Abstract
In heavy nuclei the ratio between local densities of neutrons and protons increases towards the nuclear periphery. The excess of neutrons is known as the neutron skin (NS) with a subtle difference (\(<0.5\) fm) between the r.m.s radii of the distributions of neutrons and protons. We show that the presence of NS in \(^{208}\)Pb leads to extra spectator neutrons in ultracentral \(^{208}\)Pb–\(^{208}\)Pb collisions at the CERN SPS and LHC. The yields of spectator neutrons and protons were calculated within a new version of Abrasion–Ablation Monte Carlo for Colliders model (AAMCC-MST) taking into account NS and pre-equilibrium clustering of spectator matter. While the average numbers of spectator neutrons and protons in ultracentral collisions vary insignificantly, the cross sections of emission of certain numbers of spectator neutrons in events with 0,1,...5 spectator protons are changed by 50–250%, depending on the thickness of NS. These cross sections are less sensitive to other parameters in calculations, and their measurements in the ALICE experiment at the LHC will make it possible to restrict the variety of neutron density parameterizations existing for \(^{208}\)Pb.
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no new experimental data were created or analyzed in this study.]
References
A.S. Botvina, I.N. Mishustin, M. Begemann-Blaich et al., Multifragmentation of spectators in relativistic heavy-ion reactions. Nucl. Phys. A 584, 737–756 (1995). https://doi.org/10.1016/0375-9474(94)00621-S
H. Appelshäuser, J. Bächler, S.J. Bailey et al., Spectator Nucleons in Pb+Pb Collisions at 158 A GeV. Eur. Phys. J. A 2, 383–390 (1998). https://doi.org/10.1007/s100500050135
G. Puddu, R. Arnaldi, E. Chiavassa et al., The zero degree calorimeters for the ALICE experiment. Nucl. Inst. Meth. A 581, 397–401 (2007). https://doi.org/10.1016/j.nima.2007.08.013
B. Abelev, J. Adam, D. Adamová et al., Centrality determination of Pb–Pb collisions at \(\sqrt{s_{NN}}=2.76\) TeV with ALICE. Phys. Rev. C 88, 044909 (2013). https://doi.org/10.1103/PhysRevC.88.044909
R.C. Barrett, D.F. Jackson, Nuclear sizes and structure (Clarendon Press, New York, 1977), p.566
I. Tanihata, H. Hamagaki, O. Hashimoto et al., Measurements of interaction cross sections and radii of He isotopes. Phys. Lett. B 160, 380–384 (1985). https://doi.org/10.1016/0370-2693(85)90005-X
P.G. Hansen, A.S. Jensen, B. Jonson, Nuclear halos. Annu. Rev. Nucl. Part. Sci. 45, 591–634 (1995). https://doi.org/10.1146/annurev.ns.45.120195.003111
A. Trzcińska, J. Jastrzȩbski, P. Lubiński, F.J. Hartmann, R. Schmidt, T. von Egidy, B. Kłos, Neutron density distributions deduced from antiprotonic atoms. Phys. Rev. Lett. 87, 82501 (2001). https://doi.org/10.1103/PhysRevLett.87.082501
I. Angeli, K.P. Marinova, Table of experimental nuclear ground state charge radii: an update. At. Data Nucl. Data Tables 99, 69–95 (2013). https://doi.org/10.1016/j.adt.2011.12.006
B.A. Brown, Neutron radii in nuclei and the neutron equation of state. Phys. Rev. Lett. 85, 5296–5299 (2000). https://doi.org/10.1103/PhysRevLett.85.5296
M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Origin of the neutron skin thickness of \(^{208}\)Pb in nuclear mean-field models. Phys. Rev. C 82, 054314 (2010). https://doi.org/10.1103/PhysRevC.82.054314
