Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Neutron and weak-charge distributions of the 48Ca nucleus

Nature Physics volume 12, pages 186–190 (2016)Cite this article

Subjects

Abstract

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. Although the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus 48Ca. We show that the neutron skin (difference between the radii of the neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities that are at present targeted by precision measurements. Based on ab initio results for 48Ca, we provide a constraint on the size of a neutron star.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Ab initio computations for atomic nuclei.
Figure 2: Predictions for observables related to the neutron distribution in 48Ca.
Figure 3: Weak-charge observables in 48Ca.
Figure 4: Properties of the nuclear equation of state and neutron-star radii based on chiral interactions.

Similar content being viewed by others

References

  1. Angeli, I. & Marinova, K. P. Table of experimental nuclear ground state charge radii: An update. At. Data Nucl. Data Tables 99, 69–95 (2013).

    Article  ADS  Google Scholar 

  2. Erler, J. et al. The limits of the nuclear landscape. Nature 486, 509–512 (2012).

    Article  ADS  Google Scholar 

  3. Tanihata, I. et al. Measurements of interaction cross sections and nuclear radii in the light p-shell region. Phys. Rev. Lett. 55, 2676–2679 (1985).

    Article  ADS  Google Scholar 

  4. Wienholtz, F. et al. Masses of exotic calcium isotopes pin down nuclear forces. Nature 498, 346–349 (2013).

    Article  ADS  Google Scholar 

  5. Steppenbeck, D. et al. Evidence for a new nuclear ‘magic number’ from the level structure of 54Ca. Nature 502, 207–210 (2013).

    Article  ADS  Google Scholar 

  6. Brown, B. A. Neutron radii in nuclei and the neutron equation of state. Phys. Rev. Lett. 85, 5296–5299 (2000).

    Article  ADS  Google Scholar 

  7. Lattimer, J. M. & Prakash, M. The physics of neutron stars. Science 304, 536–542 (2004).

    Article  ADS  Google Scholar 

  8. Hebeler, K., Lattimer, J. M., Pethick, C. J. & Schwenk, A. Equation of state and neutron star properties constrained by nuclear physics and observation. Astrophys. J. 773, 11 (2013).

    Article  ADS  Google Scholar 

  9. Zenihiro, J. et al. Neutron density distributions of 204,206,208Pb deduced via proton elastic scattering at Ep = 295 MeV. Phys. Rev. C 82, 044611 (2010).

    Article  ADS  Google Scholar 

  10. Tarbert, C. M. et al. Neutron skin of 208Pb from coherent pion photoproduction. Phys. Rev. Lett. 112, 242502 (2012).

    Article  ADS  Google Scholar 

  11. Abrahamyan, S. et al. Measurement of the neutron radius of 208Pb through parity violation in electron scattering. Phys. Rev. Lett. 108, 112502 (2012).

    Article  ADS  Google Scholar 

  12. Donnelly, T. W., Dubach, J. & Sick, I. Isospin dependences in parity-violating electron scattering. Nucl. Phys. A 503, 589–631 (1989).

    Article  ADS  Google Scholar 

  13. Tamii, A. et al. Complete electric dipole response and the neutron skin in 208Pb. Phys. Rev. Lett. 107, 062502 (2011).

    Article  ADS  Google Scholar 

  14. Hashimoto, T. et al. Dipole polarizability of 120Sn and nuclear energy density functionals. Phys. Rev. C 92, 031305(R) (2015).

    Article  ADS  Google Scholar 

  15. Rossi, D. M. et al. Measurement of the dipole polarizability of the unstable neutron-rich nucleus 68Ni. Phys. Rev. Lett. 111, 242503 (2013).

    Article  ADS  Google Scholar 

  16. Riordan, S. et al. CREX proposal to Jefferson Lab (2013); http://hallaweb.jlab.org/parity/prex/c-rex2013_v7.pdf.

  17. Horowitz, C. J., Kumar, K. S. & Michaels, R. Electroweak measurements of neutron densities in CREX and PREX at JLab, USA. Eur. Phys. J. A 50, 48 (2014).

    Article  ADS  Google Scholar 

  18. Bender, M., Heenen, P.-H. & Reinhard, P.-G. Self-consistent mean-field models for nuclear structure. Rev. Mod. Phys. 75, 121–180 (2003).

    Article  ADS  Google Scholar 

  19. Reinhard, P.-G. & Nazarewicz, W. Information content of a new observable: The case of the nuclear neutron skin. Phys. Rev. C 81, 051303(R) (2010).

    Article  ADS  Google Scholar 

  20. Piekarewicz, J. et al. Electric dipole polarizability and the neutron skin. Phys. Rev. C 85, 041302 (2012).

    Article  ADS  Google Scholar 

  21. Reinhard, P.-G. et al. Information content of the weak-charge form factor. Phys. Rev. C 88, 034325 (2013).

    Article  ADS  Google Scholar 

  22. Epelbaum, E., Hammer, H.-W. & Meißner, U.-G. Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009).

    Article  ADS  Google Scholar 

  23. Machleidt, R. & Entem, D. Chiral effective field theory and nuclear forces. Phys. Rep. 503, 1–75 (2011).

    Article  ADS  Google Scholar 

  24. Ekström, A. et al. Accurate nuclear radii and binding energies from a chiral interaction. Phys. Rev. C 91, 051301(R) (2015).

    Article  ADS  Google Scholar 

  25. Hagen, G., Papenbrock, T., Hjorth-Jensen, M. & Dean, D. J. Coupled-cluster computations of atomic nuclei. Rep. Prog. Phys. 77, 096302 (2014).

    Article  ADS  Google Scholar 

  26. Emrich, H. J. et al. Radial distribution of nucleons in isotopes 48Ca, 40Ca. Nucl. Phys. A 396, 401c–408c (1983).

    Article  ADS  Google Scholar 

  27. Bacca, S. et al. Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon–nucleon interactions. Phys. Rev. C 90, 064619 (2014).

    Article  ADS  Google Scholar 

  28. Ahrens, J. et al. Total nuclear photon absorption cross-sections for some light elements. Nucl. Phys. A 251, 479–492 (1975).

    Article  ADS  Google Scholar 

  29. Hebeler, K., Bogner, S. K., Furnstahl, R. J., Nogga, A. & Schwenk, A. Improved nuclear matter calculations from chiral low-momentum interactions. Phys. Rev. C 83, 031301 (2011).

    Article  ADS  Google Scholar 

  30. Kortelainen, M. et al. Nuclear energy density optimization: Shell structure. Phys. Rev. C 89, 054314 (2014).

    Article  ADS  Google Scholar 

  31. Lattimer, J. M. & Lim, Y. Constraining the symmetry parameters of the nuclear interaction. Astrophys. J. 771, 51 (2013).

    Article  ADS  Google Scholar 

  32. Lattimer, J. M. & Prakash, M. Neutron star structure and the equation of state. Astrophys. J. 550, 426–443 (2001).

    Article  ADS  Google Scholar 

  33. Lattimer, J. M. & Steiner, A. W. Neutron star masses and radii from quiescent low-mass X-ray binaries. Astrophys. J. 784, 123 (2014).

    Article  ADS  Google Scholar 

  34. Bogner, S. K., Furnstahl, R. J. & Perry, R. J. Similarity renormalization group for nucleon-nucleon interactions. Phys. Rev. C 75, 061001(R) (2007).

    Article  ADS  Google Scholar 

  35. Entem, D. R. & Machleidt, R. Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001(R) (2003).

    Article  ADS  Google Scholar 

  36. Holt, J. D., Menéndez, J., Simonis, J. & Schwenk, A. Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes. Phys. Rev. C 90, 024312 (2014).

    Article  ADS  Google Scholar 

  37. Hagen, G. et al. Coupled-cluster theory for three-body Hamiltonians. Phys. Rev. C 76, 034302 (2007).

    Article  ADS  Google Scholar 

  38. Roth, R. et al. Medium-mass nuclei with normal-ordered chiral NN + 3N interactions. Phys. Rev. Lett. 109, 052501 (2012).

    Article  ADS  Google Scholar 

  39. Taube, A. G. & Bartlett, R. J. Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces. J. Chem. Phys. 128, 044110 (2008).

    Article  ADS  Google Scholar 

  40. Gour, J. R., Piecuch, P., Hjorth-Jensen, M., Włoch, M. & Dean, D. J. Coupled-cluster calculations for valence systems around 16O. Phys. Rev. C 74, 024310 (2006).

    Article  ADS  Google Scholar 

  41. Bacca, S., Barnea, N., Hagen, G., Orlandini, G. & Papenbrock, T. First principles description of the giant dipole resonance in 16O. Phys. Rev. Lett. 111, 122502 (2013).

    Article  ADS  Google Scholar 

  42. Hagen, G., Papenbrock, T. & Dean, D. J. Solution of the center-of-mass problem in nuclear structure calculations. Phys. Rev. Lett. 103, 062503 (2009).

    Article  ADS  Google Scholar 

  43. Kanungo, R. et al. Exploring the anomaly in the interaction cross section and matter radius of 23O. Phys. Rev. C 84, 061304(R) (2011).

    Article  ADS  Google Scholar 

  44. Olive, K. A. & (Particle Data Group), et al. Review of particle physics. Chin. Phys. C 38, 090001 (2014).

    Article  ADS  Google Scholar 

  45. Horowitz, C. J. & Piekarewicz, J. Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei. Phys. Rev. C 86, 045503 (2012).

    Article  ADS  Google Scholar 

  46. Kortelainen, M. et al. Neutron-skin uncertainties of Skyrme energy density functionals. Phys. Rev. C 88, 031305 (2013).

    Article  ADS  Google Scholar 

  47. Drischler, C., Somà, V. & Schwenk, A. Microscopic calculations and energy expansions for neutron-rich matter. Phys. Rev. C 89, 025806 (2014).

    Article  ADS  Google Scholar 

  48. van Kolck, U. Few-nucleon forces from chiral Lagrangians. Phys. Rev. C 49, 2932–2941 (1994).

    Article  ADS  Google Scholar 

  49. Epelbaum, E. et al. Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002).

    Article  ADS  Google Scholar 

  50. Entem, D. R. & Machleidt, R. Accurate nucleon–nucleon potential based upon chiral perturbation theory. Phys. Lett. B 524, 93–98 (2002).

    Article  ADS  Google Scholar 

  51. Bernard, V., Epelbaum, E., Krebs, H. & Meißner, U.-G. Subleading contributions to the chiral three-nucleon force. II. Short-range terms and relativistic corrections. Phys. Rev. C 84, 054001 (2011).

    Article  ADS  Google Scholar 

  52. Chen, C. R., Payne, G. L., Friar, J. L. & Gibson, B. F. Convergence of Faddeev partial-wave series for triton ground state. Phys. Rev. C 31, 2266–2273 (1985).

    Article  ADS  Google Scholar 

  53. Carlson, J. Green’s function Monte Carlo study of light nuclei. Phys. Rev. C 36, 2026–2033 (1987).

    Article  ADS  Google Scholar 

  54. Pudliner, B. S., Pandharipande, V. R., Carlson, J. & Wiringa, R. B. Quantum Monte Carlo calculations of A = 6 nuclei. Phys. Rev. Lett. 74, 4396–4399 (1995).

    Article  ADS  Google Scholar 

  55. Wiringa, R. B., Pieper, S. C., Carlson, J. & Pandharipande, V. R. Quantum Monte Carlo calculations of A = 8 nuclei. Phys. Rev. C 62, 014001 (2000).

    Article  ADS  Google Scholar 

  56. Mihaila, B. & Heisenberg, J. H. Microscopic calculation of the inclusive electron scattering structure function in 16O. Phys. Rev. Lett. 84, 1403–1406 (2000).

    Article  ADS  Google Scholar 

  57. Pieper, S. C., Varga, K. & Wiringa, R. B. Quantum Monte Carlo calculations of A = 9,10 nuclei. Phys. Rev. C 66, 044310 (2002).

    Article  ADS  Google Scholar 

  58. Navrátil, P., Gueorguiev, V. G., Vary, J. P., Ormand, W. E. & Nogga, A. Structure of A = 10–13 nuclei with two- plus three-nucleon interactions from chiral effective field theory. Phys. Rev. Lett. 99, 042501 (2007).

    Article  ADS  Google Scholar 

  59. Maris, P. et al. Origin of the anomalous long lifetime of 14C. Phys. Rev. Lett. 106, 202502 (2011).

    Article  ADS  Google Scholar 

  60. Hergert, H., Binder, S., Calci, A., Langhammer, J. & Roth, R. Ab initio calculations of even oxygen isotopes with chiral two-plus-three-nucleon interactions. Phys. Rev. Lett. 110, 242501 (2013).

    Article  ADS  Google Scholar 

  61. Cipollone, A., Barbieri, C. & Navrátil, P. Isotopic chains around oxygen from evolved chiral two- and three-nucleon interactions. Phys. Rev. Lett. 111, 062501 (2013).

    Article  ADS  Google Scholar 

  62. Bogner, S. K. et al. Nonperturbative shell-model interactions from the in-medium similarity renormalization group. Phys. Rev. Lett. 113, 142501 (2014).

    Article  ADS  Google Scholar 

  63. Jansen, G. R., Engel, J., Hagen, G., Navrátil, P. & Signoracci, A. Ab initio coupled-cluster effective interactions for the shell model: Application to neutron-rich oxygen and carbon isotopes. Phys. Rev. Lett. 113, 142502 (2014).

    Article  ADS  Google Scholar 

  64. Lähde, T. et al. Lattice effective field theory for medium-mass nuclei. Phys. Lett. B 732, 110–115 (2014).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with C. Horowitz, J. Piekarewicz, P.-G. Reinhard and A. Steiner. This material is based on work supported by the US Department of Energy, Office of Science, Office of Nuclear Physics under Award Numbers DEFG02-96ER40963 (University of Tennessee), DOE-DE-SC0013365 (Michigan State University), DE-SC0008499 and DE-SC0008511 (NUCLEI SciDAC collaboration), the Field Work Proposal ERKBP57 at Oak Ridge National Laboratory and the National Science Foundation with award number 1404159. It was also supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT, IG2012-5158), by the European Research Council (ERC-StG-240603), by NSERC Grant No. 2015-00031, by the US-Israel Binational Science Foundation (Grant No. 2012212), by the ERC Grant No. 307986 STRONGINT, and the Research Council of Norway under contract ISPFysikk/216699. TRIUMF receives funding via a contribution through the National Research Council Canada. Computer time was provided by the INCITE program. This research used resources of the Oak Ridge Leadership Computing Facility located at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract No. DEAC05-00OR22725; and computing resources at the Jülich Supercomputing Center.

Author information

Authors and Affiliations

  1. Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    G. Hagen, A. Ekström, C. Forssén, G. R. Jansen, W. Nazarewicz, T. Papenbrock & K. A. Wendt

  2. Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

    G. Hagen, A. Ekström, C. Forssén, G. R. Jansen, T. Papenbrock & K. A. Wendt

  3. Department of Fundamental Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

    C. Forssén & B. Carlsson

  4. Department of Physics and Astronomy and NSCL/FRIB, Michigan State University, East Lansing, Michigan 48824, USA

    W. Nazarewicz & M. Hjorth-Jensen

  5. Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

    W. Nazarewicz

  6. TRIUMF, 4004 Wesbrook Mall Vancouver, British Columbia V6T 2A3, Canada,

    S. Bacca & M. Miorelli

  7. Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

    S. Bacca

  8. Racah Institute of Physics, Hebrew University, 91904 Jerusalem, Israel

    N. Barnea

  9. Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany

    C. Drischler, K. Hebeler, A. Schwenk & J. Simonis

  10. ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany

    C. Drischler, K. Hebeler, A. Schwenk & J. Simonis

  11. Department of Physics, University of Oslo, N-0316 Oslo, Norway

    M. Hjorth-Jensen

  12. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada

    M. Miorelli

  13. Dipartimento di Fisica, Università degli Studi di Trento, I-38123 Trento, Italy

    G. Orlandini

  14. Istituto Nazionale di Fisica Nucleare, TIFPA, I-38123 Trento, Italy

    G. Orlandini

Authors
  1. G. Hagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ekström
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Forssén
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. R. Jansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. Nazarewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. T. Papenbrock
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. K. A. Wendt
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. S. Bacca
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. N. Barnea
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. B. Carlsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. C. Drischler
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. K. Hebeler
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. M. Hjorth-Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. M. Miorelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. G. Orlandini
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. A. Schwenk
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. J. Simonis
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.H. initiated and led the project. G.H., A.E., G.R.J., T.P., K.A.W., S.B., N.B., B.C., C.D., K.H., M.H.-J., M.M., G.O., A.S. and J.S. developed computational tools utilized in this study. G.H., G.R.J., K.A.W., C.D., K.H. and M.M. performed calculations. G.H., A.E., C.F., G.R.J., W.N., T.P., K.A.W., S.B., N.B., C.D., K.H., M.H.-J., M.M., G.O. and A.S. discussed and interpreted the results. G.H., A.E., C.F., G.R.J., W.N., T.P., K.A.W., K.H. and A.S. wrote the paper with input from all co-authors.

Corresponding author

Correspondence to G. Hagen.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 403 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hagen, G., Ekström, A., Forssén, C. et al. Neutron and weak-charge distributions of the 48Ca nucleus. Nature Phys 12, 186–190 (2016). https://doi.org/10.1038/nphys3529

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3529

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing