Abstract.
The density dependence of the symmetry energy around saturation density, characterized by the slope parameter L , is studied using information provided by the neutron skin thickness in finite nuclei. An estimate for L is obtained from experimental data on neutron skins extracted from antiprotonic atoms. We also discuss the ability of parity-violating elastic electron scattering to obtain information on the neutron skin thickness in 208Pb and to constrain the density dependence of the nuclear symmetry energy. The size and shape of the neutron density distribution of 208Pb predicted by mean-field models is briefly addressed. We conclude with a comparative overview of the L values predicted by several existing determinations.
Article PDF
Similar content being viewed by others
References
A. Steiner, M. Prakash, J. Lattimer, P. Ellis, Phys. Rep. 411, 325 (2005)
B. Alex Brown, Phys. Rev. Lett. 85, 5296 (2000)
S. Typel, B.A. Brown, Phys. Rev. C 64, 027302 (2001)
R. Furnstahl, Nucl. Phys. A 706, 85 (2002)
C.J. Horowitz, J. Piekarewicz, Phys. Rev. Lett. 86, 5647 (2001)
B.G. Todd-Rutel, J. Piekarewicz, Phys. Rev. Lett. 95, 122501 (2005)
A.E.L. Dieperink, Y. Dewulf, D. Van Neck, M. Waroquier, V. Rodin, Phys. Rev. C 68, 064307 (2003)
A.W. Steiner, B.-A. Li, Phys. Rev. C 72, 041601 (2005)
M.K. Gaidarov, A.N. Antonov, P. Sarriguren, E.M. de Guerra, Phys. Rev. C 85, 064319 (2012)
D.T. Khoa, W. von Oertzen, A. Ogloblin, Nucl. Phys. A 602, 98 (1996)
T. Gaitanos, M.D. Toro, S. Typel, V. Baran, C. Fuchs, V. Greco, H. Wolter, Nucl. Phys. A 732, 24 (2004)
V. Baran, M. Colonna, V. Greco, M.D. Toro, Phys. Rep. 410, 335 (2005)
B.-A. Li, L.-W. Chen, C.M. Ko, Phys. Rep. 464, 113 (2008)
D.V. Shetty, S.J. Yennello, G.A. Souliotis, Phys. Rev. C 76, 024606 (2007)
M.A. Famiano, T. Liu, W.G. Lynch, M. Mocko, A.M. Rogers, M.B. Tsang, M.S. Wallace, R.J. Charity, S. Komarov, D.G. Sarantites et al., Phys. Rev. Lett. 97, 052701 (2006)
M.B. Tsang, Y. Zhang, P. Danielewicz, M. Famiano, Z. Li, W.G. Lynch, A.W. Steiner, Phys. Rev. Lett. 102, 122701 (2009)
L. Trippa, G. Colò, E. Vigezzi, Phys. Rev. C 77, 061304 (2008)
LAND Collaboration (A. Klimkiewicz et al.), Phys. Rev. C 76, 051603 (2007)
X. Roca-Maza, G. Pozzi, M. Brenna, K. Mizuyama, G. Colò, Phys. Rev. C 85, 024601 (2012)
A. Carbone, G. Colò, A. Bracco, L.G. Cao, P.F. Bortignon, F. Camera, O. Wieland, Phys. Rev. C 81, 041301 (2010)
X. Roca-Maza, M. Brenna, B.K. Agrawal, P.F. Bortignon, G. Colò, L.-G. Cao, N. Paar, D. Vretenar, Phys. Rev. C 87, 034301 (2013)
J. Guéna, M. Lintz, M.A. Bouchiat, Mod. Phys. Lett. A 20, 375 (2005)
