- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Mechanisms for charge transfer (or for the capture of any light particle) at asymptotically high impact velocities

Robin Shakeshaft and Larry Spruch*

Robin Shakeshaft

  • Physics Department, Texas A&M University, College Station, Texas 77843

Larry Spruch*

  • Physics Department, New York University, New York, New York 10003 and Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138

  • *Permanent address.
PDF

Rev. Mod. Phys. 51, 369 – Published 1 April, 1979

DOI: https://doi.org/10.1103/RevModPhys.51.369

Abstract

Within the nonrelativistic approximation the authors discuss three different mechanisms for the capture of a light particle from a bare heavy nucleus by another bare heavy nucleus which is incident with a very high relative velocity. The emphasis is on physical interpretation. For each mechanism a "physical" (i.e., more readily comprehensible) derivation is given of the asymptotic form of the total cross section, and a comparison is made of the relative importance of the different mechanisms in the case of electron capture from hydrogenlike "atoms." (Electron capture is normally referred to as charge transfer). The first mechanism is knock-on capture, where the two nuclei have equal masses and simply switch places. The second mechanism is radiative capture, which occurs with the emission of a photon. The third mechanism, which is perhaps the most interesting one, is double scattering, first suggested within the framework of classical mechanics by Thomas in 1927. In this mechanism the light particle undergoes two collisions, the first with the incident nucleus, and the second with the target nucleus; the light particle finally has almost the same velocity as the incident nucleus and therefore has a reasonable probability of being captured. The capture process in the asymptotic domain is a fascinating one theoretically since radiative capture can dominate over nonradiative capture; what is perhaps more remarkable is that for nonradiative capture integrated over the forward direction the second Born contribution dominates over the first in the asymptotic limit. For the capture of an electron bound in a high Rydberg state, capture via the knock-on the double scattering mechanisms are describable classically (Thomas' result becomes exact!) and (near the forward direction) the second Born(Born again) term dominates over the first at much lower energy. (Changing only the notation and the kinematics, the results can be used to study mass transfer processes in which one of a massive gravitationally pound pair of astrophysical objects is captured by a third massive object). A number of results for capture into a true bound state can be readily carried over to "capture to the continuum," with the electron emerging with a small positive energy relative to the incident nucleus. An understanding of the asymptotic form of the capture cross section is of considerable interest in its own right; it may also be helpful in understanding the dynamics of the capture process in the medium velocity range where applications are important. At medium velocities electron capture is of interest in many areas of physics such as astrophysics, chemical physics, plasma physics, and atomic physics; it is also of practical interest, having applications in laser and fusion research.

View figure in article

References (86)

