> **V. THEORETICAL PHYSICS**
>
> **OVERVIEW**
>
> Our research addresses the five key questions that comprise the
> Nation\'s nuclear physics agenda. We place heavy emphasis on the
> prediction of phenomena accessible at Argonne\'s ATLAS facility, at
> JLab, and at other laboratories around the world; and on anticipating
> and planning for RIA. [Our program in theoretical and computational
> nuclear astrophysics addresses such issues as the origin of the
> heaviest elements through the actinide region and the basic mechanisms
> of supernova explosions, and serves to identify critical nuclear
> parameters and systematic properties to be explored with RIA.]{.mark}
> We employ quantum chromodynamics to explore the structure of light-
> and heavy-hadrons: in vacuum, as relevant to programs such as those
> pursued at JLab; and in-medium, as appropriate to the early universe,
> compact astrophysical objects, and the RHIC program. Interactions
> between light hadrons are studied via the development of reaction
> theories that exploit modern ideas of hadron structure, which are then
> used to predict the outcomes of experiments at; e.g., JLab, MIT-Bates
> and Mainz. The structure of atomic nuclei is explored in *ab-initio*
> many-body calculations based on the realistic two- and three-nucleon
> potentials we have constructed. These potentials give excellent fits
> to nucleon-nucleon elastic scattering data and the properties of light
> nuclei. In addition, we use quantum Monte-Carlo methods to, e.g.,
> compute nucleon-nucleus scattering phase shifts, transition
> amplitudes, and a variety of electroweak reactions important to
> astrophysics. Our nuclear structure and reaction program includes:
> coupled-channels calculations of heavy-ion reactions near the Coulomb
> barrier; calculations of observables in breakup reactions of nuclei
> far from stability, the determination of radiative capture rates from
> Coulomb dissociation experiments, and studies of high-spin deformation
> and the structure of the heaviest elements. Our programs provide much
> of the scientific basis for the drive to physics with rare isotopes.
> Additional research in the Group focuses on: atomic and neutron
> physics; fundamental quantum mechanics; quantum computing; and tests
> of fundamental symmetries and theories unifying all the forces of
> nature, and the search for a spatial or temporal variation in
> Nature\'s basic parameters. The pioneering development and use of
> massively parallel numerical simulations using hardware at Argonne and
> elsewhere is a major component of the Group\'s research.

**C. NUCLEAR ASTROPHYSICS**

The objective of this research program is to investigate nuclear
processes that take place in stars, in the big bang, and in interstellar
and intergalactic space. Nuclear phenomena are ubiquitous in the
universe. The stars shine by nuclear energy, and the chemical
compositions observed in the solar system and elsewhere are the results
of nuclear processes that occurred in the big bang and inside the
several generations of stars that have formed since then. Many
astrophysical phenomena may only be understood by a combination of
nuclear physics with methods more familiar to astrophysicists.

A particularly important problem is to determine rates for the nuclear
reactions that occur in astrophysical environments. There are many
applications (for example, the rapid neutron capture process) where
large contributions from theoretical nuclear physics -- particularly
masses and cross sections - will always be necessary as input, and we
maintain research interests in these areas. We have applied advances in
the theoretical descriptions of light nuclei to compute cross sections
important for big-bang nucleosynthesis, the solar neutrino flux, and
seeding of the\
*r*-process. This work continues in close connection with our other work
on light nuclei, and the main goals at present are to improve the wave
functions and computational methods as described in section b.2. In the
last year, we have participated in work to improve the computational
methods used to compute weak-interaction rates important for the
collapse and subsequent supernova explosions of massive stars. In
addition, studies are underway of electroweak reaction rates relevant to
astrophysical processes in dense nuclear matter. These are a part of our
attempt to predict observable features of quark matter in compact
astrophysical objects.

Understanding nucleosynthesis and energy generation in a particular
astrophysical environment requires calculations of nuclear reaction
networks. Even for cases in which the detailed astrophysical phenomena
can only be understood from difficult calculations coupling a reaction
network and hydrodynamics, simpler network calculations can identify the
crucial reactions and other nuclear properties to be determined by more
detailed theoretical and experimental work. Ongoing work in this area
involves big-bang nucleosynthesis, nuclear burning in low-mass stars,
and photon-nucleus reactions in high-energy cosmic rays.

A major goal of nucleosynthesis studies is to determine the specific
physical conditions that gave rise to abundance patterns seen in nature:
what mix of different kinds of stellar environments gave rise to
observed chemical compositions? Large amounts of important new data on
abundance patterns are now being collected, with important evidence
arising from low-metallicity stars in our own galaxy, absorption-line
systems backlit by distant quasars, and primitive inclusions and
pre-solar grains embedded in meteorites. These data contain important
clues about the nucleosynthetic history of the universe, both locally
and globally, and the effort to disentangle the clues into information
on stellar sources and galactic chemical evolution is necessarily
coupled to our work on nucleosynthesis. Close connections between these
observational studies and researchers in the theory group have been
fostered by participation in the Joint Institute of Nuclear Astrophysics
(JINA).

