The strong nuclear interaction between nucleons (protons and neutrons) is the effective force that holds the atomic nucleus together. This force stems from fundamental interactions between quarks and gluons (the constituents of nucleons) that are described by the equations of quantum chromodynamics. However, as these equations cannot be solved directly, nuclear interactions are described using simplified models, which are well constrained at typical inter-nucleon distances1,2,3,4,5 but not at shorter distances. This limits our ability to describe high-density nuclear matter such as that in the cores of neutron stars6. Here we use high-energy electron scattering measurements that isolate nucleon pairs in short-distance, high-momentum configurations7,8,9, accessing a kinematical regime that has not been previously explored by experiments, corresponding to relative momenta between the pair above 400 megaelectronvolts per c (c, speed of light in vacuum). As the relative momentum between two nucleons increases and their separation thereby decreases, we observe a transition from a spin-dependent tensor force to a predominantly spin-independent scalar force. These results demonstrate the usefulness of using such measurements to study the nuclear interaction at short distances and also support the use of point-like nucleon models with two- and three-body effective interactions to describe nuclear systems up to densities several times higher than the central density of the nucleus.
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The raw data from this experiment are archived in Jefferson Lab’s mass storage silo.
Carlson, J. et al. Quantum Monte Carlo methods for nuclear physics. Rev. Mod. Phys. 87, 1067 (2015).
Epelbaum, E., Hammer, H. W. & Meißner, U. G. Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009).
Machleidt, R., Holinde, K. & Elster, C. The Bonn meson-exchange model for the nucleon–nucleon interaction. Phys. Rep. 149, 1–89 (1987).
Wiringa, R. B., Stoks, V. G. J. & Schiavilla, R. Accurate nucleon–nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995).
Gezerlis, A. et al. Quantum Monte Carlo calculations with chiral effective field theory interactions. Phys. Rev. Lett. 111, 032501 (2013).
Lattimer, J. M. & Prakash, M. Neutron star observations: prognosis for equation of state constraints. Phys. Rep. 442, 109–165 (2007).
Hen, O., Miller, G. A., Piasetzky, E. & Weinstein, L. B. Nucleon–nucleon correlations, short-lived excitations, and the quarks within. Rev. Mod. Phys. 89, 045002 (2017).
Ciofi degli Atti, C. In-medium short-range dynamics of nucleons: recent theoretical and experimental advances. Phys. Rep. 590, 1–85 (2015).
Frankfurt, L. & Strikman, M. High-energy phenomena, short-range nuclear structure and QCD. Phys. Rep. 76, 215–347 (1981).
Subedi, R. et al. Probing cold dense nuclear matter. Science 320, 1476–1478 (2008).
Korover, I. et al. Approaching the nucleon–nucleon short-range repulsive core via the 4He(e, e′pN) triple coincidence reaction. Phys. Rev. Lett. 113, 022501 (2014).
Hen, O. et al. (Jefferson Lab CLAS Collaboration). Momentum sharing in imbalanced Fermi systems. Science 346, 614–617 (2014).
Duer, M. et al. (CLAS Collaboration). Direct observation of proton–neutron short-range correlation dominance in heavy nuclei. Phys. Rev. Lett. 122, 172502 (2019).
Kelly, J. J. Nucleon knockout by intermediate-energy electrons. In Advances in Nuclear Physics (eds Negele, J. W. & Vogt, E.) 75–294 (1996).
Piasetzky, E., Sargsian, M., Frankfurt, L., Strikman, M. & Watson, J. W. Evidence for the strong dominance of proton–neutron correlations in nuclei. Phys. Rev. Lett. 97, 162504 (2006).
Cohen, E. O. et al. (CLAS Collaboration). Center of mass motion of short-range correlated nucleon pairs studied via the A(e, e′pp) reaction. Phys. Rev. Lett. 121, 092501 (2018).
Frankfurt, L., Sargsian, M. M. & Strikman, M. Recent observation of short range nucleon correlations in nuclei and their implications for the structure of nuclei and neutron stars. Int. J. Mod. Phys. A 23, 2991–3055 (2008).
Colle, C., Cosyn, W. & Ryckebusch, J. Final-state interactions in two-nucleon knockout reactions. Phys. Rev. C 93, 034608 (2016).
Sargsian, M. M. Selected topics in high energy semi-exclusive electro-nuclear reactions. Int. J. Mod. Phys. E 10, 405–458 (2001).
Mecking, B. A. et al. The CEBAF large acceptance spectrometer (CLAS). Nucl. Inst. Meth. A 503, 513–553 (2003).
De Forest, T. Off-shell electron–nucleon cross sections: the impulse approximation. Nucl. Phys. A 392, 232–248 (1983).
Weiss, R., Korover, I., Piasetzky, E., Hen, O. & Barnea, N. Energy and momentum dependence of nuclear short-range correlations – spectral function, exclusive scattering experiments and the contact formalism. Phys. Lett. B 791, 242–248 (2019).
