**SCIDAC PROPOSAL**

**NSLER: Nuclear Structure and Low-Energy Reactions**

**Applicant/Institution:** The University of Tennessee

**Street Address/City/State/Zip:** 1534 White Avenue\
Knoxville, TN 37996-1529

**Principal Investigator:** David J. Dean

**Address:** 401 Nielsen Physics Building

> 1408 Circle Drive\
> Knoxville, TN 37996-1200

**Telephone Number:** 865-576-5229

**Email:** <deandj@ornl.gov>

**Lead Applicant/Institution:** The University of Tennessee

**Lead Principal Investigator:** David J. Dean

**Address:** 401 Nielsen Physics Building

> 1408 Circle Drive\
> Knoxville, TN 37996-1200

**Telephone Number:** 865-576-5229

**Email:** <deandj@ornl.gov>

**DOE/Office of Science Program Office:** Nuclear Physics

> **Technical Contact:** Sidney A. Coon, 301-903-7878

**Collaborating Institutions and senior personnel:**

Ames Lab: M. Sosonkina\*

ANL: S. C. Pieper\*, K. Nollett, R. B. Wiringa; E. Lusk, J. Moré, B.
Norris

Arizona State University: K. Schmidt\*\*

Iowa State University: J. P. Vary\*\*

U. Arizona: B. R. Barrett

LANL: J. Carlson\*, G. Hale, T. Kawano, P. Moller, P. Talou

LBNL: E. Ng\*, C. Yang

LLNL: W. E. Ormand\*, J. Escher, R. D. Falgout, P. Navratil, B. de
Supinski, I. Thompson

Michigan State University: B. A. Brown\*\*, T. Duguet, F. Nunes, V.
Zelevinsky; P. Piecuch\*\*

Central Michigan: M. Horoi; Florida State: A. Volya

Old Dominion University: R. Schiavilla\*\*

University of Tennessee: D .J. Dean\*, W. Nazarewicz, T. Papenbrock

ORNL: D.E. Bernholdt\*, G. Fann, K. Roche, W. Shelton, G. Arbanas

University of Washington: G. F. Bertsch\*\*, A. Bulgac

Ohio State University: R. Furnstahl,Yale University: Yoram Alhassid

\*will submit FWP

\*\*will submit University grant application

#   {#section .Style4 .unnumbered}

# ABSTRACT {#abstract .Style4}

Our long-term vision is to arrive at a comprehensive and unified
description of nuclei and their reactions that is grounded in the
interactions between the constituent nucleons. We will replace current
phenomenological models of nuclear structure and reactions with a
well-founded microscopic theory that will deliver maximum predictive
power with minimal uncertainties that are well quantified.  To achieve
this goal requires a national effort linking theoretical physics and
computational science together to develop forefront software for
state-of-the-art architectures. We will build a national capability to
calculate nuclear structure and low-energy nuclear cross sections, and
assess their uncertainties relevant to several DOE programs. Nuclear
structure and reactions play an essential role in the science to be
investigated at the Rare Isotope Accelerator (RIA) and in nuclear
physics applications to the Science-Based Stockpile Stewardship Program,
next-generation reactors, and threat reduction.  In order to build this
capability, we will develop a multi-pronged program of theoretical,
algorithmic, and computational developments that will deliver nuclear
cross section information critical to DOE programs that is more accurate
than is currently available. We anticipate an expansion of the
computational techniques and methods we currently employ, and
developments of new treatments, to take advantage of petascale
architectures and demonstrate the capability of the leadership class
machines to deliver new science heretofore impossible.

# **I. Executive Summary** {#i.-executive-summary .Style4}

Our long-term vision is to arrive at a comprehensive and unified
description of nuclei and their reactions that is grounded in the
fundamental interactions between the constituent nucleons. We seek to
replace current phenomenological models of nuclear structure and
reactions with a well-founded microscopic theory that delivers maximum
predictive power with uncertainties that are well quantified.

In order to achieve this goal, we propose to build a national capability
to calculate nuclear structure and low-energy cross sections, and assess
their uncertainties. This capability requires a multi-pronged program of
theoretical, algorithmic, and computational developments that will
utilize leadership-class computation to solve several long-standing
fundamental problems in nuclear physics, and will deliver cross section
information that is more accurate than is currently available. DOE needs
this capability because in many instances experimental data are not
available or obtainable even with the construction of advanced exotic
beam facilities. Thus, a reliance on theory or extrapolations from known
data is required in order to make predictions. The proposed effort
entails both improving the predictive power of nuclear calculations by
connecting microscopic effective interactions to the basic nuclear
interactions, and assessing quantitative error estimates of the results.
We also anticipate an expansion of the computational techniques and
methods we currently employ, and developments of new treatments, to
utilize petascale architectures for new scientific discoveries in this
area.

The need to develop better theory for the description of nuclear
structure and reaction cross sections for various applications has been
pointed out in several high-level documents including the Nuclear
Science Advisory Committee (NSAC) 2004 Report: *A vision for Nuclear
Theory*; the NSAC 2005 Report: *Guidance for Implementing the 2002
Long-Range Plan*; and the DOE *Path to Sustainable Nuclear Energy*
(2005), which points to the need for cross sections in planning for the
advanced reactor technology.

During the past 10 years, the nuclear theory community has been pursuing
developments of sophisticated computational techniques to investigate
properties of nuclei based only on the underlying nuclear forces. These
developments have led to a new understanding of light nuclei using ab
initio many-body methods and heavier nuclei using self-consistent
mean-field techniques. Furthermore, the first steps have been taken to
understand nuclear reactions using ab initio techniques. This proposal
focuses on significantly expanding both our many-body and density
functional methods to calculate nuclear cross sections for a variety of
nuclei across the chart of nuclei. We have targets of opportunity that
are relevant to DOE missions. Light nuclear cross sections are important
in NIF and NNSA-related work; cross sections of drip-line nuclei will
shed light on their structure and dynamics relevant to Rare Isotope
Accelerator (RIA) research; neutron-induced reactions on a wide variety
of targets are important to the Stockpile Stewardship Program and
advanced reactor technology programs. Indeed, if we are to close the
fuel cycle in advanced-reactor technology, we will need to understand
neutron cross sections, nuclear decay, and fission on many nuclei
ranging from light to heavy systems. Calculation of neutron cross
sections requires a detailed knowledge of nuclear properties, and our
proposal addresses this issue. Theoretical error estimates for our cross
sections will be relevant to covariance studies for network evaluations.

The specific goals of this proposal are to *i)* calculate light nuclear
structure and reaction information using realistic nuclear potentials;
*ii)* describe medium mass and heavy nuclei with nuclear density
functional theory and its extensions; *iii)* incorporate new density
functional information into reaction cross section calculations
including the building of theoretically based optical potentials; *iv)*
develop a robust computational description of nuclear level densities;
*v)* integrate mathematical algorithms with science applications for
optimal performance; and *vi)* deliver to the community open-source
software for the calculation of nuclear cross sections relevant to the
various DOE missions. Verification of different methods with each other
and validation with experimental data will play an important role in our
efforts.

Summarizing, our team involves expertise in nuclear structure and
reactions ranging from light to heavy nuclei. We have our sights set on
a new generation of codes that will scale to the leadership-class
computers. These advances will enable us to use those new computers to
make calculations of ab-inito cross sections in light to medium-mass
nuclei, extensions to nuclear mean-field theory to enable calculations
of relevant information in medium-mass to heavy nuclei, and construction
of modern optical potentials based on these mean-field extensions.

# II. Background and Recent Accomplishments {#ii.-background-and-recent-accomplishments .Style4}

Virtually all microscopic theories for nuclear processes represent a
substantial computational challenge, and the past decade has seen the
exploitation of emerging computational capabilities to make spectacular
progress in a fundamental description of the structure of nuclei.
Confidence in our ability to accurately calculate nuclear structure and
dynamics has increased dramatically over the past ten years, due to
advances in theory, algorithms, and the historic advances in
computational power. In particular, first-principles approaches to light
nuclei - Green's Function Monte Carlo (GFMC), No-core Shell Model
(NCSM), and Coupled Cluster (CC) theory - have yielded important
information about nuclei, including uncovering the role played by the
three-nucleon interaction.

We now have firm evidence that the basic paradigm is correct; that
nuclear properties can be obtained starting from a realistic
nucleon-nucleon interaction and nuclear currents, with the addition of
comparatively smaller multi-nucleon interactions and currents. Our
confidence in this picture is based mostly on ab initio calculations in
the lightest nuclei, up to mass A = 12. Both GFMC and NCSM methods have
been used to accurately calculate the spectra of light nuclei, and both
methods were recently expanded in preliminary calculations of nuclear
reactions. CC methods were recently employed to investigate closed-shell
medium-mass nuclei and selected valence systems with 15 and 17 nucleons
from an ab initio point of view. We are unable to use ab-initio
techniques for all nuclei, and we turn to nuclear DFT for calculations
of global low-energy nuclear properties. Initial work using complex
basis states in shell- model diagonalization codes shows promise for
expansions to calculations of doorway states and other inputs that will
enable improvements of nuclear optical potentials and coupled-channel
reactions calculations. In the following, we briefly describe the
current status of techniques we will employ to reach our goal of
significantly improved nuclear cross section calculations.

**GFMC and AFDMC:** GFMC calculations \[[^1]\] using the AV18+IL2
interaction developed by members of this group, reproduce some 60
nuclear levels up to A = 12 with a RMS error of 0.7 MeV
\[[^2],[^3],[^4]\]. The reliability of GFMC, NCSM, and other methods has
been demonstrated in a benchmark calculation of ^4^He \[[^5]\].
Electroweak currents have also been successfully used with our wave
functions \[[^6]\]. Since the nucleon-nucleon interaction is strongly
spin- and isospin-dependent, these calculations are much more
computationally intensive than typical for a few-body quantum mechanical
problem. A GFMC calculation of the ^12^C ground state with a realistic
two- and three-nucleon interaction requires approximately 55,000 node
hours on the Bassi machine at NERSC. The code presently runs at 1.46
Gflops or 19% of peak on Bassi, but only at 9% of peak on Blue Gene
Light. GFMC is essentially a branching random walk with large sparse
linear algebra calculations on each node. Parallel efficiencies are
typically greater than 95% up to 2,048 processors for calculations up to
A = 10. However, the parallel efficiency for ^12^C is 70% of linear
speedup on only 256 and 384 processors due to the relatively large
granularity (in both memory and CPU time) of the current parallelization
scheme. Computer software approaches described in this proposal are
designed to improve both single-node performance and parallel efficiency
for the largest problems. We now believe the Hamiltonians and
computational algorithms are mature enough to address low-energy
scattering problems important in nuclear astrophysics and NNSA
applications. We previously completed calculations mixing microscopic
techniques with experimental data on low-energy scattering to calculate
low-energy capture reactions such as alpha-d and alpha-t capture
\[[^7],[^8]\]. These results have encouraged us to begin to develop
purely microscopic methods to treat low-energy scattering.

Auxiliary-Field Diffusion Monte Carlo (AFDMC) \[[^9]\] uses
auxiliary-fields to sample the spin and isospin degrees of freedom, and
diffusion Monte Carlo to sample the spatial degrees of freedom. The same
realistic Hamiltonians used by GFMC are used by AFDMC. Simulating
fermions requires a constraint similar to the fixed-node method. This
method has been very successful in calculating the properties of neutron
\[[^10]\] matter, including the equation of state and s-wave super-fluid
gap at low densities \[[^11]\]. These results are crucial to the
structure and cooling of neutron stars. Computationally, AFDMC is very
attractive in that it scales with a low-degree polynomial of the number
of particles. The calculations involve branching random walks with
significant computational effort in linear algebra at each step of the
walk. Simulations of more than 100 neutrons with realistic interactions
have been achieved.

**No-core Shell Model:** The No-core Shell Model (NCSM) is an ab initio
configuration-interaction (CI) approach based on effective interactions
derived from realistic two- and three-nucleon interactions \[[^12]\].
The CI basis is constructed within a harmonic oscillator basis, where an
exact separation between intrinsic and center-of-mass degrees of freedom
is possible. Convergence towards the exact result for a given nuclear
Hamiltonian is achieved by either 1) increasing the number of basis
states through the maximum number of oscillator quanta (N~max~), and/or
2) increasing the number of nucleons in the effective interaction
cluster. Computer codes to derive the effective interaction and to find
the eigenvalues of the many-body systems have been written in Fortran90
with MPI and MPI-I/O. Calculations with three-body effective
interactions with basis dimensions approaching 4 × 10^7^ have been
performed using approximately 3500 processors on THUNDER at LLNL. The
largest of these calculations typically require on the order of 30 PFlop
to find the fifteen lowest states, using the Lanczos algorithm with 500
iterations. The codes have led to a recent investigation of NN and NNN
potentials based on effective-field theory. The first-generation
reaction formalism in the NCSM has been developed \[[^13]\] and applied
to S-factors for reactions important for solar models such as
^7^Be(p,γ)^8^B \[[^14]\]. The NCSM codes are poised to exploit the
anticipated leadership class of computers and obtain forefront results
for nuclei in the sd shell and to bridge with the DFT approach by
producing *ab initio* nuclear wave functions.

**Coupled-cluster Method:** During the last three years, we have
developed a set of powerful theoretical tools
\[[^15],[^16],[^17],[^18],[^19]\] for the description of nuclear
properties using coupled-cluster theory \[[^20],[^21]\]. These
techniques solve for ground and excited states of a quantum many-body
system using exponentiated cluster excitation amplitudes. The
coupled-cluster equations are coupled, non-linear, algebraic equations
for the cluster amplitudes, which are solved iteratively.
Coupled-cluster methods for excited states \[[^22],[^23],[^24]\] require
the additional diagonalizations of non-Hermitian effective Hamiltonians.
We investigated single-reference methods and cluster expansions
involving one-particle one-hole (*1p-1h*) and *2p-2h* cluster amplitudes
(CCSD and EOMCCSD approximations), while computing estimates for the
contributions of *3p-3h* cluster amplitudes through a posteriori energy
corrections taken from \[[^25]\]. We also developed the CCSD/EOMCCSD
codes for density matrices and ground and excited states of valence
systems dominated by 1*p* and 1*h* excitations from the corresponding
closed-shell nuclei. The nuclear CCSD codes are written in Fortran90
with MPI and MPI-I/O. The remaining nuclear CC/EOMCC programs are, at
this time, efficient, fully vectorized serial codes. We performed
several calculations for ^4^He, ^16^O, and the A=15, 17 systems around
^16^O \[Error: Reference source not found,Error: Reference source not
found,Error: Reference source not found,Error: Reference source not
found,Error: Reference source not found\]. The largest calculation we
have attempted so far for ^40^Ca in a model space of seven shells
involves 2 million unknowns using 1024 processors of Seaborg at NERSC
(with 4 processors per node for computations at 400 Mflop/s/processor).
The total computation on this type of run is 7.2 peta-ops. The
computational requirements of CCSD and EOMCCSD scale as
*n~o~^2^n~u~^4^*. Here, $n_{o}$is the number of single-particle orbitals
below the Fermi surface, and $n_{u}$ is the number of orbitals above the
Fermi surface. Approximate inclusion of 3*p*-3*h* connected cluster
components can be accomplished with the relatively inexpensive
*n*~o~^3^*n~u~^4^* steps.

**Nuclear Density Functional Theory:** The main tool for understanding
heavier nuclei is mean-field theory. From the early days of restricted
application to magic nuclei and to qualitative justification of the
phenomenological shell model, the theory has blossomed in the 1990s to
become a powerful quantitative tool for all aspects of nuclear structure
in medium to heavy nuclei \[[^26]\]. The present self-consistent mean-
field theories are much like the density functional theory of condensed
matter, and the name "DFT" is used for the nuclear theory as well.
Essential to the success of the nuclear DFT was the development of
realistic energy-density functionals and increased computer resources.
We believe we can make a qualitative improvement in the reliability and
accuracy of the theory with another generation of functionals coupled
with the high-performance computing that is now available. This is
urgently needed for several reasons. DFT is the microscopic method of
choice to interpret the data from the upcoming generation of exotic beam
facilities. Also, DFT is at the basis of theories of dynamic processes
such as the ones controlling fission and low-energy reactions.

Highlights from DFT include the systematic application of the theory
over the entire chart of nuclei to calculate nuclear masses. In the
strict DFT approach, the achieved accuracy \[[^27],[^28]\] is a factor
of two better than the liquid drop model. For binding-energy
differences, however, the agreement with the data can be quite
impressive \[[^29]\]. Still, at present, comparable accuracy to the
benchmark finite-range liquid drop model \[[^30]\] is only obtained by
adding phenomenological terms for correlation energies \[[^31]\].

Recently, we performed a full DFT mass table evaluation for even-even
nuclei. Such global calculations require approximately 40
peta-operations to complete and were performed on 200 processors of an
IBM Power-3. These calculations did not restore the broken symmetries
present in the DFT, and they did not consider all nuclei. Future
progress will involve algorithmic developments that enable symmetry
restoration and nuclei with odd numbers of protons and/or neutrons. We
estimate a factor of 1,000 increase in computational needs in order to
accomplish this task.

Another major highlight is a qualitative improvement on the description
of excited-state properties using extensions of the DFT such as
particle-number and angular momentum projection, the Generator
Coordinate Method (GCM), and the fully self-consistent Quasiparticle
Random Phase Approximation (QRPA). In these extensions, there are no
parameters beyond those already fixed in the DFT functional. Two highly
non-trivial examples are a recent DFT/GCM treatment of coexisting
excited 0^+^ states \[[^32]\] and a DFT/QRPA description of multipole
strength in weakly bound nuclei \[[^33]\].

**Continuum Shell Model:** The nuclear shell model is the cornerstone of
our understanding of nuclei. In its standard realization, the shell
model assumes that the many-nucleon system is perfectly isolated from an
external environment of scattering states and decay channels. The
validity of such a closed quantum system framework is sometimes
justified by relatively high one-particle (neutron or proton) separation
energies in nuclei close to the valley of beta stability. However,
weakly bound or unbound nuclear states cannot be treated in the closed
quantum system formalism.

One possible strategy of tackling the continuum challenge is by using
the resonant state expansions, e.g., the Berggren ensemble
\[[^34],[^35]\] which consists of Gamow (Siegert or resonant) states and
the complex non-resonant continuum. The resonant states are the
generalized eigenstates of the time-independent Schroedinger equation;
they are regular at the origin and satisfy purely outgoing boundary
conditions. They correspond to the poles of the S-matrix in the complex
energy plane lying on or below the positive real axis. We generate a
single-particle basis using these states and use diagonalization
techniques to construct the many-body basis. Hence, both continuum
effects and correlations between nucleons are taken into account
simultaneously. These calculations are formative and have not yet been
ported to large parallel computers. They involve Krylov space
diagonalization techniques for very large non-Hermitian matrices. We
anticipate advancing the code to parallel systems in the early stages of
this proposal.

**Nuclear Level Density:** The level density is undoubtedly the most
important statistical nuclear property \[[^36],[^37],[^38]\]. Level
densities are needed to estimate transition rates (through Fermi's
golden rule) and are an integral part of the Hauser-Feschbach theory of
nuclear reaction cross sections. They therefore appear in numerous
nuclear physics applications, such as the neutron and proton capture
reactions in nucleosynthesis \[[^39],[^40],[^41]\] and reactions
pertinent to nuclear reactor engineering.

The level density and partition function are difficult to calculate in
the presence of correlations, and most theoretical estimates rely on
empirical modifications of Fermi gas models to account for shell
structure and pairing correlations. While the shell model is a suitable
framework for the microscopic calculation level densities, the required
model space is many orders of magnitude larger than spaces that are
treatable with conventional diagonalization methods.

This problem was largely overcome with the recent development of
auxiliary field Monte Carlo (AFMC) methods, also known as the shell
model Monte Carlo (SMMC), which enable calculations in very large model
spaces \[[^42],[^43],[^44]\]. Using a thermodynamical approach, SMMC
methods were implemented to calculate partition functions and level
densities \[[^45], [^46], [^47], [^48]\]. The sign problem was overcome
using good sign interactions that include the dominating collective
components of the nuclear interaction. Applications to iron-region
nuclei (A \~ 50-70) provided level densities that agree very well with
the experimental densities without any adjustable parameters \[Error:
Reference source not found\]. The SMMC code (with continuing software
and hardware performance enhancements) performs at roughly 300
Mflops/processor (and up to 350 depending on the application) on
Seaborg. Further enhancements beyond raw speed have given the code
another factor of 10 in overall efficiency. Code memory requirements are
roughly 200-400 Mbytes/processor. The code is also running on the XT3
and on BGL. In all cases, scaling is excellent to at least 2000
processors.

Another promising method is based on nuclear statistical spectroscopy,
in which the first few moments of the Hamiltonian are used to estimate
the level density \[[^49],[^50]\]. Improved results are obtained when
the model space is partitioned by single-particle configurations
\[[^51],[^52],[^53]\]. The ground-state energy needed for determining
the excitation energy can be calculated using AFMC or the exponential
convergence method \[[^54]\].

**Coupled-channels:** The coupled-channels technique has been applied to
elastic, inelastic, transfer, fusion and breakup \[[^55]\], and other
reactions. In many cases, it is important to include continuum states of
the projectile. One of the most successful ways of doing this is through
the Continuum Discretized Coupled Channels (CDCC) method \[[^56]\]. CDCC
was applied for instance to the two-body breakup reactions of ^8^B,
^11^Be, and ^17^F on light and heavy targets
\[[^57],[^58],[^59],[^60]\]. In all these, the projectile is taken as a
single-particle two-body system. In general, as the mass of the
projectile increases, more configuration mixing is to be expected. Thus,
it is essential for progress in this field to replace the
single-particle assumption for the projectile in the standard CDCC with
a multi-channel description. This has been our main goal: to develop an
eXtended theory of CDCC (XCDCC), where each projectile state is a
composition of several configurations. The first applications (to the
breakup of ^11^Be on ^9^Be) take one- half to one day on 16 processors
of an SGI Altix 3700. Presently, a new version of the code can run on a
loosely coupled AMD cluster with up to 256 threads. Test runs on the MSU
cluster machine are in progress.

**Reaction Models:** The Hauser-Feshbach statistical model has been used
over the years to calculate nuclear reaction cross sections for a wide
range of nuclei and incident energies. It is well established and has
been applied successfully to analyze and predict a large body of
experimental data. However, current implementations of this model are
limited in several ways. The model includes many phenomenological
parameters, and this weakens its predictive power. Only the total
emission energy spectra for the emitted particles and the inclusive
reaction cross sections can be assessed. Also, only the fission cross
section is calculated within this approach, and the subsequent decay of
the fission fragments is not tackled.

The pre-equilibrium process was formulated in a quantum mechanical
framework, which is an extension of the distorted-wave Born
approximation (DWBA) to the continuum. The model was applied to analyze
experimental data at high energies, and an effective interaction
obtained from the g-matrix theory gave a good agreement with
experimental data without any adjustable parameters.  However, the
current model has deficiencies in predicting cross sections at low
energies, and we need to validate the effective interaction in the low
energy region. In fission, the shape of a nucleus evolves from a single
ground-state shape to two separated fission fragments.  From observed
fission properties, one can conclude that at least five shape degrees of
freedom are required for studies of the potential energy of the system
as it evolves in shape. We identify the optimum saddle points by varying
all shape coordinates independently. Our calculated fission barrier
heights agree with experimentally deduced values fairly well.

# ![](media/image1.jpeg){width="1.7597222222222222in" height="3.3993055555555554in"}III. Proposed Research {#iii.-proposed-research .Style4}

Figure 1 illustrates our research path within this proposal. We begin
with nuclear interactions that describe the nucleon-nucleon scattering
data well. These interactions include those derived through effective
field theory \[[^61]\] as well as their slightly more phenomenological
cousins \[[^62],[^63]\]. These interactions, augmented by three-nucleon
potentials, serve as direct input into the various ab initio methods for
calculating nuclear structure and reactions. Our proposed efforts will
bring these methods to a new level of sophistication and will also
enable each method to be used for calculations of reaction data. The
investment in computational capability will enable us to explore how we
might reach mass-100 nuclei within an ab initio framework. The
improvements will also lead to better constraints on the energy
functional relevant to nuclear Density Functional Theory. For heavier
nuclei, DFT will be used to calculate nuclear properties relevant to a
description of nuclear reaction mechanisms. These include descriptions
of the ground-state energies, nuclear density, deformation, improved
optical potentials, and single-particle energies. Improved
energy-density functionals will also come from global fits to existing
nuclear data. Restoration of symmetries within the DFT framework is
computationally demanding and represents an important aspect of this
effort. Further developments will enable calculations of time-dependent
correlations such as giant-resonance states and nuclear lifetimes which
enter into a description of nuclear decay and reactions. We will also
investigate dynamical fission and calculate fission barriers of heavy
nuclei within this effort. Nuclear level densities enter into any
description of nuclear reactions, and we will enhance SMMC calculations
to tackle this important input for nuclei up to mass 250. We also
anticipate improvements to coupled-channel calculations (by improving
our theoretical descriptions of the optical potentials) and through
developments of codes that can predict pre-equilibrium emission.

In Section III.A, we outline the physics we propose to pursue in the
context of this proposal using several different methods of attack. All
methods are tied to reaction theory as they are going to be used to
directly calculate reactions or to calculate necessary input to reaction
calculations. Furthermore, the numerical techniques required to push the
physics forward will be explored. While several of our basic codes
currently perform on a variety of parallel platforms, they will require
significant modifications and improvements to reach our physics goals.
We outline several of the key issues in Section III.B.

## III.A. Nuclear Structure and Reactions {#iii.a.-nuclear-structure-and-reactions .Style-Heading-2-+-Justified}

The ab initio methods described in Section II employ already moderately
mature multiprocessor programs for structure calculations. Here we
propose extensions of the methods to larger nuclei than can currently be
done and, more importantly, extensions to computing scattering and
reactions. The first extension requires mostly computer science
developments, while the second requires both physics and computer
science work. An important part of this proposal is work with computer
scientists to enable use of leadership computers that will be needed for
the calculations being proposed. In addition, we also propose important
improvements in the physics done with these techniques. In almost all
cases, significant increases in computational capability are needed in
order to achieve physics results.

**Green's Function Monte Carlo:** (Carlson, Nollett, Pieper, Wiringa) In
addition to providing important benchmarks (see below), ^12^C
calculations have great scientific interest. We will work on computing
the first 0^+^ excited state which is the famous triple-alpha burning
resonance. GFMC calculations of the 0^+^ excited state require the
development of a suitable variational trial wave function that expresses
the 4p4h nature of this state. We expect to do this by making a
three-alpha particle wave function which is orthogonal to the ground
state. These and the benchmark ^12^C calculations require significantly
more computer power than we presently have routine access to. For
example, a single GFMC ^12^C ground state calculation needs 200 peta
operations. As is mentioned in Sec. II, ^12^C calculations are less
efficient than those for light nuclei; Sec III.B describes work to
address this problem.

Some preliminary results for the GFMC treatment of scattering are
currently being obtained by studying *n*-^4^He scattering and mapping
out the well-known 3/2^-^ and 1/2^-^ resonances, as well as the
non-resonant 1/2^+^ phase shifts. These GFMC results, again with and
without three-nucleon potentials, should provide good benchmarks for
other methods. We propose to extend the GFMC scattering calculations in
a number of directions during the next five years.

A straightforward extension is to low-energy scattering of nucleons from
other targets. Scientifically interesting cases are n-^6^He, n-^8^He,
and n-^9^Li. In the n-^8^He case, there is the experimentally unsettled
question of the parity of the ^9^He ground state, while n-^9^Li
scattering will investigate the also uncertain spectrum of ^10^Li. These
calculations will be relevant to experiments with unstable beams.
Calculations of n-^3^H will be compared to already existing reliable CHH
calculations as a further verification of the GFMC method and to data as
a validation of the isospin dependence of our best three-nucleon
potentials.

Electroweak capture reactions on light nuclei have great relevance to
nuclear astrophysics and to NNSA applications (Carlson, Hale,
Schiavilla). They are often suppressed processes (e.g., ^3^He(n,γ)^4^He
or ^7^Be(p,e+,ν~e~)^8^B) and therefore sensitive to small components in
the initial and final wave functions, the treatment of initial continuum
pre-capture states, and the contributions of many-body terms in the
nuclear electroweak current operator. Thus, comparison to experiment
will validate many aspects of our structure and scattering calculations
and the currents. Our present models of these currents are quite
successful, although some discrepancies between theory and experiment
persist, e.g., a 9% over-prediction of thermal-neutron capture on ^2^H
in which many-body currents contribute about 50% of the total cross
section.

We propose to make further refinements in the modeling of the nuclear
electroweak currents and to use them in GFMC calculations of weak and
radiative captures involving up to A=8 nuclei, such as ^4^He(d,γ)^6^Li
and ^4^He(t,γ)^7^Li. This will involve the development of
cluster-cluster boundary conditions and the coupling of the pre-capture
state to other open channels in the GFMC. A comparison of the GFMC (and
also NCSM) predictions for the ^3^He(n,γ)^4^He process with those
expected to be obtained from the hyper-spherical harmonics method in the
next three years will be an important verification of our results.

Individual scattering calculations are comparable in CPU needs to
bound-state calculations for the same number of nucleons, but one has to
do many more of them to map out the phase shifts as functions of the
scattering energy. The scattering energy, i.e., the energy above
threshold, which is the difference of two total energies, each with its
own statistical error, requires smaller individual statistical errors.

**No-core Shell Model:** The NCSM is a powerful ab initio method that
has been applied to nuclei up to A = 16 with three-body clusters and
excitations up to 6 oscillator quanta (N~max~ = 6). Better convergence
can be obtained by increasing the model space, i.e., N~max~, or the size
of the effective interaction cluster. We (Ormand, Navratil, Vary,
Barrett) plan several improvements and extensions to the NCSM formalism.
One goal is to extend calculations with three-body interactions to
N~max~ = 8 throughout the p-shell nuclei. The configuration space
dimensions are approximately 10 times larger than our current maximum
and over 30 GB of information is needed to specify just the effective
Hamiltonian. A rough estimate is that the computational effort would
increase by two orders of magnitude over the current scale. We will make
algorithm and code improvements to reduce this to a range of a factor of
10 which will be obtainable on peta-scale computers.

Next we will extend the effective interaction up to four-body clusters.
This may provide substantial improvement in describing not only the
low-lying states but also represents the best hope to correctly describe
alpha-clustering in the NCSM. Here the information needed to describe
the Hamiltonian increases dramatically, while the decrease in sparseness
leads to memory demands for the many-body matrices that are
approximately a factor of ten greater than currently used for three-body
clusters at N~max~ = 6. New codes to compute the effective interaction
and to diagonalize the many-body matrices will be built in collaboration
with computer scientists and mathematicians.

We will also "derive" a two-body interaction for sd-shell nuclei through
large N~max~ calculations for A=18, and using the Okubo-Lee-Suzuki
transformation \[[^64]\] projected to N~max~=0. The resulting two-body
interaction will be compared with empirically derived shell-model
interactions.

We will explore extensions and improvements to the NCSM formalism and
their computational implementation. An intriguing possibility involves
the formulation of the ω−οperator in the Okubo-Lee-Suzuki procedure
\[Error: Reference source not found\] for A-body calculations. In
current applications the ω−οperator does not satisfy the decoupling
condition in the many-body space between the active, P, and excluded, Q,
space. One can achieve decoupling to leading order by formulating the
ω-operator in terms of two-, three-, or *a*-body cluster excitations
from P-space states to the Q-space. With this formulation, we need to
find the eigenvalues of the product matrix of the form A^-1/2^BA^-1/2^,
where both A and B are matrices in the full model space. This may lead
to better overall convergence and solve several issues relating to
effective operators used to compute transition amplitudes. We will
devise and test algorithms to efficiently compute the inverse square
root and the eigenvalues of the product matrix. We will also use a
Hartree-Fock (HF) basis derived from a larger space, say N~max~=20. The
HF solutions, and the unitary transformation to the original oscillator
basis, form a new CI basis. With the HF basis, high lying 1p-1h
excitations are automatically included in the CI basis, giving an
improved description of the single-particle radial wave functions. We
will also analyze and mitigate the effect of spurious center-of-mass
motion induced by HF.

An extension of the NCSM to describe dynamic properties, such as nuclear
reactions, is an important step towards a complete description of
nuclear properties. We (Navratil) utilize an approach that builds upon
existing techniques such as the resonating-group method \[[^65]\], which
provides a microscopic formulation of the equations of motion. In order
to set up these equations one has to calculate a norm matrix of the
cluster basis states as well as the Hamiltonian matrix \[[^66]\], which
describes the intrinsic motion within the clusters as well as the
relative motion of the clusters. For the cluster basis states, we employ
projectile and target eigenstates obtained in their respective intrinsic
frame by diagonalizing the NCSM effective Hamiltonian. The task is to
calculate matrix elements of transposition operators as well as matrix
elements of products of interaction operators and transposition
operators. The NCSM allows this to be done while still preserving the
translational invariance of the problem. The formalism leads to a system
of coupled-channels integro-differential equations describing the
relative motion of the nuclei involved that needs to be solved
numerically.

