ORNL Review Vol. 34, No. 2, 2001

ORNL Theorists and the Nuclear Shell Model

In 1997 ORNL physicist David Dean received the Presidential Early Career Award for Scientists and Engineers for his leadership role in developing the Quantum Shell Model Monte Carlo technique for solving the nuclear many-body problem. He performed this work with Steve Koonin and collaborators at the California Institute of Technology and has continued developing the technique during his time at ORNL. The techniques are particularly well suited to investigating thermal properties of nuclei such as phase transitions and critical temperature phenomena that can be induced by bombarding a nucleus with projectile ions and other particles.

The idea of independent neutrons and protons that make up a nucleus moving in a common potential, an attractive force created by the self-interaction of the nucleons that binds them into a nucleus, is central to the description of atoms, metals, and hadrons. It is also realized in nuclei and was first put on a firm theoretical basis in 1949 by Maria Goeppert-Mayer and Hans Jensen, who later shared a Nobel Prize for their work.

In contrast to other quantal systems cited above, the residual interaction between the protons and neutrons in a nucleus is strong and severely perturbs the naive picture of the nucleus as a collection of independent particles. This interaction mixes together many different independent-particle configurations, generating phenomena such as superfluidity (pairing), deformation (non-spherical ground-state shapes), and collective rotations and vibrations (where many neutrons and protons are involved in the motion) that are common properties of nuclei.

In the 1960s scientists developed one of the first shell model codes to solve the nuclear structure problem by diagonalization. This work—carried out by Bruce French (University of Rochester) and by Cheuk-Yin Wong, Joe McGrory, and Edith Halbert (all from ORNL), among others—was seminal in providing an understanding of nuclei with up to 30 nucleons (neutrons and protons). With advancing computational technology, a second generation of shell model codes was developed in the late 1970s and 1980s, using ideas of the U.K. theorist John Whitehead.

Currently, a Joint Institute for Heavy Ion Research postdoctoral fellow, Andrius Juodagalvis (from Lithuania), is working with Dean to develop a parallel implementation of the Whitehead scheme on modern parallel supercomputers.

Quantum Monte Carlo methods (pursued by Dean and collaborators) solve this same problem with path-integral techniques and are used to investigate both the ground-state and thermal properties of nuclei. These methods are based on a quantum Monte Carlo integration technique. This technique allows for the integration of very large, multidimensional integrals that naturally arise in the nuclear structure problem. The methods are also applied to other areas of science where the particles involved are quantum-mechanically strongly correlated. The differing approaches are complementary and, thus, allow a more complete picture of the nucleus to emerge.

Shell model diagonalization has recently been used to understand the structure of nickel-56 (⁵⁶Ni). This nucleus has 28 neutrons and 28 protons, so it is a doubly magic nucleus. In 2000 an ORNL/UT experimental group led by Cyrus Baktash—along with Dean, Witek Nazarewicz, and collaborators—published a scientific paper on ⁵⁶Ni entitled "Rotational Bands in the Doubly Magic Nucleus ⁵⁶Ni" in the 82nd volume of Physical Review Letters (1999). The paper won a Technical Achievement Award from UT-Battelle in 2000.

According to Dean, the nuclear shell model indicated both a spherical ground-state band and a highly deformed rotational band at higher excitation energies, and experimental and theoretical results agreed. At the time, these calculations were among the largest performed using the shell model diagonalization approach.

HRIBF offers physicists a unique capability for understanding both nuclear structure and certain astrophysical phenomena, using similar experimental techniques (see ORNL's Search for Rare Isotopes and Beam Technologies Enable HRIBF Experiments).

Results of Shell Model Monte Carlo calculations

Understanding the nucleus and its interactions with other particles requires significant interplay between experimental and theoretical efforts. Shown are results of Shell Model Monte Carlo calculations of Gamow-Teller excitations within various iron-group nuclei compared to experiment (a). Low-energy electrons cause this excitation through their weak interaction with nucleons in the nucleus. The quality of these results required a significant investment in computational algorithm development and computer time. They have influenced our understanding of element production in supernovae. The bright dot at the top of the galaxy M98 is the supernova SN1997bu (b). Many of the tools of nuclear theory are common to other quantum-mechanical, many-body systems (clusters, quantum dots, atoms) in which the interacting particles are highly correlated (c).

"We are using our quantum Monte Carlo techniques developed for nuclear structure studies to understand the microphysics of supernova explosions and other astrophysical phenomena," Dean says.

For example, electron capture on iron-group nuclei plays a key role in determining energy release and subsequent element production in supernova explosions. Understanding the underlying nuclear structure turns out to be quite important in obtaining reliable electron capture rates.

"Through electron capture by a nucleus, a proton can become a neutron, producing a more neutron-rich nucleus," Dean explains. "What happens is that an electron is absorbed onto a nucleus where it reacts with a proton to produce a neutron and neutrino. Emitted neutrinos can drive the supernova explosion and aid in the synthesis of elements. With our current shell-model technologies, we are modeling various aspects of these nuclear reactions."

Dean and his colleagues run the Quantum Shell Model Monte Carlo codes at the Department of Energy's National Energy Research Supercomputing Center in Berkeley, California, and on the IBM supercomputer at DOE's Center for Computational Sciences at ORNL. They recently received funding from DOE's Scientific Discovery through Advanced Computing (SciDAC) program to continue to develop the new parallel shell model diagonalization codes and quantum Monte Carlo algorithms.

These researchers have contributed to the theoretical understanding of the structure of the atomic nucleus and the microphysics of exploding stars.

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