Abstract
It is shown that a consistent treatment of nuclear bulk and surface effects leads to an improved version of the liquid-drop mass formula with modified symmetry and Coulomb terms. If in addition shell effects are modelled through the counting of the number of valence nucleons, a very simple mass formula is obtained with an rms deviation from the 2003 database of atomic masses of about 800keV. As an application, the volume and surface symmetry energy for A \( \rightarrow\) ∞ are determined. A similar description of nuclear radii is suggested with specific reference to the neutron skin.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003).
S. Goriely, M. Samyn, J.M. Pearson, Nucl. Phys. A 773, 279 (2006).
W.D. Myers, W.J. Swiatecki, Nucl. Phys. 81, 1 (1966).
P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995).
J. Duflo, Nucl. Phys. A 576, 29 (1994).
A.P. Zuker, Nucl. Phys. A 576, 65 (1994).
J. Duflo, A.P. Zuker, Phys. Rev. C 52, R23 (1995).
H. Koura, T. Tachibana, M. Uno, M. Yamada, Prog. Theor. Phys. 113, 305 (2005).
G. Royer, Nucl. Phys. A 807, 105 (2008).
P. Danielewicz, Nucl. Phys. A 727, 203 (2003).
A.W. Steiner, M. Prakash, J.M. Lattimer, P.J. Ellis, Phys. Rep. 411, 325 (2005).
G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003).
P. Van Isacker, in Capture Gamma-Ray Spectroscopy and Related Topics, edited by Andreas Woehr and Ani Aprahamian, AIP Conf. Proc. 819, 57 (2006).
A.E.L. Dieperink, P. Van Isacker, Eur. Phys. J. A 32, 11 (2007).
F. Iachello, A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, England, 1987).
R. Fossion, C. De Coster, J.E. García-Ramos, T. Werner, K. Heyde, Nucl. Phys. A 697, 703 (2002).
I. Talmi, Simple Models of Complex Nuclei. The Shell Model and Interacting Boson Model (Harwood, Chur, 1993).
R.F. Casten, Nucl. Phys. A 443, 1 (1985).
P. Danielewicz, arXiv:nucl-th/0411115v2.
P. Danielewicz, J. Lee, in Nuclear Physics and Applications, AIP Conf. Proc. 947, 301 (2007).
P. Danielewicz, J. Lee, Int. J. Mod. Phys. E 8, 892 (2009).
J. Jänecke, T.W. O’Donnell, Phys. Lett. B 605, 87 (2005).
B.A. Brown, A. Derevianko, V.V. Flambaum, Phys. Rev. C 79, 035501 (2009).
I. Angeli, At. Data Nucl. Data Tables 87, 185 (2004).
J. Duflo, A.P. Zuker, Phys. Rev. C 66, 051304(R) (2002).
M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Phys. Rev. Lett. 102, 122502 (2009).
A.P. Zuker, J. Duflo, S.M. Lenzi, G. Martínez-Pinedo, A. Poves, J. Sánchez-Solano, Phys. Rev. Lett. 89, 142502 (2002).
A.E.L. Dieperink, P. Van Isacker, in preparation.
W.D. Myers, K.-H. Schmidt, Nucl. Phys. A 410, 61 (1983).
A. Trzcińska, J. Jastrzębski, P. Lubiński, F.J. Hartmann, R. Schmidt, T. von Egidy, B. Kłlos, Phys. Rev. Lett. 87, 082501 (2001).
B.A. Brown, G. Shen, G.C. Hillhouse, J. Meng, A. Trzcińska, Phys. Rev. C 76, 034305 (2007).
W.D. Myers, W.J. Swiatecki, Nucl. Phys. A 336, 267 (1980).
P. Sarriguren, M.K. Gaidarov, E. Moya de Guerra, A.N. Antonov, Phys. Rev. C 76, 044322 (2007).
Lead radius experiment (PREX) at Jlab, E06002.
J. James, P.G.H. Sandars, J. Phys. B 32, 3295 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by W. Nazarewicz
Rights and permissions
About this article
Cite this article
Dieperink, A.E.L., Van Isacker, P. Shell corrections to a liquid-drop description of nuclear masses and radii. Eur. Phys. J. A 42, 269 (2009). https://doi.org/10.1140/epja/i2009-10869-3
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/i2009-10869-3