Weiss, R., Bazak, B. & Barnea, N. Generalized nuclear contacts and momentum distributions. Phys. Rev. C 92, 054311 (2015).
Weiss, R., Cruz-Torres, R., Barnea, N., Piasetzky, E. & Hen, O. The nuclear contacts and short-range correlations in nuclei. Phys. Lett. B 780, 211–215 (2018).
Cruz-Torres, R. et al. Scale and scheme independence and position–momentum equivalence of nuclear short-range correlations. Preprint at https://arxiv.org/abs/1907.03658 (2019).
Hoppe, J., Drischler, C., Furnstahl, R. J., Hebeler, K. & Schwenk, A. Weinberg eigenvalues for chiral nucleon–nucleon interactions. Phys. Rev. C 96, 054002 (2017).
Ciofi degli Atti, C., Simula, S., Frankfurt, L. L. & Strikman, M. I. Two-nucleon correlations and the structure of the nucleon spectral function at high values of momentum and removal energy. Phys. Rev. C 44, 7–11 (1991).
Norton, P. R. The EMC effect. Rep. Prog. Phys. 66, 1253–1297 (2003).
Kulagin, S. A. & Petti, R. Global study of nuclear structure functions. Nucl. Phys. A 765, 126–187 (2006).
The CLAS Collaboration. Modified structure of protons and neutrons in correlated pairs. Nature 566, 354–358 (2019).
Hakobyan, H. et al. A double-target system for precision measurements of nuclear medium effects. Nucl. Instrum. Meth. A 592, 218–223 (2008).
Cruz-Torres, R. et al. Short-range correlations and the isospin dependence of nuclear correlation functions. Phys. Lett. B 785, 304–308 (2018).
Weiss, R., Schmidt, A., Miller, G. A. & Barnea, N. Short-range correlations and the charge density. Phys. Lett. B 790, 484–489 (2019).
Sargsian, M. M., Abrahamyan, T. V., Strikman, M. I. & Frankfurt, L. L. Exclusive electrodisintegration of 3He at high Q 2. II. Decay function formalism. Phys. Rev. C 71, 044615 (2005).
Frankfurt, L. L., Sargsian, M. M. & Strikman, M. I. Feynman graphs and generalized eikonal approach to high energy knock-out processes. Phys. Rev. C 56, 1124–1137 (1997).
Rvachev, M. et al. Quasielastic 3He(e, e′p)2H reaction at Q 2 = 1.5 GeV2 for recoil momenta up to 1 GeV/c. Phys. Rev. Lett. 94, 192302 (2005).
Benmokhtar, F. et al. Measurement of the 3He(e, e′p)pn reaction at high missing energies and momenta. Phys. Rev. Lett. 94, 082305 (2005).
Egiyan, K. S. et al. (CLAS Collaboration) Experimental study of exclusive 2H(e, e′p)n reaction mechanisms. Phys. Rev. Lett. 98, 262502 (2007).
Boeglin, W. U. et al. Probing the high momentum component of the deuteron at high Q 2. Phys. Rev. Lett. 107, 262501 (2011).
Dutta, D., Hafidi, K. & Strikman, M. Color transparency: past, present and future. Prog. Part. Nucl. Phys. 69, 1–27 (2013).
The CLAS Collaboration. Measurement of transparency ratios for protons from short-range correlated pairs. Phys. Lett. B 722, 63–68 (2013).
The CLAS Collaboration. Measurement of nuclear transparency ratios for protons and neutrons. Phys. Lett. B 797, 134792 (2019).
Colle, C. et al. Extracting the mass dependence and quantum numbers of short-range correlated pairs from A(e, e′p) and A(e, e′pp) scattering. Phys. Rev. C 92, 024604 (2015).
Ciofi degli Atti, C. & Morita, H. Universality of many-body two-nucleon momentum distributions: correlated nucleon spectral function of complex nuclei. Phys. Rev. C 96, 064317 (2017).
Tang, A. et al. (EVA Collaboration) n–p short-range correlations from (p, 2p + n) measurements. Phys. Rev. Lett. 90, 042301 (2003).
Shneor, R. et al. (Jefferson Lab Hall A Collaboration) Investigation of proton–proton short-range correlations via the 12C(e, e′pp) reaction. Phys. Rev. Lett. 99, 072501 (2007).
Lonardoni, D., Gandolfi, S., Wang, X. B. & Carlson, J. Single- and two-nucleon momentum distributions for local chiral interactions. Phys. Rev. C 98, 014322 (2018).
Wiringa, R. B., Schiavilla, R., Pieper, S. C. & Carlson, J. Nucleon and nucleon-pair momentum distributions in A ≤ 12 nuclei. Phys. Rev. C 89, 024305 (2014).
Ciofi degli Atti, C. & Simula, S. Realistic model of the nucleon spectral function in few and many nucleon systems. Phys. Rev. C 53, 1689–1710 (1996).
Colle, C., Cosyn, W., Ryckebusch, J. & Vanhalst, M. Factorization of exclusive electron-induced two-nucleon knockout. Phys. Rev. C 89, 024603 (2014).
