New analysis improves theoretical understanding of hyperfine splitting in hydrogen

NEWPORT NEWS, VA – While it’s commonplace for many scientists to collaborate on nuclear physics experiments at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility, it’s rarer for the lab’s individual experiments to collaborate with each other. But that’s exactly what g2p in Jefferson Lab’s Experimental Hall A and EG4 in Experimental Hall B did.

The two collaborations combined their complementary data on the proton’s inner structure to improve calculations of a phenomenon in atomic physics: the hyperfine splitting of hydrogen.

An atom of hydrogen, the simplest and most abundant element in the universe, is made up of an electron orbiting a proton. Both of these particles have a property known as angular momentum, commonly known as spin, which can be oriented “up” or “down.”

The overall energy level of hydrogen depends on the spin orientation of the proton and electron. If one is up and one is down, the atom will be in its lowest energy state, like two dipole magnets who want to be anti-aligned. On the other hand, if the spins of these particles are the same, the energy level of the atom will increase by a small, or hyperfine, amount. These spin-born differences in the energy level of an atom are known as hyperfine splitting.

Since the discovery of hyperfine splitting in the 1930s, scientists have measured this energy difference in hydrogen very precisely. However, theory hasn’t been able to keep up.

“Our theoretical understanding of it is a million times worse than our experimental measurement of it,” said David Ruth, a postdoctoral associate at the University of New Hampshire. “Different things contribute to that, but what dominates our uncertainty in the calculations is a lack of understanding of the internal structure of the proton.”

Fortunately, g2p and EG4 happened to probe exactly that.

Greater than the sum of their parts

Ultimately, hyperfine splitting in hydrogen is caused by the interaction of the proton and the electron. Unlike the electron, the proton is not a fundamental particle: it’s made up of smaller particles called quarks and gluons. As a result, precise calculations of hyperfine splitting need to include information about the proton’s internal structure. But the inside of the proton is complicated and not fully understood, making it difficult to describe with theory alone.

The g2p and EG4 experiments were both designed to study how the proton’s constituent quarks make up its overall spin. To do so, these experiments aimed the electron beam generated in the Continuous Electron Beam Accelerator Facility (CEBAF), A DOE Office of Science user facility, at a polarized proton target – a target of protons whose spins are all oriented in the same direction.

In g2p, the proton target was transversely polarized, or the spins were oriented perpendicular to the electron beam. In EG4, the proton target was longitudinally polarized, or the spins were oriented parallel to the electron beam.

Detecting the beam electrons, which were also polarized, after they interacted with the polarized targets allowed these experiments to measure different aspects of the proton’s spin structure.

“We collected this data for our own purpose, to learn more about the internal structure of the proton and test theories related to the proton, but we produced the same data needed for better understanding hyperfine splitting,” said Alexandre Deur, a staff scientist at Jefferson Lab who worked on EG4. “It was a stroke of good luck.”

In a paper recently published in Physics Letters B, experimentalists from g2p and EG4 applied their distinct but compatible proton spin structure data to calculations of hyperfine splitting in hydrogen.

This cut the uncertainty related to proton structure in hyperfine splitting calculations in half, advancing theoretical understanding of this effect and atomic structure in general.

“The g2p and EG4 experiments were two gargantuan efforts, but, independently, neither of them could have answered this question,” said Karl Slifer, professor of physics at the University of New Hampshire who worked on g2p. “Together, the data were the perfect complement. This paper is the distillation of countless hours and hundreds of people's efforts.”

In addition to bridging Jefferson Lab’s experimental halls, this work connected fields.

The experimentalists of g2p and EG4 worked closely with Carl Carlson, Franziska Hagelstein and Vladimir Pascalutsa, nuclear theorists knowledgeable in atomic physics who ensured the calculations were as precise as possible.

“During every step of this analysis, we were having a back-and-forth conversation with the theorists,” said Ruth, who worked on the g2p experiment as a graduate student. “I think the result is pretty cool because it's a lot more of a direct collaboration between experiment and theory than usual.”

Over a year and a half, Ruth spearheaded the analysis and coordinated the meetings for this work.

“David did a great job,” said Jian-Ping Chen, a principal staff scientist at Jefferson Lab who worked on the g2p experiment. “He got all the experimentalists and theorists together to discuss this work. It is because of his persistence that we got this result out.”

The ultimate goal is for theorists in atomic physics to use these results to precisely and completely calculate hyperfine splitting of hydrogen from theory.

A muonic future

These hyperfine splitting calculations are also relevant to an exotic form of hydrogen called muonic hydrogen. In muonic hydrogen, the electron is replaced by a muon, which is 200 times heavier. This weight pulls the muon closer to the proton, where it is more sensitive to the proton’s internal structure.

In 2010, atomic physicists at the Paul Scherrer Institute (PSI) in Switzerland measured the radius of a proton in muonic hydrogen and found it was smaller than previously thought. This unexpected discovery was dubbed the proton radius puzzle.

“That was a big surprise,” Deur said. “And that came about simply because they started playing with muonic hydrogen.”

An upcoming experiment at PSI will again probe muonic hydrogen, this time in an attempt to precisely measure its hyperfine splitting. The results of the new analysis from g2p and EG4 will help to guide this PSI measurement.

There are multiple ways to define the proton’s radius. The measurement in the proton radius puzzle was of the proton’s charge radius. In addition to carrying out calculations related to hyperfine splitting, the collaborators of this work used g2p and EG4’s data to refine the value of the proton’s Zemach radius, which is a combination of its charge radius and its magnetic radius. Previous measurements and theoretical calculations of this type of radius disagree, but the extracted value bridges this gap.

“This new extraction of the Zemach radius of the proton gives us a better understanding of the physical dimensions of the proton and its messy composite structure,” Slifer said.

There’s still more to learn about the proton. Future experiments at Jefferson Lab will further probe this particle’s internal structure, and Chen hopes they also find use outside of nuclear physics.

“I’d like future experiments at Jefferson Lab to have more broad collaboration among different halls, with theorists, and even with other fields,” Chen said. “It’s important to go in all these directions to give the results as much impact as possible.”

By Chris Patrick

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