Atomic versus molecular diffraction: Influence of breakups and finite size

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 3, 1998, Pages 2021-2029

  Hegerfeldt, Gerhard C ^a   Köhler, Thorsten ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001462109     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.2021     Document Type: Article

References (34)

1. For an overview see Appl. Phys. B: Photophys. Laser Chem. 54(1992), special issue on atom optics, edited by J. Mlynek, V. Balykin, and P. Meystre;
2. C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).PRPLCM
3. O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 2689 (1991); PRLTAO
4. Phys. Rev. Lett.D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Prichard, 66, 2693 (1991).
5. W. Schöllkopf and J. P. Toennies, Science 266, 1345 (1994).SCIEAS
6. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, R. A. Rubenstein, J. Schmiedmayer, S. Wehinger, and D. E. Prichard, Phys. Rev. Lett. 74, 4783 (1995).PRLTAO
7. Diffraction of molecules by surface lattices was already observed by I. Estermann and O. Stern, Z. Phys. 61, 95 (1930).ZEPYAA
8. F. Luo, G. C. Mc Bane, G. Kim, C. F. Giese, and W. R. Gentry, J. Chem. Phys. 98, 3564 (1993).JCPSA6
9. K. T. Tang, J. P. Toennies, and C. L. Yiu, Phys. Rev. Lett. 74, 1546 (1995).PRLTAO
10. F. Luo, C. F. Giese, and W. R. Gentry, J. Chem. Phys. 104, 1151 (1995).JCPSA6
11. L. D. Faddeev, Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory (Sivan, Jerusalem, 1965).
12. E. O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. B 2, 167 (1967).NUPBBO
13. W. Schöllkopf and J. P. Toennies, J. Chem. Phys. 104, 1155 (1996).JCPSA6
14. G. C. Hegerfeldt, T. Köhler, W. Schöllkopf, and J. P. Toennies (unpublished).
15. (Formula presented) could also have an attractive part, but this is not considered here.
16. W. Glöckle, The Quantum Mechanical Few-Body Problem, edited by W. Beiglböck (Springer, Berlin, 1983).
17. W. Sandhas, Acta Phys. Austriaca, Suppl. IX, 57 (1972).APAUAV
18. A. G. Sitenko, Theory of Nuclear Reactions (World Scientific, Singapore, 1990).
19. R. G. Newton, Scattering Theory of Waves and Particles (Springer, Berlin, 1982);
20. C. J. Joachain, Quantum Collision Theory (North-Holland, Amsterdam, 1975).
21. This weak dependence is also used in Ref. 16 and in T. A. Osborn, Ann. Phys. (N.Y.) 58, 417 (1970).APNYA6
22. It is noteworthy that the structure of the rhs of Eq. (41) is very similar to the deuteron transition amplitude for elastic diffraction scattering by a “black” nucleus (see Ref. 16, p. 354).
23. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Pt. II, p. 1551. Due to Eq. (27) and the remarks following it (Formula presented) is almost normal to the grating and we can neglect possible effects from the finite bar depth. This presupposes that the bar depth is not much larger than the bar width.
24. There is an irrelevant overall phase factor depending on the position of the grating.
25. M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1959), consider the square of this.
26. It should be noted that for diffraction of point particles the amplitude (Formula presented) can, without loss of generality, be replaced by the usual slit function of Ref. 22, which is proportional to (Formula presented), where (Formula presented). This is seen by using the addition formula for the sin in Eq. (45) and by noting that for (Formula presented), (Formula presented), i.e., for the main maxima of the grating function, one has (Formula presented) and (Formula presented). We also note that in optics one usually considers gratings that are closed at the two ends and not open like ours. This leads to a change in the zeroth-order peak.
27. This corroborates the interpretation of nondestructive mass selection given for the experiments in Refs. 311.
28. The appearance of the grating function in (Formula presented) can be understood as follows. The potentials of the individual bars are translates (Formula presented) of a fixed bar potential and similarly for the corresponding (Formula presented) and (Formula presented) matrices in Eqs. (10) and (13). The associated amplitude differs just by a phase factor (Formula presented) from the fixed bar amplitude since (Formula presented) and (Formula presented) are eigenvectors of (Formula presented). Summation over (Formula presented) gives the general form in Eq. (47), up to an overall phase factor.
29. In view of recent results by M. Arndt, M. Ben Dahan, D. Guéry-Odelin, M. W. Reynolds, and J. Dalibard, Phys. Rev. Lett. 79, 625 (1997), there also may be a weakly bound large cesium dimer. We thank P. S. Julienne for pointing this out to us.PRLTAO
30. S. W. Rick, D. L. Lynch, and J. D. Doll, J. Chem. Phys. 95, 3506 (1991); JCPSA6
31. J. Chem. Phys.M. Lewerenz, 104, 1028 (1996).
32. W. Schöllkopf and J. P. Toennies (unpublished).
33. V. Efimov, Phys. Lett. 33B, 563 (1970); PYLBAJ
34. B. D. Esry, C. D. Lin, and C. H. Greene, Phys. Rev. A 54, 394 (1996), and references therein. PLRAAN