Nuclear Forces

The fundamental theory for the strong interaction is quantum chromodynamics (QCD) with quark and gluon degrees of freedom, but it is very difficult to solve in the non-perturbative regime of atomic nuclei.  In fact, over a substantial range of energy and momenta, the structure and reactions of nuclei and nucleonic matter can be understood starting from a non-relativistic Hamiltonian with nucleons as the only active degrees of freedom.  Such interaction models can be used to understand which nuclei are stable, the decay modes for those that are not, and the interactions of nuclei with electroweak probes and with each other.  They form the basic input to our ab initio studies of nuclear systems ranging from the deuteron to neutron stars. 

There is a wealth of nucleon-nucleon (NN) scattering data available that severely constrains possible NN interaction models.  We use our knowledge of meson and nucleon resonance degrees of freedom, along with the underlying symmetries of QCD, to guide our construction of such models.  Theory also tells us to expect many-nucleon interactions, starting at the three-nucleon (3N) level.  Nuclear interactions have been obtained that provide accurate fits to NN data, both in phenomenological models and in chiral effective field theory (χEFT).  The Argonne Theory Group has played an active role in the construction of phenomenological potentials, such as the Argonne NN and Urbana / Illinois 3N models.  We have also helped develop and test χEFT models such as the Norfolk NV2+3 interactions.   

Our ab initio studies of nuclear systems can utilize a wide range of possible nuclear interactions, both to see how well they reproduce known data, and to make predictions for nuclear systems that are not (as yet), or cannot, be measured in the laboratory.

Light Nuclei       

We aim at understanding how the structure and the dynamics of atomic nuclei emerges from the individual interactions of their constituent protons and neutrons. Sophisticated nucleon-nucleon (NN) and three-nucleon (3N) potentials, which we help develop, are the main input to our calculations. Solving the Schrödinger equation is made particularly difficult by the non-perturbative nature of these forces and their strong spin/isospin dependence. We tackle this problem by using and developing state-of-the-art quantum Monte Carlo methods, which are ideally suited to accurately describe long- and short-range nuclear dynamics on the same footing.

The variational Monte Carlo and the Green’s function Monte Carlo methods can take as input the most sophisticated Hamiltonians and compute the spectrum and electroweak transitions of light nuclei with percent-level accuracy. The Green’s function Monte Carlo method is also used to study the electroweak response function, which determines the electron and neutrino-nucleus cross sections that are relevant for electron-scattering carried out at Jefferson Lab and for the accelerator-neutrino program.  

The auxiliary-field diffusion Monte Carlo method can treat larger nuclei, up to 16O, and infinite neutron matter, but is currently limited to somewhat simplified interactions. To extend the reach of the AFDMC to larger nuclei and more sophisticated interactions, we are actively investigating the use of artificial neural network representations of the nuclear wave functions.

Medium-mass and heavy nuclei  

Up until a little over a decade ago, ab initio many-body methods using two-body and three-body forces could only reach light nuclei up to mass A=12-16. Since then, developments in polynomial-scaling methods and renormalization group techniques have enabled converged computations of nuclei up to mass A=100, and more recently, up to A=208.  We use the in-medium similarity renormalization group (IMSRG) approach to solving the many-body problem. This highly versatile method can access open-shell nuclei, including excited states, opening the door for a number of interesting applications, including the structure of exotic neutron-rich nuclei present in extreme astrophysical environments, and searches for physics beyond the standard model.  

In order to circumvent the curse of dimensionality and reach heavy open-shell nuclei, one must inevitably make approximations in the solution of the many-body problem. The typical approximations made in the IMSRG, and other polynomially-scaling methods like coupled cluster, yield high accuracy--especially for bulk properties like binding energies and radii—and are systematically improvable. However, a more rigorous prescription for generating theoretical error bars in the absence of experimental data is absolutely essential. This is a current frontier in ab initio theory. 

Dense Nuclear Matter 

The matter inside a neutron star consists primarily of neutrons, with a few protons, electrons, and other sub-atomic particles. This matter is so dense that an entire neutron star, with a mass greater than the Sun, would fit inside a city of the size of Chicago. As such, multi-messenger astrophysical observations on neutron stars allow us to probe the matter in extreme conditions not accessible in terrestrial laboratories. These observations include gravitational-wave signals and electromagnetic emissions from merging events, mass measurements of pulsars, and X-ray timing with NASA’s Neutron Star Interior Composition Explorer instrument. 

We model neutron-star matter as an infinite system of neutrons that interact by the same nuclear force that binds protons and neutrons in atomic nuclei. Using sophisticated numerical techniques, most notably quantum Monte Carlo methods, that take advantage of leadership-class computers, we compute the neutron matter equation of state, i.e., how the pressure of matter changes as a function of its density. This quantity provides us information on how massive the star can be before gravity crushes it into a black hole and how large the star is. In addition, the ​“stiffness” of the equation of states is imprinted in the gravitational-wave signal measured by the LIGO / VIRGO collaboration.  

In addition to shedding light on neutron-star properties, these calculations help us understand nuclear interactions, particularly the force acting between triplets of neutrons. Terrestrial experiments poorly constrain the latter, but it plays a crucial role in the dense matter found in the interior of neutron stars. 

Funding Sources:

• U.S. Department of Energy Office of Science, Office of Nuclear Physics
• Laboratory Directed Research and Development (LDRD)