What Is the Size of the Atomic Nucleus?

The neutron skin of the nucleus calcium-48 is much thinner than previously thought.

X-Ray Laser
Image courtesy of Oak Ridge National Laboratory; conceptual art by LeJean Hardin and Andy Sproles
Conceptual art connects the atomic underpinnings of the neutron-rich calcium-48 nucleus with the Crab Nebula, which has a neutron star at its heart. Zeros and ones depict the computational power needed to explore objects that differ in size by 18 orders of magnitude.

The Science

Directly computing the size of the atomic nucleus of calcium-48 revealed that the neutron skin, or difference between proton and neutron radii, is significantly smaller than previously thought. The calculations also showed that the neutron skin does not depend on the interaction between the constituent nucleons. These calculations also constrain the size of a neutron star.

The Impact

This study, which is being validated by scientists in the United States and Germany, could help constrain future theoretical models. This research also impacts the number of nuclei that can exist, and the size of neutron stars, thereby connecting objects that differ by 18 orders of magnitude in length scale.


The “neutron skin” of the nucleus of a calcium-48 atom is much thinner than thought. An international team of nuclear physicists led by Dr. Gaute Hagen of the Department of Energy's Oak Ridge National Laboratory used the Titan supercomputer to compute the neutron distribution and related observables of the atomic nucleus of calcium-48, which consists of 20 protons and 28 neutrons. Computing the nucleus from scratch revealed that the difference between the radii of neutron and proton distributions (called the neutron skin) is considerably smaller than previously thought. The collaboration also made predictions for the electric dipole polarizability and the weak form factor, quantities that are currently targeted by precision measurements worldwide. These calculations also constrain the size of a neutron star, thereby connecting objects that differ in size by 18 orders of magnitude.


Gaute Hagen
Oak Ridge National Laboratory
(865) 576-4295


This work is funded 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.


G. Hagen, A. Ekström C. Forssén, G. R. Jansen, W. Nazarewicz, T. Papenbrock, K. A. Wendt, S. Bacca, N. Barnea, B. Carlsson, C. Drischler, K. Hebeler, M. Hjorth-Jensen, M. Miorelli, G. Orlandini, A. Schwenk, and J. Simonis, “Neutron and weak-charge distributions of the 48Ca nucleus.” Nature Physics (2015). [DOI: 10.1038/nphys3529].

Related Links

Neutron Skin of 48-Calcium Thinner than Previously Thought

Computing the Size of the Atomic Nucleus

Computing Nuclei from First Principles

Pushing Boundaries of Atomic Nuclei Research 

How Big is a Nucleus?

Computing the Heart of Matter

Highlight Categories

Program: ASCR , NP

Performer: University , DOE Laboratory , SC User Facilities , ASCR User Facilities , OLCF

Additional: Collaborations , Non-DOE Interagency Collaboration , International Collaboration