**RIA Theory Bluebook: A Road Map**

**A Report from the RIA Theory Group**

**May 2005**

![](media/image1.png){width="4.024305555555555in"
height="5.990972222222222in"}

Ode to Nature: IV, Copyright Julio Mateo, 1985

> Used by permission from the artist.
> [www.mateo.net](http://www.mateo.net/).

[Executive Summary 3](#executive-summary)

[I. Overview of RIA Theory 5](#i.-overview-of-ria-theory)

[II. Scientific Connections and Societal Impacts of RIA Physics
6](#ii.-scientific-connections-and-societal-impacts-of-ria-physics)

[II.A. Intersections of nuclear physics and astrophysics
6](#ii.a.-intersections-of-nuclear-physics-and-astrophysics)

[II.B Connections to neutrinos and fundamental symmetries
6](#ii.b.-connections-to-neutrinos-and-fundamental-symmetries)

[II.C. Connections to mesoscopic systems
6](#ii.c.-connections-to-mesoscopic-systems)

[II.D. Connections to computational sciences
6](#ii.d.-connections-to-computational-sciences)

[III. RIA Theory Detailed Road Map: Goals and Strategies
6](#iii.-ria-theory-detailed-road-map-goals-and-strategies)

[III.A. Nuclear structure 6](#iii.a.-nuclear-structure)

[III.A.1. Develop ab initio structure and reaction theory
6](#iii.a.1.-develop-ab-initio-structure-and-reaction-theory)

[III.A.2. Develop an understanding of the nature of effective
interactions and operators used in nuclear structure models
6](#iii.a.2.-develop-an-understanding-of-the-nature-of-effective-interactions-and-operators-used-in-nuclear-structure-models)

[III.A.3. Develop predictive density-functional theory for nuclei and
nuclear matter
6](#iii.a.3.-develop-predictive-density-functional-theory-for-nuclei-and-nuclear-matter)

[III.A.4. Develop many-body theories of nuclear collective dynamics,
including the large amplitude collective motion and nuclear decays
6](#iii.a.4.-develop-many-body-theories-of-nuclear-collective-dynamics-including-the-large-amplitude-collective-motion-and-nuclear-decays)

[III.A.5. Develop unified treatment of bound states and open channels
6](#iii.a.5.-develop-unified-treatment-of-bound-states-and-open-channels)

[III.B. Nuclear reactions 6](#iii.b.-nuclear-reactions)

[III.B.1. Understand the essential role of intermediate and final
continuum states in reactions with weakly bound and exotic nuclei
6](#iii.b.1.-understand-the-essential-role-of-intermediate-and-final-continuum-states-in-reactions-with-weakly-bound-and-exotic-nuclei)

[III.B.2. Extend reaction models to include the dynamics of two-particle
continuum
6](#iii.b.2.-extend-reaction-models-to-include-the-dynamics-of-two-particle-continuum)

[III.B.3. Incorporate new structure information in peripheral reaction
models of collective and/or valence nucleon transitions
6](#iii.b.3.-incorporate-new-structure-information-in-peripheral-reaction-models-of-collective-andor-valence-nucleon-transitions)

[III.B.4. Improve the microscopic structure in cluster reaction models
6](#iii.b.4.-improve-the-microscopic-structure-in-cluster-reaction-models)

[III.B.5. Develop theoretical techniques to extract reaction rate
information from indirect methods
6](#iii.b.5.-develop-theoretical-techniques-to-extract-reaction-rate-information-from-indirect-methods)

[III.B.6. Develop theoretical methods that describe fusion of heavy
nuclei
6](#iii.b.6.-develop-theoretical-methods-that-describe-fusion-of-heavy-nuclei)

[III.C. Nuclear matter equation of state
6](#iii.c.-nuclear-matter-equation-of-state)

[III.C.1. Develop statistical approaches to phase transitions and
cluster formation in asymmetric nuclear matter
6](#iii.c.1.-develop-statistical-approaches-to-phase-transitions-and-cluster-formation-in-asymmetric-nuclear-matter)

[III.C.2. Develop a quantum transport theory for complex reactions
6](#iii.c.2.-develop-a-quantum-transport-theory-for-complex-reactions)

[III.C.3. Identify the role of isospin degree of freedom in the dynamics
from peripheral to central reactions
6](#iii.c.3.-identify-the-role-of-isospin-degree-of-freedom-in-the-dynamics-from-peripheral-to-central-reactions)

[III.C.4. Determine observables constraining the equation of state and
phases of asymmetric matter from sub- to supra-normal nuclear densities
6](#iii.c.4.-determine-observables-constraining-the-equation-of-state-and-phases-of-asymmetric-matter-from-sub--to-supra-normal-nuclear-densities)

[III.D. Nuclear astrophysics 6](#iii.d.-nuclear-astrophysics)

[III.D.1. Understand nucleosynthesis in the first generation of stars
6](#iii.d.1.-understand-nucleosynthesis-in-the-first-generation-of-stars)

[III.D.2. Develop quantitative nuclear microphysics for core-collapse
supernova to understand the explosion mechanism and the origin of the
heavy elements
6](#iii.d.2.-develop-quantitative-nuclear-microphysics-for-core-collapse-supernova-to-understand-the-explosion-mechanism-and-the-origin-of-the-heavy-elements)

[III.D.3. Understand the nucleosynthesis of thermonuclear supernovae
6](#iii.d.3.-understand-the-nucleosynthesis-of-thermonuclear-supernovae)

[III.D.4. Understand nova nucleosynthesis
6](#iii.d.4.-understand-nova-nucleosynthesis)

[III.D.5. Use X-ray binaries to understand neutron star structure
6](#__RefHeading___Toc99943723)

[III.D.6. Understand low-mass giants and the s-process
6](#iii.d.6.-understand-low-mass-giants-and-the-s-process)

[IV. Summary: Challenges and Opportunities
6](#iv.-summary-challenges-and-opportunities)

[Appendix: development of this report and its authors
6](#appendix-development-of-this-report-and-its-authors)

# Executive Summary

RIA theory covers a range of activities from nuclear structure and
reactions, to nuclear equation-of-state issues. Furthermore, many
nuclear issues are relevant to processes in astrophysical environments.
Since all nuclei heavier than carbon are made in stars, this synergy is,
in fact, natural. Understanding both the basic nature of the nuclear
many-body problem and understanding the effects of nuclear physics on
stellar evolution and nucleosynthesis constitutes major intellectual
efforts. Furthermore, low-energy nuclear science remains important in
matters of national safety and security.

This document describes a number of theoretical challenges that must be
met during the next decade in order to facilitate the success of an
experimental program focused on short-lived isotopes. These efforts
include:

-   Development of ab initio approaches to medium mass nuclei.

-   Development of self-consistent nuclear DFT methods for static and
    dynamic problems.

-   Development of reaction theory that incorporates relevant degrees of
    freedom for weakly bound nuclei.

-   Exploration of the isospin degrees of freedom of the
    density-dependent nuclear force.

-   Development and synthesis of nuclear theory, and its consequent
    predictions, into various astrophysical models to determine the
    nucleosynthesis in stars.

Present research facilities and projected upgrades to them, and the
future RIA experimental facility, are measuring or will measure nuclear
structure and reactions for nuclei that have very short half-lives and
live close to the neutron (or proton) drip line. Many of these
experiments will be relevant to astrophysics and will enable a
comparison of theoretical predictions to experimental data. There will
be numerous (in fact, many) nuclei and nuclear properties that we cannot
measure. For an understanding of those systems, a robust
nuclear-theoretical capability is required.

Certain critical investments in nuclear theory research over the last 10
years are yielding significant knowledge and understanding of properties
of nuclei. Continued success will require investments in the following
areas.

-   Several approaches to the nuclear many-body problem have enabled
    both few- and many-body calculations to proceed in an ab initio way,
    starting from the basic two- and three-nucleon interactions.
    Critical investments for nuclear theory will include extensions of
    ab initio techniques to heavier nuclei and drip-line systems.

-   Self-consistent mean-field theories offer a robust and global
    approach to a wide range of nuclei and nuclear properties. Critical
    to the success of this endeavor will be a full description of the
    energy density functional, and the development of methods to treat
    excited states and giant resonances on the same footing.

-   The treatment of the continuum in both structure and reaction
    theories has been, and will continue to be, a critical area that
    requires both new ideas and potentially new computational techniques
    in order to be successfully applied to nuclear scattering of
    near-drip-line nuclei.

-   An understanding of the isospin dependence of the nuclear equation
    of state will be an important outcome of the medium-energy collision
    work performed at RIA. Theorists also need to develop methods to
    extract from experimental data relevant quantities that will enable
    a description of the nuclear equation of state.

-   The interplay of astrophysics and low-energy nuclear theory requires
    some level of coordination. This is taking place through two
    supernova SciDAC efforts for nuclear physics relevant to supernova
    production. We identified several other astrophysically interesting
    sites that would benefit from nuclear theory input.

While significant progress on the basic theoretical underpinnings of the
nuclear many-body problem will require an enhanced workforce development
and research effort, one challenge will be to export the knowledge
gained from these research activities to the broader nuclear physics and
nuclear astrophysics communities. One component of future research will
be to assess the validity of models used in nuclear science applications
(for example, in nuclear astrophysics), and that assessment hinges on
our ability to perform calculations in ever larger nuclei and in nuclei
far from stability.

We also identified several important areas and elements of theoretical
nuclear astrophysics that should be actively supported. Each scientific
area involves interdisciplinary challenges for both nuclear theory and
astrophysics theory. Progress requires mutually beneficial and
coordinated research in theoretical astrophysics and nuclear physics.
This will allow us to combine leading-edge nuclear physics with the
latest astrophysical models to answer the major open questions in
nuclear astrophysics.

# I. Overview of RIA Theory

Nuclear theory strives to build a unified and comprehensive microscopic
framework in which bulk nuclear properties, nuclear excitations, and
nuclear reactions can all be described. A new and exciting focus in this
endeavor lies in the description of exotic and short-lived nuclei. The
extreme isospin of these nuclei and their weak binding bring new
phenomena to the fore which isolates and amplifies important features of
the nuclear many-body problem. The new arena of nuclei with large
neutron excess is therefore key to building a unified theoretical
foundation for understanding the nucleus in all its
manifestations---from the stable nuclei that exist around us to the most
exotic nuclei, and even to exotic forms of nucleonic matter which exist,
e.g., in neutron stars. Nuclei also play key roles in stellar evolution
and nucleosynthesis. Various nuclear properties and interaction cross
sections are important ingredients in astrophysical simulations of
stars, supernova, and nova.

RIA theory and associated experimental investigations will enable us to
answer several long-standing questions in nuclear physics. These include
understanding the following issues:

-   *Changes in the effective nuclear interaction and the nuclear matter
    equation of state as a function of neutron excess:* What is the
    isospin dependence of the effective nuclear interaction? What is the
    density dependence of the effective interaction? How does one
    characterize the transition from finite nuclei to bulk nucleonic
    matter?

-   *Foundations of independent particle motion:* How does shell
    structure change as a function of increasing neutron number? What is
    the role of the continuum in weakly bound nuclei?

-   *Excitation and decay properties of weakly bound systems:* How does
    one quantify nucleon halos and skins in near-drip-line nuclei? What
    are the soft modes of excitation of these weakly bound systems?

-   *Element production in the universe and the nuclear structures in
    stars:* What is the origin of the heavy elements in the universe?
    What role does nuclear structure play in supernovae explosion
    mechanisms? What are the properties of neutron stars?

-   *Weak nuclear processes:* What are the nuclear uncertainties in
    fundamental symmetry measurements in atomic nuclei? How can unstable
    nuclei be used as laboratories for the fundamental symmetry tests?

Currently, a variety of nuclear research facilities within the United
States, in Europe, and in Japan provide experimental data concerning the
properties of both exotic and stable nuclei. In order to address
astrophysical questions related to nuclear physics, the National Science
Foundation (NSF) recently created the Joint Institute for Nuclear
Astrophysics. In addition to the current U.S. facilities, efforts are
ongoing to build the Rare Isotope Accelerator (RIA), the next-generation
low-energy nuclear facility. RIA is a near-term number-three priority of
the U.S. Department of Energy, Office of Science (and the top priority
within the Division of Nuclear Physics).

RIA and other exotic beam facilities allow unique insights into the
quantum many-body nature of nuclei by providing access to their most
extreme manifestations and by providing precise control of the number of
nucleons in these systems. Recent theoretical and experimental
achievements, coupled with the experimental discoveries that RIA will
provide, are focusing new attention on a number of unsolved issues in
nuclear structure and reactions, and offer excellent scientific
opportunities for the next decade and beyond. Given the advent of
research on radioactive nuclei, particularly with the coming of the RIA,
it is extremely important to prepare nuclear theory for its realization.
The RIA Theory Group consists of about 160 scientists who share the
common purpose of moving theory forward to understanding the unique
features of nuclei far from stability and related questions in nuclear
astrophysics and mesoscopic physics.

The purpose of this RIA Theory Bluebook is to establish overall goals
and strategies to meet the challenges of the RIA Theory Group in the
coming years. In the following sections we discuss the scientific and
societal ties that nuclear theory enjoys with other areas of science. We
then turn to a detailed road map of required scientific developments
that will enable the description of rare nuclei in the coming years.

# II. Scientific Connections and Societal Impacts of RIA Physics

Low energy nuclear physics is "one of the cornerstones of the nation's
technological edifice" according to a 1999 survey of nuclear science by
the National Research Council, *Nuclear Physics: the core of matter the
fuel of stars*. Clearly, nuclear physics plays a major role in medicine,
including modern imaging techniques, and the widespread use of
radioisotopes for therapy and diagnosis. Furthermore, various nuclear
properties are important to understand in light of the nuclear stockpile
and its stewardship. Nuclei play an extremely important role in our
understanding of the universe around us. In fact, elements heavier than
carbon were all made in stars. The nucleus also shares common roots with
other physical systems where many-body quantum mechanics plays an
essential role. Nuclear theory research also provides an excellent
educational opportunity for the Nation's highly technical workforce
needs.

## II.A. Intersections of nuclear physics and astrophysics

The physics of atomic nuclei governs the nature of most of the visible
universe. Nuclear dynamics and structure are directly reflected in the
nature of stars, the light curves of stellar explosions, and the
abundances of chemical elements in the cosmos. Element abundance
patterns produced by various nucleosynthesis events become increasingly
important as tracers of large scale astrophysical processes such as
galaxy formation. This will broaden the relevance of nuclear
astrophysics for astronomy considerably. In addition many key questions
in astrophysics such as the origin of the heavy elements, the physics of
stellar explosions, nuclear and mixing processes in stars, the nature of
compact objects such as white dwarfs and neutron stars and thermonuclear
explosions on their surfaces like novae and X-ray bursts are directly
linked to open questions in nuclear physics. This is particularly true
for extremely unstable nuclei created in the extreme environments of
stellar explosions and compact objects. With RIA we will be able to
delineate experimentally the properties of many of these unstable nuclei
for the first time. Simultaneously the next generation of astronomical
observatories will provide data of unprecedented quality on element
abundances and stellar explosions. This includes a next generation of
more sensitive X-ray, few MeV γ-ray and optical telescopes, and also the
large-scale spectroscopic surveys, like SEGUE in the SLOAN-II and
emerging multi-object fiber-optics systems together with refined
analysis methods of star dust, for example from meteorites. Continuing
advances in nuclear theory, theoretical astrophysics, and computational
astrophysics will enable a unified interpretation of these new data and
give an understanding of the nuclear processes in nature that ultimately
are responsible for our existence.

A close collaboration between nuclear physics and astrophysics will
therefore maximize the impact of RIA science. The experimental results
of RIA must be interpreted in terms of nuclear theory and then be
incorporated into astrophysical simulations to be translated into
astrophysical observables that can be directly compared with telescope
data. This requires that new experimental and theoretical nuclear
physics data are merged with existing data into an evaluated and
documented data archive for nuclear astrophysics. At the same time new
observations and their astrophysical modeling needs to be considered
when prioritizing the RIA nuclear physics program.

## II.B. Connections to neutrinos and fundamental symmetries

Nuclear theory advances during the next decade will significantly impact
research programs associated with searches for physics beyond the
Standard Model. Experimentally, RIA promises to generate a great variety
of radioactive isotopes with high intensities that will provide
unprecedented opportunities to search for physics beyond the
Electro-Weak Standard Model. For example, RIA will allow for
orders-of-magnitude improvements on limits of the CP-violating atomic
Electric Dipole Moment (EDM) and on the determination of the Weinberg
angle from measurements of parity violation in Fr atoms. New
measurements of  β−decay using ion or atom traps will produce much
higher precision for searches for non V-A contributions to the weak
interaction. Finally, β-decay measurements, coupled with new information
on the spectroscopy and masses of the appropriate nuclei far from
stability, could provide definitive information on the apparent
nonunitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

The research portfolio in nuclear physics also encompasses
neutrino-nucleus interactions and the search for neutrino properties.
One of the central questions in neutrino science today concerns whether
the neutrino is its own antiparticle. The recent discovery that
neutrinos oscillate and have a finite (albeit small) mass makes neutrino
science an interesting area of discovery that will require nuclear
theory input for its interpretation. For example, if a 0νββ-decay
experiment sees a definitive signal, then experimentally we would
understand that neutrinos are Majorana particles with a definite mass.
There is no other realistic way to determine the nature (Dirac or
Majorana) of massive neutrinos. Furthermore, precise theoretical
knowledge of the nuclear 0νββ-decay matrix element would allow us to
interpret the neutrino mass spectrum. Thus, advances in nuclear theory
will be crucial to the success of a neutrino science program.

## II.C. Connections to mesoscopic systems

The scientific community is witnessing the birth of a new area of
physics that will supplement traditional macrophysics of large systems
and physics of the micro-world, namely mesoscopic physics. This name can
be applied to systems that are sufficiently large to display generic
statistical regularities but at the same time sufficiently small to
allow the researchers to study in detail, theoretically and
experimentally, individual quantum states. The future successes of
fundamental physics and technology are in the direction of mesoscopic
systems, such as atomic and metal clusters, complex molecules including
fullerenes and biological molecules, quantum dots and nanoscale solid
state devices, Bose and Fermi gases in atomic traps, and the elementary
units (qubits) of future quantum computers.

Although on a much shorter length scale, nuclei are also prototype
mesoscopic systems. Mesoscopic systems display a variety of common
phenomena. For instance, shell structure, collective surface
excitations, and pairing and superfluidity are found both in nuclei and
in other mesoscopic systems like atomic clusters, quantum dots, small
metallic grains, and trapped atom gases. On the one hand, nuclear
theorists have made important contributions to the theory of mesoscopic
physics when applying their expertise to these nanoscale problems. On
the other hand, nuclear theorists are also employing techniques and
methods that originated in other fields of physics. This
cross-fertilization generates vitality and yields an appreciation of
nuclear theory outside the field. RIA physics offers several
opportunities for interdisciplinary research. Some broad categories of
com-mon problems are outlined in the following.

