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  • Letter
  • Open Access

Nuclear binding, correlations, and the A dependence of the EMC effect

Omar Benhar1,* and Alessandro Lovato2,3,4,5,†

  • *Contact author: omar.benhar@roma1.infn.it
  • †Contact author: lovato@anl.gov

Phys. Rev. C 114, L042501 – Published 20 October, 2026

DOI: https://doi.org/10.1103/wyx6-8lcz

Abstract

The measurements of inclusive electron scattering from nuclear targets carried out at the Thomas Jefferson National Accelerator Facility in the mid 2000s have provided valuable novel information on the A dependence of the modifications of nuclear structure functions known as the EMC effect. We argue that these data are best described in terms of the scaling variable ỹ, designed to take into account dynamical effects in interacting many-particle systems, and analyze the A dependence of the slope of the inclusive cross-section ratios, RA=(σA/A)/(σ2/2), providing a measure of the size of the EMC effect in the region where nuclear binding plays a leading role. The results of our study clearly hint at a linear correlation between dRA(ỹ)/dỹ and the average nucleon removal energy 〈EA〉. The role of correlation effects in the determination of 〈EA〉 is highlighted.

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References (56)

  1. CERN Hints from high energy muons, CERN Cour. 9, 362 (1982).
  2. J. J. Aubert et al., The ratio of the nucleon structure functions F2N for iron and deuterium, Phys. Lett. B 123, 275 (1983).
  3. G. Bari et al. (BCDMS Collaboration), A measurement of nuclear effects in deep inelastic muon scattering on deuterium, nitrogen and iron targets, Phys. Lett. B 163, 282 (1985).
  4. J. Ashman et al., Measurement of the ratios of deep inelastic muon-nucleus cross sections on various nuclei compared to deuterium, Phys. Lett. B 202, 603 (1988).
  5. J. Gomez, R. G. Arnold, P. E. Bosted, C. C. Chang, A. T. Katramatou, G. G. Petratos, A. A. Rahbar, S. E. Rock, A. F. Sill, Z. M. Szalata, A. Bodek, N. Giokaris, D. J. Sherden, B. A. Mecking, and R. M. Lombard-Nelsen, Measurement of the A dependence of deep-inelastic electron scattering, Phys. Rev. D 49, 4348 (1994).
  6. K. Ackerstaff et al. (HERMES Collaboration), Nuclear effects on R=σ/σ in deep-inelastic scattering, Phys. Lett. B 475, 386 (2000).
  7. A. Airapetian et al. (HERMES Collaboration), Erratum to: “Nuclear effects on R=σL/σT in deep-inelastic scattering”: [Phys. Lett. B 475 (2000) 386–394], Phys. Lett. B 567, 339 (2003).
  8. J. Seely, A. Daniel, D. Gaskell, J. Arrington, N. Fomin, P. Solvignon, R. Asaturyan, F. Benmokhtar, W. Boeglin, B. Boillat, P. Bosted, A. Bruell, M. H. S. Bukhari, M. E. Christy, B. Clasie, S. Connell, M. M. Dalton, D. Day, J. Dunne, D. Dutta, et al., New measurements of the European Muon Collaboration effect in very light nuclei, Phys. Rev. Lett. 103, 202301 (2009).
  9. J. Arrington, A. Daniel, D. B. Day, N. Fomin, D. Gaskell, and P. Solvignon, Detailed study of the nuclear dependence of the EMC effect and short-range correlations, Phys. Rev. C 86, 065204 (2012).
  10. B. Schmookler et al. (CLAS Collaboration), Modified structure of protons and neutrons in correlated pairs, Nature (London) 566, 354 (2019).
  11. J. Arrington, J. Bane, A. Daniel, N. Fomin, D. Gaskell, J. Seely, R. Asaturyan, F. Benmokhtar, W. Boeglin, P. Bosted, M. H. S. Bukhari, M. E. Christy, S. Connell, M. M. Dalton, D. Day, J. Dunne, D. Dutta, L. El Fassi, R. Ent, H. Fenker, et al., Measurement of the EMC effect in light and heavy nuclei, Phys. Rev. C 104, 065203 (2021).
  12. A. Karki et al. (Hall C Collaboration), First measurement of the EMC effect in B10 and B11, Phys. Rev. C 108, 035201 (2023).
  13. D. W. Higinbotham, G. A. Miller, O. Hen, and K. Rith, The EMC effect still puzzles after 30 years, CERN Cour. 53, 24 (2013).
  14. M. Arneodo, Nuclear effects in structure functions, Phys. Rep. 240, 301 (1994).
  15. D. F. Geesaman, K. Saito, and A. W. Thomas, The nuclear EMC effect, Annu. Rev. Nucl. Part. Sci. 45, 337 (1995).
  16. P. R. Norton, The EMC effect, Rep. Prog. Phys. 66, 1253 (2003).
  17. S. Malace, D. Gaskell, D. W. Higinbotham, and I. C. Cloët, The challenge of the EMC effect: Existing data and future directions, Int. J. Mod. Phys. E 23, 1430013 (2014).
  18. C. C. degli Atti and S. Liuti, Classical European-Muon-Collaboration effect from few-body systems to nuclear matter: Can binding effects explain it? Phys. Rev. C 44, R1269 (1991).
  19. O. Benhar, V. R. Pandharipande, and I. Sick, Nuclear binding and deep inelastic scattering, Phys. Lett. B 410, 79 (1997).
  20. L. B. Weinstein, E. Piasetzky, D. W. Higinbotham, J. Gomez, O. Hen, and R. Shneor, Short range correlations and the EMC effect, Phys. Rev. Lett. 106, 052301 (2011).
  21. O. Hen, E. Piasetzky, and L. B. Weinstein, New data strengthen the connection between short range correlations and the EMC effect, Phys. Rev. C 85, 047301 (2012).
  22. N. Fomin, J. Arrington, R. Asaturyan, F. Benmokhtar, W. Boeglin, P. Bosted, A. Bruell, M. H. S. Bukhari, M. E. Christy, E. Chudakov, B. Clasie, S. H. Connell, M. M. Dalton, A. Daniel, D. B. Day, D. Dutta, R. Ent, L. El Fassi, H. Fenker, B. W. Filippone, et al., New measurements of high-momentum nucleons and short-range structures in nuclei, Phys. Rev. Lett. 108, 092502 (2012).
  23. J. Arrington and N. Fomin, Searching for flavor dependence in nuclear quark behavior, Phys. Rev. Lett. 123, 042501 (2019).
  24. N. Fomin et al., Long range outlook for short-range correlations, arXiv:2601.09568.
  25. O. Benhar and I. Sick, Nuclear binding, correlations, and the origin of the EMC effect, arXiv:1207.4595.
  26. O. Benhar, V. R. Pandharipande, and I. Sick, Many-body theory interpretation of deep inelastic scattering, Phys. Lett. B 489, 131 (2000).
  27. R. T. Azuah, W. G. Stirling, H. R. Glyde, M. Boninsegni, P. E. Sokol, and S. M. Bennington, Condensate and final-state effects in superfluid He4, Phys. Rev. B 56, 14620 (1997).
  28. I. Sick, D. Day, and J. S. McCarthy, Nuclear high-momentum components and y scaling in electron scattering, Phys. Rev. Lett. 45, 871 (1980).
  29. O. Benhar, D. Day, and I. Sick, Inclusive quasielastic electron-nucleus scattering, Rev. Mod. Phys. 80, 189 (2008).
  30. O. Nachtmann, Positivity constraints for anomalous dimensions, Nucl. Phys. B 63, 237 (1973).
  31. R. L. Jaffe, in Relativistic Dynamics and Quark Nuclear Physics, edited by M. B. Johnson and A. Picklesimer (Wiley-Interscience, New York, 1986).
  32. O. Benhar, D. Day, and I. Sick, An archive for quasi-elastic electron-nucleus scattering data, arXiv:nucl-ex/0603032.
  33. O. Benhar, A. Fabrocini, and S. Fantoni, The nucleon spectral function in nuclear matter, Nucl. Phys. A 505, 267 (1989).
  34. O. Benhar, A. Fabrocini, and S. Fantoni, Nuclear-matter Green functions in correlated-basis theory, Nucl. Phys. A 550, 201 (1992).
  35. O. Benhar, A. Fabrocini, S. Fantoni, and I. Sick, Spectral function of finite nuclei and scattering of GeV electrons, Nucl. Phys. A 579, 493 (1994).
  36. A. M. Ankowski, O. Benhar, and M. Sakuda, Determination of the proton spectral function of C12 from (e,e′p) data, Phys. Rev. C 110, 054612 (2024).
  37. D. S. Koltun, Total binding energies of nuclei, and particle-removal experiments, Phys. Rev. Lett. 28, 182 (1972).
