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Study ofpf-shell nuclei with a symmetry conserving generator coordinate method

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Zeitschrift für Physik

Abstract

Bands based on the 0+ ground state and the first excited 0+ pairing vibrational state of48Ti,52Cr and56Fe are studied with the generator coordinate method. The generating wave functions for each value of the angular momentumJ are angular momentum and particle number projected selfconsistent Hartree-Fock-Bogoliubov states where the constrained amount of pairing correlations serves as the generator coordinate. The interaction is given by reaction matrix elements derived from the Hamada-Johnston force. The basis includes the four lowest oscillator shells.

The excitation energies of the pairing vibrational states can be reproduced fairly well by the present choice of the generating wave functions, whereas the ground band is not much improved compared to projected Hartree-Bogoliubov calculations. We find that the strength of the pairing correlations in the 0+ and 2+ states of the ground state and the pairing vibrational bands can be related to data of two-particle transfer reactions. The angular momentum dependence of the pairing correlations and of the moments of inertia are studied. The results show that for a strongly paired ground state the ground state band and the pairing vibrational band intersect. This may produce in the yrast band the anomaly of the moment of inertia known from rare earth nuclei.

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References

  1. Hill, D.L., Wheeler, J.A.: Phys. Rev.89, 1102, (1953)

    Google Scholar 

  2. Griffin, J.J., Wheeler, J.A.: Phys. Rev.108, 312, (1957)

    Google Scholar 

  3. Griffin, J.J.: Phys. Rev.108, 328, (1957)

    Google Scholar 

  4. Wong, C.W.: Nucl. Phys. A147, 545, (1970).

    Google Scholar 

  5. Banerjee, B., Brink, D.M.: Z. Physik258, 46, (1973).

    Google Scholar 

  6. Jancovici, B., Schiff, D.H.: Nucl. Phys.58, 678, (1964).

    Google Scholar 

  7. Brink, D.M., Weiguny, A.: Nucl. Phys. A120, 59, (1968).

    Google Scholar 

  8. Ripka, G., Padjen, R.: Nucl. Phys. A132, 489, (1969).

    Google Scholar 

  9. Generator coordinate method for nuclear bound states and reactions. Review of contributions and discussions at the working seminar Ljubljana, August 13–September 1, 1972, ed. by M.V. Mihailovic and M. Rosina. Europhysics Journal, Fizika5 (1973) supplement

  10. Justin, D., Mihailovic, M.V., Rosina, M.: Phys. Lett.,32 B, 23, (1970).

    Google Scholar 

  11. Justin, D., Mihailovic, M.V., Rosina, M.: Nucl. Phys. A,182, 54, (1972).

    Google Scholar 

  12. Siegal, C.D., Sorensen, R.A.: Nucl. Phys. A,184, 81, (1972).

    Google Scholar 

  13. Siegal, C.D., Gambhir, Y.K.: Phys. Lett.39 B, 151, (1972).

    Google Scholar 

  14. Sorensen, R.A.: Phys. Lett.,38 B, 376, (1972).

    Google Scholar 

  15. Faessler, A., Grümmer, F., Plastino, A.: Z. Physik,260, 305, (1973).

    Google Scholar 

  16. Faessler, A., Grümmer, F., Piastino, A., Krmpotic, F.: Nucl. Phys. A217, 420, (1973).

    Google Scholar 

  17. Goeke, K., Garcia, J., Faessler, A.: Phys. Lett.,41 B, 557, (1972).

    Google Scholar 

  18. Goeke, K., Garcia, J., Faessler, A.: Nucl. Phys. A208, 477 (1973).

    Google Scholar 

  19. Goeke, K., Faessler, A., Müther, H., Allaart, K.: Contribution to the International Conference on Nuclear Physics, Munich, August 27–September 1, 1973, and to be published in Phys. Rev.

