Department of Physics and Astronomy

Research summary, computing, funding, graduate students

Professors: Volker E. Oberacker and A. Sait Umar

graduate student: David Pigg (adviser: Prof. Umar)

Research summary

The aim of nuclear theory is to study the quantum many-particle aspects of two of nature's four fundamental forces: the strong and the weak interaction. The majority of nuclear phenomena are non-perturbative, i.e. the effective coupling constants involved are large. Hence, most basic quantum many-body theories require large-scale numerical computations.

One of the fundamental questions of nuclear structure physics is: what are the limits of nuclear stability? How many neutrons or protons can we add to a given nucleus before it becomes unstable against spontaneous neutron or proton emission? If one connects the isotopes with zero neutron separation energy, S_n=0, in the nuclear chart one obtains the neutron dripline. Similarly, the proton dripline is defined by the condition S_p=0. Another limit to stability is the superheavy element region around Z=124-126 and N=184.

The nuclear chart shows less than 300 stable nuclear isotopes, and about 2700 additional isotopes have been synthesized and studied in accelerator experiments. Nuclei in between the proton and neutron driplines are unstable against beta-decay. Nuclei outside the driplines decay by spontaneous neutron emission or proton radioactivity. The neutron-rich side, in particular, exhibits thousands of nuclear isotopes still to be explored ('terra incognita'). Some of these exotic nuclei can be studied with existing first-generation Radioactive Ion Beam Facilities (e.g. HRIBF at Oak Ridge and NSCL at Michigan State University). Several countries are constructing new 'second generation' RIB facilities, in particular for the exploration of neutron rich isotopes. In the United States, the  DOE/NSF Long Range Plan for Nuclear Physics (Dec. 2007) gives highest priority for new construction to FRIB (Facility for Rare Isotope Beams).

Theories predict profound differences between the known isotopes near stability and the exotic nuclei at the driplines: for n-rich nuclei, as the Fermi level approaches the particle continuum at E=0, weakly bound neutron states couple strongly to the continuum giving rise to neutron halos and neutron skins. Theories also expect large pairing correlations and new collective modes (e.g. 'pygmy resonance'), a weakening of the spin-orbit force leading to a quenching of the shell gaps, and perhaps new magic numbers.

Furthermore, FRIB will allow us to address fundamental questions in nuclear astrophysics: more than half of all elements heavier than iron are thought to be produced in supernovae explosions by the rapid neutron capture process (r-process). The r-process path contains many exotic neutron-rich nuclei which can only be studied with FRIB. Also, the predicted neutron skins would allow us to measure the properties of pure neutron matter which is of great interest for the study of neutron stars.

Specifically, our current research concentrates on the following topics:

1.  Fusion of neutron-rich nuclei above and below the Coulomb barrier, using the time-dependent Hartree-Fock (TDHF) mean field theory.

Computational Aspects: Fortran 95/03 Software and Algorithms

Our Fortran 95/03 source code development and production runs are carried out on local LINUX workstations with INTEL Core 2 processors. In the past, we have used the IBM-SP massively parallel supercomputer (~6000 processors) at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California.

We have developed a portable Fortran 95/03 library of Basis-Spline routines; both the collocation and the Galerkin method are implemented, either for periodic or fixed boundary conditions. This library has been documented in numerous publications and is used by researchers in various disciplines. It is highly modular and suitable for parallel computers.

computational techniques:
* 3-D spatial discretization of PDE's via Basis-Spline collocation method, periodic boundary conditions
* Iterative solutions of N-body coupled PDE's (damped gradient iteration)
* Fast Poisson solver
* Gram-Schmidt orthonormalization
* time-development: Taylor-series expansion of propagator for small time step
* parallelization (OPENMP, MPI) is achieved by spreading the wavefunctions of the N colliding nucleons onto N processors

* 2-D lattice (cylindrical coordinates), Basis-Spline representation of wavefunctions and differential operators using collocation and Galerkin method, fixed endpoint boundary conditions.
* Direct diagonalization of 2-D coupled PDE's using LAPACK95 library

Funding of our research group

The Vanderbilt Computational Nuclear Theory group receives external funding from:

* U.S. Department of Energy, Division of Nuclear Physics

Computational awards

* DOE Grand Challenge Award, High-Performance Computing and Communications Program, project entitled 'The Quantum Structure of Matter', Vanderbilt-ORNL collaboration, five CO-PI's (1992)

Graduate students

David Pigg (entered Ph.D. program in summer 2007; adviser: Prof. Umar)

Artur Blazkiewicz (Ph.D. in December 2005, '2D Coordinate Space Hartree-Fock-Bogoliubov Calculations for Neutron-Rich Nuclei in the A~100 Mass Region', Adviser: Prof. Oberacker); software designer, Glasgow, KY (2006-)

Edgar Teran (Ph.D. in May 2003, 'Hartree-Fock-Bogoliubov Calculations for Nuclei far from Stability', Adviser: Prof. Umar), postdoc at San Diego State University (2003-2006); Associate Scientist, PROS software company in Houston, TX (Sep. 2006 - )

Jun Chen, (1998 -2001, Adviser: Prof. Oberacker); Computational Analyst at Bloomberg Financial Services, New York City

Alan C. Calder, (Ph.D. 1997, 'Multidimensional simulations of core collapse supernovae using multigroup neutrino transport', Adviser: Prof. Umar); Research Associate, U. Illinois (Urbana); currently Research Associate, U. Chicago.

D. Russell Kegley, (Ph.D. 1996, 'Spline techniques for modeling weakly bound nuclear systems' , Adviser: Prof. Oberacker); senior staff member, ITT Corporation, Roanoake, Virginia; currently Manager of Reliability Engineering, Silicon Wireless Corp.

Mehmet Cem Guclu, (Ph.D. 1995, 'Monte-Carlo Calculations of Lepton-Pair Production in Relativistic Heavy-Ion Collisions', Adviser: Prof. Umar); currently Associate Professor, Istanbul Technical University, Turkey

Dr. Jack Wells, (Ph.D. 1994, 'Electromagnetic Lepton-Pair Production with Capture in Relativistic Heavy-Ion Collisions', Adviser: Prof. Oberacker); postdoc at Harvard-Smithsonian Center for Astrophysics; received a Wigner Fellowship at Oak Ridge Nat. Laboratory; currently group leader at Center for Computational Sciences, Oak Ridge Nat. Lab.

Dr. David Dean, (Ph.D. 1991, 'The String-Parton Model', Adviser: Prof. Umar); postdoc at Caltech; received DOE's Young Scientist Award and a Presidential Early Career Award; currently group leader of Nuclear Theory group, Oak Ridge Nat. Lab.

Dwight P. Russell (1983-1986); Asst. and Assoc. Professor, University of Texas at El Paso; currently Assoc. Professor at Baylor University, Waco, Texas.

Mohammad W. Katoot (1983 - 1986), Chairman and CEO, MK Industries, Tucker, GA; deceased Aug. 2000