Abstract
We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential \( \Delta\) \( \lambda\) = \( \lambda_{{n}}^{}\) - \( \lambda_{{p}}^{}\) beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.
Similar content being viewed by others
References
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Berlin, Heidelberg, 1980).
W.D. Myers, W.J. Swiatecki, Ann. Phys. (N.Y.) 55, 395 (1969).
M.B. Tsang, C.K. Gelbke, X.D. Liu, Phys. Rev. C 64, 054615 (2001).
A. Ono, P. Danielewicz, W.A. Friedman, Phys. Rev. C 68, R051601 (2003).
J.B. Natowitz, K. Hagel, R. Wada., Phys. Rev. C 52, R2322 (1995).
J. Cibor, R. Wada, K. Hagel, Phys. Lett. B 473, 29 (2000).
M. Veselsky, R.W. Ibbotson, R. Laforest, Phys. Lett. B 497, 1 (2001).
W.A. Friedman, Phys. Rev. C 42, 667 (1990).
H.S. Xu, M.B. Tsang, T.X. Liu, Phys. Rev. Lett. 85, 716 (2000).
V.E. Viola, Nucl. Phys. A 734, 487 (2004).
W.D. Myers, W.J. Swiatecki, Phys. Rev. C 57, 3020 (1998).
W.D. Myers, W.J. Swiatecki, Phys. Rev. C 63, 034318 (2001).
P.-G. Reinhard, M. Bender, W. Nazarewicz, T. Vertse, Phys. Rev. C 73, 014309 (2006).
W. Satula, R.A. Wyss, M. Rafalski, Phys. Rev. C 74, 011301R (2006).
W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965).
D.A. Kirznitz, Field Theoretical Methods in Many Body Systems (Pergamon, London, 1967).
M. Brack, C. Guet, H.-B. Håkansson, Phys. Rep. 123, 275 (1985).
M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).
A. Bohr, B.R. Mottelson, Nuclear Structure, Vol. 1 (W. A. Benjamin, New York, 1969).
K.-F. Liu, H. Luo, Z. Ma, O. Shen, Nucl. Phys. A 534, 25 (1991).
E. Chabanat, P. Bonche, P. Haensel,, Nucl. Phys. A 627, 25 (1991).
K.C. Chung, C.S. Wang, A.J. Santiago, J.W. Zhang, Eur. Phys. J. A 10, 27 (2001).
M.J. Martin, Nucl. Data Sheets 108, 1583 (2007).
L.D. Landau, E.M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1958).
Author information
Authors and Affiliations
Corresponding author
Additional information
W. Nazarewicz
Rights and permissions
About this article
Cite this article
Kolomietz, V.M., Sanzhur, A.I. Equation of state and symmetry energy within the stability valley. Eur. Phys. J. A 38, 345–354 (2008). https://doi.org/10.1140/epja/i2008-10679-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epja/i2008-10679-1