  1. Aaron, R., R. D. Amado, and B. W. Lee, 1961, Phys. Rev. 121, 319
  2. Abramowitz, M., and I. Stegun, 1970, Handbook of Mathematical Functions (Dover, New York)
  3. Abrines, R., and I. C. Percival, 1966, Proc. Phys. Soc. Lond. 88, 861
  4. Bates, D. R., and R. McCarroll, 1958, Proc. R. Soc. A 245, 175
  5. Bates, D. R., C. J. Cook, and F. J. Smith, 1964, Proc. Phys. Soc. Lond. 83, 49
  6. Bates, D. R., and R. A. Mapleton, 1965, Proc. Phys. Soc. Lond. 85, 605
  7. Bates, D. R., and R. A. Mapleton, 1966, Proc. Phys. Soc. Lond. 87, 657
  8. Belkić Dž., 1977, J. Phys. B 10, 3491
  9. Bethe, H. A., and E. E. Salpeter, 1957, Quantum Mechanics of One- and Two-Electron Atoms (Academic, New York), p. 322
  10. Bohr, N., 1948, K. Dan Vidensk. Selsk. Mat.-Fys. Medd. 18
  11. Bonham, R. A., 1972, J. Chem. Phys. 57, 1604
  12. Bransden, B. H., 1972, Rep. Prog. Phys. 35, 949
  13. Briggs, J. S., 1977, J. Phys. B 10, 3075
  14. Briggs, J. S., and K. Dettmann, 1974, Phys. Rev. Lett. 33, 1123
  15. Briggs, J. S., and K. Dettmann, 1977, J. Phys. B 10, 1113
  16. Briggs, J. S., and L. Dube, 1978, J. Phys. B, to be published
  17. Brinkman, H. C., and H. A. Kramers, 1930, Proc. K. Ned. Akad. Wet. 33, 973
  18. Bussard, R. W., R. Ramaty, and K. Omidvar, 1978, Astrophys. J. 220, 353
  19. Chen, J. C. Y., A. C. Chen, and P. J. Kramer, 1971, Phys. Rev. A 4, 1982
  20. Chen, J. C. Y., and P. J. Kramer, 1972, Phys. Rev. A 5, 1207
  21. Cheshire, I. M., 1964, Proc. Phys. Soc. Lond. 84, 89
  22. Corbett, J. F., 1968, J. Math. Phys. 9, 891
  23. Das, J. N., 1976, J. Phys. B 9, L539
  24. Dettmann, K., 1971, Springer Tracts Mod. Phys. 58, 119
  25. Dettmann, K., K. G. Harrison, and M. W. Lucas, 1974, J. Phys. B 7, 269
  26. Dettmann, K., and G. Leibfried, 1966, Phys. Rev. 148, 1271
  27. Dettmann, K., and G. Leibfried, 1969, Z. Phys. 218, 1
  28. Dewangan, D. P., 1977, J. Phys. B 10, 1083
  29. Dirac, P. A. M., 1958, The Principles of Quantum Mechanics (Clarendon, Oxford), 4th edition, p. 244
  30. Drisko, R. M., 1955, Ph.D. thesis, Carnegie Institute of Technology, unpublished
  31. Gardner, L. D., 1978, Ph.D. thesis, Yale University, unpublished
  32. Gradshteyn, I. S., and I. W. Ryzhik, 1965, Tables of Integrals, Series, and Products, translated by Scripta Technica Inc., edited by A. Jeffrey (Academic, New York), 4th edition
  33. Halpern, A. M., and J. Law, 1973, Phys. Rev. Lett. 31, 4
  34. Heitler, W., 1954, The Quantum Theory of Radiation (Clarendon, Oxford), 3rd edition
  35. Hills, J. G., 1975, Astron. J. 80, 809
  36. Hills, J. G., 1976, Mon. Not. R. Astr. Soc. 175, p. 1
  37. Hills, J. G., 1977, Astron. J. 82, 626
  38. Jackson, J. D., and H. Schiff, 1953, Phys. Rev. 89, 359
  39. Joachain, C. J., 1977, Comments At. Mol. Phys. 6, 69
  40. Kleber, M., and D. Jakubassa, 1975, Nucl. Phys. A 252, 152
  41. Kleber, M., and M. A. Nagarajan, 1975, J. Phys. B 8, 643
  42. Kramer, P. J., 1972, Phys. Rev. A 6, 2125
  43. Lapicki, G., and W. Losonsky, 1977, Phys. Rev. A 15, 896
  44. LeBellac, M., and J. M. Levy-LeBlond, 1973, Nuovo Cimento B 14, 217
  45. Macek, J., 1970, Phys. Rev. A 1, 235
  46. Mapleton, R. A., 1964, Proc. Phys. Soc. Lond. 83, 895
