When a nucleus has too many protons or neutrons, a neutron will transform into a proton, or a proton will transform into a neutron. The process - beta decay - brings the nucleus closer to a region of stability. For half a century, nuclear physicists have been dogged by something of a problem of scale: why was it they could calculate the beta decay rate of a single neutron, but using that information for an atomic nucleus resulted in a too-fast decay?
Thomas Papenbrock, professor of theoretical nuclear physics at the University of Tennessee, Knoxville, and co-author on theNature Physicspaper, explained that the adjustment for this discrepancy came in the form of "quenching" - reducing a fundamental coupling constant between decay rates for a free neutron and the decay rate scientists observed in an atomic nucleus. The puzzle was that there was no first-principles theoretical understanding for why quenching worked.
"Our work shows that the beta decay of a nucleus is more complicated", Thomas Papenbrock stated. "Even if we think of it as a decay of a neutron to a proton inside the nucleus, this decay is influenced by processes where two neutrons interact and transition into a proton and a neutron. Taking these effects into account, and using state-of-the art nuclear models and supercomputers, we were able to solve the puzzle of 'quenched' beta decays."
Availing themselves of the Cray XK7 Titan Supercomputer at ORNL, the researchers simulated the decay of tin-100 into indium-100. Tin-100 is known as a "doubly-magic" nucleus: it has 50 protons and 50 neutrons in complete shells, making it strongly-bound. The relative simplicity of its structure makes tin-100 an ideal candidate for the sort of large-scale calculations where scientists need to understand the forces between the protons and neutrons in an atomic nucleus. The two elements share the same number of nucleons (protons and neutrons), with tin-100 possessing 50 protons to indium-100's 49.
"For decades, scientists have lacked a first-principles understanding of nuclear beta decay, in which protons convert into neutrons, or vice versa, to form other elements", stated ORNL staff scientist Gaute Hagen, who led the study. "Our team demonstrated that theoretical models and computation have progressed to the point where it is possible to calculate some decay properties with enough precision to allow for direct comparison to experiment."
Calculating beta decay precisely required the team to not only accurately simulate the structure of the mother and daughter nuclei but also account for the correlated interactions between two nucleons during the transition. This additional treatment presented an extreme computational challenge due to the combination of strong nuclear correlations and interactions involving the decaying nucleon.
In the past, nuclear physicists worked around this problem by inserting a fundamental constant to reconcile observed beta-decay rates of neutrons inside and outside the nucleus, a practice known as "quenching". But with machines like ORNL's Titan supercomputer, Gaute Hagen's team demonstrated that this mathematical crutch is no longer necessary.
"Nobody really understood why this quenching factor worked. It just did", stated ORNL computational scientist Gustav Jansen. "We found that it could largely be explained by including two nucleons in the decay - for example, two protons decaying into a proton and a neutron, or a proton and a neutron decaying into two neutrons."
The team, which included partners from Lawrence Livermore National Laboratory, University of Tennessee, University of Washington, TRIUMF in Canada, and Technical University Darmstadt in Germany, performed a comprehensive study of beta decays from light to medium-heavy nuclei up to tin-100.
The achievement gives nuclear physicists increased confidence as they search for answers to some of the most perplexing mysteries related to the formation of matter in the universe. Beyond regular beta decay, scientists are looking to compute neutrinoless double beta decay, a theorized form of nuclear decay that, if observed, would explore important new physics and help to determine the mass of the neutrino.
Many elements have isotopes that decay over long periods of time. For example, the half-life of carbon-14, the nucleus used in carbon dating, is 5,730 years. Other nuclei, however, exist only for fractions of a second before ejecting particles in an attempt to stabilize.
In neutron beta decay, an electron and an anti-neutrino are emitted. When tin-100 transforms into indium-100, the nucleus undergoes beta-plus decay, expelling a positron and a neutrino when converting a proton to a neutron.
With its equal number of protons and neutrons, tin-100 exhibits an unusually high rate of beta decay, giving the ORNL team a strong signal from which to verify its results. Furthermore, the tin-100 nucleus is "doubly magic", meaning the nucleons fill out defined shells inside the nucleus that make it strongly bound and relatively simple in structure. The ORNL team's NUCCOR code, which is programmed to solve the nuclear many-body problem, excels at describing doubly magic nuclei up and down the nuclear chart.
"A doubly magic nucleus like tin-100 isn't as complicated as many other nuclei", stated Thomas Papenbrock. "This means we can reliably compute it using our coupled cluster method, which calculates properties of large nuclei by accounting for forces between the individual nucleons."
To model beta decay, however, the team also had to calculate the structure of indium-100, a more complex nucleus than the doubly magic tin-100. This required a more precise treatment of the strong correlations between the nucleons. By borrowing ideas from quantum chemistry, which treats electrons as waves, Gaute Hagen's team successfully developed techniques to model these processes.
"In our case we are dealing with nucleons instead of electrons, but the quantum chemistry concepts have helped us branch out from doubly magic nuclei and expand into these open-shell regions", stated ORNL physicist Titus Morris.
Now that Gaute Hagen's team has shown its understanding of beta decay is on par with experiment, it's looking to take advantage of new supercomputers like ORNL's Summit, the world's most powerful, to guide current and future experiments.
Researchers are currently using Summit to simulate how calcium-48, another doubly magic nucleus, would undergo neutrinoless double beta decay - a process in which two neutrons beta decay into protons, but without emitting any neutrinos. The results could aid experimentalists in the selection of an optimal detector material for the potential discovery of this rare phenomenon.
"Currently, calculations using different nuclear models of neutrinoless double beta decay may differ by as much as a factor of six", Gaute Hagen stated. "Our goal is to provide a benchmark for other models and theories."
The results of this study are consistent with experimental data and could also inform predictions for the matrix element that governs neutrino-less double beta decay. This is a hypothetical process where two neutrons decay into protons at the same time, but without emitting neutrinos. Neutrino-less double beta decay, as theNature Physicspaper points out, has its own puzzle in terms of understanding the scale of mass in neutrinos, which up until 1998 were thought to have no mass at all.
The Nature Physics paper includes two authors with UT Physics ties: Thomas Papenbrock and Gaute Hagen, adjunct assistant professor.
This research was supported by the DOE Office of Science.