*The transition from microscopic to mesoscopic to macroscopic* - The
general challenge for theory of mesoscopic systems is to understand the
principles of building up complexity out of \"elementary\" blocks, which
in fact have a complicated structure of their own, similar to how
quantum chemistry builds complex molecules, including biological, of
simpler atoms. RIA data will challenge theory to explain how
increasingly complex nuclei are build from protons and neutrons. Heavy
and super-heavy nuclei form a bridge between nuclear drops and nuclear
matter similar to what can be studied in nanoscience.

*Loosely bound and open systems* - RIA will produce loosely bound nuclei
that will require theoretical advances in the physics of marginally
stable and open systems that are tied to those needed for negatively
charged molecules, and quantum wires and other solid state
micro-devices.

*Coherent phenomena* - Collective excitations and the coherent response
to external fields play a crucial role in all mesoscopic systems. New
examples of collective modes will be presented by RIA. Superfluidity,
shape transformations, shape coexistence, and other quantum phase
transitions, which will be encountered in new forms in nuclei far from
the valley of stability, will require new approaches, possibly close to
those used for atomic clusters, metallic grains, and ultra-cold Fermi
gases. We definitely need a much deeper understanding of thermodynamics
and precursors of phase transitions in finite systems.

It is necessary to continue the study of quantum chaos with interplay of
one-body and many-body effects common for complex nuclei and quantum
dots and vitally important for future quantum computers.

*Quantum transport* - Quantum transport is another topic of general
interest. In energetic central reactions of heavy nuclei, the nuclear
medium gets excited and its density is increased compared to that normal
for nuclei. Under those circumstances, the de Broglie wavelength of
nucleons becomes comparable to the nucleon mean-free path, signifying
the quantum nature of nucleon transport across the reaction zone. The
mesoscopic character of the transport is further underscored by the fact
that the interaction range becomes comparable to the mean-free path. The
method of non-equilibrium Green\'s functions developed for nuclear
physics has been adapted and expanded to semi-conducting devices, memory
effects, plasmas and decay through barriers in conjunction with
dissipation. Overall, with regard to this difficult topic, a
synchronized effort is needed, with any significant development
impacting different areas simultaneously.

## II.D. Connections to computational sciences

The entire field of low-energy nuclear physics and nuclear astrophysics
utilizes resources available to perform large-scale calculations. The
definition of 'large-scale' changes each year as raw computational power
increases: today it is common for various theoretical projects to use
tens of Teraflop-hours of computing time per month in order to solve
some of our current problems. Computational efforts in the field will
grow, and it is important to take advantage of the new generation of
machines that will become available. As examples, we mention Green's
Function Monte Carlo for nuclei, neutron drops, and nuclear matter,
no-core shell model for nuclei and effective operators, coupled-cluster
theory for nuclei, shell-model Monte Carlo studies of medium-mass
nuclei, HFB calculations of mass tables, hydrodynamic and transport
codes that probe the nuclear equation of state, and multidimensional
core-collapse supernova simulations (requiring nuclear theory input).
These computational problems are just a few examples of the rich variety
of theory that can utilize the large-scale technology available for
scientific computing.

The revolution in scientific computing technology will continue its
torrid pace over the next few years, and nuclear theory must take
advantage of the resources available. The challenges will be to provide
numerical algorithms that scale across hundreds to thousands of
processors. This involves rethinking common algorithmic structures. For
example, in the last few years Lanczos algorithms have become
efficiently developed for parallel application; nuclear coupled-cluster
theory has recently been developed with scaling in mind. Quantum Monte
Carlo algorithms are naturally parallel and have taken significant
advantage of parallel machines. SciDAC funds two efforts in supernova
simulations (including nuclear structure components), and the field
should continue to take advantage of this funding stream when
appropriate.

Many of the future directions discussed in section III will be tied to
continuing advances in high-performance computing. Our field should take
the time and effort required to develop efficient numerical algorithms
that will scale to large processor numbers since these algorithms will
allow us to pursue far more science than would otherwise be possible.

# III. RIA Theory Detailed Road Map: Goals and Strategies

In this chapter, we discuss a detailed road map that will enable
progress toward rare nuclei. The key components in moving forward
involve placing the nuclear many-body problem on a more firm footing,
and increasing the number of degrees of freedom that can be investigated
in nuclear reaction models, thereby decreasing the parameterizations
used, and identifying key low-energy nuclear physics input to
astrophysics. We organize this section according to various sub-fields,
recognizing that efforts in several of the fields actually overlap.

## III.A. Nuclear structure

Atomic nuclei are extraordinarily interesting quantum many-body systems
that exhibit a diverse range of phenomena. While comprised of a very
limited number of particles, nuclear structure manifests both individual
particle dynamics as well as collective dynamics at the same energy
scale. Remarkably, although nuclei have been the object of intense study
for over 70 years, the ability to execute, theoretically, the
conceptually simple task of "building" a nucleus up from its constituent
parts, the protons and neutrons, has yet to be fully realized. This is
largely due to the complex nature of both the interaction between
constituent nucleons and the solution of the quantum many-body problem.
The leading two-nucleon interaction is characterized by a strong
short-range repulsion and strong spin and isospin components. In
addition, there is now mounting evidence that three-body forces
significantly affect nuclear structure. For the most part, because of
these complexities, progress in nuclear structure theory has largely
relied on approximate methods of solutions with effective interactions
renormalized to experimental data. While largely successful, this
approach is unsatisfying, as the renormalizations are essentially based
on approximations, and extrapolations into regions where experimental
data are absent, as will be the case for RIA, have uncertainties that
are not quantifiable. The goal of nuclear theory in the future must be
to go beyond it empirical roots, and to arrive at a fundamental
understanding of nuclear properties from a unified theoretical
standpoint rooted in the fundamental forces between nucleons.

Our overarching goal for the future is to ground our approaches within
the fundamental interactions between nucleons, whether we utilize bare
interactions in ab initio calculations, effective interactions in
large-scale microscopic calculations, or applications of density
functional theory for mean-field treatments.

### III.A.1. Develop ab initio structure and reaction theory

A long-standing goal in nuclear physics has been an exact treatment of
nuclei utilizing the fundamental interactions between nucleons. Due to
the advent of new theoretical techniques and exceptional improvements in
computational capabilities, this goal is finally beginning to be
realized in light nuclei. The prospects look bright, and it is likely
that within the next decade, exact results for medium-mass nuclei may be
attained. With these powerful new methods and a full determination of
inter-nucleon interactions, it will be possible to explore the rich
diversity of properties exhibited in light nuclei, such as clustering
phenomena, deformation, the locations of the proton and neutron drip
lines, neutron halos, and low-energy nuclear reactions important for
stellar physics.

The starting point is the nuclear Hamiltonian. Much work has been done
to explore the properties of the nucleon-nucleon interaction, and today
several high-quality versions derived from nucleon-nucleon scattering
and the properties of the deuteron are available. These range from local
potential models such as Argonne V18 to non-local interactions based on
meson exchange, such as CD-Bonn, and QCD-based interactions derived
within the framework of effective field theory. It is well known that
all of these high-quality two-nucleon interactions fail to reproduce the
binding energy of even the simplest complex nuclei, namely the
three-body system, and that three-body interactions are required. While
three-nucleon interactions provide a modest amount of binding, about 6%
to the total binding energy, there is mounting evidence that spin-orbit
and isospin-dependent components in the three-body interaction strongly
affect the structure of nuclear levels and even the location of the drip
line. All realistic nucleon-nucleon interactions that reproduce the
scattering phase shifts predict the wrong ground state for ^10^B. The
stronger spin-orbit components in three-nucleon interactions can correct
not only this deficiency, but also strongly modify the amplitudes of
transition operators, such as Gamow-Teller.

![](media/image2.wmf){width="4.141732283464567in"
height="3.0736220472440943in"}Three-nucleon interactions are also
required to adequately describe the binding energy changes in an A-chain
as one increases the proton-neutron difference towards the drip line.
Progress towards a complete ab initio description of nuclei, including
those near the drip lines, requires a full understanding of the two- and
three-body components of the nuclear interaction. Many of the features
of the three-nucleon interaction are manifested in many-body nuclear
systems. Consequently efforts to determine the full form of the
inter-nucleon interactions must go hand-in-hand with solutions to the
many-body problem.

To date, several complementary methods have been employed in ab initio
studies. The most successful has been the Green's Function Monte Carlo
(GFMC), which is now providing "exact" results for ^12^C including both
two- and three-nucleon potentials. A serious first attempt has been made
to determine the full form of the three-nucleon interaction by examining
its effects on the structure of nuclei. Shown in Figure 1 is the current
state-of-the-art GFMC method for p-shell nuclei up to ^12^C. The results
obtained so far are impressive, and a full determination of the
three-nucleon force and its effect on nuclear structure will likely be
determined in the coming years. Going beyond ^12^C with the current
formulation, however, is computationally difficult, and algorithm
changes may be required. One possibility is to utilize the
Hubbard-Stratonovich transformation on the quadratic spin and isospin
operators in the imaginary-time propagator. While this method may
significantly reduce computational requirements and permit calculations
of heavy nuclear systems, it is unclear if the sign-problem, which is
endemic in Monte Carlo applications to fermion systems, can be overcome.

A complementary approach is the No-Core, Shell Model (NCSM), which is
based on the application of effective-interaction theory within the
context of the shell model. A key feature of the NCSM is that because of
the separation between the allowed and excluded spaces, the effective
interaction has two-, three-, up to A-body components even if the
Hamiltonian is only two-body in character. In this context, convergence
to exact results can be achieved by increasing the number of clusters
included in the effective interaction and/or by increasing the size of
the allowed space. The NCSM can also provide a bridge to heavier nuclei
by giving important guidance on the nature of effective interactions
that can then be used with other "conventional" many-body approaches
such as the shell model. Another promising method for ab initio studies
is the coupled-cluster technique. An advantage of coupled-clusters is
that it is a size-extensive method that can provide very accurate
results in many-body systems.

In the coming decade, ab initio studies of nuclear structure will
continue, and key questions, such as the nature of the nuclear
Hamiltonian, level ordering, Gamow-Teller transition amplitudes,
root-mean square radii, and clustering will be answered. In addition to
the rich diversity of structure exhibited in the light p-shell nuclei,
their reactions have important consequences for the fate of the
universe. Indeed, low-energy fusion reactions are the primary energy
generation mechanism for stars, and help determine the course of stellar
evolution. Further, much of what we know about neutrino oscillations is
determined from neutrinos emerging from the Sun following the beta decay
of reaction products and, in particular, ^8^B. If solar neutrinos are to
provide even more precise information on the oscillation properties, the
light-ion fusion rates comprising the standard solar model need to be
improved. Structure also plays an important role in these reactions.
Perhaps the most complex and most important astrophysical reactions are
the fusion of three alpha-particles to form ^12^C, and the fusion of
^12^C nucleus and an alpha-particle to form ^16^O. Both fusion reactions
are dominated by the contributions of resonances and/or subthreshold
states. Here, ab-initio description of the structure of these states in
the many-body framework is a formidable challenge. Here, an ab initio
description of the structure of these resonances in the many-body
framework is a formidable challenge. Indeed, presently a fundamental
description of coupling reaction mechanisms with nuclear structure has
yet to be realized. An important goal for the next decade will be to
extend the ab initio efforts into a fundamental reaction formalism that
will be capable of accurately calculating reaction cross sections,
break-up reactions, and the alpha-capture reactions leading to the
production of ^12^C and ^16^O in stellar environments.

### III.A.2. Develop an understanding of the nature of effective interactions and operators used in nuclear structure models 

Typical large-basis shell-model calculations, which are some of the most
successful detailed microscopic descriptions of nuclei, start with an
effective interaction derived for a given shell-model space. Experience
shows that while a derived effective interaction is a good starting
point, agreement with experimental data is often lacking. At this point,
the effective interaction is then empirically tuned to experimental
data. Changes with respect to the original effective interaction are
usually small; however, the exact nature of these changes is not known.
While applications have generally been successful, the fact remains that
calculations carry with them an uncertainty that is difficult to
quantify. This is particularly true for extrapolations to nuclei outside
the region where the Hamiltonian has been empirically determined.
Furthermore, without a more formal approach to these effective
interactions, it is difficult, if not impossible, to determine an
effective interaction that would be applicable to new regions of nuclear
structure, where data do not yet exist.

With any truncation of the active model space, not only do we have an
effective interaction, but each and every operator must also be
renormalized, leading to effective operators. The general procedure has
been to be guided by theoretical formalism; however, to determine
effective charges, g-factors, etc., one requires that they reproduce
known experimental data. Again, we have the situation where the nature
of the renormalizations is not well understood.

Concurrent with developing a more formal mechanism to determine the
effective interaction is the ability to utilize them while including the
relevant degrees of freedom. While the computational challenges incurred
in microscopic models can be daunting, the methods often provide rich
rewards, leading to an increased capability to manage an ever larger
number of many-body basis states. In addition, Monte Carlo sampling of
shell-model basis states has also proven to be successful, and solutions
that can be reliably extrapolated to the exact result can be obtained
for nuclei in the middle of the fp-shell region, where the number of
basis states exceeds 2 billion. Factorization methods, truncations based
on symmetry groups, and density-renormalization group methods may also
prove successful in extending detailed microscopic calculations to
nuclei not thought possible before.

The nature of effective interactions and operators is critical to the
study of nuclear structure. It is vital to note that the effective
interaction is determined by the choice of the active Hilbert space, and
formal theories based on realistic inter-nucleon interactions, or
effective field theories need to be formulated. While promising
approaches exist (for example, similarity transformations to the active
Hilbert space, or ladder summations, etc.) they do not yet fully
incorporate the realistic three-body interaction. This issue is
particularly important in the next decade (prior to the advent of RIA)
where detailed nuclear theory studies of nuclei away from the valley of
stability will be carried out, and some degree of confidence and
certainty (hopefully quantifiable) can be achieved.

### III.A.3. Develop predictive density-functional theory for nuclei and nuclear matter

Density functional theory (DFT) is built on theorems showing the
existence of universal energy functionals for many-body systems, which
include, in principle, all many-body correlations. Condensed matter
physicists and computational chemists have developed such functionals
for the Coulomb interaction that describe properties of a wide range of
systems with chemical accuracy.

In nuclear physics, self-consistent methods based on the DFT, e.g., the
Hartree-Fock-Bogoliubov theory with Skyrme parameterizations, have
achieved a level of sophistication that allows analyses of experimental
data for a wide range of properties and for arbitrarily heavy nuclei. A
recent example is shown in Figure 2, where HFB calculations were used to
explore the rich physics exhibited by super-heavy nuclei.

![](media/image3.wmf){width="2.8318897637795275in" height="3.75in"}The
achieved accuracy and predictive power of mean-field calculations,
however, still leaves much to be desired. This is illustrated in Figure
3, where two-neutron separation energies for Sn isotopes resulting from
Hartee-Fock-Bogoliubov calculations utilizing a wide range of Skyrme
potentials are shown. On the left, the comparison with present
experiment can be quite good. However, each of the various Skyrme
potentials extrapolates to different results as one advances to the
neutron drip line where data do not exist to constrain theory. The quest
for a truly universal DFT of nuclei, including dynamical effects and
symmetry restoration, is one of the main themes of theoretical nuclear
structure worldwide.

We believe that a concerted effort rooted in a fundamental understanding
of inter-nucleon interactions offers promise to achieve corresponding
qualitative improvements in the accuracy and applicability for nuclear
physics. Current functionals lack a sufficient understanding of density
and isospin dependences and an adequate treatment of many-body
correlations, which are required for robust and controlled
extrapolations to low densities, large asymmetries, and higher
temperatures. New challenges not generally faced by Coulomb DFT are the
essential roles of symmetry breaking and pairing, and the need for
symmetry restoration in finite, self-bound systems. The functional
should have a solid foundation based on microscopic inter-nucleon
interactions with an ultimate goal of quantitative matching to
microscopic theory (as in Coulomb DFT). Addressing these challenges will
require us to exploit advances in the study of microscopic inter-nucleon
interactions, in the development of many-body computational techniques,
and in raw computer power, as well as to further develop DFT itself as
applied to finite, self-bound systems.

![](media/image4.wmf){width="3.958267716535433in"
height="3.072834645669291in"}The first, most general question to be
addressed is just what is the form of the nuclear energy density
functional? Limitations of current functionals in describing isovector
and density dependences reflect both insufficient constraints from data
(e.g., for time-odd fields) and incomplete physics encoded in the
functionals.

To make progress, a concerted effort will be required to study new
functionals when applied to finite nuclei and infinite or semi-infinite
nuclear matter. For instance, in the particle-hole channel, one would
like to enrich the density dependence of the effective mass in order to
differentiate between its value in the bulk and at the Fermi surface.
Another goal is to understand connections between the symmetry energy
and isoscalar and isovector mean fields, and in particular the influence
of effective mass and pair correlations on symmetry energy versus
isospin. Such an understanding will allow us to better determine isospin
corrections to nuclear mean fields and energy density functionals. In
the self-consistent method, the average nucleonic field is obtained from
the nucleonic density. Consequently, in the nuclear state with nonzero
angular momentum, the self-consistent potential acquires time-odd
components. These terms are expected to play a significant role at very
high angular momentum when the nucleus is strongly polarized, but they
should also influence properties of beta decay and the ground states of
odd-mass and odd-odd nuclei.

Fundamental questions, such as constraints on the most general form for
functionals and the existence of DFT for intrinsic densities, need to be
addressed. Effective field theory (EFT) methods, now widely applied for
few-nucleon systems, can provide systematic insight into the density
dependences along with error estimates.

Little is known about the basic properties of the pairing force. Up to
now, the microscopic theory of the pairing interaction has only seldom
been applied in realistic calculations for finite nuclei. A
"first-principle" derivation of pairing interaction from the bare NN
force still encounters many problems such as, e.g., the treatment of
core polarization. Hence, phenomenological density-dependent pairing
interactions are usually introduced. It is not obvious how the density
dependence should be parametrized, although nuclear-matter calculations
and some experimental data (e.g., isotope shifts and odd-even mass
staggering) suggest that pairing is strongly affected by the nuclear
surface. This is why neutron-rich nuclei play such an important role in
this discussion. Indeed, because of strong surface effects, the
properties of these nuclei are sensitive to the density dependence of
pairing. The investigation of the density and isospin dependence of
pairing interactions is a significant part of this program.

A better understanding of the symmetry energy appears to be a key
element in resolving the question of the proton-neutron (p-n) pairing.
The isoscalar p-n pairing is our current best explanation for the
additional binding of N=Z nuclei, the so-called Wigner energy. However,
basic questions regarding the collectivity of such a phase still remain
unanswered.

Spontaneous symmetry-breaking effects are at the heart of the mean-field
description of highly correlated many-body systems. A large part of
those correlations can indeed be included by considering
symmetry-breaking product states. Within the mean-field approach, one
can understand many physical observables by directly employing
broken-symmetry states; however, for finite systems, a quantitative
description often requires symmetry restoration. For this purpose, one
can apply a variety of theoretical techniques; in particular, projection
methods and the generator-coordinate method.