  38. M. Harada, Separation energies of nucleons and the energy sum rule of the Green's function method, Lett. Nuovo Cimento 15, 566 (1976).
  39. J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schiavilla, K. E. Schmidt, and R. B. Wiringa, Quantum Monte Carlo methods for nuclear physics, Rev. Mod. Phys. 87, 1067 (2015).
  40. R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Accurate nucleon-nucleon potential with charge-independence breaking, Phys. Rev. C 51, 38 (1995).
  41. S. C. Pieper, The Illinois extension to the Fujita-Miyazawa three-nucleon force, AIP Conf. Proc. 1011, 143 (2008).
  42. D. Lonardoni, A. Lovato, S. C. Pieper, and R. B. Wiringa, Variational calculation of the ground state of closed-shell nuclei up to A=40, Phys. Rev. C 96, 024326 (2017).
  43. B. S. Pudliner, V. R. Pandharipande, J. Carlson, and R. B. Wiringa, Quantum Monte Carlo calculations of A≤6 nuclei, Phys. Rev. Lett. 74, 4396 (1995).
  44. K. E. Schmidt and S. Fantoni, A quantum Monte Carlo method for nucleon systems, Phys. Lett. B 446, 99 (1999).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/wyx6-8lcz for details of the CVMC/FHNC validation and the χEFT removal energy analysis, which also includes Refs.  [46]– [50].
  46. A. Gnech, A. Lovato, and N. Rocco, Static and dynamic properties of atomic nuclei with high-resolution potentials, Phys. Rev. C 111, 024314 (2025).
  47. R. B. Wiringa and S. C. Pieper, Evolution of nuclear spectra with nuclear forces, Phys. Rev. Lett. 89, 182501 (2002).
  48. A. Lovato, I. Bombaci, D. Logoteta, M. Piarulli, and R. B. Wiringa, Benchmark calculations of infinite neutron matter with realistic two- and three-nucleon potentials, Phys. Rev. C 105, 055808 (2022).
  49. M. Piarulli, A. Baroni, L. Girlanda, A. Kievsky, A. Lovato, E. Lusk, L. E. Marcucci, S. C. Pieper, R. Schiavilla, M. Viviani, and R. B. Wiringa, Light-nuclei spectra from chiral dynamics, Phys. Rev. Lett. 120, 052503 (2018).
  50. J. E. Lynn, I. Tews, J. Carlson, S. Gandolfi, A. Gezerlis, K. E. Schmidt, and A. Schwenk, Chiral three-nucleon interactions in light nuclei, neutron-α scattering, and neutron matter, Phys. Rev. Lett. 116, 062501 (2016).
  51. I. Sick and D. Day, The EMC effect of nuclear matter, Phys. Lett. B 274, 16 (1992).
  52. D. B. Day, J. S. McCarthy, Z. E. Meziani, R. C. Minehart, R. M. Sealock, S. T. Thornton, J. Jourdan, I. Sick, B. W. Filippone, R. D. McKeown, R. G. Milner, D. H. Potterveld, and Z. Szalata, Nuclear matter response function, Phys. Rev. C 40, 1011 (1989).
  53. A. Akmal and V. R. Pandharipande, Spin-isospin structure and pion condensation in nucleon matter, Phys. Rev. C 56, 2261 (1997).
  54. C. Marchand, M. Bernheim, P. C. Dunn, A. Gérard, J. M. Laget, A. Magnon, J. Morgenstern, J. Mougey, J. Picard, D. Reffay-Pikeroen, S. Turck-Chieze, P. Vernin, M. K. Brussel, G. P. Capitani, E. De Sanctis, S. Frullani, and F. Garibaldi, High proton momenta and nucleon-nucleon correlations in the reaction He3(e,e′p), Phys. Rev. Lett. 60, 1703 (1988).
  55. J. J. van Leeuwe, H. P. Blok, J. F. J. van den Brand, H. J. Bulten, G. E. Dodge, R. Ent, W. H. A. Hesselink, E. Jans, W. J. Kasdorp, J. M. Laget, L. Lapikás, S. I. Nagorny, C. J. G. Onderwater, A. R. Pellegrino, C. M. Spaltro, J. J. M. Steijger, R. Schiavilla, J. A. Templon, and O. Unal, High-missing-momentum components in the He4(e,e′p)H3 reaction, Phys. Rev. Lett. 80, 2543 (1998).
  56. D. Rohe et al. (E97-006 Collaboration), Correlated strength in the nuclear spectral function, Phys. Rev. Lett. 93, 182501 (2004).

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