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News & views external member of the Max-Planck Institute 8. Xu, J., Du, Y. & Deng, H. Cell Stem Cell 16, 119–134 describing the high-density cores of of Biochemistry, Martinsried. (2015). stars. We know that the NN inter­action is attrac­ 9. Takahashi, K. & Yamanaka, S. Cell 126, 663–676 (2006). −15 e-mails: giacomo.masserdotti@ 10. Pang, Z. P. et al. Nature 476, 220–223 (2011). tive down to about 1 (10 ). helmholtz-muenchen.de; 11. Caiazzo, M. et al. Nature 476, 224–227 (2011). At smaller distances, very strong repulsion sets [email protected] 12. Son, E. Y. et al. Cell Stem Cell 9, 205–218 (2011). in2,3. In atomic nuclei, consequently 13. Victor, M. B. et al. Neuron 84, 311–323 (2014). position themselves close enough to take 1. Vierbuchen, T. et al. Nature 463, 1035–1041 (2010). 14. Mertens, J. et al. Cell Stem Cell 17, 705–718 (2015). 2. Mangold, O. & Spemann, H. Wilhelm Roux Arch. Entwickl. 15. Hu, W. et al. Cell Stem Cell 17, 204–212 (2015). advantage of the attraction, but shy away from Mech. Org. 111, 341–422 (1927). 16. Victor, M. B. et al. Nature Neurosci. 21, 341–352 (2018). the notoriously hard core of their neighbours 3. Gurdon, J. B. J. Embryol. Exp. Morphol. 10, 622–640 (1962). 17. Wapinski, O. L. et al. Cell 155, 621–635 (2013). at the shortest distances. 4. Davis, R. L., Weintraub, H. & Lassar, A. B. Cell 51, 987–1000 18. Rouaux, C. & Arlotta, P. Nature Cell Biol. 15, 214–221 (2013). (1987). 19. Gascon, S., Masserdotti, G., Russo, G. L. & Götz, M. For the description of most nuclear 5. Heins, N. et al. Nature Neurosci. 5, 308–315 (2002). Cell Stem Cell 21, 18–34 (2017). properties, nucleons can be approximated 6. Buffo, A. et al. Proc. Natl Acad. Sci. USA 102, 18183–18188 20. von Schimmelmann, M. et al. Nature Neurosci. 19, as independent particles subjected to a mean (2005). 1321–1330 (2016). 7. Barker, R. A., Götz, M. & Parmar, M. Nature 557, 329–334 field created by the other nucleons. But about 4 (2018). This article was published online on 24 February 2020. 20% of the time , as a result of density fluctu­ ations in nuclei, two nucleons come close Nuclear enough to form a short-range correlated pair that defies the mean-field description. Accord­ ing to Heisenberg’s uncertainty principle, such large local density fluctuations are associated Nuclear probed with large fluctuations in momentum5. Schmidt and collaborators have now tested at short distances the details of effective theories of the nuclear force — that is, theories based on effective Alexandra Gade NN interactions — using the particle detector system known as the CEBAF Large Acceptance The dense soup of matter in the core of neutron stars is hard Spectrometer (CLAS) at the Thomas Jefferson to model, but particle-accelerator experiments in which National Accelerator Facility in Newport News, energetic electrons scatter off atomic nuclei could help to Virginia. They scattered energetic electrons off pairs of nucleons that were separated by explore this high-density regime. See p.540 very small distances (and which have charac­ teristically high momenta) in nuclei to study the NN repulsion, and used the data to test the Modelling the fundamental strong force are phenomenological — they are based on accuracy of effective NN interactions at these between and — collectively experimental data obtained by scattering distances. Their pushes the investiga­ called nucleons — is tricky. But on page 540, nucleons from each other3. Others2 are derived tion of such pairs to the highest momenta yet Schmidt and collaborators1 demonstrate a from first principles and exploit symmetries attained. way to explore these interactions in atomic manifested in QCD. In optics, the resolving power of an instru­ nuclei, and compare experimental measure­ Because of the way they were developed, we ment is the smallest distance at which two ments against calculations that use various can be fairly confident that the effective NN closely spaced objects can be separated. models of the strong nuclear interaction. They inter­actions accurately represent the actual This distance is typically proportional to do so at the shortest inter- distances interactions at typical inter-nucleon distances the wavelength of light used: the smaller the yet probed, by poking nucleon pairs using in nuclei, but not necessarily at the tiny dis­ wavelength, the better the resolving power. high- electrons and focusing on a pre­ tances that are relevant, for example, when In , to resolve nucleons in a viously unexplored regime of short-distance, nucleus, a resolution of about 1 fm is required. high-momentum interactions in a nucleus. The high-energy electron scattering used (QCD) is the by Schmidt et al. achieves this resolution fundamental theory of the strong inter­ because high-energy electrons have a tiny action, one of the four in nature. In that Nucleus wavelength (the de Broglie wavelength) and theory, the nucleon–nucleon (NN) interaction a high momentum, which they impart to the that binds protons and neutrons into atomic nucleon systems being studied. nuclei is largely determined by the underlying From data taken using the CLAS detector, dynamics of and (quarks being Schmidt and collaborators picked out reac­ the elementary particles that combine to form tions in which a scattered high-energy electron e– protons, neutrons and other, less stable parti­ (e,e′, where e is the incoming electron and e′ is cles; gluons are the carriers of the strong force the scattered electron) liberated a (p) that ‘glues’ the quarks together). Figure 1 | High-energy electron scattering probes from a target nucleus (A); these reactions are 1 However, because the unwieldy nature of the strong nuclear interaction. Schmidt et al. described as A(e,e′p) events. More specifically, studied nuclear reactions in which high-energy QCD makes it impossible to model atomic the authors selected scattering reactions in electrons (e�) scattered off systems of nucleons nuclei computationally, we still lack a truly which a property of the liberated proton known (protons and neutrons; blue and pink, respectively), quantitative understanding of the NN force and in which high-momentum protons were as the missing momentum was measured to be from QCD. Instead, modellers have resorted liberated. The resulting data were used to more than 400 megaelectronvolts­ per c (where to approximations known as effective NN investigate the interactions that occur between c is the speed of light). For the high-energy inter­actions for use in models of nuclear nucleons separated by very small distances, and conditions studied, this missing momentum 2,3 properties . These treat nucleons as point- to show that current models of nucleon–nucleon is approximately equal to the initial momen­ like objects. Some effective interactions interactions might be valid at these short distances. tum of the struck proton inside the nucleus.

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A proton momentum of 400 MeV c−1 is almost the nucleon systems that were previously optimized at low to describe nuclear twice that of ordinary mean-field protons, studied experimentally and which were used to systems up to densities well above the central which indicates that the knocked-out proton develop some of the effective NN interactions. density of nuclei. Thus, Schmidt et al. have was part of a short-range correlated pair. They also greatly exceed the range for which opened an exciting path to exploring NN inter­ Out of these A(e,e′p) events, Schmidt and some of the theor­etically derived effective NN actions at the distances relevant, for example, collaborators then selected a subset in which interactions — including those derived from a for neutron stars. a second, high-momentum ‘recoil’ proton was much-used approach known as chiral effective Interestingly, the effective NN interaction released (Fig. 1). These reactions — which are field theory — might be expected to be reliable. derived from chiral described as A(e,e′pp) events — are the telltale Nevertheless, the team found that both fares less well than the phenomenological signatures of short-range correlated proton types of effective NN interaction — the effective NN interaction that was tested — the pairs in which the two protons have high and chiral interaction is not as good at predicting opposite momenta. “The approximations absolute yields as it is at predicting ratios. As The reaction yields for the two types of methods and computational approaches for event can be numerically modelled such that could be used in models modelling many-body systems (such as nuclei) the reaction dynamics and associated nuclear to reproduce the new advance, it will be possible to examine experi­ structure factorize (they can be separated experimental data mental data using the diverse tools of the trade out from each other). This allows the initial astonishingly well.” but with fewer approximations. The ball is in structure of the nuclei in the experiments to the court of nuclear theory now. be reconstructed from the observed reac­ tion yields. By using the phenomenological and chiral ones — could still Alexandra Gade is at the National calculated from effective NN interactions to be used in models to reproduce the new experi­ Superconducting Cyclotron Laboratory, predict yields, and comparing these predicted mental data astonishingly well. In particular, Michigan State University, East Lansing, yields with the experimentally observed ones, as the momentum between two nucleons in Michigan 48824, USA. Schmidt et al. tested whether effective inter­ a pair increases (and the distance between e-mail: [email protected] actions accurately describe NN interactions at them consequently decreases), the data reflect very short inter-nucleon distances. subtle but important changes in the details of 1. Schmidt, A. et al. Nature 578, 540–544 (2020). 2. Epelbaum, E., Hammer, H.-W. & Meißner, U.-G. Rev. Mod. The team calculated the reaction-yield the force, as predicted by the models. Phys. 81, 1773–1825 (2009). ratios A(e,e′pp)/A(e,e′p) for different nuclear The results demonstrate the potential of 3. Wiringa, R. B., Stoks, V. G. J. & Schiavilla, R. Phys. Rev. C targets and for proton momenta ranging from using such data to dissect the nuclear inter­ 51, 38–51 (1995). −1 9 4. Subedi, R. et al. Science 320, 1476–1478 (2008). 400 MeV c to 1 gigaelectronvolt (10 eV) per c. action at short distances. They might justify 5. Hen, O., Miller, G. A., Piasetzky, E. & Weinstein, L. B. These momenta far exceed the energetics of the use of effective interactions that were Rev. Mod. Phys. 89, 045002 (2017).

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