**Coupled-Cluster Method:** We will extend the coupled-cluster (CC)
formalism to treat three-nucleon forces (TNF) (Dean, Papenbrock,
Piecuch). This implementation will be based on the factorized form of
the coupled-cluster equations for computations on parallel
architectures. With the inclusion of TNF, we will eventually have to
incorporate the connected 3*p*-3*h* clusters, at least approximately,
since they contribute to the first-order wave function when the TNF
terms are present in the Hamiltonian (they are second-order terms in the
wave function when only two-body forces are present). We will compute
the structure of medium mass nuclei with the TNF included. The results
will show us what part of the structure in heavier nuclei is affected by
the TNF. Possible deviations between theory and experiment will enable
us to better determine the TNF itself. An important question concerns
computational reductions of the TNF (through implementation of
*Higher-Order SVDs*, see below). Progress in this matter will enable us
to extend calculations with TNF to larger model spaces, and might also
improve our understanding of effective two-body interactions in
traditional shell-model problems with a core.

We will incorporate continuum states (for a description of resonances
and scattering states) into CC theory (Papenbrock, Dean). This approach
links CC theory with the Continuum Shell Model and is based on recent
work \[[^67]\]. This method allows for stable numerical calculations of
binary bound states, resonances, and anti-bound states. It determines a
complex on-shell and off-shell scattering matrix from realistic
nucleon-nucleon interaction. The combination of the contour deformation
and the CC methods will allow us to investigate scattering cross
sections in unprecedentedly large model spaces.

The single-reference coupled-cluster methods we have employed so far are
expected to work quite well for closed- and open-shell nuclei if the
unrestricted Hartree-Fock state can be used as a reference determinant.
In mid-shell and other open-shell cases, a symmetry-adapted
multi-reference description, where several determinants are used as
references, is usually more appropriate. The multi-reference
coupled-cluster (MRCC) methods are broadly classified as genuine
multi-state methods based on the Bloch wave operator formalism
\[22,Error: Reference source not found,[^68]\] and state-selective
approaches \[[^69]\] (see, e.g., \[[^70],[^71]\] and references therein
for further details). None of these MRCC methods have ever been tested
in nuclear studies. Based on the experience of quantum chemistry, we
believe that approximations as the state-universal MRCC (SUMRCC) theory
\[22,Error: Reference source not found\] will be useful for the nuclear
problems (Piecuch).

Recent years have witnessed large progress in application of these
methods using incomplete model spaces \[[^72]\], non-iterative
corrections due to higher-than-two-body clusters to SUMRCCSD energies
\[Error: Reference source not found,[^73]\], and the determination of
the most numerous core-virtual cluster amplitudes via arguments based on
many-body perturbation theory \[Error: Reference source not
found,[^74]\]. We also plan to investigate state-selective or
active-space CC/EOMCC approaches (Piecuch) \[Error: Reference source not
found,[^75]\] in which the most essential elements of MRCC are
incorporated into the usual single-reference CC/EOMCC formalism.

**Auxiliary-Field Diffusion Monte Carlo:** Auxiliary-Field Diffusion
Monte Carlo (AFDMC) will provide a link between microscopic studies of
light nuclei and density-functional studies of larger nuclei, and
calculate properties of nuclear and neutron-star matter. We will extend
present codes to study arbitrary mixtures of neutrons and protons and
then use these methods for light nuclei (comparing with other
techniques), larger nuclei, neutron drops, and nuclear matter (Schmidt,
Carlson). Since it samples the spins and isospins exactly, AFDMC can
provide accurate thermodynamic quantities for large systems.

We will also improve the accuracy of these methods to treat nuclei and
nuclear matter. Proposed AFDMC calculations include studies of
neutron-rich isotopes with a background potential used to simulate the
protons. These calculations can be directly compared with GFMC (Carlson,
Pieper) and could provide useful input for density-functional theory
(Carlson, Bertsch). We will also improve the trial wave functions which
provide the constraint to include pairing correlations. In the third
year of this proposal, we will perform studies of light nuclei with the
AV8 interaction to compare with GFMC and the NCSM. Subsequently, we will
study larger nuclei, including neutron-rich systems, with microscopic
interactions.

**Verification and Validation of GFMC, NCSM, CC, and AFDMC:** A few
years ago, a number of us participated in a successful benchmark paper
that verified seven methods for computing the ground state of ^4^He. We
propose to verify the GFMC, NCSM, and CC codes for the much more
difficult case of ^12^C and in some cases ^16^O (Pieper, Carlson,
Schmidt, Dean, Ormand, Piecuch). The first comparison will be for the
ground state using just a two-nucleon interaction. Subsequent further
tests will involve a three-nucleon potential and computation of excited
states and transitions between states. Finally, validation by comparison
with experimental values will also be done, although in this case, each
method will use its own best nuclear models, rather than the common
models used for verification.

We will also apply the computational theories that we use for light
nuclei to a problem related to trapped atomic condensates (Bulgac). This
is the theory of the two-component Fermi gas in the so-called unitary
limit. This is a particularly appealing theoretical problem because 1)
the Hamiltonian is simple and very well defined; 2) it can serve as a
testing ground for a large number of theoretical many-body techniques;
3) computational aspects are very demanding; 4) it is an approximate
model for dilute neutron matter; 5) its properties are relevant to
several physics fields. We will incorporate the Hamiltonian as an input
option to the codes for GFMC, CC, AFDMC, and NCSM, and compare the codes
on identical systems (number of particles and external potentials or
boundary conditions).

**Nuclear Density Functional Theory:** In many instances, particularly
in heavier nuclei, our method of choice to describe both structure and
inputs to reaction calculations is density functional theory. The
challenges we will address include: 1) developing a universal nuclear
DFT for reliable extrapolation; 2) developing the computer programs to
solve the DFT equations and its extensions without the computationally
motivated approximations needed in the past (i.e., artificially imposed
symmetries); 3) finding the optimal degrees of freedom for nuclear
many-body dynamics. Answering the above fundamental questions will be a
step toward our long-term goal of a reliable theory of the nuclear
large-amplitude collective motion, including fission and fusion, as well
as a microscopic theory of low-energy reactions.

In the near term, we will refit the Skyrme energy functional including
data on fission isomers, superdeformed states, and fission barriers.
This will help determine more reliably the surface terms such as the
surface-symmetry energy (Nazarewicz, Stoitsov). The goal is to improve
on the ability of the functional to describe highly deformed nuclei.

It is clear that current energy functionals, rooted in the Skyrme force,
are inadequate to go below the 0.7 MeV limit in the mass accuracy. Also,
current functionals leave room for significant improvement \[[^76]\]. In
particular, the pairing interaction should be re-parameterized with
microscopic guidance \[[^77]\], as it is not well determined in detail
by available data (masses and spectroscopy) (Duguet). We look for
guidance from the more fundamental ab initio methods presented in this
proposal, which emphasize the role of the pion as the longest distance
interaction and the dominant source of nuclear binding (Bertsch,
Furnstahl); one has reason to believe that inclusion of the pion in the
DFT functional may ameliorate some problems of the spectroscopy
\[[^78]\]. This requires a new DFT computer code that includes explicit
exchange, a computational challenging task (Bertsch). Finally, in the
region of nuclei overlapping the domains of ab initio theory and of DFT,
we will use the ab initio densities to first assess the reliability of
the DFT and then to modify the functionals to better reproduce the ab
initio results. We propose a comparison of density matrices for ^16^O,
^24^O, and ^24^Mg. The first two allow us to assess the reliability of
the DFT for isospin densities, an observable needed in weak current
studies, but one that cannot be measured well in other ways. The third
nucleus has important long-range correlations and will allow extensions
of DFT discussed below to be tested (Vary, Bertsch).

The present globally fitted DFT mass tables do not include time-odd
fields. Although they are significant for nuclei with an odd number of
protons and/or neutrons, those fields are largely unknown. As a
near-term project, we will use existing codes that treat time-odd fields
to perform new global fits of the Skyrme energy functional (Stoitsov,
Nazarewicz). In the longer term, we will develop and apply a code to
carry out the rotational GCM extension of the DFT for odd/rotating
nuclei (Duguet, Bender).

**Time-Dependent Nuclear DFT:** Time-dependent density functional theory
provides a robust approximation for calculating the nuclear response to
external fields such as the electric dipole response for the E1
absorption strength, the quadrupole response for E2 transition
strengths, and the axial vector response for beta decay and neutrino
absorption strengths. There are many different algorithmic formulations
for the theory applied to the response, otherwise known as RPA or
quasi-particle RPA. We will use the real time method \[[^79]\] for the
E1 absorption strength (Bertsch). It has the advantages that the
interaction kernel is automatically consistent with the static DFT, that
the entire spectrum can be calculated to a specified accuracy in a
single computation, and that the accuracy in the continuum threshold can
be readily enhanced by changing the box boundary conditions. We will
also use the matrix QRPA method to perform a systematic calculation of
β-decay rates across the chart of nuclides. Of particular interest are
the neutron-rich, r-process nuclei, in which deformation, pairing, and
continuum effects compete.

The DFT in the Kohn-Sham approximation incorporates short-range
correlation effects very well, but at present the long-range
correlations are most effectively treated explicitly. Most obviously,
the DFT states break symmetries such as translational and rotational
invariance, and restoration of those symmetries gives a very important
contribution to the energy for mass-table accuracies. There are two
approaches that will be pursued simultaneously. The first is to carry
out parameter-free microscopic calculations based on the DFT functional
treating the correlation degrees of freedom as described below (e.g. for
the quadrupole degree of freedom, cf. \[[^80]\]) (Duguet). As those
calculations are computationally difficult, we will also develop
approximate expressions for the correlation term that will capture the
essence of results of the microscopic calculations (Nazarewicz). In this
way, the hope is to develop a tractable parametrization of the
correlation energy in terms of simple properties of the DFT solution
that would allow an explicit inclusion of dynamical effects into the
energy functional.

We will also investigate methods that incorporate many degrees of
freedom into the DFT formalism. *(i) GCM:* A very promising extension of
the DFT is the Generator Coordinate Method (GCM); it treats collective
degrees of freedom at low excitation energy very well. Up to now, global
studies have been limited to a single degree of freedom, the axial
quadrupole deformation. The pairing field should be considered a dynamic
degree of freedom as well in global studies, and there are many nuclei
in which the octupole deformation plays a dynamic role \[[^81]\]. We
will first extend an existing code to treat simultaneously mass
quadrupole and pairing collective coordinates, together with projection
on angular momentum and particle number, and perform global applications
on masses and spectroscopy (Duguet, Bender). Next, the axial octupole
degree of freedom will be added. As this will require several orders of
magnitude greater computer resources than has been used in the past
\[Error: Reference source not found\], we will look for accurate
approximations in view of including even more modes. *(ii) Shell model
interface:* The configuration-interaction shell model (CISM) is another
major approach in nuclear structure physics. It has been successful in
describing the low-energy spectroscopy of nuclei and in providing
improved correlation energies. However, this approach often requires
many parameters, and they are different in various mass regions. At the
heart of nuclear structure physics are the single-particle degrees of
freedom, and improved DFT functionals can provide the necessary input to
shell-model treatment of these degrees of freedom. We intend to team
with shell-model practitioners to gain the benefits of both approaches,
namely the global applicability of the DFT approach, and the more
accurate treatment of the shell-model approach (Bertsch, Alhassid). In
addition to the single-particle Hamiltonian, there is also the promise
that some aspects of the effective shell-model interaction can be
extracted from the DFT \[[^82]\]. We plan to pursue this idea further.
Such a mapping of the DFT on a CISM Hamiltonian could provide a global
theory for calculating improved correlation energies and other
spectroscopic information.

We will also investigate fission barriers and dynamics in the context of
time-dependent DFT. Our mid-term goal is to calculate reliable potential
energy surfaces, including the fission and fusion barriers, for all
nuclei that are accessed by experiment or created in astrophysical and
other processes (Stoitsov, Nazarewicz, Goutte). This will be followed by
calculations of spontaneous fission lifetimes and mass and charge
divisions using dynamic adiabatic approaches based on the adiabatic
and/or semi-classical approximation. The DFT codes require treating
several constraining fields simultaneously. This is a challenging
computational problem and our first goal will be to compare existing and
proposed representations to determine which is the most efficient for
this problem. Contenders are harmonic oscillator representations and
coordinate space grid representations, including multiscale adaptive
grids. The long-term goal is to calculate the full fission dynamics,
including mass and energy distributions. We will investigate novel
microscopic (non-adiabatic) methods to do so. First the GCM provides a
clear conceptual framework for the dynamics which we want to pursue. The
first step in that direction has been already taken to describe the
barrier-top fission of Pu-240 with two collective degrees of freedom
\[[^83]\]. Second, we will assess whether the imaginary time method can
be used in practical self-consistent calculations.

**Gamow Shell Model:** The main challenge in the Gamow shell model is to
develop a realistic effective interaction. To better take into account
density-dependence and continuum-coupling effects, calculations with a
finite-range density-dependent interaction inspired by the Gogny force
are now in progress. The remaining major problems related to the
realistic Gamow shell-model calculations are the treatment of the center
of mass (essential, especially in the context of halo nuclei), and the
handling of very large shell-model spaces. The successful application of
the Gamow shell model to heavier nuclei is ultimately related to the
progress in optimization of the Gamow shell-model basis, related to the
inclusion of the non-resonant continuum configurations. A promising
development is the adaptation of the density matrix renormalization
group method \[[^84]\] to the genuinely non-Hermitian Gamow shell-model
problem in the complex-k plane using the j-scheme angular momentum
coupling.

The Gamow shell model can be used to describe direct reactions,
including transfer cross sections, spectroscopic factors, and
one-particle overlap integrals. We also propose to apply the Berggren
ensemble formalism and the complex-energy Hartree-Fock method to the
microscopic description of optical potentials in medium-mass and heavy
nuclei (Arbanas, Nazarewicz). An inherently poor energy resolution of
optical model potentials is a consequence of coarse averaging over many
compound resonances in a using a customary interval of 0.5 MeV; the lack
of information on nuclear structure that prohibits finer energy
resolution. With expected improvements in understanding of nuclear
structure of heavy nuclei, we can realistically attempt to develop a new
generation of optical potentials with energy resolution increased by at
least one order of magnitude. This new generation of optical potentials
ought to reproduce well-known intermediate structure in nuclear
reactions \[[^85]\]. We will accomplish this by explicitly accounting
for doorway states (e.g., 2p1h excitations), and hallway states (e.g.,
3p2h excitations) on the ground state of a heavy target, and by
incorporating their effects into the potential. This methodology will
also yield improved calculations of multi-step nuclear reactions
\[[^86]\], including radiative neutron capture.

**Level Densities:** A critical input to many reaction theories is the
density of states in the nucleus. While the optical potential defines
the overall magnitude of the reaction cross section, the level density
governs the decay probability through each of the open channels. In
particular, radiative capture is highly sensitive to the magnitude of
the level density, as is the threshold behavior for (n,2n) reactions.
Previously, most applications utilized variations of the Fermi-gas
estimate. We propose several microscopic approaches that include the
full effect of the residual interaction to compute level densities.
Again, an important goal is the integration of theoretical level
densities into existing reaction-theory codes, such as Hauser-Feshbach,
so that sensitivities error estimates in the computed cross sections can
be studied.

The first approach implemented here is the Auxiliary-Field Monte Carlo
(AFMC) \[Error: Reference source not found,Error: Reference source not
found,Error: Reference source not found\] applied to a shell-model basis
and Hamiltonian (Dean, Ormand). The AFMC approach readily yields the
energy of the system as a function of temperature in the canonical
ensemble. One then computes the level density by use of either the
saddle-point approximation or maximum-entropy reconstruction methods.
Projection of symmetries such as parity, angular momentum, partial
densities, and isospin can also be achieved in the AFMC method
\[[^87],[^88],[^89]\]. A limitation of the AFMC method is the fermionic
sign problem, and first studies will be limited semi-realistic pairing
plus multipole-multipole interactions \[[^90]\] that are free from this
problem. Later, the feasibility of a new approach to the sign problem,
called the shifted-contour method \[[^91]\], will be explored and
applied to finite nuclei. We plan to utilize the AFMC approach to
compute level densities and gamma-transition strength functions for a
wide range of nuclei important to DOE programs. The extension to heavier
nuclei, especially deformed nuclei in the *A*\~150-200 region, remains a
substantial computational challenge, and is a focus of this proposal.

The second approach is based on statistical spectroscopy \[Error:
Reference source not found,Error: Reference source not found\] in which
the first few moments of the shell-model Hamiltonian are computed
(Horoi, Brown, Zelevinsky, Volya). Here, configuration moments of the
Hamiltonian within the shell-model basis are computed, and the full
level density can be reconstructed using modified Gaussians or functions
suitable to reproducing the third and fourth configuration moments. If
fourth moments prove necessary, substantial improvements of existing
algorithms will be required. One obtains parity projection, and partial
level densities are obtained automatically through the partitions of the
model space. Projection onto angular momentum can be achieved with
suitable moment formulae \[[^92], Error: Reference source not found\].
The effective interactions will be obtained from the G-matrix and
applications of DFT. A systematic application to nuclei in the mass
region *A*\~50-250 is planned.

A significant challenge for shell-model approaches to level densities is
accurately accounting for excitations into multiple shells. Several
reactions of interest require the level density for excitation energies
up to 20-30 MeV. We will accomplish this by increasing the model space
to include multiple shells, or with methods that can extend the effect
of the mean field to higher temperatures \[[^93]\]. In addition to
increasing the computational complexity when several shells are
introduced, issues relating to spurious excitations of the
center-of-mass and the effect of the residual interaction coupling the
active shells \[[^94]\] must be addressed. With the powerful computer
programs developed in this proposal, we will investigate several
mitigation schemes for both of these issues.

**Microscopic Optical Potential:** A key input to theoretical
descriptions of many nuclear reaction theories is the optical potential.
For neutron-induced reactions, which are typically based on statistical
reaction theories such as Hauser-Feshbach, the optical potential defines
the reaction cross section. Optical potentials are also critically
important for theories of breakup reactions such as CDCC, as well as
direct reactions, such as transfer. The latter is a cornerstone of
indirect experimental methods such as surrogate reactions. At present,
empirical potentials fit to data are used. For nuclei lying outside the
range of the fits, such as those important for RIA, r-process,
Stockpile-stewardship, and advanced reactor applications, this can lead
to an unquantifiable uncertainty. 

We will develop computer codes to compute the optical potential from a
fully microscopic foundation (Thompson, Escher). The starting points for
deriving the optical potential are the bound and continuum wave
functions in the mean field obtained from accurate CI and/or DFT
calculations. Excitations around this configuration are then modeled to
find additional real and imaginary contributions to the optical
potential in the surface region. The leading part of these will
initially be derived from perturbation theory for particle-hole
excitations with a set of two-particle, one-hole equations within a
continuum basis using either Green's function or coupled-channels
methods to yield the dynamic polarization potentials. Later,
coupled-channels solutions (Thompson, Nunes) will be used to find the
effects of continuum-continuum couplings. Further effects of the
spreading width of these 2p-1h excitations can be included from later
coupled-channels or second-RPA calculations for three-particle, two-hole
excitation modes, possibly with some de-coherence assumptions, but
providing a yet more microscopically based optical potential. We plan to
first address spherical systems where definable symmetries exist that
simplify the equations, and then extend the formalism to deformed
nuclei. There are similarities between the perturbation approach here
and the continuum shell model. The methods will be compared for selected
nuclei where both approaches are valid.

**Coupled-channel Calculations:** We will continue developments of our
coupled-channel techniques to go beyond a single-particle description of
the projectile (Nunes, Thompson), thus allowing incorporation of two
degrees of freedom of the projectile in the reaction model
\[[^95],[^96]\]. These reaction models include core degrees of freedom
and require parallel algorithm development. Such a calculation scales
cubically with the number of channels. Ultimately, we will apply the
method to the extraction of capture reactions for which the breakup
reaction is often the only tool to extract the desired cross section.
Old techniques need to be reassessed for both memory requirements per
node and speedup. For example, it is not clear at present that partial
wave expansion of the scattering amplitude, used for over 40 years, is
still the most effective way of handling the numerical challenges.

**Improved Reaction Codes:** We will implement a full Monte Carlo
simulation of the Hauser-Feshbach statistical decay of a compound
nucleus, following the entire decay sequence, including the neutrons and
gamma-rays evaporated from the fission fragments (Kawano, Talou). In
each component, we utilize physical quantities obtained by the
microscopic theories such as effective two-body interaction, optical
potentials, and level densities. In this approach, exclusive cross
sections and spectra can be calculated exactly. In addition, important
correlations (in energies and angular distributions) among the emitted
particles can be studied. Those correlations are particularly relevant
to several programs of national security interest. Following the decay
of the fission fragments will also require significant improvements in
the modeling of the fission fragments mass and kinetic energy
distribution predictions.

For the fission model, a challenge is to reduce the high-dimensional
potential energy surfaces to some type of barrier (or barriers in the
case of multimode fission), and develop reaction cross section models
with enhanced predictability compared to earlier approaches based on
more phenomenological barriers (Moller). A goal is to develop models for
mass distributions, kinetic energies of the fission fragments, and the
number of neutrons emitted by the fragments.

## III.B. Computational and Applied Math Research Components {#iii.b.-computational-and-applied-math-research-components .Style-Heading-2-+-Justified}

The physics goals in III.A can only be realized with a close cooperation
between the physics and computer science collaborators in this proposal.
The issues range from algorithic, finding the optimal methodology, to
optimization on current artitechtures, to producing the scalable codes
appropriate for pentascale computers. All production codes will be
open-source and freely available.