  20. Goeke, K., Müther, H., Faessler, A.: Nucl. Phys. A201, 49 (1973).

    Google Scholar 

  21. Allaart, K., Goeke, K., Faessler, A.: Z. Physik263, 407, (1973).

    Google Scholar 

  22. Allaart, K., Faessler, A., Goeke, K., Grümmer, F.: Contribution to the International Conference on Nuclear Physics, Munich, August 27–September 1, 1973, and to be published in Nucl. Phys.

  23. Baranger, M.: 1962 Cargese Lectures in Theoretical Physics, ed. by M. Levy. New York: Benjamin, 1963.

    Google Scholar 

  24. Goeke, K., Faessler, A., Wolter, H.H.: Nucl. Phys., A183, 352, (1972).

    Google Scholar 

  25. Barrett, B.R., Hewitt, R.G.L., McCarthy, R.J.: Phys. Rev. C2, 1199 (1970).

    Google Scholar 

  26. Barrett, B.R., Hewitt, R.G.L., McCarthy, R.J.: Phys. Rev. C3, 1137 (1971)

    Google Scholar 

  27. Baranger, M.: Proceedings of the International Summer School “Enrico Fermi”, Course XL. 1968

  28. Bethe, H.A., Brandow, B.H., Petschek, A.G.: Phys. Rev.12A, 225 (1963)

    Google Scholar 

  29. Chandra, H., Rustgi, M.L.: Phys. Rev. C6, 1281 (1972)

    Google Scholar 

  30. Ernst, D.J., Shakin, C.M., Thaler, R.M.: Phys. Rev. C8, 440 (1973)

    Google Scholar 

  31. Jänecke, J.: Nucl. Phys.73, 97 (1965)

    Google Scholar 

  32. Satpathy, L., Goeke, K., Faessler, A.: Nucl. Phys. A179, 177 (1972)

    Google Scholar 

  33. McDonald, N., Morrison, I., Watt, A.: Nucl. Phys. A217, 429 (1973) and private communication

    Google Scholar 

  34. Morrison, I., Watt, A., Whitehead, J.: J. Phys. A7, No. 6, L75 (1974)

    Google Scholar 

  35. Khadkikar, S.B., Gunye, M.R.: Nucl. Phys. A144, 289 (1970)

    Google Scholar 

  36. Sandhya Devi, K.R., Khadkikar, S.B., Parikh, J.K., Banerjee, B.: Phys. Lett.32B, 179 (1970)

    Google Scholar 

  37. Banerjee, B., Khadkikar, S.B., Sandhya Devi, K.R.: Phys. Rev. C7, 1010 (1973)

    Google Scholar 

  38. Bloch, C., Messiah, A.: Nucl. Phys.39, 65 (1962)

    Google Scholar 

  39. Goodman, A.L.: Thesis 1969. University of California, Lawrence Radiation Laboratory, Berkeley, UCRL-19514

    Google Scholar 

  40. Wolter, H.H., Faessler, A., Sauer, P.U.: Nucl. Phys. A167, 108 (1971)

    Google Scholar 

  41. Chandra, H., Rustgi, M.L.: Phys. Rev. C7, 180 (1973)

    Google Scholar 

  42. Faessler, A., Sauer, P.U., Wolter, H.H.: Nucl. Phys.A129, 21 (1969)

    Google Scholar 

  43. Sorensen, B.: Nucl. Phys. A134, 1 (1969)

    Google Scholar 

  44. Mottelson, B.R., Valatin, J.C.: Phys. Rev. Lett.5, 511 (1960)

    Google Scholar 

  45. Faessler, A., Lin, L., Wittmann, F.: Phys. Lett.44B, 127 (1973)

    Google Scholar 

  46. Faessler, A., Grümmer, F., Lin, L., Urbano, J.: Phys. Lett.48B, 87 (1974)

    Google Scholar 

  47. Faessler, A., Goeke, K., Müther, H.: Physica Scripta6, 255 (1972)

    Google Scholar 

  48. Kleber, M.: Z. Physik231, 421 (1970)

    Google Scholar 

  49. Broglia, R.A., Riedel, C., Sorensen, B.: Nucl. Phys. A107, 1 (1968)

    Google Scholar 

  50. Bes, D.R., Broglia, R.A., Perazzo, R.P.J., Kumar, K.: Nucl. Phys. A143, 1 (1970)

    Google Scholar 

  51. Broglia, R.A.: Symposium on Two-Nucleon Transfer and Pairing Excitations. Argonne National Laboratory, Argonne, Illinois, March 20–21, 1972, p. 113

