耦合通道光学势方法研究低能下电子同钠原子的碰撞
摘要
低能电子同原子的相互作用,存在着一种重要的物理现象:共振,即入射电子和靶原子能够形成不稳定的准束缚态(quasi-bound states),其会在散射相移和散射截面上引起剧烈的变化。对共振现象的研究对理解多体体系的基本对称性和相互作用动力学等都起着非常重要的作用。
1995年,Johnston and Burrow的电子跃迁光谱实验发现了在电离阈值以下电子碰撞碱金属原子中存在着一个复杂的共振序列(series resonance),并且在所有的碱金属之间能够形成一个“家族式”共振(family resemblance);但是到目前为止,还没有一个理论方法能够完整地预言低能情况下电子同碱金属原子碰撞所产生的共振序列,尤其是在接近电离阈值的区域。在本文工作中,我们首次将耦合通道光学势方法(CCO)应用于低能情况下的电子同钠原子的碰撞,计算了其电离阈值以下的总散射截面,并且从中得到了共振序列。
从我们的计算结果可以看出,低激发态附近的几个共振与其他理论和实验结果都符合的非常好,我们在4.166、4.502和4.578 eV发现了三个峰值,这三个峰值能够确认Johnston and Burrow的实验结果,这是他们的实验结果在十多年后首次被我们的计算证实。此外我们还在1.80 eV预言了一个峰值,总散射截面与Rubin et al.的测量结果符合的非常好,由于其他理论和实验都没有得到这一峰值,其尚未被证明是由共振引起的,在将来的工作中,我们会对这一现象做进一步的研究。我们在5s激发阈值(4.128 eV)至电离阈值(5.14 eV)之间的能量范围内预言了许多新的共振,这些共振和低激发态附近的共振一起组成一个较为完整的共振序列。对电子碰撞钠原子共振序列的成功验证,使得我们相信CCO方法能够用来研究其他碱金属原子的共振序列,并且进一步地研究碱金属原子间的“家族式”共振。
早在1966年Mittleman就指出,由于吸引的偶极势的存在,正电子与氢原子的碰撞同样能够产生共振。最近,CCO方法被成功地用于正电子同氢原子碰撞的共振研究,并且取得了很好的结果。钠原子由于其简单的类氢壳层结构为研究正电子同更复杂原子的共振现象奠定了基础。
CCO方法在电子-钠原子体系和正电子-氢原子体系的共振研究上的成功,使得我们能够应用此方法来研究正电子-钠原子的共振现象。我们计算了10 eV以下的正电子同钠原子的总散射截面并与已知的理论和实验数据进行了比较,取得了很好的结果。迄今为止只有少数的理论方法被用来研究钠原子的前几个分波的共振,他们的计算结果集中在2 - 4 eV,而我们的计算也在这一区域显示出明显的共振现象。具体的分波共振在进一步的计算中。
Low-energy electron collision with sodium exhibits dramatic negative-ion resonances, consisting of the temporary bounding of the incident electron with target atom, which have significant contributions to the total cross sections.
In the present work we employed the momentum space coupled-channel optical potential (CCO) method to calculate the low-energy scattering of electrons by sodium at incident energies up to ionization threshold and predict the positions and the configurations for most of the lower-lying resonances. The present results are in good agreement with available experimental data and previous theoretical calculations. Furthermore, some higher-lying resonances are put forth propositionally at the energies near the ionization threshold, which are especially agreement with the resonance series observed by Johnston and Burrow.
We also calculated the total cross sections for low-energy positron-Sodium scattering and the present results have shown significant resonances in the region of 2-4 eV. Further calculation will be performed in the future work.
