Quantum shell structure reveals new rule for proton-neutron pairing inside nuclei

Nuclear physicists used a little magic in their latest experiment conducted at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility, and the result has revealed surprising new information about the behavior of protons and neutrons inside the atom’s nucleus. Specifically, the research revealed another requirement that determines how protons and neutrons pair up.

The result is reported in the journal Nature.

The research involves short-range correlations (SRCs). This phenomenon describes when a proton and a neutron, or two protons or two neutrons, briefly pair up inside the nucleus.

Research into short-range correlations has helped to explain why there are high-momentum (fast-moving) protons and neutrons in the nucleus, some details about how such correlations form, and also how they may affect the quark structure of the protons and neutrons themselves.

Using magic nuclei to compare

To continue unraveling the mystery of how SRCs affect nuclear structure, the physicists needed more detailed information about how pair partners are chosen. Their experiments compared ordinary nuclei and how their SRCs change as the number of protons and neutrons increase.

Previous SRC experiment results had shown that nuclei with more neutrons had more protons that were paired up. But according to Or Hen, a professor of physics at the Massachusetts Institute of Technology, there wasn’t enough information to disentangle which variable, specifically, was causing this behavior.

“We changed the nuclei both in terms of their mass and also in the proton to neutron ratio at the same time. So, it was not this unique CaFe setup,” said Hen.

To better control for both variables, the collaboration of 30 physicists working on this experiment turned to a little bit of magic. The CaFe experiment compares how SRCs behave in “magic” and “doubly magic” nuclei.

In this view of nuclear structure, the protons and neutrons are arranged by discrete energy levels, much like the electron energy levels in the atom. Each level is called a shell, and higher shells only become available once all the lower ones have filled.

A magic nucleus is one in which either all the places for a proton or all the places for a neutron have been filled in the outermost available shell. A doubly magic nucleus has all the places for both protons and neutrons fully filled. Iron-54 (Fe) is a magic nucleus, with a filled neutron outer shell. Calcium-40 and Calcium-48 (Ca) are both doubly magic nuclei. The CaFe experiment is named after these two elements.

What the comparisons revealed

Calcium-48 (20 protons, 28 neutrons) has eight more neutrons than Calcium-40 (20 protons, 20 neutrons). According to Larry Weinstein, a professor of physics and eminent scholar at Old Dominion University, comparing these two nuclei was the first step in the analysis process. Comparing the two is the equivalent of adding just eight neutrons to a nucleus.

“What we found was that when you add those eight extra neutrons, not much happens. If the neutron dominance theory is right, then adding 40% more neutrons should get your protons a lot more correlated. And they didn’t. They only got about 10% more,” Weinstein said.

Then, they took the next step in the analysis process and compared Calcium-48 (20 protons, 28 neutrons) to Iron-54 (26 protons, 28 neutrons). This comparison is the equivalent of adding just six protons to a nucleus.

“And if you just do simple proton counting, you’d expect 30% more SRCs, because there are 30% more protons. But instead, we got 50%. And that really surprised us,” Weinstein said.

When the experimental collaboration reviewed the combined result, it revealed a completely unexpected twist.

“We were saying, okay, is this mass or is this neutron excess? And the answer was no. It’s actually shell structure; it’s quantum effects. And that’s cool,” explained Weinstein. “Adding eight neutrons in this outer shell, those neutrons don’t really couple to the protons in inner shells. But if we had six more protons in the same shell, they couple really well to those eight neutrons in that shell.”

Hen summed it up another way.

“We have discovered new quantum selection rules for who can pair. And that was not known before,” said Hen.

How the experiment was run

The result came from just four days of run-time in one of the Continuous Electron Beam Accelerator Facility’s four end stations. More than 1,700 nuclear physicists worldwide use CEBAF, a DOE Office of Science user facility, to conduct their research.

In this experiment, electrons with 10.5 GeV (billion electron-volts) of energy were directed into targets consisting of Calcium-40, Calcium-48, Iron-54 and gold-197, as well as a range of lighter elements, including beryllium-9, boron-10, boron-11 and carbon-12. Electrons coming out of the target were detected in the Super High Momentum Spectrometer.

SRC protons that were knocked out of the target were collected and measured in the High Momentum Spectrometer. The entire experiment, including the additional nuclei not included in this first analysis, took only eight days of data taking.

The experimental data taking and analysis were led by Dien Nguyen (Jefferson Lab and University of Tennessee), Carlos Yero (Old Dominion University and Catholic University), and Holly Szumila-Vance (Jefferson Lab and Florida International University), with help from graduate student Noah Swan (Old Dominion University) and the Jefferson Lab Hall C Collaboration.

“The reason this was a quick and easy experiment to run and to do was because of almost two decades of work at Jefferson Lab, where we have developed and devised this methodology of identifying correlations,” Hen said. “Developing the method and the understanding of how to do this well took a long time. But now that we know how to do it right, we can run with it. And we can do quick measurements and get a ton of insight.”

From proposal to next steps

Yet, the experiment almost didn’t happen. It was first presented to the lab’s Program Advisory Committee (PAC) in 2016. This committee reviews all proposed experiments and rates them based on their scientific merit, feasibility and support. That first proposal was not approved to be placed on CEBAF’s schedule.

In 2017, the collaboration brought a new proposal to the committee. It addressed all of the recommendations made by the previous PAC, whose review was led by David Dean, a committee member who would later become the lab’s chief research officer and deputy director for science.

“I suggested to the proponents that they describe specifically how SRC measurements would affect our understanding of the physics of the nucleus. The team took this to heart and submitted a much stronger proposal,” said Dean. “It has been gratifying to follow the development of CaFe from the ground up and to see the results appear in Nature.”

As far as the next step, the collaboration already has the next result in the works. A second result will include the data taken on the lighter nuclei that was not the focus of this particular study. That result is currently in the analysis phase. Meanwhile, another related experiment using the CEBAF Large Acceptance Spectrometer, located in another of CEBAF’s end stations, took data in 2021-2022 and is in the review phase.

Further experiments will be determined by these results and the lively discussions that are sure to follow among collaboration members. Hen and Weinstein credit the very active and involved research collaboration for the success of these experiments.

“It started off with just a few of us working together for many years, and now we have this amazing generation from students to postdocs to junior faculty, like Holly Szumila-Vance, Carlos Yero, and Dien Nguyen. And they’re challenging us. They’re pushing and they’re arguing with us,” said Hen. “And through that conversation, that back and forth, eventually that conversation leads to new insight.”

Who’s behind this story?

Sadie Harley

BSc Life Sciences & Ecology. Microbiology lab background with pharmaceutical news experience in oil, gas, and renewable industries.

Full profile →

Robert Egan

Bachelor’s in mathematical biology, Master’s in creative writing. Well-traveled with unique perspectives on science and language.

Full profile →