M. Warda, X. Viñas, X. Roca-Maza, M. Centelles, Analysis of bulk and surface contributions in the neutron skin of nuclei. Phys. Rev. C 81, 054309 (2010). https://doi.org/10.1103/PhysRevC.81.054309
C.M. Tarbert, D.P. Watts, D.I. Glazier et al., Neutron skin of \(^{208}\)Pb from coherent pion photoproduction. Phys. Rev. Lett. 112, 242502 (2014). https://doi.org/10.1103/PhysRevLett.112.242502
D. Adhikari, H. Albataineh, D. Androic et al., Accurate determination of the neutron skin thickness of \(^{208}\)Pb through parity-violation in electron scattering. Phys. Rev. Lett. 126, 172502 (2021). https://doi.org/10.1103/PhysRevLett.126.172502
J. Dobaczewski, W. Nazarewicz, T.R. Werner, Neutron radii and skins in the Hartree–Fock–Bogoliubov calculations. Z. Phys. A 354, 27–35 (1996). https://doi.org/10.1007/s002180050009
C.J. Horowitz, J. Piekarewicz, Neutron star structure and the neutron radius of \(^{208}\)Pb. Phys. Rev. Lett. 86, 5647 (2001). https://doi.org/10.1103/PhysRevLett.86.5647
A.W. Steiner, M. Prakash, J.M. Lattimer, P.J. Ellis, Isospin asymmetry in nuclei and neutron stars. Phys. Rep. 411, 325–375 (2005). https://doi.org/10.1016/j.physrep.2005.02.004
D.Q. Fang, Y.G. Ma, X.Z. Cai, W.D. Tian, H.W. Wang, Effects of neutron skin thickness in peripheral nuclear reactions. Chin. Phys. Lett. 28, 10–13 (2011). https://doi.org/10.1088/0256-307X/28/10/102102
D.Q. Fang, Y.G. Ma, X.Z. Cai, W.D. Tian, H.W. Wang, Neutron removal cross section as a measure of neutron skin. Phys. Rev. C 81, 047603 (2010). https://doi.org/10.1103/PhysRevC.81.047603
T.-Z. Yan, S. Li, Impact parameter dependence of the yield ratios of light particles as a probe of neutron skin. Nucl. Sci. Tech. 30, 43 (2019). https://doi.org/10.1007/s41365-019-0572-8
T. Aumann, C.A. Bertulani, F. Schindler, S. Typel, Peeling off neutron skins from neutron-rich nuclei: constraints on the symmetry energy from neutron-removal cross sections. Phys. Rev. Lett. 119, 262501 (2017). https://doi.org/10.1103/PhysRevLett.119.262501
C.A. Bertulani, J. Valencia, Neutron skins as laboratory constraints on properties of neutron stars and on what we can learn from heavy ion fragmentation reactions. Phys. Rev. C 100, 015802 (2019). https://doi.org/10.1103/PhysRevC.100.015802
S. De, The effect of neutron skin on inclusive prompt photon production in Pb + Pb collisions at Large Hadron Collider energies. J. Phys. G: Nucl. Part. Phys. 44, 045104 (2017). https://doi.org/10.1088/1361-6471/aa5689
H. Paukkunen, Neutron skin and centrality classification in high-energy heavy-ion collisions at the LHC. Phys. Lett. B 745, 73–78 (2015). https://doi.org/10.1016/j.physletb.2015.04.037
M. Alvioli, M. Strikman, Spin-isospin correlated configurations in complex nuclei and neutron skin effect in W\(^\pm \) production in high-energy proton-lead collisions. Phys. Rev. C 100, 024912 (2019). https://doi.org/10.1103/PhysRevC.100.024912
H. Li, H.-J. Xu, Y. Zhou, X. Wang, J. Zhao, L.-W. Chen, F. Wang, Probing the neutron skin with ultrarelativistic isobaric collisions. Phys. Rev. Lett. 125, 222301 (2020). https://doi.org/10.1103/physrevlett.125.222301
I.A. Pshenichnov, N.A. Kozyrev, R.S. Nepeivoda, A.O. Svetlichnyi, N.A. Dmitrieva, Properties of spectator matter in nuclear collisions at NICA. Phys. Part. Nucl. 52, 591–597 (2021). https://doi.org/10.1134/S1063779621040493
U. Dmitrieva, N. Kozyrev, A. Svetlichnyi, I. Pshenichnov, Spectator nucleons in most central collisions of heavy nuclei at NICA. AIP Conf. Proc. 2377, 030005 (2021). https://doi.org/10.1063/5.0063284
N. Kozyrev, A. Svetlichnyi, R. Nepeivoda, I.A. Pshenichnov, Spectator nucleons in ultracentral \(^{208}\)Pb-\(^{208}\)Pb collisions as a probe of nuclear periphery. In: Proceedings of The Ninth Annual Conference on Large Hadron Collider Physics - PoS(LHCP2021), p. 223. Sissa Medialab, Trieste, Italy (2021). https://doi.org/10.22323/1.397.0223. https://pos.sissa.it/397/223
I.A. Pshenichnov, N.A. Kozyrev, A.O. Svetlichnyi, U.A. Dmitrieva, What one can learn by studying spectator remnants in central nucleus–nucleus collisions? Phys. Part. Nucl. 53, 335–341 (2022). https://doi.org/10.1134/S1063779622020691
L.-M. Liu, C.-J. Zhang, J. Zhou, J. Xu, J. Jia, G.-X. Peng, Probing neutron-skin thickness with free spectator neutrons in ultracentral high-energy isobaric collisions (2022) arXiv:2203.09924
A. Svetlichnyi, R. Nepeyvoda, I. Pshenichnov, Using spectator matter for centrality determination in nucleus–nucleus collisions. Particles 4, 227–235 (2021). https://doi.org/10.3390/particles4020021
A. Svetlichnyi, I. Pshenichnov, Formation of free and bound spectator nucleons in hadronic interactions between relativistic nuclei. Bull. Russ. Acad. Sci. Phys. 84, 911–916 (2020). https://doi.org/10.3103/S1062873820080110
R.S. Nepeivoda, A.O. Svetlichnyi, Dependence of n/p-ratio in spectator matter on the energy and mass of colliding nuclei. Mem. Faculty Phys. (1), 2110302 (2021)
R. Nepeivoda, A. Svetlichnyi, N. Kozyrev, I. Pshenichnov, Pre-equilibrium clustering in production of spectator fragments in collisions of relativistic nuclei. Particles 5, 40–51 (2022). https://doi.org/10.3390/particles5010004
C. Loizides, J. Kamin, D. D’Enterria, Improved Monte Carlo Glauber predictions at present and future nuclear colliders. Phys. Rev. C 97, 054910 (2018). https://doi.org/10.1103/PhysRevC.97.054910
T. Ericson, The statistical model and nuclear level densities. Adv. Phys. 9, 425–511 (1960). https://doi.org/10.1080/00018736000101239
V.F. Weisskopf, D.H. Ewing, On the yield of nuclear reactions with heavy elements. Phys. Rev. 57, 472–485 (1940). https://doi.org/10.1103/PhysRev.57.472
E. Fermi, High energy nuclear events. Prog. Theor. Phys. 5, 570–583 (1950). https://doi.org/10.1143/ptp/5.4.570
J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Statistical multifragmentation of nuclei. Phys. Rep. 257, 133–221 (1995). https://doi.org/10.1016/0370-1573(94)00097-M
S. Agostinelli, J. Allison, K. Amako, J. Apostolakis et al., Geant4—a simulation toolkit. Nucl. Inst. Meth. A 506, 250–303 (2003). https://doi.org/10.1016/S0168-9002(03)01368-8
C. Loizides, Glauber modeling of high-energy nuclear collisions at the subnucleon level. Phys. Rev. C 94, 024914 (2016). https://doi.org/10.1103/PhysRevC.94.024914
J.J. Gaimard, K.H. Schmidt, A reexamination of the abrasion–ablation model for the description of the nuclear fragmentation reaction. Nucl. Phys. A 531, 709–745 (1991). https://doi.org/10.1016/0375-9474(91)90748-U
C. Scheidenberger, I.A. Pshenichnov, K. Sümmerer et al., Charge-changing interactions of ultrarelativistic Pb nuclei. Phys. Rev. C 70, 014902 (2004). https://doi.org/10.1103/PhysRevC.70.014902
D.D. Chinellato, et al. Data-driven model for the emission of spectator nucleons as a function of centrality in Pb-Pb collisions at LHC energies, ALICE-PUBLIC-2020-001 (2020). http://cds.cern.ch/record/2712412
A.S. Botvina, N. Buyukcizmeci, M. Bleicher, Evolution of the statistical disintegration of finite nuclei toward high energy. Phys. Rev. C 106, 014607 (2022). https://doi.org/10.1103/PhysRevC.106.014607
R.C. Prim, Bell Syst. Tech. J. 36, 1389–1401 (1957). https://doi.org/10.1002/j.1538-7305.1957.tb01515.x
V.E. Viola, K. Kwiatkowski, J.B. Natowitz, S.J. Yennello, Breakup densities of hot nuclei. Phys. Rev. Lett. 93, 132701 (2004). https://doi.org/10.1103/PhysRevLett.93.132701
J.N. De, S.K. Samaddar, X. Viñas, M. Centelles, Nuclear expansion with excitation. Phys. Lett. B 638, 160–165 (2006). https://doi.org/10.1016/j.physletb.2006.05.046
J. Allison, K. Amako, J. Apostolakis, P. Arce, M. Asai, T. Aso, E. Bagli, A. Bagulya, S. Banerjee, G. Barrand et al., Recent developments in Geant4. Nucl. Instrum. Methods A 835, 186–225 (2016). https://doi.org/10.1016/j.nima.2016.06.125
V. Weisskopf, Statistics and nuclear reactions. Phys. Rev. 52, 295–303 (1937). https://doi.org/10.1103/PhysRev.52.295
U. Dmitrieva, I. Pshenichnov, On the performance of Zero Degree Calorimeters in detecting multinucleon events. Nucl. Instrum. Methods Phys. Res. Sect. A 906, 114–119 (2018). https://doi.org/10.1016/j.nima.2018.07.072
M. Alvioli, H. Holopainen, K.J. Eskola, M. Strikman, Initial-state anisotropies and their uncertainties in ultrarelativistic heavy-ion collisions from the monte carlo glauber model. Phys. Rev. C 85, 034902 (2012). https://doi.org/10.1103/PhysRevC.85.034902
M. Alvioli, M. Strikman, Beam fragmentation in heavy ion collisions with realistically correlated nuclear configurations. Phys. Rev. C 83, 044905 (2011). https://doi.org/10.1103/PhysRevC.83.044905
M. Alvioli, H.J. Drescher, M. Strikman, A Monte Carlo generator of nucleon configurations in complex nuclei including nucleon–nucleon correlations. Phys. Lett. B 680, 225–230 (2009). https://doi.org/10.1016/j.physletb.2009.08.067
B. Abelev, J. Adam, D. Adamová et al., Measurement of the cross section for electromagnetic dissociation with neutron emission in Pb–Pb collisions at \(\sqrt{s_{{\rm N}N}}=2.76\) TeV. Phys. Rev. Lett. 109, 252302 (2012). https://doi.org/10.1103/PhysRevLett.109.252302
Acknowledgements
One of the authors (I.P.) is grateful to Dariusz Miskowiec and Chiara Oppedisano for the discussions which stimulated the investigation of the effects of neutron skin in ultrarelaticistic \(^{208}\)Pb–\(^{208}\)Pb collisions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Additional information
Communicated by Vittorio Somá
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kozyrev, N., Svetlichnyi, A., Nepeivoda, R. et al. Peeling away neutron skin in ultracentral collisions of relativistic nuclei. Eur. Phys. J. A 58, 184 (2022). https://doi.org/10.1140/epja/s10050-022-00832-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epja/s10050-022-00832-5