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# Neutron and weak-charge distributions of the 48Ca nucleus

## 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.

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## 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

### 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)

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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

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

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