  47. Mapleton, R. A., 1966, Proc. Phys. Soc. Lond. 87, 219
  48. Mapleton, R. A., 1972, Theory of Charge Exchange (Wiley, New York)
  49. May, R. M., 1964, Phys. Rev. A 136, 669
  50. McDowell, M. R. C., and J. P. Coleman, 1970, Introduction to the Theory of Ion-Atom Collisions (North-Holland, Amsterdam)
  51. McGuire, J. H., 1973, Phys. Rev. A 8, 2760
  52. Mittleman, M. H., 1964, Proc. Phys. Soc. Lond. 84, 453
  53. Oppenheimer, J. R., 1928, Phys. Rev. 31, 349
  54. Percival, I. C., and D. Richards, 1975, in Advances in Atomic and Molecular Physics, edited by D. R. Bates and B. Bederson (Academic, New York), Vol. II, p. 1
  55. Potapov, V. S., 1972, Zh. Eksp. Teor. Fiz. 63, 2094 [Sov. Phys.—JETP 36, 1105 (1973)]
  56. Raisbeck, G., and F. Yiou, 1971, Phys. Rev. A 4, 1858
  57. Rosenberg, L., 1963, Phys. Rev. 129, 968
  58. Rudd, M. E., C. A. Sautter, and C. L. Bailey, 1966, Phys. Rev. 151, 20
  59. Salin, A., 1969, J. Phys. B 2, 631
  60. Saslaw, W. C., M. J. Valtonen, and S. J. Aarseth, 1974, Astrophys. J. 190, 253
  61. Schiff, L. I., 1968, Quantum Mechanics (McGraw-Hill, New York), 3rd edition, p. 292
  62. Schnopper, H. W., H. D. Betz, J. P. Delvaille, K. Kalata, A. R. Sohval, K. W. Jones, and H. E. Wegner, 1972, Phys. Rev. Lett. 29, 898
  63. Shakeshaft, R., 1974a, J. Phys. B 7, 1059
  64. Shakeshaft, R., 1974b, Phys. Rev. A 10, 1906
  65. Shakeshaft, R., 1974c, J. Phys. B 7, 1734
  66. Shakeshaft, R., 1977, Phys. Rev. A 16, 1458
  67. Shakeshaft, R., 1978a, Phys. Rev. A 18, 2047
  68. Shakeshaft, R., 1978b, Phys. Rev. A 17, 1011
  69. Shakeshaft, R., and L. Spruch, 1973, Phys. Rev. A 8, 206
  70. Shakeshaft, R., and L. Spruch, 1977, Phys. Rev. Lett. 38, 175
  71. Shakeshaft, R., and L. Spruch, 1978a, J. Phys. B 11, L621
  72. Shakeshaft, R., and L. Spruch, 1978b, J. Phys. B 11, L457
  73. Shakeshaft, R., and L. Spruch, 1978c, Phys. Rev. Lett. 41, 1037
  74. Shastry, C. S., A. K. Rajagopal, and J. Callaway, 1972, Phys. Rev. A 6, 268
  75. Slater, J. C., 1960, Quantum Theory of Atomic Structure (McGraw-Hill, New York), Vol. 1, p. 368
  76. Sohval, A. R., 1975, Ph.D. thesis, Massachusetts Institute of Technology, unpublished
  77. Sohval, A. R., J. P. Delvaille, K. Kalata, K. Kirby-Docken, and H. W. Schnopper, 1976, J. Phys. B 9, L25
  78. Spindler, E., H.-D. Betz, and F. Bell, 1977, J. Phys. B 10, L561
  79. Spruch, L., 1969, in Lectures in Theoretical Physics—Atomic Collisions, edited by S. Geltman, K. T. Mahanthappa, and W. E. Britten (Gordon and Breach, New York), Vol. XIC, p. 77
  80. Spruch, L., 1978, Phys. Rev. A 18, 2016
  81. Spruch, L., and R. Shakeshaft, 1979, Phys. Rev. A 19, 1023
  82. Suter, M., C. R. Vane, I. A. Sellin, S. B. Elston, G. D. Alton, R. S. Thoe, and R. Laubert, 1978, Phys. Rev. Lett. 41, 399
  83. Thomas, L. H., 1927, Proc. R. Soc. 114, 561
  84. Tuan, T. F., and E. Gerjuoy, 1960, Phys. Rev. 117, 756
  85. Vane, C. R., I. A. Sellin, M. Suter, G. D. Alton, S. B. Elston, P. M. Griffin, and R. S. Thoe, 1978, Phys. Rev. Lett. 40, 1020
  86. Wilets, L., and S. J. Wallace, 1968, Phys. Rev. 169, 84

Outline

Information

Rev. Mod. Phys. 51, 369– Published 1 April, 1979

    © 1979 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation