[Formula Presented] transition and Siegert’s theorem

Physical Review C - Nuclear Physics

Volumn 58, Issue 4, 1998, Pages 2478-2488

  Buchmann, A J ^a   Hernandez E ^b   Meyer, U ^a   Faessler, Amand ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345911569     PISSN: 05562813     EISSN: 1089490X     Source Type: Journal    
DOI: 10.1103/PhysRevC.58.2478     Document Type: Article

References (55)

1. R. Beck, et al., Phys. Rev. Lett. 78, 606 (1997).
2. G. Blanpied, Phys. Rev. Lett. 79, 4337 (1997).
3. F. Kalleicher, U. Dittmayer, R. W. Gothe, H. Putsch, T. Reichelt, B. Schoch, and M. Wilhelm, Z. Phys. A 359, 201 (1997).
4. J. R. Comfort, Proceedings of the Seventh International Sym-posium on Meson-Nucleon Physics and the Structure of the Nucleon, Vancouver, 1997[πN Newsletter 13, 55 (1997)]; ZZZZZZC. N. Papanicolas and S. E. Williamson, Proceedings of the International Conference on Hadron Spectroscopy (Hadron ’91), College Park, 1991, p. 145.
5. M. A. B. Beg, B. W. Lee, and A. Pais, Phys. Rev. Lett. 13, 514 (1964).
6. R. H. Dalitz and D. G. Sutherland, Phys. Rev. 146, 1180 (1966).
7. O. Hanstein, D. Drechsel, and L. Tiator, Phys. Lett. B 385, 45 (1996)
8. O. HansteinD. DrechselL. Tiatorsee, also, Nucl. Phys.A632, 561 (1998).
9. N. Isgur, G. Karl, and R. Koniuk, Phys. Rev. D 25, 2394 (1982).
10. S. S. Gershtein and G. V. Dzhikiya, Sov. J. Nucl. Phys. 34, 870 (1982).
11. J. Dey and M. Dey, Phys. Lett. 138B, 200 (1984).
12. D. Drechsel and M. M. Giannini, Phys. Lett. 143B, 329 (1984).
13. A. Wirzba and W. Weise, Phys. Lett. B 188, 6 (1987)
14. T. D. Cohen and W. Broniowski, Phys. Rev. D 34, 3472 (1986)
15. A. Abada, H. Weigel, and Hugo Reinhardt, Phys. Lett. B 366, 26 (1996)
16. H. Walliser and G. Holzwarth, Z. Phys. A 357, 317 (1997).
17. M. Fiolhais, B. Golli, and S. Širca, Phys. Lett. B 373, 229 (1996).
18. Chr. V. Christov, A. Blotz, H.-C. Kim, P. Pobylitsa, T. Watabe, Th. Meissner, E. Ruiz Arriola, and K. Goeke, Prog. Part. Nucl. Phys. 37, 91 (1996).
19. S. Kumano, Phys. Lett. B 214, 13 (1988)
20. R. M. Davidson, N. C. Mukhopadhyay, and R. S. Wittman, Phys. Rev. D 43, 71 (1991).
21. M. Weyrauch and H. J. Weber, Phys. Lett. B 171, 13 (1986).
22. M. Bourdeau and N. C. Mukhopadhyay, Phys. Rev. Lett. 58, 976 (1987).
23. S. Capstick and G. Karl, Phys. Rev. D 41, 2767 (1990).
24. A. De Rujula, Howard Georgi, and S. L. Glashow, Phys. Rev. D 12, 147 (1975).
25. Instead of classifying the quark-quark interactions in terms of relativistic invariants, one can also classify them in terms of the five nonrelativistic invariants: spin-independent central, spin-dependent central, spin-orbit, tensor, quadratic spin-orbit. For each of these invariants and for each meson, the lowest nonvanishing contribution is kept. The leading-order potential of each diagram is considered to be of the same order as the nonrelativistic kinetic energy, which is of order (Formula presented)
26. A. M. Kusainov, V. G. Neudatchin, and I. T. Obukhovsky, Phys. Rev. C 44, 2343 (1991)
27. F. Fernandez, A. Valcarce, U. Straub, and A. Faessler, J. Phys. G 19, 2013 (1993)
28. A. Valcarce, A. Buchmann, F. Fernandez, and A. Faessler, Phys. Rev. C 50, 2246 (1994)
