No Matter the Size of a Nuclear Party, Some Protons and Neutrons Will Always Pair up and Dance

A team led by MIT simulated the behavior of protons and neutrons in different types of atomic nuclei and found that the formulas describing the behavior of atoms in a gas can be generalized to predict how protons and neutrons will behave in the near vicinity in the nucleus to interact. Photo credit: collage from MIT News. Neutron constellation: X-ray (NASA / CXC / ESO / F. Vogt et al.); Optical (ESO / VLT / MUSE & NASA / STScI)

Findings on short-range nuclear interactions will help scientists study neutron stars and heavy radioactive nuclei.

Atoms in a gas can appear like parties at a nanoscopic rave, with particles walking around, pairing, and seemingly randomly flying away. Yet physicists have developed formulas that predict this behavior, even when the atoms are extremely close together and can pull and pull each other in complicated ways.

The environment at the core of an individual atom seems to be similar, with protons and neutrons dancing around too. But because the nucleus is such a compact space, scientists have tried to determine the behavior of these particles, known as nucleons, in the nucleus of an atom. Models that describe the interactions of nucleons that are far apart collapse when the particles pair and interact at close range.

Well one WITHThe -led team has simulated the behavior of protons and neutrons in different types of atomic nuclei using some of the most powerful supercomputers in the world. The team studied a variety of nuclear interaction models and surprisingly found that the formulas describing the behavior of atoms in a gas can be generalized to predict how protons and neutrons interact in the nucleus at close range.

When nucleons are less than 1 femtometer – 1 quadrillionth of a meter – apart, the researchers found another surprise: the particles pair in the same way, regardless of whether they inhabit a small nucleus like helium or a crowded one like calcium.

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“These short-range couples don’t really care about their surroundings – whether they’re in a large group or a group of five, it doesn’t matter – they will mate in the same universal way,” says Reynier Cruz-Torres who led the work as a physics student at MIT.

This near-range behavior is likely to be universal for all types of atomic nuclei, such as the much denser, more complex nuclei in radioactive atoms.

“People didn’t expect this type of model to capture cores, which are some of the most complicated objects in physics,” says Or Hen, assistant professor of physics at MIT. “Despite a density difference of more than 20 orders of magnitude between an atom and a nucleus, we can still find this universal behavior and apply it to many open problems in nuclear physics.”

The team published its results in the magazine Natural physics. MIT’s co-authors include Axel Schmidt, a research member of the Laboratory for Nuclear Science, as well as employees at Hebrew University, Los Alamos and Argonne National Laboratories, and various other institutions.

Party couples

Hen tries to understand the chaotic interactions between protons and neutrons at extremely short distances, where pulling and pulling between nucleons in the very small, dense environment of the nucleus was known to be difficult to determine. For years he has wondered whether a concept of atomic physics known as contact formalism could also apply to nuclear physics and the inner workings of the nucleus.

In the broadest sense, contact formalism is a general mathematical description that proves that the behavior of atoms in a cloud depends on their size: those that are far apart follow a certain physics, while atoms that are very close together follow one completely separate set of physics follow. Each group of atoms performs its interactions without considering the behavior of the other group. For example, according to contact formalism, there will always be a certain number of ultra-clear pairs regardless of what other, more distant atoms in the cloud are doing.

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Hen wondered whether contact formalism could also describe the interactions within the atomic nucleus.

“I thought that you can’t be seeing this beautiful formalism that was a revolution in atomic physics, and yet we can’t make it work for nuclear physics,” says Hen. “It was just too big a connection.”

“On a human scale”

The researchers initially worked with Ronen Weiss and Nir Barnea of ​​Hebrew University, who led the development of a theoretical generalization of atomic contact formalism to describe a general system of interacting particles. They then wanted to simulate particles in a small, dense, nuclear environment to see if behavior patterns would occur between short-range nucleons in a completely different way than long-range nucleons, as predicted by generalized contact formalism.

The group simulated particle interactions within several light atomic nuclei, ranging from three nucleons in helium to 40 in calcium. For each atomic nucleus type, they ran a random sampling algorithm to create a movie of where each of the protons and neutrons in a given nucleus could be over time.

“At a certain point in time, these particles can be distributed in one direction and interact with one another with a certain scheme, for example this is paired with this and a third particle is kicked instead. At a different point in time they will be distributed differently, ”explains co-lead author Diego Lonardoni, a physicist at Los Alamos National Laboratory and Michigan State University. “So we repeat these calculations over and over again to find equilibrium.”

To discover an equilibrium or pattern, the team had to simulate all of the physics possible between each individual particle and take thousands of snapshots for each type of nucleus. This number of calculations would typically take millions of hours of processing time to complete.

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“It would take my laptop more than the age of the universe to complete the calculation,” says Hen. “If you spread the computation across 10,000 processors, you can get your result on a human scale at a time.”

So the team used supercomputers in Los Alamos and the Argonne National Laboratory – some of the most powerful computers in the world – to split the work in parallel.

After running the simulations, they recorded a distribution of nucleons for each nucleus type they simulated. For example, for an oxygen nucleus, they found a certain percentage of nucleons 1 Fermi apart and another percentage a little closer, and so on.

Surprisingly, they found that the distribution of long-range nucleons varied greatly from nucleus type to nucleons. With short-range nucleons that were less than 1 femtometer apart, the distributions across atomic types looked exactly the same, regardless of whether the nucleons lived in an ultra-light helium nucleus or a denser carbon nucleus. In other words, short-range nucleons behaved independently of their environment on a larger scale, similar to how atomic behavior is described by contact formalism.

“Our result offers a new and easy way to pin down at short distance that part of the core distribution that, along with the existing theory, essentially enables complete distribution,” says Hen. “Among other things, we can use this to test the nature of neutrinos and calculate the cooling rates of neutron stars.”

Reference: “Many-body factorization and position-momentum equivalence of core correlations in the near range” by R. Cruz-Torres, D. Lonardoni, R. Weiss, M. Piarulli, N. Barnea, DW Higinbotham, E. Piasetzky, A. Schmidt, LB Weinstein, RB Wiringa and O. Hen, November 9, 2020, Natural physics.
DOI: 10.1038 / s41567-020-01053-7

This research was supported in part by the US Department of Energy, the Pazy Foundation, the Israeli Science Foundation, and the Clore Foundation.

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