Our goal is to achieve a description of nuclear systems ranging in size from the deuteron to nuclear matter and neutron stars using a single parameterization of the nuclear forces. Our work includes both the construction of two- and three-nucleon potentials and the development of many-body techniques for computing nuclear properties with these interactions. Detailed quantitative, computationally intense studies are essential parts of this work.

In the last decade we have constructed several realistic two- and
three-nucleon potential models.
The *NN* potential, Argonne v18,
has a dominant charge-independent piece plus additional charge-dependent
and charge-symmetry-breaking terms, including a complete electromagnetic
interaction.
It fits 4301 *pp* and *np* elastic scattering data with a
*chi***2 of 1.09/datum, as well as low-energy *nn* scattering
parameters and deuteron properties.
Argonne v18, which has become a standard used by many groups in the nuclear
structure community, was built in collaboration with Vincent Stoks (Flinders
University) and
Rocco Schiavilla (Jefferson Lab & Old Dominion University) [1].

Recently we have built a new family of *NNN* potentials, the Illinois
models, in collaboration with
Vijay Pandharipande (University of Illinois) and
Joe Carlson
(Los Alamos National Lab).
These models incorporate standard two-pion-exchange diagrams, including both
the dominant P-wave and chirally-required S-wave pi-nucleon scattering.
In addition, three-pion ring diagrams provide an extra degree of freedom
for the isospin dependence while a shorter-range repulsive term helps provide
saturation in dense matter [2].

With these interactions we make quantum Monte Carlo (QMC) calculations of a
wide range of many-nucleon systems [3-8].
The QMC methods include both variational Monte Carlo (VMC) and Green's
function Monte Carlo (GFMC).
In the VMC method we construct trial functions from products of pair and
triplet correlation operators and then evaluate energy expectation values
using a Metropolis Monte Carlo procedure.
We vary parameters in the trial functions to minimize the energy, and then
use these optimized wave functions to study other nuclear properties,
such as one-body densities amd
two-body densities, and various
momentum distributions including both nucleon
and nucleon-cluster distributions.
We have also studied electromagnetic elastic and transition
form factors for ^{6}Li [9],
spectroscopic factors in ^{7}Li(*e,e'p*) reaction [10],
transition densities for pion elastic
and inelastic scattering [11],
low-energy radiative capture reactions [12-13], and weak decay rates [14].

The GFMC calculations take these trial functions as a starting point and
systematically improve on them by a propagation in imaginary time with
an exponential of the Hamiltonian.
This method produces essentially exact (~1-2%) binding energies for the
lowest states of given spin and parity, but also produces good estimates for
higher-lying excited states.
At present, using both VMC and GFMC methods, we have calculated the energies
of nearly 100 ground or low-lying excited states in nuclei up to ^{12}C.
Using the Hamiltonian containing the Argonne v18 and Illinois-2 potentials,
we get an excellent reproduction of the experimental spectrum for
*A*=4-8 and
*A=*9-12.
We have used these methods to demonstrate how sensitive the spectra of
light nuclei are to details of the nuclear force, which has considerable
influence on the chemical composition of the universe [15].

We are also studying neutron drops, i.e., collections of neutrons held together by an external well, by GFMC methods in collaboration with Carlson, Pandharipande, Kevin Schmidt (Arizona State University) and others [16]. We have examined the ground states and spin-orbit splitting in drops with from 2 to 14 neutrons. The properties of these drops can be used as "data" for fitting simpler effective interaction models that are employed in the study of large neutron-rich nuclei and the crusts of neutron stars. We have also demonstrated that recent experimental claims of a bound four-neutron system are not consistent with our knowledge of nuclear forces and nuclei [17].

The QMC calculations are numerically intensive, and would not be possible without the tremendous advances in parallel computing that have been made over the past decade. We have benefitted from a series of advanced parallel machines in Argonne's Mathematics and Computer Science Division (MCS) and from computers at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, as well as support at different times from NSF centers at Urbana and Cornell. Most of our current efforts are being made using the Argonne Jazz Linux cluster and IBM Blue Gene/L and the NERSC IBM SP Seaborg.

[1] R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla,
Phys. Rev. C **51**, 38 (1995)

[2] S. C. Pieper, V. R. Pandharipande, R. B. Wiringa, and J. Carlson,
Phys. Rev. C **64**, 014001 (2001)

[3] B. S. Pudliner, V. R. Pandharipande, J. Carlson, and R. B. Wiringa,
Phys. Rev. Lett. **74**, 4396 (1995)

[4] B. S. Pudliner, V. R. Pandharipande, J. Carlson, S. C. Pieper,
and R. B. Wiringa,
Phys. Rev. C **56**, 1720 (1997)

[5] R. B. Wiringa, S. C. Pieper, J. Carlson, and V. R. Pandharipande,
Phys. Rev. C **62**, 014001 (2000)

[6] S. C. Pieper and R. B. Wiringa,
Annu. Rev. Nucl. Part. Sci. **51**, 53 (2001)

[7] S. C. Pieper, K. Varga, and R. B. Wiringa,
Phys. Rev. C **66**, 044310 (2002)

[8] Steven C. Pieper, R. B. Wiringa, and J. Carlson,
Phys. Rev. C **70**, 054325-1:11 (2004)

[9] R. B. Wiringa and R. Schiavilla,
Phys. Rev. Lett. **81**, 4317 (1998)

[10] L. Lapikas, J. Wesseling, and R. B. Wiringa,
Phys. Rev. Lett. **82**, 4404 (1999)

[11] T.-S. H. Lee and R. B. Wiringa,
Phys. Rev. C **63**, 014006 (2001)

[12] K. M. Nollett, R. B. Wiringa, and R. Schiavilla,
Phys. Rev. C **63**, 024003 (2001)

[13] K. M. Nollett,
Phys. Rev. C **63**, 054002 (2001)

[14] R. Schiavilla and R. B. Wiringa,
Phys. Rev. C **65**, 054302 (2002)

[15] R. B. Wiringa and S. C. Pieper,
Phys. Rev. Lett. **89**, 182501 (2002)

[16] B. S. Pudliner, A. Smerzi, J. Carlson, V. R. Pandharipande,
S. C. Pieper, and D. G. Ravenhall,
Phys. Rev. Lett. **76**, 2416 (1996)

[17] S. C. Pieper,
Phys. Rev. Lett. **90**, 252501 (2003)

Nuclear dynamics with sub-nucleonic degrees of freedom

Theoretical Physics Research

Heavy-ion reactions and nuclear structure