29. Phys. Rev. CA. ValcarceA. BuchmannF. FernandezA. Faessler51, 1480 (1995).
30. P. Stichel and E. Werner, Nucl. Phys. A145, 257 (1970).
31. N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978)
32. Phys. Rev. DN. IsgurG. Karl19, 2653 (1979).
33. M. M. Giannini, Rep. Prog. Phys. 54, 453 (1990).
34. Steven Weinberg, Phys. Rev. Lett. 65, 1181 (1990).
35. A. Buchmann, Y. Yamauchi, and A. Faessler, Nucl. Phys. A496, 621 (1989).
36. A. Buchmann, E. Hernández, and K. Yazaki, Nucl. Phys. A569, 661 (1994).
37. J. L. Friar, Ann. Phys. (N.Y.) 104, 380 (1977).
38. M. Chemtob and M. Rho, Nucl. Phys. A163, 1 (1971).
39. W. Lucha, F. F. Schöberl, and D. Gromes, Phys. Rep. 200, 127 (1991).
40. The two-body pion and gluon exchange charge densities are of order (Formula presented) and (Formula presented) respectively, and the question concerning the convergence of such an expansion arises. However, we have repeatedly argued that it is more important to include the lowest nonvanishing exchange currents for each degree of freedom than to insist on formal consistency of all operators in a given relativistic order (Formula presented) Our approach of keeping for each degree of freedom the lowest nonvanishing order is phenomenologically successful. For example, the lowest nonvanishing order pion and gluon exchange terms in the charge operator contain a tensor in spin space (Formula presented) not present in the one-body charge operator. This leads to nonvanishing (Formula presented) and via Siegert’s theorem also to a nonvanishing (Formula presented) transition amplitude of the right sign and magnitude. Evidently, one should not discard these terms. We have pointed out a similar effect in connection with Eq. (1). The color-magnetic term in the one-gluon exchange potential of Eq. (4) is a relativistic correction of order (Formula presented) which is, however, the lowest nonvanishing (Formula presented) type term resulting from one-gluon exchange. This term is crucial for explaining the difference between (Formula presented) and (Formula presented) masses in the quark model.
41. A. D. Jackson, A. Lande, and D. O. Riska, Phys. Lett. 55B, 23 (1975)
42. Phys. Lett.M. Beyer, D. Drechsel, and M. M. Giannini, 122B, 1 (1983)
43. A. J. Buchmann, H. Henning, and P. U. Sauer, Few-Body Syst. 21, 149 (1996).
44. A. J. Buchmann, Z. Naturforsch. Teil A 52, 877 (1997).
45. R. Koniuk and N. Isgur, Phys. Rev. D 21, 1868 (1980).
46. A. J. F. Siegert, Phys. Rev. 52, 787 (1937).
47. T. de Forest and Dirk Walecka, Adv. Phys. 15, 1 (1966); ADPHAH
48. C. Ciofi degli Atti, Prog. Part. Nucl. Phys. 3, 163 (1980).
49. H. Arenhövel, Z. Phys. A 302, 25 (1981).
50. A. Buchmann, E. Hernández, and K. Yazaki, Phys. Lett. B 269, 35 (1991).
51. A. J. Buchmann, E. Hernández, and Amand Faessler, Phys. Rev. C 55, 448 (1997).
52. Particle Data Group, R. M. Barnett, Phys. Rev. D 54, 1 (1996).
53. R. C. E. Devenish, T. S. Eisenschitz, and J. G. Körner, Phys. Rev. D 14, 3063 (1976).
54. H. F. Jones and M. D. Scadron, Ann. Phys. (N.Y.) 81, 1 (1973).
55. Georg Wagner, A. J. Buchmann, and Amand Faessler, Phys. Rev. C58, 1745 (1998).