Abstract
The relevance of exchange effects for the stability of superheavy nuclei is examined within a linear QHD-II model by comparing Hartree-Fock with meanfield results. To allow a scan of the complete superheavy regime the recently developed local density approximation (LDA) for the exchange potential is employed for the Hartree-Fock level calculations. It turns out that, while many nuclear properties obtained with the LDA approach differ significantly from the corresponding mean-field results, the predictions of the two methods for shell closures are very similar. Furthermore, a comparison with a nonlinear variant of QHD-II shows that many nuclear properties obtained with the LDA in the framework of linear QHD-II are somewhere in-between the corresponding linear and nonlinear mean-field results. This indicates that the LDA exchange partially includes nonlinear contributions, which supports the interpretation of the meson self-coupling as a parametrization of many-body effects.
Similar content being viewed by others
References
U. Mosel and W. Greiner,Z. Phys. 222, 261 (1969).
S. G. Nilsson, C. F. Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, I.-L. Lamm, P. Möller, and B. Nilsson,Nucl. Phys. A 131, 1 (1969).
K. Kumar,Superheavy Elements (Adam Hilger, Bristol, 1989).
S. Hofmann, V. Ninov, F. P. Hessberger, P. Armbruster, H. Folger, G. Münzenberg, H. J. Schött, A. G. Popeko, A. V. Yeremin, A. N. Andreyev, S. Saro, R. Janik, and M. Leino,Z. Phys. A 350, 277 (1995),Z. Phys. A 350, 281 (1995).
S. Hoffmann, V. Ninov, F. P. Hessberger, P. Armbruster, H., Folger, G. Münzenberg, H. J. Schött, A. G. Popeko, A. V. Yeremin, S. Saro, R. Janik, and M. Leino,Z. Phys. A 354, 229 (1996).
Yu. Lazarev, Yu. V. Lobanov, Yu. Ts. Oganessian, V. K. Utyonkov, F. Sh. Abdullin, A. N. Polyakov, J. Rigol, I. V. Shirokovsky, S. Iliev, V. G. Subbotin, A. M. Sukhov, G. V. Buklanov, B. N. Gikal, V. B. Kutner, A. N. Mezentsev, K. Subotic, J. F. Wild, R. W. Lougheed, and K. J. Moody,Phys. Rev. C 54 620 (1996).
S. Ćwiok, J. Dobaczewski, P.-H. Heenen, P. Magierski, and W. Nazarewicz,Nucl. Phys. A 611, 211 (1996).
K. Rutz, M. Bender, T. Bürvenich, T. Schilling, P.-G. Reinhard, J. A. Maruhn, and W. Greiner,Phys. Rev. C 56, 238 (1997).
G. A. Lalazissis, M. M. Sharma, P. Ring, and Y. K. Gambhir,Nucl. Phys. A 608, 202 (1997).
Z. Patyk and A. Sobiczewski,Nucl. Phys. A 533, 132 (1991).
P. Möller and J. R. Nix:Nucl. Phys. A 549, 84 (1992);J. Phys. G 20, 1681 (1994).
Y. K. Gambhir, P. Ring, and A. Thimet,Ann. Phys. (N.Y.) 198, 132 (1990).
B. D. Serot, and J. D. Walecka, inAdvances in Nuclear Physics, J. W. Negele and E. Vogt, eds. (Plenum, New York, 1986), Vol. 16.
B. D. Serot,Rep. Prog. Phys. 55, 1855 (1992).
H. F. Boersma,Phys. Rev. C 48, 472 (1993).
J.-K. Zhang, Y. Jin, and D. S. Onley,Phys. Rev C 48, 2697 (1993).
R. N. Schmid, E. Engel, and R. M. Dreizler,Phys. Rev. C 52, 164 (1995).
R. N. Schmid, E. Engl, and R. M. Dreizler,Phys. Rev. C 52, 2804 (1995).
C. Speicher, R. M. Dreizler, and E. Engel,Ann. Phys. (N. Y.) 213, 312 (1992).
A. Bouyssy, J.-F. Mathiot, Nguyen Van Giai, and S. Marcos,Phys. Rev. C 36, 380 (1987).
H. F. Boersma and R. Malfliet,Phys. Rev. C 49, 233 (1994);Phys. Rev. C 49, 1495 (1994).
M. Rufa, P.-G. Reinhard, J. A. Maruhn, W. Greiner, and M. R. Strayer,Phys. Rev. C 38, 390 (1988).
R. O. Jones and O. Gunnarsson,Rev. Mod. Phys. 61, 689 (1989).
S. A. Chin,Ann. Phys. (N. Y.) 108, 301 (1977).
Unfortunately, this inversion leads to numerical difficulties in the asymptotic regime with its exponentially decaying densities. To deal with this problem one resorts to a perturbative evaluation ofe INM x (ρ p , ρ n , ρ s ), in which the difference between ρ s and\(\tilde \rho _s \) is taken into account to first order,\(e_x^{INM} (\rho _s ) \approx \tilde e_x^{INM} (M^* ) + \frac{{d\tilde e_x^{INM} }}{{dM^* }}(M^* )\left( {\frac{{d\tilde \rho _s }}{{dM^* }}(M^* )} \right)^{ - 1} (\rho _s - \tilde \rho _s )\) withM * (x) taken from (14) (for fixed ρ p and ρ n , which are here suppressed for brevity).
M. Prakash, P. J. Ellis, E. K. Heide, S. Rudaz,Nucl. Phys. A 575, 583 (1994).
W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen,Phys. Rev. Lett. 52, 2141 (1984).
H. de Vries, C. W. de Jager, and C. de Vries,Atomic and Nuclear Data Tables 36, 495 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schmid, R.N., Engel, E. & Dreizler, R.M. Relativistic models for nuclear structure calculations: Comparative study of mean-field and Hartree-Fock approximation for superheavy nuclei. Found Phys 27, 1257–1274 (1997). https://doi.org/10.1007/BF02551527
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02551527