1995年,Johnston and Burrow的电子跃迁光谱实验发现了在电离阈值以下电子碰撞碱金属原子中存在着一个复杂的共振序列(series resonance),并且在所有的碱金属之间能够形成一个“家族式”共振(family resemblance);但是到目前为止,还没有一个理论方法能够完整地预言低能情况下电子同碱金属原子碰撞所产生的共振序列,尤其是在接近电离阈值的区域。在本文工作中,我们首次将耦合通道光学势方法(CCO)应用于低能情况下的电子同钠原子的碰撞,计算了其电离阈值以下的总散射截面,并且从中得到了共振序列。
从我们的计算结果可以看出,低激发态附近的几个共振与其他理论和实验结果都符合的非常好,我们在4.166、4.502和4.578 eV发现了三个峰值,这三个峰值能够确认Johnston and Burrow的实验结果,这是他们的实验结果在十多年后首次被我们的计算证实。此外我们还在1.80 eV预言了一个峰值,总散射截面与Rubin et al.的测量结果符合的非常好,由于其他理论和实验都没有得到这一峰值,其尚未被证明是由共振引起的,在将来的工作中,我们会对这一现象做进一步的研究。我们在5s激发阈值(4.128 eV)至电离阈值(5.14 eV)之间的能量范围内预言了许多新的共振,这些共振和低激发态附近的共振一起组成一个较为完整的共振序列。对电子碰撞钠原子共振序列的成功验证,使得我们相信CCO方法能够用来研究其他碱金属原子的共振序列,并且进一步地研究碱金属原子间的“家族式”共振。
早在1966年Mittleman就指出,由于吸引的偶极势的存在,正电子与氢原子的碰撞同样能够产生共振。最近,CCO方法被成功地用于正电子同氢原子碰撞的共振研究,并且取得了很好的结果。钠原子由于其简单的类氢壳层结构为研究正电子同更复杂原子的共振现象奠定了基础。
CCO方法在电子-钠原子体系和正电子-氢原子体系的共振研究上的成功,使得我们能够应用此方法来研究正电子-钠原子的共振现象。我们计算了10 eV以下的正电子同钠原子的总散射截面并与已知的理论和实验数据进行了比较,取得了很好的结果。迄今为止只有少数的理论方法被用来研究钠原子的前几个分波的共振,他们的计算结果集中在2 - 4 eV,而我们的计算也在这一区域显示出明显的共振现象。具体的分波共振在进一步的计算中。
Low-energy electron collision with sodium exhibits dramatic negative-ion resonances, consisting of the temporary bounding of the incident electron with target atom, which have significant contributions to the total cross sections.
In the present work we employed the momentum space coupled-channel optical potential (CCO) method to calculate the low-energy scattering of electrons by sodium at incident energies up to ionization threshold and predict the positions and the configurations for most of the lower-lying resonances. The present results are in good agreement with available experimental data and previous theoretical calculations. Furthermore, some higher-lying resonances are put forth propositionally at the energies near the ionization threshold, which are especially agreement with the resonance series observed by Johnston and Burrow.
We also calculated the total cross sections for low-energy positron-Sodium scattering and the present results have shown significant resonances in the region of 2-4 eV. Further calculation will be performed in the future work.
引文
1. E. P. Wigner, Phys. Rev. 73, 1002 (1948)
2. B. Bederson and L. J. Kieffer, Rev. Mod. Phys. 43, 601 (1971)
3. S. J. Buckman and C. W. Clark, Rev. Mod. Phys. 66, 539 (1994)
4. I. I. Fabrikant and V. S. Lebedev, J. Phys. B: At. Mol. Opt. Phys. 33, 1521 (2000)
5. A.Z. Msezane, Z. Felfli and D. Sokolovski, Chem. Phys. Lett. 456, 96 (2008)
6. D. R. Bates, Adv. At. Mol. Opt. Phys. 27, 1 (1991)
7. A. Kasdan and W. C. Lineberger, Phys. Rev. A 10, 1658 (1974)
8. T. Andersen, Phys. Scr. T 34, 23 (1991)
9. C. Blondel, Phys. Scr. T 58, 31 (1995)
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11. R. B. Brode, Phys. Rev. 34, 673 (1929)
