GFMC and AFDMC mini-justification

The principal goal of nuclear physics is to explain the structure and
reactions of nuclei as systems of nucleons which interact by, and hence are
correlated by, realistic forces.  These realistic forces must also provide
accurate descriptions of two- and three-nucleon scattering.  Green's Function
Monte Carlo (GFMC) and Auxiliary Field Diffusion Monte Carlo (AFDMC) are two
related approaches to attaining this goal.

GFMC allows essentially exact (up to statistical errors) solution of the
nuclear Schroedinger equation for slightly simplified Hamiltonians and up to 7
nucleons.  Larger systems require the introduction of constrained-path methods
that, while no longer theoretically exact, appear to give eigenenergies with
less than 2% systematic errors up to A=10.  The computer requirements of GFMC
increase very rapidly with A, so that 12C or slightly larger neutron systems
are our present limit.  Requirements for AFDMC grow much more slowly with A
and it has been applied to as many as 114 neutrons in a box.  However, the
need for a simpler constraint than is used in GFMC results in somewhat less
accuracy and at present limits AFDMC to pure neutron systems.

Recent successes:

1) Benchmark calculations showed that GFMC, NCSM, and 5 other methods agreed
to 0.3% for the 4He energy computed with Argonne v8'.  We have also shown
that GFMC and NCSM calculations of A=6,7 levels with AV8' are in agreement.

2) We used GFMC to construct the Illinois NNN potentials in a fit up to A=8.
Our subsequent calculations reproduce some 60 levels up to A=12 with an RMS
error of 0.7 MeV.

3) We showed that AFDMC agrees well with GFMC for up to 14-neutron systems
(which is the present GFMC limit) and gives converged neutron-matter results
by computing up to 114 neutrons in a box.

4) The preservation of orthogonality by GFMC propagation for multiple states
with the same quantum numbers has been demonstrated.

5) The A=5,8 mass gaps and other aspects of A <= 10 nuclear structure were
shown to require much of the complex structure of realistic NN potentials.

6) Our calculations of the astrophysically-important (alpha,gamma) capture
reactions on 2H, 3H, and 3He compare well with laboratory data.

Current work:

1) GFMC calculations of scattering states are being studied in detail for
n+4He in both resonant and nonresonant partial waves.

2) High-precision GFMC calculations for the charge radii of 6,8He and 6,7,8,9Li 
are being made for comparison to recent and future isotope-shift experiments.

3) Studies of 1-hbar-omega intruder states in A=9,10 nuclei are in progress.

4) Alternate starting wave functions for 12C GFMC are being investigated.

5) A path-integral approach to AFDMC is being developed to avoid the
dependence on the starting wave function.

6) Pairing starting wave functions are being studied to extend AFDMC to
systems of both protons and neutrons.

Work that could be done in the next five years with adequate support (both
computational and personnel).  All of these are relevant to the Nuclear
Physics Long-range Plan milestones:

1) A good theoretical understanding of the 12C nucleus is of fundamental
importance.  The RIA theory Bluebook identifies the triple-alpha burning
reaction, which is the source of 12C, and the subsequent 12C(alpha,gamma)16O
reaction as perhaps the most important astrophysical reactions; a Nuclear
Physics Long-range Plan milestone is to reduce the uncertainty in such
reactions by a factor of two.  In the next four years we will do much to
elucidate the properties of 12C by GFMC calculations of multiple 12C states
and transitions between them.  Benchmark comparisons with other methods such
as NCSM and CC will be crucial.

2) We are expanding the range of the QMC methods to include unbound states
treated as such and the computation of phase shifts and reaction cross
sections.  The result will be a more diverse set of tests for the nuclear
interactions and currents.  Continuum calculations will open the door to
accurate quantitative predictions of reaction cross sections in the light
systems important for solar neutrinos, big-bang nucleosynthesis, and seeding
the r-process in neutron-rich freeze-out.  Applications will include
7Be(p,gamma)8B radiative capture, 6,7,8Li(n,gamma)7,8,9Li, and 4He(alpha
n,gamma)9Be.  Comparison of our ab-initio neutron-capture cross sections with
other more approximate methods will provide useful calibrations for neutron
captures on larger nuclei.

3) Another important issue is the structure of the NNN potential, particularly
its isospin dependence and the question of whether current forms are adequate
to get both p- and sd-shell levels simultaneously.  GFMC calculations of
neutron-rich halo nuclei like 11Li and 1- & 2-hbar-omega intruder states in 
A=9-11 nuclei will provide important tests of NNN potential models.

4) The extension of AFDMC will allow much larger nuclei to be studied than
can be done with GFMC.  Comparisons with CC for such cases will be made.

5) The path-integral approach to AFDMC should allow finite-temperature
calculations relevant to equations of state for supernova simulations.

6) GFMC calculations relevant to fundamental symmetries will be made; examples
are 10C super-allowed beta decay and parity violation in few nucleon systems.

Computational needs:

Each 12C GFMC calculation (single level) requires ~200 Petaops.  Other nuclei
require less.  Over the five-year period we could use ~6000 Petaops.

An AFDMC calculation for 114 neutrons takes a few Petaops. The addition of
protons increases this by about an order of magnitude.  Some improved wave
functions may scale with an additional power of the number of particles with
would increase these numbers by 1 or 2 orders of magnitude. It is likely that
the AFDMC calculations would use several thousand Petaops over five years.

Computer science needs:

The 12C calculations also require a lot of memory -- more than 1 Gigabyte per
processor in the present implementation.  However, a number of the latest
supercomputer designs are for thousands of processors with significantly
smaller memories instead of hundreds of processors with large memories.  An
example is IBM's Blue Gene/L which has only 256 Megabytes per processor.
Therefore the GFMC program needs to be reworked to distribute the calculation
of individual Monte Carlo samples across many processors.  Keeping all the
processors usefully occupied will be nontrivial.  In general asynchronous
methods of distributing and balancing work between processors would be very
helpful and certainly of use to other applications also.