Laser spectroscopy measurements of the size of neutron-rich potassium isotopes at CERN/ISOLDE combined with first principles simulations on the OLCF’s Summit supercomputer indicate that 32 may not actually be a ‘magic number’ for neutrons

Using the power of the Summit supercomputer, researchers at the US Department of Energy’s (DOE’s) Oak Ridge National Laboratory (ORNL) and the University of Tennessee, Knoxville, have verified the results of a groundbreaking experiment to precisely measure the charge radii of neutron-rich potassium isotopes. The findings challenge current nuclear theory and its description of the atomic nucleus.

In a paper recently published in Nature Physics, an international team of scientists led by Ágota Koszorús (Institute for Nuclear Radiation Physics at KU Leuven, Belgium) and Xiaofei Yang (Peking University, Beijing, China) reported the measurements of nuclear charge radii made at the Isotope mass Separator On-Line facility (ISOLDE) at CERN, the particle physics laboratory in Geneva managed by the European Council for Nuclear Research. Previous research had indicated that isotopes with 32 neutrons have a closed “shell” in the nucleus, making these nuclei “magic.” However, the experiment’s findings—backed up by large-scale modeling conducted on Summit—indicate that this hypothesis might not be correct: the potassium isotope 51K consisting of 32 neutrons is not more compact than its neighbors.

“We revealed some deficiencies in the most modern and state-of-the-art theory of the atomic nucleus,” said Gaute Hagen, an ORNL staff scientist in the Nuclear Structure and Nuclear Astrophysics Group. “Measurements of masses and excitation energies in calcium isotopes suggested that neutron number 32 is magic, but this new finding indicates that it might not be as magic as one had thought.”

Measured changes in the charge radii of potassium isotopes compared with the predictions of ab initio coupled cluster and density functional theory. The trend of the charge radii across the neutron number 32 does not follow behavior around the magic number N = 28.

At CERN, Koszorús and Yang and their team combined ionization measurements with beta-decay studies to extend charge radii measurements of the potassium isotopes beyond 32 neutrons. Charge radii measurements have revealed that a “kink” in the charge radius in isotope chains is a clear indicator of compactness and magicity. But Koszorús and Yang’s precise measurements revealed that there is no kink in the charge radius at neutron number 32. So, is 32 a magic neutron number after all?

Meanwhile, at ORNL, Hagen conducted concurrent simulations on Summit as part of his project, Ab initio Nuclear Structure and Nuclear Reactions, which was awarded compute time by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. The IBM AC922 Summit supercomputer is the flagship system of the Oak Ridge Leadership Computing Facility, a DOE Office of Science user facility at ORNL. Seeking to describe nuclei, nuclear reactions, and nucleonic (i.e., consisting or protons and neutrons) matter from first principles (i.e., ab initio), the project uses a quantum many-body code called NUclear Coupled Cluster Oak Ridge (NUCCOR) to calculate the properties of atomic nuclei. The simulations arrived at the same results as the experiment.

“Up until the magic number 28, we reproduced the radii quite well, including fine details,” Hagen said. “At neutron number 28, we found a clear kink in the radius, indicating a completely filled and magic shell. But beyond 28, the radius just keeps increasing quite dramatically, which is what Koszorús and Yang found experimentally. We do not know what causes this very rapid increase in radii in neutron-rich isotopes of potassium and also in calcium isotopes, so that’s an open problem on our side.”

NUCCOR was originally written at ORNL in the mid-2000s but has been rewritten almost from scratch several times since then, with Hagen and ORNL computational scientist Gustav Jansen currently leading its development. As part of their work, the Nuclear Tensor Contraction Library was built. It is a domain-specific, architecture-agnostic, high-performance distributed library, optimized for both NVIDIA and AMD GPUs. Jansen made some key code improvements to allow for detailed isotope modeling beyond the established magic number of 28 neutrons, which required very large calculations.

“One key algorithm that increased node-level performance enabled the calculations done for this paper,” Jansen said. “In short, the algorithm enabled the calculation of distributed sparse tensor contractions as a series of local dense tensor contractions. This unlocked additional performance gains from the GPUs on Summit. Without it, these calculations would have been too computationally expensive to run on Summit.”

These performance gains were critical to NUCCOR’s newly added ability to break specific symmetries of the nucleus, a much more computationally demanding approach than previous methods to describe medium-sized nuclei.

“The computational complexity grew at least an order of magnitude compared with what we did before. But it also allows us now to study, for the first time, the whole isotope chain of an atomic nuclei within the same framework,” Hagen said. “Before, having to impose symmetry of the nucleus in the calculation, we were restricted to specific nuclei around what we call ‘closed-shell’ or ‘sub-shell’ closures. So only very few nuclei were accessible to be described within this framework.”

Beyond this paper, NUCCOR’s findings in a variety of nuclear simulations will be further tested by experiments conducted at the Facility for Rare Isotope Beams (FRIB), a DOE Office of Science user facility scheduled to open at Michigan State University in 2022. FRIB is supported by the DOE Office of Science’s Office of Nuclear Physics and will enable scientists to make discoveries about the properties of rare isotopes, nuclear astrophysics, fundamental interactions, and applications for society, including in medicine, homeland security, and industry.

FRIB building

A rendering of the Facility for Rare Isotope Beams (FRIB), a DOE Office of Science user facility scheduled to open at Michigan State University in 2022. Many of the predictions made by Hagen’s project at ORNL will become ‘day one’ experiments at FRIB. Image courtesy FRIB.

“Many of the predictions that we now do within our approach will become what they call ‘day one’ experiments at FRIB,” Hagen said. “Calcium 60, for example, is one of the more exotic nuclei that exists, but we don’t know much about its structure, and that structure would impact how many more neutrons you can add onto the calcium isotopes. Does calcium 70 exist? I think a lot of the nuclei that we will be able to address and explore when FRIB comes online are highly relevant to what we are doing now. Our calculations will be confronted by experiments—there’s this feedback loop between theory and experiment to make progress in science.”

Related Publication:
Á. Koszorús, X. F. Yang, W. G. Jiang, S. J. Novario, S. W. Bai, J. Billowes, C. L. Binnersley, M. L. Bissell, T. E. Cocolios, B. S. Cooper, R. P. de Groote, A. Ekström, K. T. Flanagan, C. Forssén, S. Franchoo, R. F. Garcia Ruiz, F. P. Gustafsson, G. Hagen, G. R. Jansen, A. Kanellakopoulos, M. Kortelainen, W. Nazarewicz, G. Neyens, T. Papenbrock, P.‑G. Reinhard, C. M. Ricketts, B. K. Sahoo, A. R. Vernon, and S. G. Wilkins. “Charge Radii of Exotic Potassium Isotopes Challenge Nuclear Theory and the Magic Character of N = 32,” Nature Physics (2021).

The research was supported by DOE’s Office of Science Nuclear Physics program. UT-Battelle LLC manages Oak Ridge National Laboratory for DOE’s Office of Science, the single largest supporter of basic research in the physical sciences in the United States. DOE’s Office of Science is working to address some of the most pressing challenges of our time. For more information, visit