12. J. Perel, P. Englander and B. Bederson, Phys. Rev. 128, 1148 (1962)
13. K. Rubin, B. Bederson, M. Goldstein and R. E. Collins, Phys. Rev. 182, 201 (1969)
14. A. Kasdan, T. M. Miller and B. Bederson, Phys. Rev. A 8, 1562 (1973)
15. W. Gehenn and E. Reichert, Z. Phys. 254, 28 (1972)
16. D. Andrick, M. Eyb and M. Hofmann, J. Phys. B: At. Mol. Opt. Phys. 5, L15 (1972)
17. M. Eyb and M. Hofmann, J. Phys. B: At. Mol. Opt. Phys. 8, 1095 (1975)
18. T. A. Patterson, H. Hotop, A. Kasdan, D. W. Norcross and W. C. Lineberger, Phys. Rev. Lett. 32, 189 (1974)
19. A. R. Johnston and P. D. Burrow, J. Phys. B: At. Mol. Opt. Phys. 15, L745 (1982)
20. A. R. Johnston and P. D. Burrow, Phys. Rev. A 51, 406 (1995)
21. C. K. Kwan, W. E. Kauppila et al. Phys. Rev. A 44, 1620 (1991)
22. D. W. Norcross, J. Phys. B: At. Mol. Opt. Phys. 4, 1458 (1971)
23. E. Karule, J. Phys. B: At. Mol. Opt. Phys. 5, 2051 (1972)
24. D. L. Moores and D. W. Norcross, J. Phys. B: At. Mol. Opt. Phys. 5, 1482 (1972)
25. A. L. Sinfailam and R. K. Nesbet, Phys. Rev. A 7, 1987 (1973)
26. Y. Nakamura and J. Lucas, J. Phys. D 11, 325 (1978)
27. I. I. Fabrikant, Opt. Spectrosc. 53, 131 (1982)
28. A. C. Fung and J. J. Matese, Phys. Rev. A 5, 22 (1972)
29. A. W. Weiss, Phys. Rev. 166, 70 (1968)
30. H. R. J. Walters, J. Phys. B: At. Mol. Opt. Phys. 9, 227 (1976)
31. I. Bray, Phys. Rev. A 49, R1 (1994)
32. I. Bray, Phys. Rev. A 49, 1066 (1994)
33. I. Bray, Phys. Rev. Lett. 73, 1088 (1994)
34. I. E. McCarthy and A. T. Stelbovics, Phys. Rev. A 28, 2693 (1983)
35. H. S. Taylor, G. V. Nazaroff and A. Golebiewski, J. Chem. Phys. 45, 2872 (1966)
36. H. S. Taylor and L. D. Thomas, Phys. Rev. Lett. 28, 1091 (1972)
37. P. G. Burke and J. F. B. Mitchell, J. Phys. B: At. Mol. Opt. Phys. 6, L161 (1973)
38. D. L. Moores, J. Phys. B: At. Mol. Opt. Phys. 9, 1329 (1976)
39. N. S. Scott, K. Bartschat, P. G. Burke, O. Nagy and W. B. Eissner, J. Phys. B: At. Mol. Opt. Phys. 17, 3755 (1984)
40. O. I. Zatsarinny, V. I. Lengyel, E. P. Sabad and I. I. Cherlenyak, Izv. Akad. Nauk SSSR, Ser. Fiz. 50,1377 (1986)
41. M. H. Mittleman, Phys. Rev. 152, 76 (1966)
42. G. J. Seiler, R. S. Oberoi, and J. Callaway, Phys. Rev. A 3 2006 (1971)
43. K. Higgins and P. G. Burke, J. Phys. B: At. Mol. Opt. Phys. 26 4269 (1993)
44. Y. K. Ho and Z. C. Yan, Phys. Rev. A 70 032716 (2004)
45. Z. C. Yan and Y. K. Ho, Phys. Rev. A 77 030701 (2008)
46. J. Yuan, B. D. Esry, T. Morishita and C. D. Lin, Phys. Rev. A 58, R4 (1998)
47. G. Ryzhikh, J. Mitroy and K. Varga, J. Phys. B: At. Mol. Opt. Phys. 31, L265 (1998)
48. H. Han, Y. Li, X. Zhang and T. Shi, J. Chem. Phys. 128, 244314 (2008)
