Multichannel effective-range theory with long-range interactions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 3, 1998, Pages 1862-1869

  Rosenberg, Leonard ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

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[No Author keywords available]

Indexed keywords

EID: 0342604331     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.1862     Document Type: Article

References (23)

1. M. H. Ross and G. L. Shaw, Ann. Phys. (N.Y.) 13, 147 (1961).APNYA6
2. J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949); PHRVAO
3. Phys. Rev.H. A. Bethe, 76, 38 (1949).
4. E. P. Wigner, Phys. Rev. 73, 1002 (1948).PHRVAO
5. M. Gailitis and R. Damburg, Proc. Phys. Soc. London 82, 192 (1963).PPSOAU
6. Similar techniques were used to allow for a potential with a long-range attractive Coulomb tail. See M. Gailitis, Z. Eksp. Teor. Fiz. 44, 1974 (1963) [Sov. Phys. JETP 17, 1328 (1963)]. The close connection between this approach and standard quantum-defect theory is apparent.SPHJAR
7. See, e.g., P. G. Burke, J. W. Cooper, and S. Ormonde, Phys. Rev. 183, 245 (1969).PHRVAO
8. R. K. Nesbet, Variational Methods in Electron-Atom Scattering Theory (Plenum, New York, 1980), p. 104.
9. T. F. O’Malley, L. Spruch, and L. Rosenberg, J. Math. Phys. 2, 491 (1961).JMAPAQ
10. M. J. Cavagnero, Phys. Rev. A 50, 2841 (1994).PLRAAN
11. A preliminary treatment was given in Ref. 11.
12. L. Rosenberg, Phys. Rev. A 55, 2857 (1997).PLRAAN
13. S. Watanabe and C. H. Greene, Phys. Rev. A 22, 158 (1980).PLRAAN
14. D. B. Khrebtukov, J. Phys. A 26, 6357 (1993).JPHAC5
15. N. A. W. Holzwarth, J. Math. Phys. 14, 191 (1973).JMAPAQ
16. Following the method of Ref. 9, the basis functions φ and ξ (the channel index is dropped here) are constructed as linear combinations of Bessel functions (Formula presented) and (Formula presented) with (Formula presented)(Formula presented) and (Formula presented) an integer. Use of (Formula presented) in place of (Formula presented) would be inappropriate since the wave-function renormalization procedure (described below) would fail to remove singular factors of the form (Formula presented) For (Formula presented)(Formula presented) equal to an integer the basis functions φ and ξ are linearly dependent. The replacement of (Formula presented) by (Formula presented) is now necessary and unobjectionable, the factor (Formula presented) being nonsingular.
17. A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30, 257 (1958).RMPHAT
18. T. Kato, Prog. Theor. Phys. (Kyoto) 6, 394 (1951).PTPKAV
19. See, for example, H. Friedrich, Theoretical Atomic Physics (Springer, New York, 1990), pp. 226–228.
20. B. H. Bransden, Atomic Collision Theory (Benjamin, New York, 1970), pp. 152–160.
21. See Ref. 19, p. 311.
22. A systematic study of long-range power-law potentials has been made recently by W. Clark and C. H. Greene, Phys. Rev. A 56, 403 (1997).PLRAAN
23. For a physical realization of this model we may consider a system with total orbital angular momentum (Formula presented) and a target atom with (Formula presented) The long-range interaction changes the projectile angular momentum by two units and is compensated for by a corresponding change in the projection of the target’s angular momentum.