T. Sil, M. Centelles, X. Viñas, J. Piekarewicz, Phys. Rev. C 71, 045502 (2005)
J.M. Lattimer, M. Prakash, Phys. Rep. 442, 109 (2007)
T. Klähn, D. Blaschke, S. Typel, E.N.E. van Dalen, A. Faessler, C. Fuchs, T. Gaitanos, H. Grigorian, A. Ho, E.E. Kolomeitsev et al., Phys. Rev. C 74, 035802 (2006)
D.T. Loan, N.H. Tan, D.T. Khoa, J. Margueron, Phys. Rev. C 83, 065809 (2011)
M. Dutra, O. Loureno, J.S. Sá Martins, A. Delfino, J.R. Stone, P.D. Stevenson, Phys. Rev. C 85, 035201 (2012)
M.B. Tsang, J.R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C.J. Horowitz, J. Lee, W.G. Lynch, Z. Kohley et al., Phys. Rev. C 86, 015803 (2012)
J.M. Lattimer, Y. Lim, Astrophys. J. 771, 51 (2013)
M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Phys. Rev. Lett. 102, 122502 (2009)
M. Warda, X. Viñas, X. Roca-Maza, M. Centelles, Phys. Rev. C 80, 024316 (2009)
M. Warda, X. Viñas, X. Roca-Maza, M. Centelles, Phys. Rev. C 81, 054309 (2010)
M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Phys. Rev. C 82, 054314 (2010)
X. Roca-Maza, M. Centelles, X. Viñas, M. Warda, Phys. Rev. Lett. 106, 252501 (2011)
N.R. Draper, H. Smith, Applied Regression Analysis, 3rd edition (Wiley, New York, 1998)
W.D. Myers, W. Swiatecki, Ann. Phys. 55, 395 (1969)
W. Myers, W. Swiatecki, Ann. Phys. 84, 186 (1974)
W. Myers, Droplet Model of Atomic Nuclei (Plenum, New York, 1977)
M. Farine, J. Coté, J.M. Pearson, Phys. Rev. C 24, 303 (1981)
M. Brack, C. Guet, H.-B.H. Kansson, Phys. Rep. 123, 275 (1985)
K. Kolehmainen, M. Prakash, J.M. Lattimer, J.R. Treiner, Nucl. Phys. A 439, 535 (1985)
J. Treiner, H. Krivine, Ann. Phys. 170, 406 (1986)
M. Centelles, M.D. Estal, X.V. Nas, Nucl. Phys. A 635, 193 (1998)
M.D. Estal, M. Centelles, X. Vias, Nucl. Phys. A 650, 443 (1999)
M. Centelles, X.V. Nas, Nucl. Phys. A 563, 173 (1993)
P. Danielewicz, J. Lee, Nucl. Phys. A 818, 36 (2009)
M. Liu, N. Wang, Z.-X. Li, F.-S. Zhang, Phys. Rev. C 82, 064306 (2010)
L.-W. Chen, Phys. Rev. C 83, 044308 (2011)
Z. Zhang, L.-W. Chen, Phys. Lett. B 726, 234 (2013)
J. Dong, W. Zuo, J. Gu, U. Lombardo, Phys. Rev. C 85, 034308 (2012)
J. Dong, W. Zuo, J. Gu, Phys. Rev. C 87, 014303 (2013)
W. Myers, W. Swiatecki, Nucl. Phys. A 336, 267 (1980)
A. Trzcińska, J. Jastrzebski, P. Lubiński, F.J. Hartmann, R. Schmidt, T. von Egidy, B. Kłos, Phys. Rev. Lett. 87, 082501 (2001)
J. Jastrzebski, A. Trzcińska, P. Lubiński, B. Kłos, F.J. Hartmann, T. von Egidy, S. Wycech, Int. J. Mod. Phys. E 13, 343 (2004)
B. Kłos, A. Trzcińska, J. Jastrzebski, T. Czosnyka, M. Kisieliński, P. Lubiński, P. Napiorkowski, L. Pieńkowski, F.J. Hartmann, B. Ketzer et al., Phys. Rev. C 76, 014311 (2007)
A. Krasznahorkay, H. Akimune, A. van den Berg, N. Blasi, S. Brandenburg, M. Csatlos, M. Fujiwara, J. Gulyas, M. Harakeh, M. Hunyadi et al., Nucl. Phys. A 731, 224 (2004)
L.-W. Chen, C.M. Ko, B.-A. Li, Phys. Rev. Lett. 94, 032701 (2005)
L.-W. Chen, C.M. Ko, B.-A. Li, Phys. Rev. C 72, 064309 (2005)
W.J. Światecki, A. Trzcińska, J. Jastrzebski, Phys. Rev. C 71, 047301 (2005)
P. Danielewicz, Nucl. Phys. A 727, 233 (2003)
S. Mizutori, J. Dobaczewski, G.A. Lalazissis, W. Nazarewicz, P.G. Reinhard, Phys. Rev. C 61, 044326 (2000)
M. Centelles, M. Pi, X.V. Nas, F. Garcias, M. Barranco, Nucl. Phys. A 510, 397 (1990)
PREX Collaboration (R. Michaels), http://hallaweb.jlab.org/parity/prex/pbup2005.ps (2005)
C.J. Horowitz, S.J. Pollock, P.A. Souder, R. Michaels, Phys. Rev. C 63, 025501 (2001)
PREX Collaboration (S. Abrahamyan, Z. Ahmed, H. Albataineh, K. Aniol, D.S. Armstrong, W. Armstrong, T. Averett, B. Babineau, A. Barbieri, V. Bellini et al.), Phys. Rev. Lett. 108, 112502 (2012)
K. Paschke, pREX-II Proposal to Jefferson Lab., http://hallaweb.jlab.org/parity/prex/prexII.pdf (2012)
S. Ban, C.J. Horowitz, R. Michaels, J. Phys. G: Nucl. Part. Phys. 39, 015104 (2012)
J. Liu, Z. Ren, T. Dong, Nucl. Phys. A 888, 45 (2012)
J. Liu, Z. Ren, T. Dong, Nucl. Phys. A 900, 1 (2013)
S. Riordan, cREX Proposal to Jefferson Lab., http://hallaweb.jlab.org/parity/prex/c-rex2013_v7.pdf (2013)
C. Sfienti, talk at the Workshop to Explore Physics Opportunities with Intense, Polarized Electron Beams up to 300 MeV and The Calcium Radius Experiment (CREX) Workshop at Jefferson Lab (2013)
C.J. Horowitz, Z. Ahmed, C.M. Jen, A. Rakhman, P.A. Souder, M.M. Dalton, N. Liyanage, K.D. Paschke, K. Saenboonruang, R. Silwal et al., Phys. Rev. C 85, 032501 (2012)
P.J. Mohr, http://pdg.lbl.gov/2012/reviews/rpp2012-rev-phys-constants.pdf (2011)
T. Donnelly, J. Dubach, I. Sick, Nucl. Phys. A 503, 589 (1989)
C.J. Horowitz, Phys. Rev. C 57, 3430 (1998)
D. Vretenar, P. Finelli, A. Ventura, G.A. Lalazissis, P. Ring, Phys. Rev. C 61, 064307 (2000)
O. Moreno, E.M. de Guerra, P. Sarriguren, J.M. Udas, J. Phys. G: Nucl. Part. Phys. 37, 064019 (2010)
X. Roca-Maza, M. Centelles, F. Salvat, X. Viñas, Phys. Rev. C 78, 044332 (2008)
F. Salvat, A. Jablonski, C.J. Powell, Comput. Phys. Commun. 165, 157 (2005)
J. Friedrich, T. Walcher, Eur. Phys. A 17, 607 (2003)
L.-W. Chen, C.M. Ko, B.-A. Li, J. Xu, Phys. Rev. C 82, 024321 (2010)
M. Baldo, P. Schuck, X.V. Nas, Phys. Lett. B 663, 390 (2008)
I. Angeli, K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)