49. R.M.Yu, Y.Zhou, L.G.Jiao,Resonances in Positron Hydrogen Scattering,submitted to Phys.Rev.A.
50. S. J. Ward, M. Horbatsch, R. P. McEachran and A. D. Stauffer, J. Phys. B: At. Mol. Opt. Phys. 22, 1845 (1989)
51. R. N. Hewitt, C. J. Noble and B. H. Bransden, J. Phys. B: At. Mol. Opt. Phys. 26, 3663 (1993)
52. G. Ryzhikh and J. Mitroy, J. Phys. B: At. Mol. Opt. Phys. 30, 5545 (1997)
53. M. T. McAlinden, A. A. Kernoghan and H. R. J. Walters, Hyperfine Int. 89, 161 (1994)
54. A. A. Kernoghan, Ph.D. thesis, Queens’s University of Belfast. (1996)
55. C. K. Kwan, W. E. Kauppila et al. Phys. Rev. A 44, 1620 (1991)
56. W. E. Kauppila, C. K. Kwan, T. S. Stein and S. Zhou, J. Phys. B: At. Mol. Opt. Phys. 27, L551 (1994)
57. S. J. Ward, M. Horbatsch, R. P. McEachran and A. D. Stauffer, J. Phys. B: At. Mol. Opt. Phys. 22, 3763 (1989)
58. S. Kar and Y. K. Ho, Eur. Phys. J. D 35, 453 (2005)
59. H. Han, Z. Zhong, X. Zhang and T. Shi, Phys. Rev. A 77, 012721 (2008)
2. B. Bederson and L. J. Kieffer, Rev. Mod. Phys. 43, 601 (1971)
3. S. J. Buckman and C. W. Clark, Rev. Mod. Phys. 66, 539 (1994)
4. I. I. Fabrikant and V. S. Lebedev, J. Phys. B: At. Mol. Opt. Phys. 33, 1521 (2000)
5. A.Z. Msezane, Z. Felfli and D. Sokolovski, Chem. Phys. Lett. 456, 96 (2008)
6. D. R. Bates, Adv. At. Mol. Opt. Phys. 27, 1 (1991)
7. A. Kasdan and W. C. Lineberger, Phys. Rev. A 10, 1658 (1974)
8. T. Andersen, Phys. Scr. T 34, 23 (1991)
9. C. Blondel, Phys. Scr. T 58, 31 (1995)
10. G. J. Schulz, Rev. Mod. Phys. 45, 378 (1973)
11. R. B. Brode, Phys. Rev. 34, 673 (1929)
12. J. Perel, P. Englander and B. Bederson, Phys. Rev. 128, 1148 (1962)
13. K. Rubin, B. Bederson, M. Goldstein and R. E. Collins, Phys. Rev. 182, 201 (1969)
14. A. Kasdan, T. M. Miller and B. Bederson, Phys. Rev. A 8, 1562 (1973)
15. W. Gehenn and E. Reichert, Z. Phys. 254, 28 (1972)
16. D. Andrick, M. Eyb and M. Hofmann, J. Phys. B: At. Mol. Opt. Phys. 5, L15 (1972)
17. M. Eyb and M. Hofmann, J. Phys. B: At. Mol. Opt. Phys. 8, 1095 (1975)
18. T. A. Patterson, H. Hotop, A. Kasdan, D. W. Norcross and W. C. Lineberger, Phys. Rev. Lett. 32, 189 (1974)
19. A. R. Johnston and P. D. Burrow, J. Phys. B: At. Mol. Opt. Phys. 15, L745 (1982)
20. A. R. Johnston and P. D. Burrow, Phys. Rev. A 51, 406 (1995)
21. C. K. Kwan, W. E. Kauppila et al. Phys. Rev. A 44, 1620 (1991)
22. D. W. Norcross, J. Phys. B: At. Mol. Opt. Phys. 4, 1458 (1971)
23. E. Karule, J. Phys. B: At. Mol. Opt. Phys. 5, 2051 (1972)
24. D. L. Moores and D. W. Norcross, J. Phys. B: At. Mol. Opt. Phys. 5, 1482 (1972)
