrationally excited molecules of hydrogen and its isotopes // At. Data Nucl. Data Tables. – 2001. – Vol. 77(2). – P. 161-214.
20 Saxena S., Gupta G.P. and Mathur C.K. Excitation of the hydrogen atom from its ground and metastable states by positron and proton impact at intermediate energies// J.Phys. B. – 1984. – Vol. 17. – P. 3743.
21 Kondow T., Girnius R.J., Chong Y.P. and Fite W.L. Production of Lyman-α radiation in collisions of protons and hydrogen atoms // Phys. Rev. A. – 1974. – Vol. 10. – P. 1167.
22 Young R.A., Stebbings R.F. and McGowan J.W. Lyman-α Production and Polarization in He+ Collisions with H and H2 // Phys. Rev. – 1968. – Vol. 171. – P. 85; Stebbings R.F. et al. Lyman-Alpha Production in H+−H(1s) Collisions // Phys. Rev. – 1965. – Vol. 138. – P. 1312.
23 Schartner K.H., Detleffsen D. and Sommer B. Excitation of the 2p level in atomic hydrogen by He+and H+ impact between 70 and 700 keV // Phys. Lett. A. – 1989. – Vol. 136. – P. 55.
24 Park J.T., Adlag J.E., George J.M. and Peacher J.L. Cross sections for excitation of atomic hydrogen to the n=2, 3, and 4 states by 15-200-keV protons // Phys. Rev. A. – 1976. – Vol. 14. – P. 608.
25 Reinhold C.O., Olson R.E. and Fritsch W. Excitation of atomic hydrogen by fully stripped ions // Phys. Rev. A. – 1990. – Vol. 41. – P. 4837.
26 Друкарев Т.Ф. Теория столкновений электронов с атомами. – М.: Физматгиз, 1963. – 37 c.
27 Бабиков В.В. Метод фазовых функций в квантовой механике. – М.: Наука, 1976. – 287 с.
28 Ramazanov T.S., Dzhumagulova K.N., Omarbakiyeva Y.A. Effective polarization interaction potential “charge-atom” for partially ly ionized dense plasma // Phys.Plasmas. – 2005. – Vol.12.- P.092702
29 Голант В.Е., Жилинский А.П., Сахаров С.А. Основы физики плазмы. – М.: Атомиздат, 1977. – С. 47-64.
References
1 H.R.J. Walters, J. Phys. B 21, 1893–1906, (1988). doi.org/10.1088/0953-4075/21/10/021
2 A.A. Kernoghan, D.J.R. Robinson, M.T. McAlinden, and H.R.J. Walters, J. Phys. B 29, 2089–2102, (1996).
3 S. Zhou, H. Li, W.E. Kaupilla, C.K. Kwan, and T.S. Stein, Phys. Rev. A 55, 361–368, (1997).
4 G.O. Jones, M. Charlton, J. Slevin, G. Laricchia, A. Koever, M.R. Poulsen, and S. Nic Chormaic, J. Phys. B 26, 483–488, (1993).
5 L. Lugosi, B. Paripas, I.K. Gyemant, and K.Tokesi, Radiation Physics and Chemistry 68, 199–203, (2003).
6 R.E. Olson, Phys. Rev. A 24, 1726–1733, (1981).
7 D.R. Shultz, C.O. Reinhold, and R.E. Olson, Phys. Rev. A 40, 4947–4958, (1989).
8 K. Tokesi, and A. Koever, J. Phys. B 33, 3067–3077, (1996).
9 T.G. Morgan, J. Geddes and H.B. Gilbody, J. Phys. B 6, 2118, (1973).
10 Y.P. Chang and W.L. Fite, Phys. Rev. A 16, 933, (1977).
11 M. Kimura and W.R. Thorson, J. Phys. B: At. Mol. Phys. 16, 1471, (1983).
12 T.G. Winter, C.D. Lin, Phys. Rev. A 29, 567, (1984). doi.org/10.1103/PhysRevA.29.567
13 R.K. Janev and P.S. Krstic, Phys. Rev. A 46, 5554, (1992). doi.org/10.1103/PhysRevA.46.5554
14 H.J. Luedde and R.M. Dreizler, J.Phys. B 15, 2703, (1982).
15 W. Fritsch and C.D. Lin, Phys. Rev. A 27, 3361, (1977). doi.org/10.1103/PhysRevA.27.3361
16 R. Shakesshaft, Phys. Rev. A 18, 1930, (1978). doi.org/10.1103/PhysRevA.18.1930
17 E. Fitchard, A.L. Ford and J.F. Reading, Phys. Rev. A 16, 1325, (1977). doi.org/10.1103/PhysRevA.16.1325
18 E.L. Freeman and E.M. Jones, Atomic Collision Processes in Plasma Physics Experiments: I (UKAEA Rept. No. CLM-R137 (Culham Laboratory, Abingdon, England, 1974)); and: Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: II, (UKAEA Rept. No. CLM-R175 (Culham Laboratory, Abingdon, England, 1977)).
19 R. Celiberto, R.K. Janev, A. Laricchimta, M. Capitelli, J.M. Wadehra and D.E. Atems, At. Data Nucl. Data Tables 77, 161, (2001). doi: 10.1006/adnd.2000.0850
20 S. Saxena, G.P. Gupta and C.K. Mathur, J.Phys. B 17, 3743, (1984).
21 T. Kondow, R.J. Girnius, Y.P. Chong and W.L. Fite, Phys. Rev. A 10, 1167, (1974).
22 R.A. Young, R.F. Stebbings and J.W. McGowan, Phys. Rev. 171, 85, (1968). doi.org/10.1103/PhysRev.171.85; R.F. Stebbings et al. Phys. Rev. 138, 1312, (1965). doi.org/10.1103/PhysRev.138.A1312.
23 K.H. Schartner, D. Detleffsen and B. Sommer, Phys. Lett. A 136, 55, (1989). doi.org/10.1016/0375-9601(89)90676-2
24 J.T. Park, J.E. Adlag, J.M. George and J.L. Peacher, Phys. Rev. A 14, 608, (1976). doi.org/10.1103/PhysRevA.14.608
25 C.O. Reinhold, R.E. Olson and W. Fritsch, Phys. Rev. A 41, 4837, (1990).
26 T.F. Drukarev Teoriya stolknoveniy elektronov s atomami. (Moscow: Fizmatgiz, 1963), 37 p. (in Russ).
27 V.V. Babikov Metod fazovykh funktsiy v kvantovoy mekhanike (Moscow: Nauka, 1976), 287 p. (in Russ).
28 T.S. Ramazanov, K.N. Dzhumagulova, Y.A. Omarbakiyeva, Phys.Plasmas 12, 092702, (2005)
29 V.Ye. Golant, A.P. Zhilinskiy, S.A. Sakharov Osnovy fiziki plazmy (Moscow: Atomizdat, 1977), pp. 47-64. (in Russ).
2 Kernoghan A.A., Robinson D.J.R., McAlinden M.T., Walters H.R.J. Positron scatteringby atomic hydrogen // J. Phys. B. – 1996. – Vol. 29. – P. 2089–2102.
3 Zhou S., Li H., Kaupilla W.E., Kwan C.K., Stein T.S. Measurements of total and positronium formation cross section for positrons and electrons scattered by hydrogen atoms and molecules // Phys. Rev. A. – 1997. – Vol. 55. – P. 361–368.
4 Jones G.O., Charlton M., Slevin J., Laricchia G., Koever A., Poulsen M.R., Nic Chormaic S. Positron impact ionization of atomic hydrogen // J. Phys. B. – 1993. – Vol. 26. – P. 483–488.
5 Lugosi L., Paripas B., Gyemant I.K., Tokesi K. Differential cross sections for positron impact excitation of hydrogen // Radiation Physics and Chemistry – 2003. – Vol. 68. – P. 199–203.
6 Olson R.E. n 1 distributions inAq++H electroncapture collisions // Phys. Rev. A. – 1981. – Vol. 24. – P. 1726–1733.
7 Shultz D.R., Reinhold C.O., Olson R.E. Large-angle scatteringin positron-helium and positron-krypton collisions // Phys. Rev. A. – 1989. – Vol. 40. – P. 4947–4958.
8 Tokesi K., Koever A. Electron capture to the continuum at 54.4 eV positron-argon collisions // J. Phys. B. – 1996. – Vol. 33. – P. 3067–3077.
9 Morgan T.G., Geddes J. and Gilbody H.B. Formation of H(2p) and H(2s) atoms in collisions of 2-26 kev protons with hydrogen atoms // J. Phys. B. – 1973. – Vol. 6. – P. 2118.
10 Chang Y.P. and Fite W.L. Cross section for production of the metastable H(2s) state in proton collision with atomic hydrogen // Phys. Rev. A. – 1977. – Vol. 16. – P. 933.