Ideally, one would like to work out approximations that would allow
avoiding full-scale collective calculations, but would be based on
calculations performed on top of self-consistent mean fields. In this
way, we hope to develop the microscopic mass formula in which both the
mean-field mass and the dynamical corrections would be obtained from the
same energy-density functional. In this context, it is important to note
that the realistic energy-density functional does not have to be related
to any given effective force. This creates a problem if a symmetry is
spontaneously broken. While the projection can be carried out in a
straightforward manner for energy functionals that are related to a
two-body potential, the restoration of spontaneously broken symmetries
of a general density functional poses a conceptual dilemma that has not
yet been properly addressed.

Finally, a reliable extrapolation to unknown nuclei is possible only
with the establishment of theoretical error bars. Consequently,
construction of new energy density functionals should be supplemented by
a complete error and covariance analysis. It is not sufficient to just
"predict" the properties of exotic nuclei by extrapolating from a DFT
determined by reproducing experiment. It is also necessary to
quantitatively determine errors related to such an extrapolation.
Moreover, for experimental work, it is essential that an improvement
gained by measuring one or two more isotopes be quantitatively known.
From a theoretical perspective, it is important to arrive at the
confidence level with which the parameters of the functional are
determined.

### III.A.4. Develop many-body theories of nuclear collective dynamics, including the large amplitude collective motion and nuclear decays

To achieve a consistent description of nuclear excitations in open-shell
super-conducting nuclei, one has to go beyond the static mean-field
approximation. A powerful tool for understanding small amplitude
collective motion (both for low-lying collective states and giant
resonances) is the quasi-particle random-phase approximation (QRPA). For
weakly bound nuclei, an important extension to the standard treatment
involves a proper treatment of the particle continuum. Continuum
extensions are usually carried out in coordinate space, facilitating
treatment of decay channels and guaranteeing correct asymptotics.

Recently, fully self-consistent QRPAs have been developed and a limited
number of studies have been carried out to address properties of exotic
nuclei such as electromagnetic strength, nature of individual collective
states, decay properties, and electroweak processes. The main challenge
is the inclusion of symmetry-breaking effects, associated with shape
deformations and pairing, in the presence of strong coupling to the
particle continuum. Once a deformed QRPA framework is developed, the
whole range of open-shell, neutron-rich nuclei will open up for
exploration.

While QRPA investigations are useful for small-amplitude motion, large
amplitude collective motion which drives fission, fusion, cluster decay,
shape coexistence, and phase transitions, and provides a particularly
important challenge. These phenomena involve the mixing of mean fields
with different symmetries. The transition from one stable mean field to
another goes through one of several level crossings around which the
original symmetry of the system is broken. We have yet to obtain a
microscopic understanding of large-amplitude collective motion that is
comparable to what we have for ground states and small-amplitude
collective motion.

One possible approach to large amplitude collective motion is
time-dependent extensions to the static mean-field solutions of
Hartree-Fock or Hartree-Fock-Bogoliubov. While the time-dependent
Hartree-Fock theory has been well developed and employed, particularly
in the 1970s and 1980s, its application to exotic nuclei has not been
extensively undertaken. Extensions to include the self-consistent
pairing field have never been fully developed except in adiabatic
approximations to the full theory.

Another useful microscopic tool that extends the applicability of
mean-field methods to excited states, and potentially to large-amplitude
collective motion, is the Generator-Coordinate Method (GCM). The GCM
wave function is usually taken as a combination of many (projected)
intrinsic states and calculated self-consistently within constrained
mean-field theory. The GCM wave function is rich enough to accommodate
correlations absent in the mean field and is not limited to the
adiabatic regime. Moreover, GCM is based on the variational principle.
Applications of GCM face both numerical and conceptual challenges. First
among these is the choice of generator coordinates, which are usually
selected in an arbitrary way that depends on the problem and our
physical intuition. Second, many problems, such as fission or cluster
decay, require the use of several collective degrees of freedom and an
immense computational effort. Third, it is not clear how to apply GCM to
weakly bound nuclei with nearly vanishing chemical potentials. Finally,
there are fundamental problems with incorporating GCM into
density-functional theory.

Spontaneous fission is one the oldest decay modes known, but is still
not fully understood. It represents an extreme example of
large-amplitude collective motion, the tunneling of a many-body system.
The pairing interaction plays a large role here because it causes a
dramatic smoothing of single-particle crossings, thus improving the
adiabatic approximation. Many calculations of spontaneous fission
(lifetimes, sometimes mass/charge splits) are based on the adiabatic
assumption. While the majority of calculations have used
microscopic-macroscopic methods, very few self-consistent applications
have been performed in the adiabatic limit.

We also need to develop the microscopic foundation of popular
phenomenological models of collective excitations, such as, for example,
interacting boson model and other group-theoretical approaches, and
understand the physics underlying their success and deficiencies in
description of nuclear spectra and shape phase transitions. This is
important in connection to diversity of shapes and deformations possible
in exotic nuclei.

### III.A.5. Develop unified treatment of bound states and open channels

A major theoretical challenge in a full microscopic description of
nuclei, especially weakly bound ones, is the rigorous treatment of both
the many-body correlations and the continuum of positive-energy states
and decay channels. The importance of the continuum for the description
of resonances is obvious. Weakly bound states cannot be described within
the closed quantum system formalism since there always appears a virtual
scattering into the continuum phase space involving intermediate
scattering states. A unified description of excited states in weakly
bound nuclei and reactions on weakly bound nuclei (described more fully
in Sections III.B.1 and III.B.2.) is one of the main goals of modern
nuclear structure physics.

One possible strategy of tackling the continuum challenge is by use of
the resonant-state expansions, e.g., the Berggren ensemble that consists
of Gamow (or resonant) states and the complex non-resonant continuum.
Since these theories incorporate continuum states into the
single-particle basis they can be used for a microscopic description of
halo nuclei, particle-unstable nuclear states, reactions of
astrophysical interest, and a variety of nuclear structure phenomena.
Initial applications in light isotopes are proving successful. The main
challenge is to develop a realistic effective interaction that will
enable us to address physics of weakly bound nuclei such as ^11^Li.
Other major problems are the treatment of the center of mass, the
inclusion of anti-bound states, and the handling of very large
shell-model spaces. The successful application of continuum shell models
to heavier nuclei is ultimately related to the progress in optimization
of the many-body basis, which is related to the inclusion of the
non-resonant continuum configurations. One promising development is the
adaptation of the density matrix renormalization group method to the
problem in which continuum states are a part of the basis.

The recently developed approach using the effective non-Hermitian
Hamiltonian is another promising direction with the advantage of a
simultaneous description of bound states, threshold phenomena, and
reaction cross sections for the long isotope chains.