25. A. L. Sinfailam and R. K. Nesbet, Phys. Rev. A 7, 1987 (1973)
26. Y. Nakamura and J. Lucas, J. Phys. D 11, 325 (1978)
27. I. I. Fabrikant, Opt. Spectrosc. 53, 131 (1982)
28. A. C. Fung and J. J. Matese, Phys. Rev. A 5, 22 (1972)
29. A. W. Weiss, Phys. Rev. 166, 70 (1968)
30. H. R. J. Walters, J. Phys. B: At. Mol. Opt. Phys. 9, 227 (1976)
31. I. Bray, Phys. Rev. A 49, R1 (1994)
32. I. Bray, Phys. Rev. A 49, 1066 (1994)
33. I. Bray, Phys. Rev. Lett. 73, 1088 (1994)
34. I. E. McCarthy and A. T. Stelbovics, Phys. Rev. A 28, 2693 (1983)
35. H. S. Taylor, G. V. Nazaroff and A. Golebiewski, J. Chem. Phys. 45, 2872 (1966)
36. H. S. Taylor and L. D. Thomas, Phys. Rev. Lett. 28, 1091 (1972)
37. P. G. Burke and J. F. B. Mitchell, J. Phys. B: At. Mol. Opt. Phys. 6, L161 (1973)
38. D. L. Moores, J. Phys. B: At. Mol. Opt. Phys. 9, 1329 (1976)
39. N. S. Scott, K. Bartschat, P. G. Burke, O. Nagy and W. B. Eissner, J. Phys. B: At. Mol. Opt. Phys. 17, 3755 (1984)
40. O. I. Zatsarinny, V. I. Lengyel, E. P. Sabad and I. I. Cherlenyak, Izv. Akad. Nauk SSSR, Ser. Fiz. 50,1377 (1986)
41. M. H. Mittleman, Phys. Rev. 152, 76 (1966)
42. G. J. Seiler, R. S. Oberoi, and J. Callaway, Phys. Rev. A 3 2006 (1971)
43. K. Higgins and P. G. Burke, J. Phys. B: At. Mol. Opt. Phys. 26 4269 (1993)
44. Y. K. Ho and Z. C. Yan, Phys. Rev. A 70 032716 (2004)
45. Z. C. Yan and Y. K. Ho, Phys. Rev. A 77 030701 (2008)
46. J. Yuan, B. D. Esry, T. Morishita and C. D. Lin, Phys. Rev. A 58, R4 (1998)
47. G. Ryzhikh, J. Mitroy and K. Varga, J. Phys. B: At. Mol. Opt. Phys. 31, L265 (1998)
48. H. Han, Y. Li, X. Zhang and T. Shi, J. Chem. Phys. 128, 244314 (2008)
49. R.M.Yu, Y.Zhou, L.G.Jiao,Resonances in Positron Hydrogen Scattering,submitted to Phys.Rev.A.
50. S. J. Ward, M. Horbatsch, R. P. McEachran and A. D. Stauffer, J. Phys. B: At. Mol. Opt. Phys. 22, 1845 (1989)
51. R. N. Hewitt, C. J. Noble and B. H. Bransden, J. Phys. B: At. Mol. Opt. Phys. 26, 3663 (1993)
52. G. Ryzhikh and J. Mitroy, J. Phys. B: At. Mol. Opt. Phys. 30, 5545 (1997)
53. M. T. McAlinden, A. A. Kernoghan and H. R. J. Walters, Hyperfine Int. 89, 161 (1994)
54. A. A. Kernoghan, Ph.D. thesis, Queens’s University of Belfast. (1996)
55. C. K. Kwan, W. E. Kauppila et al. Phys. Rev. A 44, 1620 (1991)
56. W. E. Kauppila, C. K. Kwan, T. S. Stein and S. Zhou, J. Phys. B: At. Mol. Opt. Phys. 27, L551 (1994)
57. S. J. Ward, M. Horbatsch, R. P. McEachran and A. D. Stauffer, J. Phys. B: At. Mol. Opt. Phys. 22, 3763 (1989)
58. S. Kar and Y. K. Ho, Eur. Phys. J. D 35, 453 (2005)
59. H. Han, Z. Zhong, X. Zhang and T. Shi, Phys. Rev. A 77, 012721 (2008)