Abstract: This paper provides a study of the rotational properties of heavy and medium nuclei, particularly the paired nuclei existing in the rare-earth, including Gd, Er, …, first to have a good representation of the intrinsic prolate fundamentals of the considered nuclei. The most important residual nuclear interaction is the pairing force which makes it possible to couple the nucleons in pairs. To take it into account, we introduce the Bardeen-Cooper-Shrie formalism (BCS), developed to describe the phenomenon of superconductivity. The test wave function is then more elaborate than that of Hartree-Fock and corresponds to a state no longer of independent particles, but of independent quasi-particles. A quasi-particle state (qp) is a linear combination of particles and holes. The Routhian Hartree-Fock model through the analysis of the experimental spectra of rotation of the deformed nucleus was usewd. Knowing that this was originally expanded by Bohr-Mottelson by applying I(I+1) expansion, we modified an existing fixed code (HF) with axial symmetry, which extended in a way that allows us to add constraints on the angular momentum and kelvin rotation to the Hamiltonian known as Cr.HF (cranking version of this formalism), initially studied by P. Quentin. This modification led to good results, especially the spectra of rotation and the angular velocities as a function of the angular momentum. Besides, it led to a decrease in the moment of inertia after it was large in some models, such as in the Hartree-Fock-Bogoliubov (HFB) model. The rotational properties and the moments of inertia of the super-deformed bands of some deformed nuclei have been studied as well as in the mass regions A=190; A=160. The results were compared with experimental results which gave good agreement. This work will offer an interesting perspective necessary for certain improvements or extensions of the Cr.HF.

Keywords: Microscopic mean field, Collective nuclear rotation, Angular momentum Routhian Hartree-Fock (RHF) model, Inertia moments, Angular velocity.

 

References

[1] Yuldashbaeva, E.K., Libert, J., Quentin, P. and Girod, M., Phys. Lett. B, 461 (1999) 1.

[2] Pillet, N., Quentin, P. and Libert, J., Nucl. Phys. A, 697 (2002) 141.

[3] Gall, B., Bonche, P., Dobaczewski, J. et al., Z. Phys. A, 348 (1994) 183.

[4] Girod, M., Delaroche, J.P., Berger, J.F. and Libert, J., Phys. Lett. B, 325 (1994) 1.

[5] Bardeen, J., Cooper, L.N. and Schrieer, J.R., Phys. Rev., 108 (1957) 1175.

[6] Parry, W.E., "The Many-body Problem", (Clarendon Press, Oxford, 1973).

[7] Madland, D.G. and Rayford Nix, J., Nucl. Phys. A, 476 (1988) 1.

[8] Vautherin, D. and Brink, D.M., Phys. Rev. C, 5 (1972) 626.

[9] Waroquier, M., Heyde, K. and Wenes, G., Nucl. Phys. A, 404 (1983) 269.

[10] Dutta, A.K. and Kohno, M., Nucl. Phys. A, 349 (1980) 455-79.

[11] Prochniak, L., Quentin, P. and Imadalou, M., Int. J. Mod. Phys. E, 21 (2012) 1250036.

[12] Chabanat, E., Bonche, P., Haensel, P., Meyer, J. and Schaeffer, R., Nucl. Phys. A, 627 (1997) 710-74.

[13] Wiringa, R.B., Fiks, V. and Fabrocini, A., Phys. Rev. C, 38 (1988) 1010.

[14] Engel, Y.M., Brink, D.M., Geoeke, K., Krieger, S.J. and Vautherin, D., Nucl. Phys. A, 249 (2) (1975) 215.

[15] Bencheikh, K., Quentin, P. and Bartel, J., Nucl. Phys. A, 571 (1994) 518.

[16] Slater, J.C., Phys. Rev. C, 81 (1951) 85.

[17] Gombas, P., Ann. Phys., 10 (1952) 253.

[18] Pillet, N., Quentin, P. and Libert, J., Nucl. Phys. A, 697 (2002) 14.

[19] Inglis, D.R., Phys. Rev., 96 (1954) 1059.

[20] Bartel, J., Quentin, P., Brack, M., Guet, C. and Haakansson, H.B., Nucl. Phys. A, 386 (1982) 79.

[21] Laftchiev, H., Samsoen, D., Quentin, P. and Mikhailov, I.N., Phys. Rev. C, 67 (2003) 014301.

[22] Laftchiev, H., Libert, J., Quentin, P. and Long, H.T., Nucl. Phys. A, 845 (2010) 33.

[23] Beiner, M., Flocard, H., Van Giai, N. and Quentin, P., Nucl. Phys. A, 238 (1975) 29.

[24] Próchniak, L., Quentin, P., Samsoen, D. and Libert, J., Nucl. Phys. A, 730 (2004) 59.

[25] Audi, G. and Wapstra, A.H., Nucl. Phys. A, 595 (1995) 409.

[26] Kumar, K. and Baranger, M., Nucl. Phys. A, 92 (1967) 608.