Machine learning used to calculate nuclear landscape's limits

  • Feb 15, 2019
  • machine learning, rare isotopes, Research, Faculty
  • Homepage News, Faculty & Staff, Research, College of Natural Science, Statistics & Probability

More than 99.9 percent of the visible universe is made from 286 stable isotopes. However, the nuclear force allows many more unstable, radioactive isotopes to exist. That instability often results because it is difficult to maintain cohesion when there are many more neutrons than protons in a given nucleus.

We may never observe most of these unstable isotopes, but these short-lived inhabitants of the nuclear borderlands matter: they govern the processes in stars that create all the stuff around us, and what we are made of.

Figure showing the probability of existence of nuclei in the calcium region.
This figure shows the probability of existence of nuclei in the calcium region. The nuclei with experimentally-known masses lie to the left of the yellow line. The red line marks the limit of nuclei that have been experimentally observed, including calcium-60. Nuclei to the right of the red line await discovery. The team’s calculated limit of existence (probably greater than 50 percent) is indicated by a blue line. Beyond this line, neutrons cannot be bound to the nucleus anymore.

A collaboration between the College of Natural Science’s Department of Statistics and Probability (STT) and the Facility for Rare Isotope Beams (FRIB) at Michigan State University (MSU) has estimated the boundaries of nuclear existence by applying statistical analysis to nuclear models and assessed the impact of current and future FRIB experiments.

More than a year ago, FRIB and STT formed a new collaboration between nuclear physics and the statistical sciences. This collaboration, led by the joint hire of statistics researcher Léo Neufcourt, was initiated to get nuclear physics and statistics to work together on building predictive models that will answer fundamental questions about rare isotopes.

Recently, the STT/FRIB researchers and their collaborators discovered eight new rare isotopes of the elements phosphorus, sulfur, chlorine, argon, potassium, scandium and—most importantly—calcium (the heaviest isotopes of these elements ever found). The calcium isotope, calcium-60, has twice as many neutrons as protons. The discoveries generated excitement within the nuclear physics community and beyond.

Encouraged by these findings, the research team estimated the boundaries of nuclear existence in the calcium region and assessed the impact of the experimental discovery on nuclear structure research. The work was recently published in Physical Review Letters.

The group used a computational approach to Bayesian analysis as the statistical framework of choice. This centuries-old idea was developed by the English vicar Thomas Bayes in the 1700s. It calculates probabilities of unobserved events based on their relations with observations and on one's beliefs about them. The modern use of this idea took off about 20 years ago when computers became powerful enough to handle the massive computations involved.

Based on what is currently known about existing nuclei, the scientists used nuclear theory models to predict what new ones might be, and with what probability they might exist. To calculate these probabilities, they used Bayesian extrapolation methods employing the methodology explained in a joint paper in Physical Review C.

This computer-based analysis is a form of what is sometimes known as supervised machine learning. The computer explores myriads of possibilities and evaluates them according to the underlying probability models (that is the supervision part). It then concentrates around the most relevant ones in view of the observed data. The entire methodology allows researchers to quantify their predictions’ uncertainties precisely and reliably.

To quantify their findings, the research team introduced the new concept of Bayesian “probability of existence” that a given isotope is bound to neutron emission.

Considering the current experimental information and current global mass models, they estimate that heavier calcium isotopes, up to calcium-70, could exist. In future work, the FRIB will allow scientists to potentially create calcium-68 or even calcium-70. Based on current knowledge and models, the FRIB/STT team estimates calcium-68’s probability of existence at 76 percent and is likely to increase as scientists discover new isotopes in the same region.

The team is working on several other uses of Bayesian machine learning with applications to nuclear physics, including a project to calibrate the particle beam in the FRIB accelerator. Their methodology is expected to have direct applications to areas which need quantified data from model-based extrapolations, such as nuclear astrophysics.


Banner image: The nuclear landscape is the set of all stable and radioactive isotopes for all elements that exist in our universe, from hydrogen and helium, carbon and oxygen, to calcium and potassium, gold, lead, uranium, and beyond. Each such nucleus is identified by its number of protons and its number of neutrons, and is represented by a small box in this artistic rendition. As we move away from the 286 stable nuclei in dark blue, and closer to the edge of the landscape, we encounter isotopes which are so unstable that they may not even exist. They are shown here 'dripping' off the edge of the nuclear world. The NatSci and FRIB team explored this 'drip line' in the neighborhood of calcium. Image courtesy of Witek Nazarewicz.