Electron–positive-ion scattering near reaction thresholds: Effect of long-range polarization forces

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 4, 1998, Pages 2864-2871

  Rosenberg, Leonard ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005457377     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.2864     Document Type: Article

References (21)

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2. See Ref. 1, p. 201.
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4. R. Oppenheim-Berger and L. Spruch, Phys. Rev. 138, B1106 (1965).PRVBAK
5. F. S. Ham, Q. Appl. Math. 15, 31 (1957).QAMAAY
6. M. J. Seaton, Mon. Not. R. Astron. Soc. 118, 815 (1958).MNRAA4
7. M. H. Ross and G. L. Shaw, Ann. Phys. (N.Y.) 13, 147 (1961).APNYA6
8. M. Gailitis, Zh. Éksp. Teor. Fiz. 44, 1974 (1963) [Sov. Phys. JETP 17, 1328 (1963)].SPHJAR
9. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, Cambridge, 1946), Chap. XVI.
10. We take over some results reported in Ref. 5, with slight changes in notation. In particular the function (Formula presented) may be identified with (Formula presented) as defined by Ham.
11. G. H. Wannier, Phys. Rev. 64, 358 (1943).PHRVAO
12. The expansion is given explicitly in Eq. (19) of Ref. 5. The coefficients (Formula presented) appearing there may be determined from the relation (Formula presented) where the (Formula presented) are defined in Eq. (2.8).
13. M. Abramowitz, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Stand. Appl. Math Ser. No. 55 (U.S. GPO, Washington, D.C., 1969), p. 539.
14. This key feature follows simply from the unit amplitude condition placed on the incoming and outgoing waves, leaving the form of the linear relations amongst the different solutions unchanged by inclusion of the polarization potential.
15. L. Rosenberg, Phys. Rev. A 57, 1862 (1998).PLRAAN
16. A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30, 257 (1958).RMPHAT
17. Note that for a highly polarizable system the polarization phase can become complex. [See, for example, N. A. W. Holzwarth, J. Math. Phys. 14, 191 (1973).] This has implications 15 with regard to the form of the unitarity relation. To simplify the present discussion the phases will be taken to be real.JMAPAQ
18. See, for example, H. Friedrich, Theoretical Atomic Physics (Springer, New York, 1990), p. 307.
19. I. Waller, Z. Phys. 38, 635 (1926), quoted in Ref. 2.ZEPYAA
20. Expressions for the resonance width and shift appear in Eq. (16) of Ref. 8. Note that the T matrix defined there is obtained from that defined here by including a factor (Formula presented)
21. P. J. Davis, in Handbook of Mathematical Functions (Ref. 13), pp. 258–260.