Abstract
We investigate the Sp(2, R) model for light and heavy nuclei and compare it to recent applications of the Sp(6, R) model. The same Hamiltonian is used and the basis states will have good angular momentum. We not only confirm that the restricted space of the Sp(6, R) model gives the dominant contribution but also that there is no practical difference from the Sp(6, R) model calculations. The Sp(2, R) model is then applied to the chain of Ba-isotopes which show, according to a recent application of the geometrical model, a dominant prolate behavior with an important γ-unstable component. They represent limiting cases where the Sp(2, R) model can be put to an extreme test.
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References
M. G. Meyer,Phys. Rev. 75, 1969 (1949). O. Haxel, J. H. D. Jensen, and H. E. Suess,Phys. Rev. 75, 1766 (1949).
D. C. Zheng, J. P. Vary, and B. R. Barrett,Phys. Rev. C 50, 2841 (1994).
S. G. Nilsson,K. Dansk. Vidensk. Selsk. Mat.-Fys. Med. (Skr.) 29, 16 (1955).
J. P. Elliott,Proc. R. Soc. London A 245, 128, 562 (1958).
M. Harvey,Adv. Nucl. Phys. 1, 67 (1968).
K. T. Hecht and A. Adler,Nucl. Phys. A 137, 129 (1969).
A. Arima, M. Harvey, and K. Shimizu,Phys. Lett. B 30, 517 (1969).
J. P. Draayer and C. Bahri,Rev. Mex. Fís. 40 (Suppl. 1), 12 (1994).
O. L. Weaver, R. Y. Cusson, and L. C. Biedenharn,Ann. Phys. (N.Y.) 102, 493 (1976).
B. Buck, L. C. Biedenharn, and R. Y. Cusson,Nucl. Phys. A317, 205 (1979).
D. J. Rowe,Rep. Prog. Phys. 48, 1419 (1985) and references therein. D. J. Rowe,Prog. Part. Nucl. Phys. 17, 265 (1996) and references therein.
G. F. Filipov, V. I. Ovcharenko, and Yu. F. Smirnov, inMicroscopic Theory of Collective Motion (in Russian) (Naukova Dumka, Kiev, 1981). G. F. Filipov and Yu. F. Smirnov,Sov. J. Nucl. Phys. 27, 39 (1978).
V. Vanagas, inGroup Theory and Its Applications in Physics-1980 (A.I.P. Conference Procedings No. 71), T. Seligman, ed. (American Institute of Physics, 1981), p. 220.
M. Moshinsky and C. Quesne,J. Math. Phys. 12, 1772 (1971).
O. Castaños and J. P. Draayer,Nucl. Phys. A 491, 349 (1989).
J. Carvalho and D. J. Rowe,Nucl. Phys. A 548, 1 (1992).
O. Castaños, M. Moshinsky, and C. Quesne,Phys. Rev. Lett. B 277, 238 (1992). C. Bahri, J. P. Draayer, and S. A. Moszkowski,Phys. Rev. Lett. 68, 2133 (1992).
O. Castaños, P. O. Hess, P. Rochford, and J. P. Draayer,Nucl. Phys. A 524, 469 (1991).
D. Troltenier, J. P. Draayer, P. O. Hess, and O. Castaños,Nucl. Phys. A 576, 351 (1994).
F. Arickx, P. Van Leuven, and M. Bouten,Nucl. Phys. A 252, 416 (1975), F. Arickx,Nucl. Phys A 268, 347 (1976). F. Arickx, J. Broeckhove, and E. Deumens,Nucl. Phys. A 318, 269 (1979).
O. Castaños, E. Chacón, A. Frank, P. O. Hess, and M. Moshinsky,J. Math. Phys. 23, 2537 (1982).
E. Chacón, P. O. Hess, and M. Moshinsky,J. math. Phys. 30, 970 (1989) and references therein.
P. Petkov, A. Dewald, and W. Andrejtscheff,Phys. Rev C 51, 2511 (1995).
J. M. Eisenberg and W. Greiner, inNuclear Theory I: Nuclear Models 3rd ed. (North-Holland, Amsterdam, 1987).
D. Troltenier, J. A. Maruhn, W. Greiner, and P. O. Hess,Z. Phys. A 343, 25 (1992).
M. Moshinsky and Yu. F. Smirnov, inThe Harmonic Oscillator in Modern Physics (Harwood Academic Publishers, 1996).
O. Castaños, J. P. Draayer, and Y. Leschber,Z. Phys. A 329, 33 (1988).
V. Velázquez, P. O. Hess, J. G. Hirsch, and A. Mariano,Phys. Rev. C 55, 1571 (1997).
D. Troltenier, W. Nazarewicz, Z. Szymanski, and J. P. Draayer,Nucl. Phys. A 567, 591 (1994).
O. Castaños, J. P. Draayer, and Y. Leschber,Ann. Phys. (N.Y.) 180, 290 (1987).
O. Castaños, J. P. Draayer, and Y. Leschber,Z. Phys. A 329, 33 (1988).
P. O. Hess, Fitting routine of theSp (2,R) model (ICN-UNAM, Mexico, 1996).
O. Castaños and J. P. Draayer, Fitting routine for theSp(6,R) model (Louisiana State University, U. S. A., 1988).
J. G. Hirsch, D. Troltenier, and J. P. Draayer, private communication.
S. Raman, C. H. Malarkey, W. T. Milner, C. W. Nestor, and P. H. Stelson,Atomic Data and Nuclear Data Tables 36, 1 (1987).
D. J. Rowe, P. Rochford, and J. Repka,J. Math. Phys. 29, 572 (1988). J. Carvalho, R. LeBlanc, M. Vassanji, D. J. Rowe, and J. B. McGrory,Nucl. Phys. A 452, 240 (1986).
B. Barrett and J. P. Draayer, Suggestions originated by a discussion at the Workshop on Nuclei under Extreme Conditions (Seattle, U.S.A., October 1995).
P. O. Hess, J. Schmidt, and W. Scheid,Ann. Phys. (N.Y.) 240, 22 (1995).
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Work supported by CONACyt (No. E120-550/95).
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Hess, P.O. Comparative study of theSp (2,R) and theSp(6,R) models and an application to theBa chain of isotopes. Found Phys 27, 1061–1081 (1997). https://doi.org/10.1007/BF02551153
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DOI: https://doi.org/10.1007/BF02551153