Abstract
The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF0 Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, 180Pb and 184Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF0 functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF0 functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF0 functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A 2ndrip = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A 2ndrip (SKM*) = 272.
Similar content being viewed by others
References
A. Bohr and B. Mottelson, Nuclear Structure, Vol. 1: Single-Particle Motion (Benjamin, New York, 1969).
A. Bohr and B. Mottelson, Nuclear Structure, Vol. 2: Nuclear Deformations (Benjamin, New York, 1974).
D. Vautherin and D. M. Brink, Phys. Rev. C 5, 626 (1972).
J. Dechargéand D. Gogny, Phys. Rev. C 21, 1568 (1980).
W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133 (1965).
P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864 (1964).
S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. Lett. 102, 152503 (2009).
S. Goriely, http://www-astro.ulb.ac.be/bruslib/nucdata/
J. Bartel, P. Quentin, M. Brack, et al., Nucl. Phys. A 386, 79 (1982).
E. Chabanat, P. Bonche, P. Haensel, et al., Nucl. Phys. A 635, 231 (1998).
M. Bender, P.-H. Heenen, and P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).
M. Kortelainen, J. McDonnell, W. Nazarewicz, et al., Phys. Rev. C 85, 024304 (2012).
P. Ring, Prog. Part. Nucl. Phys. 37, 193 (1996).
M. Baldo, C. Maieron, P. Schuck, and X. Viñas, Nucl. Phys. A 736, 241 (2004).
M. Baldo, P. Schuck, and X. Viñas, Phys. Lett. B 663, 390 (2008).
M. Baldo, L. M. Robledo, P. Schuck, and X. Viñas, Phys. Rev. C 87, 064305 (2013).
V. A. Khodel and E. E. Saperstein, Phys. Rep. 92, 183 (1982).
A. B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei (Nauka, Moscow, 1965; Wiley, New York, 1967).
S. A. Fayans and V. A. Khodel, JETP Lett. 17, 444 (1973).
A. B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei, 2nd ed. (Nauka, Moscow, 1981) [in Russian].
N. V. Gnezdilov, E. E. Saperstein, and S. V. Tolokonnikov, Europhys. Lett. 107, 62001 (2014).
N.V. Gnezdilov, E. E. Sapershtein, and S.V. Tolokonnikov, Phys. At. Nucl. 78, 24 (2015).
V. A. Khodel, E. E. Saperstein, and M. V. Zverev, Nucl. Phys. A 465, 397 (1987).
P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980).
A. V. Smirnov, S. V. Tolokonnikov, and S. A. Fayans, Sov. J. Nucl. Phys. 48, 995 (1988).
D. J. Horen, G. R. Satchler, S. A. Fayans, and E. L. Trykov, Nucl. Phys. A 600, 193 (1996).
I. N. Borzov, S. A. Fayans, E. Krömer, and D. Zawischa, Z. Phys. A 355, 117 (1996).
S. A. Fayans, S. V. Tolokonnikov, E. L. Trykov, and D. Zawischa, Nucl. Phys. A 676, 49 (2000).
S. V. Tolokonnikov and E. E. Saperstein, Phys. At. Nucl. 73, 1684 (2010).
E. E. Saperstein and S. V. Tolokonnikov, Phys. At. Nucl. 74, 1277 (2011).
I. N. Borzov, E. E. Saperstein, and S.V. Tolokonnikov, Phys. At. Nucl. 71, 469 (2008).
I. N. Borzov, E. E. Saperstein, S. V. Tolokonnikov, et al., Eur. Phys. J. A 45, 159 (2010).
S. V. Tolokonnikov, S. Kamerdzhiev, S. Krewald, E. E. Saperstein, and D. Voitenkov, Eur. Phys. J. A 48, 70 (2012).
S. Kamerdzhiev, S. Krewald, S. Tolokonnikov, E. E. Saperstein, and D. Voitenkov, EPJ Web Conf. 38, 10002 (2012).
S. V. Tolokonnikov, S. Kamerdzhiev, D. Voytenkov, S. Krewald, and E. E. Saperstein, Phys. Rev. C 84, 064324 (2011).
S. V. Tolokonnikov, S. Kamerdzhiev, S. Krewald, E. E. Saperstein, and D. Voitenkov, EPJ Web Conf. 38, 04002 (2012).
N. V. Gnezdilov, I. N. Borzov, E. E. Saperstein, and S. V. Tolokonnikov, Phys. Rev. C 89, 034304 (2014).
S. V. Tolokonnikov, I. N. Borzov, M. Kortelainen, Yu. S. Lutostansky, and E. E. Saperstein, J. Phys. G 42, 075102 (2015).
S. A. Fayans, JETP Lett. 68, 169 (1998).
M. V. Stoitsov, N. Schunck, M. Kortelainen, et al., Comput. Phys. Commun. 184, 1592 (2013).
M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, et al., Phys. Rev. C 68, 054312 (2003).
J. Erler, N. Birge, M. Kortelainen, et al., Nature 486, 509 (2012).
R. R. Rodrguez-Guzmán, J. L. Egido, and L. M. Robledo, Phys. Rev. C 69, 054319 (2004).
M. Bender, P. Bonche, T. Duguet, and P.-H. Heenen, Phys. Rev. C 69, 064303 (2004).
I. Angeli, Recommended Values of Nuclear Charge Radii (2008), http://cdfe.sinp.msu.ru/services/radchart/radhelp.html#rad
Yu. Gangrsky and K. Marinova (2008), http://cdfe.sinp.msu.ru/services/radchart/radhelp. html#rad
Database of the Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics. http://cdfe.sinp.msu.ru/services/radchart/radmain.html
N. J. Stone, At. DataNucl. Data Tables 90, 75 (2005).
K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011).
R. Julin, K. Helariutta, and M. Muikku, J. Phys. G 27, R109 (2001).
P. Rahkila, D. G. Jenkins, J. Pakarinen, et al., Phys. Rev. C 82, 011303(R) (2010).
M. Bender, T. Duguet, and D. Lacroix, Phys. Rev. C 79, 044319 (2009).
J. M. Yao, M. Bender, and P.-H. Heenen, Phys. Rev. C 87, 034322 (2013).
M. Bender, T. Cornelius, G. A. Lalazissis, et al., Eur. Phys. J. A 14, 23 (2002).
K. Heyde, C. de Coster, P. van Duppen, et al., Phys. Rev. C 53, 1035 (1996).
B. Friedman and V. R. Pandharipande, Nucl. Phys. A 361, 502 (1981).
J. A. Nolen, and J. P. Schiffer, Ann. Rev. Nucl. Part. Sci. 19, 471 (1969).
B. A. Brown, Phys. Rev. C 58, 220 (1998).
G. Audi, A. H. Wapstra, and C. Thibault, Nucl. Phys. A 729, 337 (2003).
M. Dutra, O. Lourenceo, J. S. SáMartins, et al., Phys. Rev. C 85, 035201 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Tolokonnikov, S.V., Borzov, I.N., Lutostansky, Y.S. et al. Deformation properties of lead isotopes. Phys. Atom. Nuclei 79, 21–37 (2016). https://doi.org/10.1134/S1063778816010208
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063778816010208