    Google Scholar 

  52. Mottelson, B.R., Valatin, J.C.: Phys. Rev. Lett.5, 511 (1960)

    Google Scholar 

  53. Stephens, F.S., Simon, R.S.: Nucl. Phys. A183, 257 (1972)

    Google Scholar 

  54. Faessler, A.: Proceedings of the Extended Seminar on Nuclear Physics 1973 in Trieste, ed. by G. Ripka and M. K. Pal

  55. Lieder, R.M., Beuscher, H., Davidson, W.F., Neskakis, A., Mayer-Böricke, C., El-Masri, Y., Monseu, P., Steyaert, J., Vervier, J.: Phys. Lett B49, 161 (1974)

    Google Scholar 

  56. Khoo, T.L., Bernthal, F.M., Boyno, J.S., Warner, R.A.: Phys. Rev. Lett.31, 1143(1973)

    Google Scholar 

  57. Grosse, E., Stephens, F.S., Diamond, R.M.: Phys. Rev. Lett.31, 840 (1973)

    Google Scholar 

  58. Lesser, P.M.S., Cline, D., Goode, P., Horoshko, R.N.: Nucl. Phys. A190, 597 (1972)

    Google Scholar 

  59. Sprague, S. W., Arns, R. G., Brunner, B. J., Caldwell, S. E., Rosza, CM.: Phys. Rev. C4, 2074 (1971)

    Google Scholar 

  60. Hinds, S., Middleton, R.: Nucl. Phys. A92, 422 (1967)

    Google Scholar 

  61. Evers, D., Assmann, W., Rudolph, K., Skorka, S., Sperr, P.: Nucl. Phys. A198, 268 (1972) Evers, D.: private communication

    Google Scholar 

  62. Baer, H.W., Kraushaar, J.J., Moss, C.E., King, N.S.P., Green, R.E.L., Kunz, P.D., Rost, E.: Ann. Phys.76, 437 (1973)

    Google Scholar 

  63. Broglia, R.A., Hansen, O., Riedel, C.: Adv. of Nucl. Phys. Vol.6, 287 (1973)

    Google Scholar 

  64. Casten, R.F., Flynn, E.R., Hansen, O., Mulligan, T.J.: Phys. Rev. C4, 130 (1971)

    Google Scholar 

  65. Chapman, R., Hinds, S., MacGregor, A.E.: Nucl. Phys. A119, 305 (1968)

    Google Scholar 

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Author notes

  1. K. Allaart

    Present address: Amsterdam Department of Theoretical Physics, Vrije Universiteit, The Neiderland

Authors and Affiliations

  1. Department of Theoretical Physics, University of Oxford, Oxford, Great Britain

    K. Goeke

  2. Institut für Kernphysik, Kernfor-schungsanlage Jülich, Jülich, West Germany

    K. Goeke, K. Allaart, H. Müther & Amand Faessler

  3. Physik-Department, Universität Bonn, Bonn, West Germany

    Amand Faessler

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  1. K. Goeke
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  2. K. Allaart
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  3. H. Müther
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  4. Amand Faessler
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On leave of absence of the Institut für Kernphysik, Kernforschungsanlage Jülich, D-517 Jülich, West Germany.

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Goeke, K., Allaart, K., Müther, H. et al. Study ofpf-shell nuclei with a symmetry conserving generator coordinate method. Z. Physik 271, 377–389 (1974). https://doi.org/10.1007/BF02126193

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  • DOI: https://doi.org/10.1007/BF02126193

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