Frankfurt, L. & Strikman, M. Short-range correlations in nuclei as seen in hard nuclear reactions and light cone dynamics. In Modern Topics in Electron Scattering (eds Frois, B. & Sick, I.) 645–694 (1992).
Artiles, O. & Sargsian, M. Multinucleon short-range correlation model for nuclear spectral functions: theoretical framework. Phys. Rev. C 94, 064318 (2016).
Miller, G. A. & Tiburzi, B. C. Relation between equal-time and light-front wave functions. Phys. Rev. C 81, 035201 (2010).
Ent, R. et al. Radiative corrections for (e, e′p) reactions at GeV energies. Phys. Rev. C 64, 054610 (2001).
Lynn, J. E. et al. Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions. Phys. Rev. C 96, 054007 (2017).
More, S. N., Bogner, S. K. & Furnstahl, R. J. Scale dependence of deuteron electrodisintegration. Phys. Rev. C 96, 054004 (2017).
We acknowledge the efforts of the staff of the Accelerator and Physics Divisions at Jefferson Lab that made this experiment possible. The analysis presented here was carried out as part of the Jefferson Lab Hall B data-mining project supported by the US Department of Energy (DOE). The research was also supported by the National Science Foundation, the Israel Science Foundation, the Pazi Foundation, the Chilean Comisión Nacional de Investigación Científica y Tecnológica, the French Centre National de la Recherche Scientifique and Commissariat a l'Energie Atomique, the French–American Cultural Exchange, the Italian Istituto Nazionale di Fisica Nucleare, the National Research Foundation of Korea, and the UK Science and Technology Facilities Council. Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility for the DOE, Office of Science, Office of Nuclear Physics under contract DE-AC05-06OR23177.
The authors declare no competing interests.
Peer review information Nature thanks Daniel Phillips and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
Diagrammatic representation and four-momentum kinematics of the two-nucleon knockout A(e, e′Np) reaction within the SRC model. The dashed red lines represent off-shell particles and solid black lines represent detected particles. The A−2 system is undetected.
Extended Data Fig. 2 Kinematical distributions and A(e, e′pp)/A(e, e′p) ratios for A = 12–208 nuclei.
a–c, Comparison of the number of A(e, e′p) event reactions versus the (e, e′p) missing momentum pmiss (a), Q2 (b) and xB (c). d–f, Comparison of the number of A(e, e′pp) event reactions versus the (e, e′p) missing momentum pmiss (d), Q2 (e) and xB (f). The total number of counts in aluminium (cyan), iron (orange), and lead (purple) was scaled to match that of carbon (dark blue). The shaded bands indicate the 1σ statistical uncertainty of the data.
a–d, Distribution of the relative angle between the momentum transfer q and the (e, e′p) missing momentum for A(e, e′p) (a, b) and A(e, e′pp) (c, d). The panels at left compare the 12C data and GCF calculations using different NN interaction models (a, c); and the panels at right compare the data for carbon (blue), aluminium (cyan), iron (orange), and lead (purple) nuclei (b, d). The total number of counts in the aluminium, iron and lead data has been scaled to match that of carbon. In a and c, the width of the band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1σ confidence level. The shaded bands in b and d indicate the 1σ statistical uncertainty of the data.
Momentum and angle distributions of scattered electrons and protons for 12C(e, e′p) (a, c, e, h) and 12C(e, e′pp) (b, d, f, g, i, j) events. Coloured bands show the various GCF calculations. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1σ confidence level.
a, Q2 versus the missing-momentum distribution of 12C(e, e′p) data. Owing to the event selection criteria, as pmiss approaches 1 GeV/c, the minimum Q2 of the data approaches 3 GeV/c. b, Emiss versus pmiss of the 12C(e, e′p) data. The red line indicates the expected Emiss–pmiss correlation for the breakup of a stationary pair.
Extended Data Fig. 6 Universal functions for pp and np pairs and the momentum dependence of their ratio.
The relative momentum distributions for different NN interaction models studied in this work, for pn (a) and pp (b). c, The momentum dependence of the fraction of protons belonging to pp SRC pairs in 12C.
Extended Data Fig. 7 Light-cone calculations of the nuclear spectral function and momentum fractions.
a–j, As in Fig. 3a–j. k, l, The reconstructed initial light-cone momentum fraction carried by the struck nucleon for (e, e′p) (k) and (e, e′pp) (l) events. m, The total pair light-cone momentum fraction for (e, e′pp) events. The data points are identical to those in Fig. 3a–j. The bands are different and show the results of the GCF calculations using light-cone formalism and various NN interaction models. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1σ confidence level.
a–c, As in Fig. 3a, b (a, b) and Fig. 2a (c), but also including the non-local N3LO (600 MeV/c) interaction. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1σ confidence level. See Methods for details.
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Schmidt, A., Pybus, J., Weiss, R. et al. Probing the core of the strong nuclear interaction. Nature 578, 540–544 (2020). https://doi.org/10.1038/s41586-020-2021-6
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