11 Kimura M.and Thorson W.R. Molecular-state studies of charge transfer in Li3+-H, Be4+-H and B5+-H collisions // J. Phys. B: At. Mol. Phys. – 1983. – Vol. 16. – P. 1471.
12 Winter T.G. and Lin C.D. Triple-center treatment of electron transfer and excitation in p-H collisions // Phys. Rev. A. – 1984. – Vol. 29. – P. 567.
13 Janev R.K. and Krstic P.S. Excitation and ionization processes in slow collisions of ground-state and excited hydrogen atoms with protons // Phys. Rev. A. – 1992. – Vol. 46. – P. 5554.
14 Luedde H.J. and Dreizler R.M. Direct and capture processes in proton hydrogen scattering. II Total cross sections for bombarding energies of 1 to 50 keV// J. Phys. B. – 1982. – Vol. 15. – P. 2703.
15 Fritsch W. and Lin C.D. Coupled-state calculations for excitation, charge transfer, and ionization in 1-75-keV proton-hydrogen-atom collisions // Phys. Rev. A. – 1983. – Vol. 27. – P. 3361.
16 Shakesshaft R. Coupled-state calculations of proton—hydrogen-atom scattering using a scaled hydrogenic basis set // Phys. Rev. A. – 1978. – Vol. 18. – P. 1930.
17 Fitchard E., Ford A.L. and Reading J.F. Hydrogen-atom excitation and ionization by proton impact in the 50- to 200-keV energy region // Phys. Rev. A. – 1977. – Vol. 16. – P. 1325.
18 Freeman E.L. and Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: I // UKAEA Rept. No. CLM-R137 (Culham Laboratory, Abingdon, England, 1974); and: Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: II // UKAEA Rept. No. CLM-R175 (Culham Laboratory, Abingdon, England, 1977).
19 Celiberto R., Janev R.K., Laricchimta A., Capitelli M., Wadehra J.M. and Atems D.E. Cross section data for electron-impact inelastic processes of vibrationally excited molecules of hydrogen and its isotopes // At. Data Nucl. Data Tables. – 2001. – Vol. 77(2). – P. 161-214.
20 Saxena S., Gupta G.P. and Mathur C.K. Excitation of the hydrogen atom from its ground and metastable states by positron and proton impact at intermediate energies// J.Phys. B. – 1984. – Vol. 17. – P. 3743.
21 Kondow T., Girnius R.J., Chong Y.P. and Fite W.L. Production of Lyman-α radiation in collisions of protons and hydrogen atoms // Phys. Rev. A. – 1974. – Vol. 10. – P. 1167.
22 Young R.A., Stebbings R.F. and McGowan J.W. Lyman-α Production and Polarization in He+ Collisions with H and H2 // Phys. Rev. – 1968. – Vol. 171. – P. 85; Stebbings R.F. et al. Lyman-Alpha Production in H+−H(1s) Collisions // Phys. Rev. – 1965. – Vol. 138. – P. 1312.
23 Schartner K.H., Detleffsen D. and Sommer B. Excitation of the 2p level in atomic hydrogen by He+and H+ impact between 70 and 700 keV // Phys. Lett. A. – 1989. – Vol. 136. – P. 55.
24 Park J.T., Adlag J.E., George J.M. and Peacher J.L. Cross sections for excitation of atomic hydrogen to the n=2, 3, and 4 states by 15-200-keV protons // Phys. Rev. A. – 1976. – Vol. 14. – P. 608.
25 Reinhold C.O., Olson R.E. and Fritsch W. Excitation of atomic hydrogen by fully stripped ions // Phys. Rev. A. – 1990. – Vol. 41. – P. 4837.
26 Друкарев Т.Ф. Теория столкновений электронов с атомами. – М.: Физматгиз, 1963. – 37 c.
27 Бабиков В.В. Метод фазовых функций в квантовой механике. – М.: Наука, 1976. – 287 с.
28 Ramazanov T.S., Dzhumagulova K.N., Omarbakiyeva Y.A. Effective polarization interaction potential “charge-atom” for partially ly ionized dense plasma // Phys.Plasmas. – 2005. – Vol.12.- P.092702
29 Голант В.Е., Жилинский А.П., Сахаров С.А. Основы физики плазмы. – М.: Атомиздат, 1977. – С. 47-64.
References
1 H.R.J. Walters, J. Phys. B 21, 1893–1906, (1988). doi.org/10.1088/0953-4075/21/10/021
2 A.A. Kernoghan, D.J.R. Robinson, M.T. McAlinden, and H.R.J. Walters, J. Phys. B 29, 2089–2102, (1996).
3 S. Zhou, H. Li, W.E. Kaupilla, C.K. Kwan, and T.S. Stein, Phys. Rev. A 55, 361–368, (1997).
4 G.O. Jones, M. Charlton, J. Slevin, G. Laricchia, A. Koever, M.R. Poulsen, and S. Nic Chormaic, J. Phys. B 26, 483–488, (1993).
5 L. Lugosi, B. Paripas, I.K. Gyemant, and K.Tokesi, Radiation Physics and Chemistry 68, 199–203, (2003).
6 R.E. Olson, Phys. Rev. A 24, 1726–1733, (1981).
7 D.R. Shultz, C.O. Reinhold, and R.E. Olson, Phys. Rev. A 40, 4947–4958, (1989).
8 K. Tokesi, and A. Koever, J. Phys. B 33, 3067–3077, (1996).
9 T.G. Morgan, J. Geddes and H.B. Gilbody, J. Phys. B 6, 2118, (1973).
10 Y.P. Chang and W.L. Fite, Phys. Rev. A 16, 933, (1977).
11 M. Kimura and W.R. Thorson, J. Phys. B: At. Mol. Phys. 16, 1471, (1983).
12 T.G. Winter, C.D. Lin, Phys. Rev. A 29, 567, (1984). doi.org/10.1103/PhysRevA.29.567
13 R.K. Janev and P.S. Krstic, Phys. Rev. A 46, 5554, (1992). doi.org/10.1103/PhysRevA.46.5554
14 H.J. Luedde and R.M. Dreizler, J.Phys. B 15, 2703, (1982).
15 W. Fritsch and C.D. Lin, Phys. Rev. A 27, 3361, (1977). doi.org/10.1103/PhysRevA.27.3361
16 R. Shakesshaft, Phys. Rev. A 18, 1930, (1978). doi.org/10.1103/PhysRevA.18.1930
17 E. Fitchard, A.L. Ford and J.F. Reading, Phys. Rev. A 16, 1325, (1977). doi.org/10.1103/PhysRevA.16.1325
18 E.L. Freeman and E.M. Jones, Atomic Collision Processes in Plasma Physics Experiments: I (UKAEA Rept. No. CLM-R137 (Culham Laboratory, Abingdon, England, 1974)); and: Jones E.M. Atomic Collision Processes in Plasma Physics Experiments: II, (UKAEA Rept. No. CLM-R175 (Culham Laboratory, Abingdon, England, 1977)).
19 R. Celiberto, R.K. Janev, A. Laricchimta, M. Capitelli, J.M. Wadehra and D.E. Atems, At. Data Nucl. Data Tables 77, 161, (2001). doi: 10.1006/adnd.2000.0850
20 S. Saxena, G.P. Gupta and C.K. Mathur, J.Phys. B 17, 3743, (1984).
21 T. Kondow, R.J. Girnius, Y.P. Chong and W.L. Fite, Phys. Rev. A 10, 1167, (1974).
22 R.A. Young, R.F. Stebbings and J.W. McGowan, Phys. Rev. 171, 85, (1968). doi.org/10.1103/PhysRev.171.85; R.F. Stebbings et al. Phys. Rev. 138, 1312, (1965). doi.org/10.1103/PhysRev.138.A1312.
23 K.H. Schartner, D. Detleffsen and B. Sommer, Phys. Lett. A 136, 55, (1989). doi.org/10.1016/0375-9601(89)90676-2
24 J.T. Park, J.E. Adlag, J.M. George and J.L. Peacher, Phys. Rev. A 14, 608, (1976). doi.org/10.1103/PhysRevA.14.608
25 C.O. Reinhold, R.E. Olson and W. Fritsch, Phys. Rev. A 41, 4837, (1990).
26 T.F. Drukarev Teoriya stolknoveniy elektronov s atomami. (Moscow: Fizmatgiz, 1963), 37 p. (in Russ).
27 V.V. Babikov Metod fazovykh funktsiy v kvantovoy mekhanike (Moscow: Nauka, 1976), 287 p. (in Russ).
28 T.S. Ramazanov, K.N. Dzhumagulova, Y.A. Omarbakiyeva, Phys.Plasmas 12, 092702, (2005)
29 V.Ye. Golant, A.P. Zhilinskiy, S.A. Sakharov Osnovy fiziki plazmy (Moscow: Atomizdat, 1977), pp. 47-64. (in Russ).
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2017-09-25
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