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A comparative study of double beta decay by shell model and quasiparticle RPA

  • Nuclear Structure and Reactions
  • Published:
Zeitschrift für Physik A Hadrons and Nuclei

Abstract

Nuclear matrix elements of the two-neutrino and neutrinolessββ decays of48Ca(0 +g.s. )→48Ti(0 +g.s. ) are calculated by shell model and QRPA. The two-neutrino matrix elementM 2v GT is rather reliably evaluated in the QRPA approach by a careful fit of the particle-particle interaction strength in the 1+ channel, which governs the spinisospin ground-state correlations. The shell-model value ofM 2v GT depends not only on the 1+ interaction but largely on the pairing and quadrupole interactions. Concerning the neutrinoless-mode nuclear matrix elements, the shell model gives generally smaller values than the QRPA. A detailed analysis indicates that the discrepancies originate mainly from the truncation of shell-model configurations (fp-space). The QRPA calculation in a larger model space well takes into account transitions from/to single-particle orbits far from the Fermi surface, and those transitions give rise to sizable contributions because of large momentum transfers due to the exchange of a virtual neutrino.

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References

  1. Haxton, W.C., Stephenson, G.J., Jr.: Prog. Part. Nucl. Phys.12, 409 (1984)

    Google Scholar 

  2. Doi, M., Kotani, T., Takasugi, E.: Prog. Theor. Phys. [Suppl.]83, 1 (1985)

    Google Scholar 

  3. Muto, K., Klapdor, H.V.: In: Klapdor, H.V. (ed.), Neutrinos. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  4. Vogel, P., Zirnbauer, M.R.: Phys. Rev. Lett.57, 3148 (1986)

    Google Scholar 

  5. Civitarese, O., Faessler, A., Tomoda, T.: Phys. Lett.194B, 11 (1987)

    Google Scholar 

  6. Muto, K., Klapdor, H.V.: Phys. Lett.201B, 420 (1988)

    Google Scholar 

  7. Muto, K., Bender, E., Klapdor, H.V.: Z. Phys. A — Atomic Nuclei334, 177 (1989)

    Google Scholar 

  8. Tomoda, T., Faessler, A.: Phys. Lett.199B, 475 (1987)

    Google Scholar 

  9. Engel, J., Vogel, P., Zirnbauer, M.R.: Phys. Rev. C37, 731 (1988)

    Google Scholar 

  10. Muto, K., Bender, E., Klapdor, H.V.: Z. Phys. A — Atomic Nuclei334, 187 (1989)

    Google Scholar 

  11. Vinh Mau, R.: Mesons in Nuclei, Vol. 1, p. 151. Rho, M., Wilkinson, D.H. (eds.). Amsterdam: North-Holland 1979

    Google Scholar 

  12. Lacombe, M., Loiseau, B., Richard, J.M., Vinh Mau, R., Côté, J., Pirès, P., Tourreil, R. de: Phys. Rev. C21, 861 (1980)