J. Zenihiro, H. Sakaguchi, T. Murakami, M. Yosoi, Y. Yasuda, S. Terashima, Y. Iwao, H. Takeda, M. Itoh, H.P. Yoshida et al., Phys. Rev. C 82, 044611 (2010)
A.W. Steiner, J.M. Lattimer, E.F. Brown, Astrophys. J. 722, 33 (2010)
K. Hebeler, J.M. Lattimer, C.J. Pethick, A. Schwenk, Phys. Rev. Lett. 105, 161102 (2010)
F.J. Fattoyev, J. Piekarewicz, Phys. Rev. Lett. 111, 162501 (2013)
H.D. Vries, C.D. Jager, C.D. Vries, At. Data Nucl. Data Tables 36, 495 (1987)
E. Friedman, A. Gal, Nucl. Phys. A 724, 143 (2003)
E. Friedman, A. Gal, J. Mares, Nucl. Phys. A 761, 283 (2005)
E. Friedman, Hyperfine Interact. 193, 33 (2009)
S. Gandolfi, J. Carlson, S. Reddy, Phys. Rev. C 85, 032801 (2012)
I. Vidaña, A. Polls, C.M.C. Providência, Phys. Rev. C 84, 062801 (2011)
M.B. Tsang, T.X. Liu, L. Shi, P. Danielewicz, C.K. Gelbke, X.D. Liu, W.G. Lynch, W.P. Tan, G. Verde, A. Wagner et al., Phys. Rev. Lett. 92, 062701 (2004)
Z. Kohley, L.W. May, S. Wuenschel, A. Bonasera, K. Hagel, R. Tripathi, R. Wada, G.A. Souliotis, D.V. Shetty, S. Galanopoulos et al., Phys. Rev. C 82, 064601 (2010)
Z. Kohley, L.W. May, S. Wuenschel, M. Colonna, M. Di Toro, M. Zielinska-Pfabe, K. Hagel, R. Tripathi, A. Bonasera, G.A. Souliotis et al., Phys. Rev. C 83, 044601 (2011)
W. Myers, W. Swiatecki, Nucl. Phys. A 601, 141 (1996)
W.D. Myers, W.J. Świaţecki, Phys. Rev. C 57, 3020 (1998)
P. Möller, W.D. Myers, H. Sagawa, S. Yoshida, Phys. Rev. Lett. 108, 052501 (2012)
B.K. Agrawal, J.N. De, S.K. Samaddar, Phys. Rev. Lett. 109, 262501 (2012)
N. Wang, L. Ou, M. Liu, Phys. Rev. C 87, 034327 (2013)
N. Wang, T. Li, Phys. Rev. C 88, 011301 (2013)
C. Xu, B.-A. Li, L.-W. Chen, Phys. Rev. C 82, 054607 (2010)
A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011)
J. Piekarewicz et al., Phys. Rev. C 85, 041302 (2012)
X. Roca-Maza, M. Brenna, G. Colò, M. Centelles, X. Viñas, B.K. Agrawal, N. Paar, D. Vretenar, J. Piekarewicz, Phys. Rev. C 88, 024316 (2013)
P.-G. Reinhard, W. Nazarewicz, Phys. Rev. C 81, 051303 (2010)
J. Meyer, P. Quentin, B. Jennings, Nucl. Phys. A 385, 269 (1982)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Ramos
Contribution to the Topical Issue “Nuclear Symmetry Energy” edited by Bao-An Li, Àngels Ramos, Giuseppe Verde, Isaac Vidaña.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Viñas, X., Centelles, M., Roca-Maza, X. et al. Density dependence of the symmetry energy from neutron skin thickness in finite nuclei. Eur. Phys. J. A 50, 27 (2014). https://doi.org/10.1140/epja/i2014-14027-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/i2014-14027-8