Nucleosynthesis and chemical evolution are increasingly important probes
of the overall star formation history of the universe. The first stars
had a very simple composition produced by the cosmological big bang:
only hydrogen, deuterium, ^3^He, ^4^He, and ^7^Li. Stars and supernovae
synthesize essentially all other nuclei, from carbon through uranium,
and eject them into the interstellar gas from which subsequent
generations of stars form. The heavy-element inventory (metallicity)
builds up over time, and the history of this process is written in the
compositions of the stars and gas in our Galaxy and other galaxies as
functions of their age. Contributions both from massive stars (*M \> 10
M~~*) with their associated Type II supernovae and from thermonuclear
(Type Ia) supernovae are particularly important in this process. Our
studies of the nuclear physics of nucleosynthesis, of the natures of the
sites of nucleosynthesis, and of the compositions of the stars as a
function of age all contribute to efforts to understand the overall star
formation history of the universe.

**c.2. Sedimentation and Type I X-Ray Bursts at Low Accretion Rates**
(F. Peng,\*

E. F. Brown,† and J. W. Truran‡)

An ionized plasma in a gravitational field develops an electric field
sufficient to levitate the ions and ensure overall charge neutrality.
When there is more than one species of ion present, the ions will
experience a differential force: lighter ions float upward (defined by
the local gravitational field) and heavier ions sink downward. The high
surface gravity of compact objects makes the timescale for isotopes to
stratify often comparable to or faster than other timescales of
interest. In particular, sedimentation of heavier isotopes is important
in understanding the surface compositions of white dwarf stars (Vauclair
*et al.* 1979) and isolated neutron stars (Chang & Bildsten 2003). For
accreting white dwarfs, diffusion between the accreted envelope and
underlying white dwarf was proposed as a means to enrich the ejecta of
classical novae in CNO isotopes (Prialnik & Kovetz 1984; Iben, Fujimoto,
& MacDonald 1992).

Accreting neutron stars, with their strong surface gravity *≈ 2 ×
10^14^* cm s^-2^, are an ideal place to look for the effects of
sedimentation. The sedimentation of heavy elements and resulting
nucleosynthesis in the envelope of isolated neutron stars cooling from
birth was first described by Rosen (1969) and has more recently been
studied in detail by Chang & Bildsten (2003, 2004). For accreting
neutron stars, the rapid stratification removes heavy nuclei from the
photosphere for accretion rates *dM/dt ≤ 10^-12^ M~~* yr^-1^ (Bildsten,
Salpeter, & Wasserman 1992). Deeper in the neutron star envelope, the
differentiation of the isotopes can alter the nuclear burning, namely
unstable H/He burning and the rapid proton-capture process
(*rp*-process), that powers Type I X-ray bursts. Some estimates of the
relative importance of sedimentation and diffusion were made by Wallace,
Woosley, & Weaver (1982), who studied accretion at rates\
*dM/dt = 2×10^-11^ M~~* yr^-1^ and argued that the partial separation
of the H and He layers might play a role in setting the ignition
conditions and subsequent burst nucleosynthesis.

Neutron stars, with their strong surface gravity, have interestingly
short timescales for the sedimentation of heavy elements. Motivated by
observations of Type I x-ray bursts from sources with extremely low
persistent accretion luminosities, *L~X~ \< 10^36^* ergs s^-1^ (*0.01*
L~Edd~), we study how sedimentation effects the distribution of isotopes
and the ignition of H and He in the envelope of an accreting neutron
star. For local mass accretion rates *dm/dt \< 10^-2^ dm~Edd~/dt* (for
which the ignition of H is unstable), where *dm~Edd~/dt = 8.8 × 10^4^* g
cm^-2^ s^-1^, the helium and CNO elements settle out of the accreted
fuel layer before the temperature is reached at which H would ignite.
Using one-zone calculations of the thermonuclear burning, we identify a
range of accretion rates for which the unstable ignition of hydrogen
does not trigger unstable helium burning. This range depends on the
emergent flux from reactions in the deep neutron star crust; for\
*F = 0.1* MeV \[*(dm/dt)/m~u~\]*, the range is

*3 × 10^-3^ dm~Edd~/dt ≤ dm/dt ≤ 10^-2^ dm~Edd~/dt*.

We speculate that sources accreting in this range will build up a
massive He layer that later produces an energetic and long X-ray burst.
At mass accretion rates lower than this range, we find that the hydrogen
flash leads to a strong mixed H/He flash. Surprisingly, even at
accretion rates dm/dt ≥ 0.1 dm~Edd~/dt, although the H and He do not
completely segregate, the H abundance at the base of the accumulated
layer is still reduced. While following the evolution of the x-ray burst
is beyond the scope of this introductory paper, we note that the reduced
proton-to-seed ratio favors the production of ^12^C, an important
ingredient for subsequent superbursts.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

\*University of Chicago, †Michigan State University, ‡Argonne National
Laboratory and University of Chicago.

**c.3. Capturing the Fire: Flame Energetics and Neutronization for Type
Ia**

**Supernova Simulations** (J. W. Truran,\* A. C. Calder,† D. M.
Townsley,†

O. E. B. Messer,‡ I. R. Seitenzahl,† F. Peng,† N. Vladimirova,† E. F.
Brown,§ and

D. Q. Lamb†)

Type Ia supernovae (SNe) are bright explosions characterized by a lack
of hydrogen spectral features and strong silicon *P Cygni* features near
maximum light. The currently favored interpretation is the disruption of
a near-Chandrasekhar-mass C/O white dwarf by a thermonuclear runaway.
These events are fascinating in and of themselves and are important both
for their contribution to the cosmic abundance of iron-peak elements and
for their role as standard candles.

Models of Type Ia SNe necessarily involve a mechanism for incinerating
the star by a thermonuclear runaway, and the nature of this mechanism is
the subject of contemporary research. In the explosion, a thermonuclear
flame propagates through the C/O fuel of the white dwarf as either a
subsonic deflagration front or a supersonic detonation wave and releases
sufficient energy to unbind the star. However, models involving either a
pure deflagration or a pure detonation have traditionally been unable to
provide an explanation for both the observed expansion velocities and
the spectra produced by ejecta that are rich in both intermediate-mass
and iron-peak elements. Recent work, however, suggests that a fast
deflagration alone may provide sufficient energy to unbind the star.

There has been considerable progress recently in hydrodynamic
simulations of deflagrations of C/O white dwarfs that model the entire
star. This is a complicated endeavor, predominantly due to the vast
range of length scales: the laminar flame width is\
*\~ 10^-3^ -- 10* cm, some 8 to 12 orders of magnitude smaller than the
stellar radius. Because the computational requirements for simulations
with these disparate scales demand resources well beyond current
capabilities, multidimensional Type Ia models must make use of an
appropriate sub-grid-scale model for the evolution of the thermonuclear
burning front. Moreover, large-scale simulations are very demanding of
computational resources, and it is not feasible at present to include
enough isotopes to allow for directly computing the reaction kinetics. A
realistic model must nevertheless accurately describe the nuclear energy
that is released, the timescale on which it is released, and the
compositional changes that occur in the flame. In addition, the burned
material continues to evolve after the passage of the flame due to both
weak interactions and hydrodynamic evolution, and realistic simulations
must describe this \"post-flame\" evolution.

This paper presents a study of the nuclear burning that occurs during
C/O deflagrations, with the goal of providing a realistic flame model
for simulations of Type Ia supernovae. Our flame model builds on the
advection-diffusion-reaction model of Khokhlov and includes electron
screening and Coulomb corrections to the equation of state in a
self-consistent way. We calibrate this model flame--its energetics and
timescales for energy release and neutronization--with self-heating
reaction network calculations that include both these Coulomb effects
and up-to-date weak interactions. The burned material evolves post-flame
due to both weak interactions and hydrodynamic changes in density and
temperature. We develop a scheme to follow the evolution, including
neutronization, of the nuclear statistical equilibrium (NSE) state
subsequent to the passage of the flame front. As a result, our model
flame is suitable for deflagration simulations over a wide range of
initial central densities and can track the temperature and electron
fraction of the burned material through the explosion and into the
expansion of the ejecta.

The importance of such a detailed consideration of the consequences of
nuclear burning and neutronization via electron captures is to provide
an accurate determination of the ^56^Ni abundance in the ejecta of a
Type Ia supernova. For a value of *Y~e~ ≈ 0.5*, the matter in nuclear
statistical equilibrium following expansion and cooling is dominated by
the self-conjugate nucleus ^56^Ni. At high densities, however, electron
captures on both protons and heavy nuclei effect neutronization of the
matter and *Y~e~* falls below *0.5*. Such neutron enrichment favors
neutron-rich isotopes at the expense of ^56^Ni. Since the brightness of
SNe Ia at maximum is a direct function of the mass of ^56^Ni ejected, an
accurate determination of the composition of the ejecta is critical to
the use of SNe Ia as distance indicators.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

\*University of Chicago and Argonne National Laboratory, †University of
Chicago, ‡University of Chicago and Oak Ridge National Laboratory,
§Michigan State University.