    Google Scholar 

  13. Anantaraman, N., Toki, H., Bertsch, G.F.: Nucl. Phys. A398, 269 (1983)

    Google Scholar 

  14. Holinde, K.: Phys. Rep.68, 121 (1981)

    Google Scholar 

  15. Haxton, W.C., Stephenson, G.J., Jr., Strottman, D.: Phys. Rev. D26, 1805 (1982)

    Google Scholar 

  16. Halbleib, J.A., Sorensen, R.A.: Nucl. Phys. A98, 542 (1967)

    Google Scholar 

  17. Muto, K., Bender, E., Klapdor, H.V.: Z. Phys. A — Atomic Nuclei333, 125 (1989)

    Google Scholar 

  18. Bertsch, G.F.: The practitioners shell model. Amsterdam: North-Holland 1972

    Google Scholar 

  19. Burrows, T.W.: Nucl. Data Sheets48, 1, 569 (1986)

    Google Scholar 

  20. Bohr, A., Mottelson, B.R.: Nuclear Structure, Vol. I. New York: Benjamin 1969

    Google Scholar 

  21. Wapstra, A.H., Audi, G., Hoekstra, R.: At. Data Nucl. Data Tables39, 281 (1988)

    Google Scholar 

  22. Shalit, A. de, Talmi, I.: Nuclear Shell Theory. New York: Academic Press 1963

    Google Scholar 

  23. Horie, H.: J. Phys. Soc. Jpn.19, 1783 (1964)

    Google Scholar 

  24. Horie, H., Oda, T.: Prog. Theor. Phys. [Suppl.], 315 (1968)

    Google Scholar 

  25. Staudt, A., Kuo, T.T.S., Klapdor, H.V.: Phys. Lett.242B, 17 (1990)

    Google Scholar 

  26. Grotz, K., Klapdor, H.V.: Nucl. Phys.A460, 395 (1986)

    Google Scholar 

  27. Klapdor, H.V., Grotz, K.: Phys. Lett.142B, 323 (1984)

    Google Scholar 

  28. Engel, J., Vogel, P., Civitarese, O., Zirnbauer, M.R.: Phys. Lett.208B, 187 (1988)

    Google Scholar 

  29. Haxton, W.C., Stephenson, G.J., Jr., Strottman, D.: Phys. Rev.D25, 2360 (1982)

    Google Scholar 

  30. Tsuboi, T., Muto, K., Horie, H.: Phys. Lett.143B, 293 (1984)

    Google Scholar 

  31. Wu, H.F., Song, H.Q., Kuo, T.T.S., Chang, W.K., Strottman, D.: Phys. Lett.162B 227 (1985)

    Google Scholar 

  32. Bardin, R.K., Gollon, P.J., Ullman, J.D., Wu, C.S.: Nucl. Phys. A158, 337 (1970)

    Google Scholar 

  33. Elliott, S.R., Hahn, A.A., Moe, M.K.: Phys. Rev. Lett.59, 2020 (1987)

    Google Scholar 

  34. Kirsten, T., Heusser, E., Kaether, D., Oehm, J., Pernicka, E., Richter, H.: In: Kotani, T., Ejiri, H., Takasugi, E. (eds.). Proc. Int. Symp. on Nuclear Beta Decays and Neutrino, p. 81. Singapore: World Scientific 1986

    Google Scholar 

  35. Schechter, J., Valle, J.W.F.: Phys. Rev. D25, 2951 (1982)

    Google Scholar 

  36. Nieves, J.F.: Phys. Lett.147B, 375 (1984)

    Google Scholar 

  37. Takasugi, E.: Phys. Lett.149B, 372 (1984)

    Google Scholar 

  38. Miller, G.A., Spencer, J.E.: Ann. Phys.100, 562 (1976)

    Google Scholar 

  39. Vergados, J.D.: Phys. Rev. C24, 640 (1981); Nucl. Phys. B218, 109 (1983)

    Google Scholar 

  40. Hirsch, J., Krmpotić, F.: Phys. Rev. C41, 792 (1990)

    Google Scholar 

  41. Muto, K.: In: Kotani, T., Ejiri, H., Takasugi, E. (eds.). Proc. Int. Symp. on Nuclear Beta Decays and Neutrino, p. 177. Singapore: World Scientific 1986

    Google Scholar 

  42. Kuo, T.T.S., Brown, G.E.: Nucl. Phys. A114, 241 (1968)

    Google Scholar 

  43. McGrory, J.B., Wildenthal, B.H.: Phys. Lett.103B, 173 (1981)

    Google Scholar 

  44. Tomoda, T., Faessler, A., Schmid, K.W., Grümmer, F.: Nucl. Phys. A452, 591 (1986)

    Google Scholar 

  45. Schmid, K.W., Grümmer, F., Faessler, A.: Nucl. Phys. A431, 205 (1984)

    Google Scholar 

  46. Caldwell, D.O., Eisberg, R.M., Grumm, D.M., Witherell, M.S.: Phys. Rev. Lett.59, 419 (1987)

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, 152, Tokyo, Japan

    K. Muto & E. Bender

  2. Max-Planck-Institut für Kernphysik, W-6900, Heidelberg, Federal Republic of Germany

    H. V. Klapdor-Kleingrothaus

Authors
  1. K. Muto
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  2. E. Bender
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  3. H. V. Klapdor-Kleingrothaus
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Additional information

Visiting scholar of Faculty of Science, Tokyo Institute of Technology

Present address: Institut für Theoretische Physik, Universität Tübingen, W-7400 Tübingen, Federal Republic of Germany

One of the authors (E.B.) is grateful for financial support to Professor E. Arai of the Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, and to the Centennial Commemoration Fund of Tokyo Institute of Technology. Numerical calculations were performed with FACOM M780/M380 computer systems of the Institute for Nuclear Study, University of Tokyo.

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Muto, K., Bender, E. & Klapdor-Kleingrothaus, H.V. A comparative study of double beta decay by shell model and quasiparticle RPA. Z. Physik A - Hadrons and Nuclei 339, 435–444 (1991). https://doi.org/10.1007/BF01288427

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  • DOI: https://doi.org/10.1007/BF01288427

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