With V. R. Pandharipande of the University of Illinois, Urbana, we are
computing the properties of light (up to 40 neutrons and protons) nuclei using
realistic two- and three-nucleon interactions. This involves developing
many-body methods for reliably computing the properties of a nucleus for
complicated forces that are strongly dependent on the spins and charge states
of the nucleons. Unlike the Coulomb force used in atomic or condensed-matter
calculations, there is no useful fundamental theory that tells us what this
force is. We can partially constrain the two-body force by fitting
nucleon-nucleon scattering data, but many-body calculations are required to
test other properties of this force as well as the three-body interaction.
Thus we are at the same time refining our knowledge of the forces and using it
to make predictions about nuclei.
We make variational calculations, in which one assumes a form for the
quantum-mechanical wave function describing a nucleus and then computes the
energy of the nucleus for a given force model. This work involves computing
multidimensional (12 to 120 dimensions) integrals using Monte Carlo methods.
The integrand is expressed in terms of large complex vectors describing the
spin and charge states of the nucleons. These calculations must be repeated
many times to find the best set of parameters for the assumed form of the
wave function. The longer a given calculation is allowed to proceed, the
smaller the statistical error from the Monte Carlo integration, and hence
the more refined the determination of the best parameters.
While the energy calculation is our main test of both the quality of the
wave function and of the correctness of the force, we can also calculate
various other properties, including low-lying excited states and a variety
of low-energy reactions. Many of these are relevant to experiments that
will be carried out at CEBAF, while others are predictions of astrophysically
interesting cross sections that cannot be measured in the laboratory.
The first calculations done on the SP1 used a new nuclear
interaction and obtained much better (when compared to experiment) results
for the binding energy and density profile of oxygen than we had previously
obtained. The better density results are specifically attributable to the
detailed variational searches made possible by the SP1. The speed of the SP1
made possible, for the first time, calculations of calcium (40 nucleons);
work on this is in progress.
The SP1 was the first parallel processor that we were able to use for
our calculations. Previously we used single processors of the most
powerful Cray computers available. Earlier parallel computers could not
be used because of their small memories; our calculations require up to 65
megabytes of memory. The RS/6000 compiler provides good speeds on each
node, allowing us to reach speeds of 48 Mflops on a single processor.
The Argonne package <#208#> p4<#208#> was used to implement the message-passing part
of the program. The calculations proceed by having the master node do
a random walk and send positions to the slaves. The calculation of the
integrand at one position is very lengthy (up to 4 minutes) so it is easy
for one master to keep all the slaves busy. The communication load is
very low. Runs on 128 nodes achieve speedups of 123, or computational
rates of 5.9 Gflops. A run using 160 nodes achieved 6.5 Gflops, but there
were also other users on some of the nodes.