### III.B.1. Performance Analysis and Code Improvements {#iii.b.1.-performance-analysis-and-code-improvements .Style-Heading-3-+-Justified .unnumbered}

**Benchmarking and Code Improvements:** We (Norris, Kaushik, Roche) will
define a suite of physical case studies for each of the key code bases.
The case studies will range in complexity from problems that were
production scale during the previous fiscal year to the problems that
define the mid- and long-term goals of the project. We will evaluate all
codes to identify performance bottlenecks and critical computational
kernels using the TAU \[[^97]\] suite of performance tools. These will
be incorporated into the code development process, enabling regular
evaluation of the effects of implementation changes. More detailed
performance evaluation, e.g., targeted memory trace analysis, cache
performance, and parallel performance, will be obtained with tools
developed by members of the PERC CET and their collaborators (Sigma++,
HPCToolkit, SvPablo, and Kojak). We will estimate performance
expectations for the code kernels by deriving performance bounds based
on source code analysis and using peak performance figures obtained from
benchmarks such as Stream instead of theoretical hardware peak numbers.

We will then focus on optimizing the performance of important numerical
kernels, working with the scientists to create high-level semantic
annotations of the computation, including optimization directives such
as memory alignments, loop unrolling, blocking, and tiling. Most of
these annotations will target multidimensional array operations (sparse
or dense). By providing a mathematical description of operations
previously hard-coded in low-level constructs, which compilers often
fail to optimize, we will enable the automated generation of optimized
code. This annotation-driven empirical optimization will have to be
redone only when the annotations are changed or the code must be ported
to a new platform.

While the above approaches are generally applicable, we have identified
some specific performance evaluation and tuning tasks. One case we will
consider is the GFMC code (Norris). Currently, each branching random
walk in the Monte Carlo simulation involves large, sparse, linear
algebra calculations on a single processor, which results in large
memory requirements and large fluctuations in CPU time on each
processor. Distributing this work over all cores of multi-core nodes
should improve performance. Other potential targets for
annotation-guided optimization include tensor-tensor products and other
array operations in very deeply nested loops (\> 4) in coupled-channel,
DFT, and other codes. We will also explore store/recompute strategies
for the large, sparse matrix diagonalizations in shell-model codes.

The alignment of the benchmarking effort with the production science
trajectory is essential for indicating barriers to algorithm scalability
(in both the physical and system parameter spaces) and provides a
baseline measure to indicate the progress made toward resolving the
science goals of this project over its duration. A reference code bank
for the case studies will be maintained and updated with regularity and
will be made available to the project participants. The codes and
completed case studies will additionally be used to calibrate novel
platforms (hardware + software) prior to production scale runs. This may
be critically important to identifying bugs in future operating systems,
compilers, or software libraries on future architectures as well as
problems with algorithms in the codes.  It will lead the task of
assisting the physicists in defining the physical suite of case studies
for their codes as well as create and maintain the actual code bank for
the project. The ORNL and ANL computer science teams will generate
baseline performance information for the case studies and subsequent
interpretation of gathered results.

For coupled-cluster application software, we will explore new
algorithms for both sparse and dense matrix-matrix and matrix-vector
operations to be computed for the four-tuple arrays that enter the
calculation matrix. For the largest applications, this code is a known
memory hog requiring the over-allocation of processing elements just to
store the problem in physical memory. The IBM Power systems and the Cray
XT3 will be the target platforms for the intial work (Roche, Dean).

DFT application software is dominated by BLAS3 operations and performs
very well. The challenge with this code will be to balance the need for
new algorithms for fast data redistribution with the need to have a very
capable load balance routine to handle mass table computations. For
instance, for light nuclei, the code over-allocates processors and thus
wastes hardware and has low system utilization, and new cutoff routines
will be incorporated to indicate how to stride through the Z-N plane
(Roche, Stoitsov).

Fault tolerance is an issue as the codes become more demanding of the
systems and systems continue to scale up the number of hardware
components. We will explore the idea of in-memory fault-tolerant
techniques starting with the AFMC application software. This code will
also be investigated on emerging hardware systems since it is naturally
parallelized, scales predictably, and reveals the behavior of some key
operations that couple the communication fabric with floating-point
computations such as global reductions. We will develop data
redistribution routines for key data decompositions (Roche, Dean).

NCSM codes have been ported to several parallel platforms utilizing MPI.
Two basic algorithms have been employed. The first (MFD) computes the
entire many-body matrix and preferably stores the matrix elements in
memory across many (1000s) processors to avoid performance degradation
caused by I/O. The second algorithm (REDSTICK) re-computes the many-body
matrix at every Lanczos iteration. Each approach has distinct advantages
and disadvantages under different conditions. We (de Supinksi, Ormand,
Vary), will profile the performance characteristics of both codes and
implement optimization procedures for both serial and massively parallel
applications. This activity will extend to the proposed versions that
will be designed to solve problems with four-body interactions.

An inefficiency for NCSM calculations is the inclusion of three-body
interaction in the effective interaction. We (Navratil) propose to
efficiently extend the current program from serial execution to exploit
massively parallel architectures. The performance characteristics of
this program will also be analyzed (de Supinksi, Navratil) and
performance optimizations will be integrated.

**Asynchronous Dynamic Load Balancing:** The GFMC code to be enhanced as
part of this proposal uses a "mananger/worker" algorithm. The
load-balancing component of this algorithm must be improved in order to
move this code from the terascale to the petascale (Lusk). The necessary
improvements are of a general nature and will be accomplished through
the design, implementation, and deployment of a dynamic asynchronous
load-balancing library (ADLB).

The present GFMC load-balancing method functions well on thousands of
processors. The execution of a work unit by a GFMC worker creates
further work units. These are kept locally in a queue, and only the
*length* of this queue is communicated to the manager. At predetermined
time steps, the manager examines the lengths of all the workers' queues,
determines an optimal redistribution, and directs workers with long
queues to send work units to workers with short queues; the latter are
told to receive the units.

This method results in 95% efficiency on various scalable machines, from
Linux clusters to the IBM Blue Gene system. In order to move into the
petascale regime, however, a new approach will be needed. With hundreds
of thousands of processors, the work units will need to be further
subdivided. A different load-balancing method, without central control
and without synchronization, will be needed.

The solution lies with *asynchronous* dynamic load balancing, in which
workers initiate load-balancing activities independently of the manager.
The idea is that a worker in need of more work directly contacts another
worker to obtain it. There obviously needs to be a way that the target
worker can be interrupted in the processing of its own current work to
give some of its queued work to the requesting worker. This requires
that the system software support, in a portable way, threads and a
thread-safe MPI implementation; such support is only now becoming
generally available. We will implement ADLB in a separate thread that
manages the work unit queue while the main thread executes work units.
Because the main thread can also initiate MPI communication, a
thread-safe MPI implementation is needed. The MPI-2 Standard \[[^98]\]
defines four levels of thread safety. ADLB will be usable regardless of
the level of thread safety implemented on a particular machine, but with
lower levels the application programmer will need to be more aware of
thread safety issues.

We will perform the following work: 1) The interface with ADLB will
allow user-defined functions for manipulating the work queue data
structures, requesting work units to work on and adding newly generated
work units to the queue. The interface will relieve the application
programmer from thread-management code and from the MPI communication
involved in load balancing. 2) The library will provide several standard
work-sharing algorithms and will also allow application-specific
load-balancing schemes. 3) The library will be written in C, but will
have bindings for various levels of Fortran, C, and C++. 4) The library
will be initially tested and refined with the GFMC code but will be
written for general use. 5) A specific goal will be the highly efficient
performance of GFMC on the next generation of leadership class machines
at Argonne, Oak Ridge, and at Berkeley. Based on our experience with
GFMC on the IBM BlueGene at Argonne, and with our prototype
multithreaded code using MPICH2 \[[^99]\], we are confident that new
scientific results from GFMC, enabled by ADLB, will be immediate. 6) In
the later years, we expect to add fault-tolerance features that we have
used in biology applications but which are not (yet) in the MPI
standard; this involves research into formulating a fault-tolerance
scheme for this type of load balancing. 7) We will incorporate ADLB into
COMPUNET as a component, in order to make it smoothly available across
this project and distribute it as high-quality, open-source,
well-documented software for use by the high-performance computing
community.

In summary, we have defined here a relatively straightforward project
with far-reaching implications. It is straightforward in that we have a
clear idea, based on experience, of what needs to be done to move GFMC
into the petascale regime on leadership class computers, producing
scientific results heretofore unavailable. Fortunately, the work needed
will produce a generally useful library for asynchronous dynamic load
balancing that can be used also by other advanced applications.

### III.B.2. Applied Math  {#iii.b.2.-applied-math .Style-Heading-3-+-Justified}

**Quadrature Schemes:** We (Fann, Shelton) will improve the quadrature
scheme for many-body calculations for certain basis (with Bertsch,
Nazarewicz and Dean). We will investigate the application of multi-scale
basis functions and multi-resolution analysis for modeling DFT and other
spectral expansions in nuclear physics. The application of low
separation rank methods for high-dimensional functions and operators
will be investigated for high-order precision (arbitrary but finite)
with a focus on overcoming the "curse of dimensionality;" (with Bertsch,
Vary, Dean, Nazarewicz, Ormand) in many-body nuclear physics. We will
also investigate the application of low separation rank methods in the
development of the CCSD method to obtain a sparse high-dimensional
tensor representation (Dean).

We will collaborate with the CET on "Advanced Algorithms and Methods for
Petascale Simulations" (AAMPS) to develop scalable generalized Gaussian
quadrature methods for fast integration of high dimensional functions.
We will apply these fast methods to nuclear density function theory and
n-body interactions problems and its formulation in terms of scattering
theory. This will be applied directly to Feshbach-Kerman-Koonin and
Hauser-Feshbach theory. We (Fann, Falgout, Ormand, Navratil) will test
NCSM improvements based on other formulations of the ω-operator and
implement efficient algorithms to compute the eigenvalues of a
symmetric, product matrix in which the inverse square root appears twice
in the product. We will also research optimal methods to solve
integro-differential equations on discretized grid with many coupled
channels for the reaction formalism of the NCSM. The 2-D work will
require production implementation \[[^100]\].

**Optimization:** The effort required to develop theories of nuclear
binding energy can be daunting due to the large number of parameters and
the large number of nuclei in the mass table. Current efforts, based on
the HFBTHO code, require new algorithms to reduce computing times and
extend our ability to handle additional parameters and nuclei. The
current approach \[28\] uses a mini-max method to fit a model to the
data, and restricts the parameter space so that linear methods can be
used. This approach reduces the amount of effort required for a fitting,
but on the other hand, is sensitive to the choice of the parameter space
and the sensitivity of the parameters, and thus requires fitting in
various subspaces. At present, there is no cost-effective, reliable
method for fitting the full nonlinear model.

We (Moré) propose to solve the fitting problem with the full nonlinear
model via algorithms in the Toolkit for Advanced Optimization (TAO). Our
work on nonlinear least squares will be extended to trust-region methods
for mini-max calculations. These methods are designed to handle
redundancy and achieve good fits to experimental data. The use of the
advanced optimization techniques in TAO is likely to achieve other
benefits such as a dramatic decrease in the number of HFBTHO binding
energy calculations when fitting the data and the ability to experiment
with different subsets of the parameters.

A mid-term aim will be the development of a toolkit that allows the use
of a wide variety of metrics. Although the current approach uses the
mini-max norm, the use of a least-squares objective, the l1 norm, or
Huber estimator may result in improved fitting procedures for a wide
range of calculations. We propose to use the ADIFOR and ADIC toolkits to
obtain the derivative information for the Skyrme energy functional.
These toolkits automatically produce accurate derivatives from the code
implementing the functional. Thus, changes can be made to the
computation of the functional without worrying about coding a new
derivative procedure. In addition, these toolkits can be used to provide
sensitivity information.

A long-term plan is to study fission pathways. These studies require the
development of optimization techniques for transition state (saddle
point) calculations. Presently, the study of transition states is
largely unexplored by the scientific computing community, but we have
developed the elastic string method that is guaranteed to find a
transition state for general problems. We will extend this work so that
all the peaks (mini-mizers) and valleys (saddle points) along the
fission pathway can be calculated by investigating the use of a p-norm
in the elastic string algorithm rather than the infinity norm. Another
approach is to subdivide the pathway into independent segments so that
multiple transition state calculations can be done.

**Higher Order SVD:** Currently the nuclear community uses spectral-type
methods with tensor product basis with global support which leads to
representations of functions which require large numbers of basis
functions. This leads to large dense matrices and the high cost of
function evaluations. Another issue is the "curse of dimensionality"
with existing methods: adding basis states and/or nucleons to our
calculations can dramatically increase the size and complexity of a
given calculation. In this section we describe some of the computational
mathematics approaches and algorithms for solving the coupled-cluster
model, the density functional theory, and further investigations into
the development and representation of high-dimensional functions and
basis for nuclear physics.

We will investigate the application of high-order singular value
decomposition (HOSVD) to 6-D tensors that arise when three-body
interactions are included in coupled-cluster computations (Fann). The
HOSVD algorithm is a generalization of the singular value decomposition
for matrices. We will be examining the HOSVD and its application to a
6-D tensor for controlled accuracy (Fann, Dean). In particular, we will
implement and test a serial HOSVD code based on alternating least square
and Zhang-Golub during the first year. In the second year, we will
develop a parallel version of this code with an optimized rank-k update
necessary for scalability \[[^101]\].

**Eigensolvers:** We will improve the performance of generalized and
real standard symmetric eigensystem solvers by using production versions
of the Parlett's holy-grail algorithm. This is currently one of the
fastest in serial and in parallel. This algorithm is coupled with a
reduction scheme that uses recursive Householder reductions. We will
couple some of these capabilities in the latest versions of LAPACK,
SCALAPACK with those of the PeIGS eigensolvers. Many of these
calculations are small (\~1K-2K) size eigen-system problems) that are
distributed. A parallel version may be required near the end for
load-balancing (Fann and Sheldon with Nazarewicz and Bertsch). This type
of load-balancing is built into the PeIGS software and will be added to
the LAPACK/SCALAPACK codes.

The No-Core Shell Model calculates the low-end of the eigen-spectrum of
a large sparse matrix using parallel implementations of the Lanczos
algorithm. For two-body interactions, the dimension of the Hamiltonian
operator reaches hundreds of million. The calculations have to be
extended to many-body interactions. As the number of nucleons increases,
the Hamiltonian becomes much sparser, but its dimension also increases
substantially. It's estimated that the dimension of the Hamiltonian can
reach billions for many-body interactions. We (Ng and Yang with Vary)
need to understand and analyze current implementations of the Lanczos
algorithm to determine its efficiency and scalability for many-body
interactions. There has been a lot of research in recent years on
efficient implementations of the Lanczos algorithms (such as in ARPACK
\[[^102]\]) and alternative approaches (including preconditioning
techniques and block algorithms \[[^103]\]) for eigen-analysis. Some of
these implementations and algorithms should be examined to determine if
they could be used to tackle the extremely large and sparse eigenvalue
problems in many-body interactions. This will provide opportunities for
new algorithmic developments.

We will study algorithms for the core parallel kernels such as the PBLAS
and parallel sparse matrix/ vector computations. It will be useful to
write a self-adapting parallel version of the key kernels that is
capable of interrogating the hardware it is running on to tune itself
for optimal performance. Another task to explore will be the behavior of
Gram-Schmidt orthogonalization without such frequent renormalization of
the vectors, which generates synchronizations that dramatically degrade
the performance due to a barrier in the communication layer. We will
also assist Fann in his efforts on these problems.

NCSM improvements based on other formulations of the w-operator might
have distinct benefits for ab initio methods that use effective
interaction theory. We (Falgout, Ormand, Navratil) will investigate the
efficacy of this extension and explore optimal algorithms for computing
the eigenvalues of the product matrix in which the inverse square-root
of a large matrix appears twice in the product.

### III.B.3. COMPUNET: The COMPUtational Nuclear EnvironmenT {#iii.b.3.-compunet-the-computational-nuclear-environment .Style-Heading-3-+-Justified}

One important goal of NSLER will be to develop a package of the relevant
computational codes that can be used by other communities
(experimentalists, NP, NNSA, and nuclear energy) to calculate relevant
cross section information. In order to meet the need, we plan to develop
the "Computational Nuclear Environment" (COMPUNET), a framework for the
integration of a broad range of nuclear physics computational tools for
the benefit of both developers and users in this project and in the
broader community.

The architecture of and approach to COMPUNET is informed by experience
with the design and implementation of other large-scale scientific
software environments. Examples are the NWChem parallel computational
chemistry package \[[^104]\] and more recent planning for the next
generation of a large-scale computational chemistry environment, as well
as the recently initiated SciDAC Center for Simulation of Wave
Interactions with Magneto-hydrodynamics (CSWIM) \[[^105]\] fusion
science project. Note that ab initio nuclear structure methods, and the
ways in which they are used, share much in common with the electronic
structure chemistry methods found in packages like NWChem.

The COMPUNET architecture will provide a very flexible and easily
extensible environment for the integration of the spectrum of nuclear
physics applications, both those specifically mentioned in this
proposal, and others from the broader community of developers and users
of nuclear structure and scattering simulations. A key idea behind our
approach is the development of common interfaces for different classes
of codes to interact (for example, structure codes with scattering
codes). Codes wishing to participate in COMPUNET should adapt their
existing interfaces to conform to the agreed common interface, and in
that way, for example, any COMPUNET scattering code should be able to
make use of any COMPUNET structure code. These interfaces may be in the
form of agreed standards for file formats, or application program
interfaces (APIs) at the software level. We expect that many COMPUNET
codes will initially exchange data via files, as they do now, but the
COMPUNET framework will facilitate the transition to a
higher-performance procedural coupling where it is needed.

A second level of integration in COMPUNET will be the reuse of utility
software across multiple codes. Disparate nuclear physics codes share
common needs for software infrastructure, both in the form of basic
utility functions, and numerical software, e.g., eigen-solvers and
linear solvers. The COMPUNET architecture will allow such functionality
to be provided in the framework, for use by any participating code. The
applied math work in this proposal will provide an additional common
link between the nuclear physics codes. Re-factoring nuclear physics
codes to use a common software infrastructure will also improve the
maintainability, robustness, and performance of the software because the
smaller code base will allow more focused work to improve it.
Throughout, we will work on an incremental and opportunistic basis --
prioritizing our work based on the needs and benefits from being
integrated into COMPUNET. The idea is to entice codes to participate in
the COMPUNET framework with the benefits such participation brings,
rather than forcing developers to conform to COMPUNET's standards.

In its implementation, COMPUNET will rely on the Common Component
Architecture (CCA) \[[^106]\] (of which Bernholdt is Lead PI, and Norris
and Sosonkina are participants) tools and techniques to aid in the
definition and use of common interfaces and to provide a plug-and-play
environment in which physics and infrastructure software components can
be assembled to execute a wide range of simulations.

As time permits, we will also pursue two other areas to extend both the
power and reach of the COMPUNET environment. The first is an archive to
allow the results of well-defined simulations to be captured, stored,
and retrieved -- avoiding the need for redundant calculations, and
facilitating scientific collaboration within the community. The second
is a simple web portal for education and for non-expert users (such as
experimentalists), providing access to some of the basic computational
capabilities of COMPUNET without the need to deploy the system locally
and worry about the details of input decks, along the lines of Vary's
Nuclear Physics Calculator \[[^107]\]. This work within the NSLER
project will focus on leveraging existing technologies from other SciDAC
and external projects, and adapting them to work with COMPUNET.

## III.C. Time table: milestones and deliverables {#iii.c.-time-table-milestones-and-deliverables .Style-Heading-2-+-Justified}

We highlight the principal goals to be achieved by the completion of
this proposal for each major component, as well as the yearly
deliverables to achieve the goals. Attaining many of these goals will
stress current and planned computational architectures, and we will
actively engage staff at the NCCS (ORNL), NERSC (Berkeley), and MCS
(ANL) to immediately use NSLER codes on leadership class machines to
pursue our important science problems.

**Ab initio nuclear structure:**

**Goal:** **Ab initio description of the ground state and excited states
of light nuclei with realistic NN and NNN interactions using Green's
Function Monte Carlo, No Core Shell Model, and Coupled Cluster methods**

**Year 1:**  Derive sd-shell interaction with the No-Core Shell Model
from A=18 nuclei and compare with empirical interactions (LLNL, ISU); 
Develop active-space open-shell coupled-cluster methods with 3*p*-2*h*
and 3*h*-2*p* excitations for nuclei with one particle or one hole
beyond the closed nuclei (MSU) and test the resulting codes on the
*A*=15,17 and *A*=39,41 systems (MSU, ORNL, UT).

**Year 2: ** Verify the Green's Function Monte Carlo (GFMC), no-core
shell model (NCSM), and coupled-cluster (CC) methods for ^12^C ground
state with NN interactions (ANL, LANL, LLNL, ORNL, ISU, MSU, UA)**; **
Extensive set of NCSM calculations for p-shell nuclei with three-body
interactions: A ≤ 16 up to N~max~=6, A ≤ 9 N~max~=8 (LLNL, ISU, UA);
**** Extend active-space CC methods to nuclei with 2 particles or two
holes beyond closed shell nuclei (MSU, ORNL, UT)

**Year 3: ** Verify GFMC, NCSM, and CC methods for ^12^C ground state
with three-nucleon interactions (ANL, LANL, LLNL, ORNL, ISU, MSU, UA)**;
** GFMC calculation of β decays and electron captures in *A*=6-8 nuclei
(ANL, LANL, ODU);  Develop computer programs for NCSM calculations with
four-body interactions (LLNL, ISU);  Complete development of
multi-reference CC algorithms for open-shell nuclei (MSU, ORNL); 
Develop tensor-tensor multiply algorithms to enhance the parallelism of
the CC codes (ORNL)**;**  Develop the initial variants of the genuine
state-universal multi-reference CC algorithms for quasi-degenerate and
open-shell nuclei (MSU) and initial tests (MSU, ORNL, UT).

**Year 4:**  Perform NCSM calculations with four-body interactions on
light p-shell nuclei (LLNL, ISU)**;**  Convert multi-reference CC
algorithms for scattering problems (MSU, ORNL, UT);  Complete work on
the nuclear state-universal multi-reference CC approach, including an
approximate treatment of 3*p*-3*h* excitations (MSU) and benchmark
calculations (MSU, ORNL, UT)**;**  Implement advanced tensor-tensor
multiply algorithms in the CC codes, enabling computations through mass
80 (ORNL, UT)

**Year 5:**  Compare experimental ^12^C ground state and excited states
(including the second 0^+^state) with computed using fully realistic
interactions by GFMC, NCSM, and CC techniques (ANL, LANL, LLNL,
ORNL)**;**  Calculate with no-core shell model four-body interactions
for 10 ≤ A ≤ 16 nuclei (LLNL, ISU)

**Ab initio nuclear reactions:**

**Goal: Complete ab initio description of light-ion reactions**

**Year 1:**  Compute scattering of n+^4^He with Green's Function Monte
Carlo (GFMC) (ANL, LANL);  Convert coupled-cluster (CC) codes to handle
complex basis states for reaction calculations (UT, ORNL);  Field
computer programs to compute the norm matrix and scattering potential
for a one-particle cluster reactions in the no-core shell model (NCSM)
formalism (LLNL)

**Year 2:**  n+^6^He and other nucleon-nucleus scattering reactions by
GFMC (ANL, LANL); **** Implement efficient algorithm to solve the
integro-differential equation for the NCSM reactions and apply to
n+^4^He (LLNL, ORNL); **** Verify GFMC and NCSM reaction methods for
n+^4^He with NN interactions**;**  Apply CC codes to a first
computation of scattering in medium mass nuclei (ORNL, UT)

**Year 3:** Extend norm matrix and scattering potential to two-particle
clusters for the NCSM reaction formalism and apply to deuteron induced
reactions (LLNL)

**Year 4:** Compute capture reactions by GFMC including many-body
current contributions (ANL, LANL, ODU)**;**  Extend norm-matrix and
scattering potential formalism to three- and four-particle clusters for
NCSM reaction formalism (LLNL)**;**  Calculate scattering processes
using CC technology developed in years 1-3 (ORNL, UT).

**Year 5:**  Multi-channel reactions like n+^6^Li → α+^3^H by GFMC
(ANL, LANL, ODU);  Apply the NCSM reaction formalism to alpha-induced
reactions (LLNL)**;**  Convert active-space and multi-reference CC
algorithms for quasi-degenerate and open-shell nuclei to investigate
nuclear scattering problems (MSU, ORNL, UT);  Develop a time-dependent
CC technology for nuclear dynamics (UT, ORNL)

**Density Functional Theory**

**Goal: Global theory of nuclear structure and improved fission
dynamics**

**Year 1:**  Include surface-sensitive data in the energy functional
(UW, UT)

**Year 2:**  Field capability of density functional theory (DFT)
mass-table calculations to include odd-mass nuclei (MSU, UT);  Improve
DFT functionals incorporating pairing, pion physics and in-medium
effects (UW, MSU, UT)

**Year 3:**  Global calculation of beta-decay rates with the
quasi-particle random-phase approximation (UT);  Global calculation of
dipole strength function by time-dependent DFT (UW, UT);  Systematic
multidimensional generator coordinate method (GCM) calculations of
masses and spectra (MSU); multidimensional-GCM/shell model interface
(MSU, UW);  Field capability of DFT mass-table calculations to include
odd-odd nuclei (MSU, UT)

**Year 4:**  Systematic calculation of fission potential energy
surfaces to the scission point including 3 GCM degrees of freedom (UT,
ORNL)

**Year 5:**  Improve methods for saddle points of energy surfaces (ANL)
and fission dynamics for actinide and transactinide nuclei (UT, ORNL); 
Calculate global nuclear mass table including ground-state correlations
(UT, UW, MSU, ANL)

**Nuclear-reaction theory**

**Goal: Theoretical description of nuclear reactions with microscopic
theories**

**Year 1:**  Develop serial and parallel computer programs to implement
algorithms to compute the optical potential for spherical nuclei (LLNL);
 Apply Auxiliary Field Monte Carlo (AFMC) and moment methods to compute
level densities for A \~ 40-60 nuclei; and compare of results (LLNL,
MSU);  Improve the treatment of the center of mass in Gamow Shell Model
(GSM) (UT, ORNL); Incorporate pre-equilibrium calculation code into
McGNASH (LANL)

**Year 2:**  Include the spreading width for intermediate states and
compute the optical potential for select spherical nuclei; compare with
experimental data and results from empirical potentials (LLNL)**; **
With singular-value-decomposition algorithms in AFMC computer codes,
extend calculations for mid-mass nuclei to multiple shells (ORNL,
LLNL)**;**  Evaluate the efficacy of methods to mitigate the sign
problem in the AFMC shell model (LLNL);  Optimize the non-resonant
component of the shell-model basis in GSM using the density matrix
renormalization group (UT, ORNL);  Apply the Berggren ensemble and the
complex-energy Hartree-Fock method to describe optical potentials in
medium-mass and heavy nuclei (UT, ORNL);  Develop a dynamic
microscopic/macroscopic fission theory (LANL);  Validate the G-matrix
two-body effective interaction used for pre-equilibrium calculations
(LANL);  Complete test of alternative methods that may represent a
solution to the bottleneck introduced by the partial wave expansion in
the extended coupled discretized continuum channels problem (MSU)

**Year 3:**  Construct the microscopic optical potential using the
Berggren ensemble (UT, ORNL);  Include microscopic optical potential
for mid-mass nuclei into Hauser-Feshbach codes (LLNL);  Include
microscopic level-densities for mid-mass nuclei into Hauser-Feshbach
codes (LLNL, ORNL);  Field serial Monte Carlo version of the McGNASH
code (LANL)  Incorporate new fission model into McGNASH to calculate
fission cross sections (LANL);  Benchmark XCDCC with a well measured
case which cannot be calculated today: ^8^B breakup into ^7^Be+p
including excitation of ^7^Be, to solve the controversy between two
independent measurements (MSU)

**Year 4:**  Extend algorithm for optical potential to deformed nuclei
and field requisite computer programs (LLNL)**;**  Validate optical
potentials derived from the continuum shell-model and perturbation
theory for select nuclei (UT, ORNL, LLNL);  Implement algorithm
improvements to extend AFMC shell model to heavier nuclei, A \~ 150
calculations (ORNL, LLNL);  Perform calculations with XCDCC for larger
mass isotopes increasing the number of configurations of the system
(MSU)

**Year 5:**  Extend AFMC shell model and moments method to A \~ 200
nuclei (ORNL, LLNL, MSU)**;**  Compute the optical potential for select
deformed nuclei and compare with experimental data and results from
empirical potentials, and integrate into Hauser-Feshbach codes (LLNL); 
Compute the optical potential for select nuclei with GSM and compare
with experimental data (UT, ORNL);  Complete full-scale Monte Carlo
Hauser-Feshbach calculations on parallel platforms (LANL);  Document
and release XCDCC code for public dissemination (MSU);  Compile results
of reaction calculations and evaluated data into data libraries for
dissemination (LANL, LLNL)

**Computer programs, algorithm development, and performance
enhancement**

**Goal: Integrate mathematical algorithms with science applications for
optimal performance**

**Year 1:**  Analyze the performance characteristics for key science
codes (ORNL, LANL, ANL, LLNL, ISU, LBNL);  Investigate and implement
higher-order singular-value-decomposition algorithms for compact
representations of 3-body forces (ORNL);  Develop implementation plan
for the COMPUNET (ORNL, ANL, Ames);  Investigate Lanzcos optimization
schemes in NCSM codes (LBNL)

**Year 2:**  Produce initial version of Asynchronous Dynamic Load
Balancing (ALDB) and integrate into GFMC code (ANL);  Incorporate TAO
methods and extensions into the HFBTHO DFT code (ANL);  Use ADIFOR and
ADIC to compute derivatives of energy functionals in DFT calculations
(ANL);  Implement singular-value-decomposition algorithms into
Auxiliary Field Monte Carlo computer codes (ORNL, LLNL);  Implement
performance enhancements in production codes (ALL);  Begin COMPUNET
implementation through common file interfaces (ORNL, ANL, Ames); 
Evaluate optimized implementations of Lanzcos and investigate
alternatives for NCSM calculations (LBNL)

**Year 3:**  Deploy general version of the ALDB library (ANL); 
Determine the efficacy of extension of the no-core shell-model to
cluster excitations from the active shell-model space -- testing of
algorithms for eigenvalues and the inverse-square root of matrices
(LLNL);  Analyze performance characteristics for new science production
codes (ALL);  Develop common utility software infrastructure for the
COMPUNET (ORNL, ANL, Ames);  Evaluate and compare alternative
eigen-solvers for NCSM (LBNL)

**Year 4:**  Documentation of science production codes intended for
public release (ALL);  Develop COMPUNET archive (Ames, ORNL, ANL); 
Optimize and implement alternative NCSM eigensolvers (LBNL)

**Year 5:**  Fault tolerant version of the ALDB library ready for
testing (ANL);  Automate system for annotation-driven code tuning (ANL,
ORNL);  Develop mechanism for public release of production codes
through the COMPUNET (ALL);  Perform final tests and installation of
alternative eigensolvers for NCSM (LBNL)

# IV. Overall budget {#iv.-overall-budget .unnumbered}

We request funds totaling \$21.6M for five years to carry out the work
and milestones outlined in Section III. We request \$4.06M in year 1,
and included escalations in out years. All institutions support travel
at an approximate level of \$4k per senior person per year. Here we list
institutional budgets and managers. The University of Tennessee (Dean)
requests \$1.4M to cover 2 post-docs, and 1 research professor. The
University of Washington (Bertsch) requests \$0.57M for 1 post-doc.
Michigan State University (Brown) requests \$1.2M for 2.5 post-docs.
Michigan State University (Piecuch) requests \$0.3M for 1.3 students.
Arizona State University (Schmidt) requests \$0.2M for 1 student. Iowa
State University (Vary) requests \$0.8M for 1 post-doc and 1 student
(joint with Barrett). Old Dominion University (Schiavilla) requests
\$0.3M for long term visitors. ORNL (Bernholdt) requests \$5M for 1.2
FTE/year and 4 post-docs. ANL (Pieper) requests \$3.5M for 0.35
FTE/year, 1.75 post-docs, and 1 programmer. LANL (Carlson) requests
\$2.3M for 0.5 FTE/year and 1.75 post-docs. LLNL (Ormand) requests
\$4.2M for 1.0/year FTE and 2.5 post-docs. Ames Lab (Sosonkina) requests
\$0.7M for 0.1 FTE/year and 1 post-doc. LBNL (Ng) requests \$1.0M for
0.3 FTE/year and 0.5 post-docs.

# V. Management plan {#v.-management-plan .Style4}

NSLER will be directed and managed by an executive committee. Initial
executive committee members are G. Bertsch (U. Washington), J. Carlson
(LANL), D.J. Dean (UT/ORNL), E. Lusk (ANL), W. E. Ormand (LLNL), S.C.
Pieper (ANL), and J. Vary (Iowa State). This executive committee cuts
across all major research efforts indicated in the proposal. The
PI/spokesperson (D.J. Dean) will represent the committee to the DOE and
other organizations supporting NSLER. The executive committee will be
responsible for organizing the two collaboration meetings per year,
produce the meeting report which will document progress on milestones,
and revise the annual budget as necessary due to changed circumstances.
The committee will be governed by majority vote with the spokesperson
casting a vote in the case of ties. Changes in composition of the
committee necessitated by circumstances will be made in consultation
with the DOE program officer(s).

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