The Gamow-state technology has also been applied to spherical and
deformed proton emitters. In particular, a nonadiabatic coupled-channel
method has been developed that properly takes into account the Coriolis
coupling due to the rotational motion of the deformed daughter nucleus.
Using this model, one obtained a consistent description of deformed
proton emitters, including proton lifetimes and branching ratios (fine
structure in proton emission). The weak point of the current approaches
to the phenomenon of proton emission is a very crude treatment of
pairing. To remedy this deficiency, the Berggren ensemble can be
utilized to solve the HFB equations. This will allow us to efficiently
take into account continuum effects and particle or quasiparticle
resonance states. Such a description is practically impossible in the
harmonic oscillator basis, and requires a huge numerical effort in the
coordinate representation, especially for deformed systems.

## III.B. Nuclear reactions

Reactions are the major tool in the study of unstable nuclei. Reliable
theoretical reaction descriptions are crucial in order to enable
accurate extraction of the desired structure information. Due to the
astrophysical motivation, further understanding of drip line properties
requires data at lower energy, where many reaction approximations are
not valid. The interplay between reaction and structure is unanimously
recognized as a prime element for a successful model.

There are several important challenges presented to reaction theory: the
one particle and two particle continuum known to be essential in the
description of reaction of drip line nuclei need to be handled
consistently, four body dynamics should be treated exactly in many
cases, core excitation needs to be taken into account, and we are
lacking a unified approach to the fusion of dripline nuclei. Many of
these challenges connect to computational issues.

### III.B.1. Understand the essential role of intermediate and final continuum states in reactions with weakly bound and exotic nuclei

![](media/image5.png){width="2.527165354330709in"
height="2.5181102362204726in"}Continuum states are necessarily populated
when nuclei near the drip lines are involved in reactions. We discussed
in Section III.A.5 their importance in the description of the structure
of weakly bound nuclei. How these states contribute to reaction
mechanisms needs to be understood for the description of a wide variety
of experimental data. This, in turn, will yield reliable structure
information from experimental data. We discuss in the following
paragraphs a variety of issues that will require focused research in the
coming years.

Intermediate continuum states play a role during particle transfer,
either as excitations of a weakly bound participant (such as a deuteron
or a nucleon in a halo nucleus) or as transfers from such participants
to the well-Q-matched low-energy continuum in the other participating
nucleus. The continuum may be in a deformed system. If transfer
reactions such as (d,p) are to be used to determine single-particle
structures, then virtual breakup in the deuteron channel must be taken
into account. Developments along these lines are in progress and will
continue.

Both virtual and real continuum states play an essential role in
moderating the fusion of weakly bound nuclei, where there is a
competition between loss of flux from real breakup and attractive
polarization potentials from virtual breakup. These must both be
understood on an equal quantum footing in order to reliably predict the
production yields of exotic nuclei by fusion mechanisms (see IVb-iv).

Near the drip lines, one often finds nuclei with valence nucleons so
loosely attached that their wave density is distributed as a halo around
a central core nucleus. Often these halo nucleons appear as pairs as in
^11^Li. For example, in two-neutron transfer reactions involving the
projectile ^6^He (which behaves like a three-body system consisting of
an alpha particle and two neutrons), the sequential transfer proceeds
through the intermediate continuum states of ^5^He. One challenge
involves including all the necessary dynamics of the two-nucleon halo
projectile into transfer reaction models.

Predictions of detailed observables are needed for comparison with rare
isotope experiments. For knock-out reactions, analysis relies on
theories of elastic and inelastic breakup (diffraction dissociation and
stripping). More powerful stripping experiments yield both integrated
cross sections and momentum or angular distributions. A great need
exists for theoretical developments that will enable us to understand,
predict, and analyze such distributions.

### III.B.2. Extend reaction models to include the dynamics of two-particle continuum

![](media/image6.png){width="2.8216535433070864in"
height="2.619291338582677in"}Due to the dominance of the 0s channel in
the nucleon-nucleon interaction, *pairing* plays an essential role in
nuclear structure. However, extraction of nuclear-pairing information
from experimental data is nontrivial. Reaction theory must be developed
so that it can be used to describe pairing in the context of
experimental data. As the drip line is approached, pairing becomes more
clearly delineated in nuclear structure (e.g., for the Borromean systems
mentioned above), and becomes completely visible from data either at
higher scattering energies, or beyond the drip line. Reaction theory
that properly treats pairing must treat the bound and continuum pairing
states in a consistent framework. Most importantly, one needs a clear
mapping between pairing fields calculated from mean-field theory and the
appearance of real nucleonic pairs available for transfer or breakup.
Also, the correlations of two particles (neutrons or protons) near
threshold, such as in halo nuclei, in both spherical and deformed
systems need to be isolated from other effects. Models for two-nucleon
breakup states must include all dynamical correlations such as two- and
three-body resonance states, two-body bound subsystems, and non-resonant
states. Finally, the excitation mechanism for two-nucleon states in RIA
reactions needs to be explored as a function of scattering energy.
Theories will have to go beyond both first-order and impulse
approximations and will need to treat to all orders the many dynamical
rearrangements possible for paired nucleons in the continuum.

### III.B.3. Incorporate new structure information in peripheral reaction models of collective and/or valence nucleon transitions

An essential tool for extracting structure information involves
peripheral reactions on the nucleus of interest. Recent efforts focused
on developments of reaction theory that extend to drip-line nuclei.
Required advances in reaction theory applications will enable
descriptions that extend beyond the separation energy prescriptions for
bound states and transitions in nuclei. One path forward involves
including microscopic structure information in reaction theory. This
includes calculations of single-particle state transitions taken from
the No-core Shell Model (see Section IV.A) instead of the approximate
single-particle transitions that are present in standard reaction codes.
In the same spirit, nucleon overlaps and coefficients of fractional
parentage calculated using Variational Monte Carlo or Greens Function
Monte Carlo methods should replace the single-particle wave functions
whenever feasible. One usually describes collective behavior in
reactions with vibrational/rotational models. These semi-classical
models should be significantly enhanced by inclusion of microscopic
descriptions of transition densities for collective excitations. One
useful path forward employs quasi-particle RPA models of nuclear level
densities. An important development will be to map the quasi-particles
onto the densities of real nucleons. Furthermore, transfer states for
nucleons derived from mean-field theory with pairing will also benefit
from a mapping of the quasi-particles and pairing densities onto
physical nucleonic densities.

### III.B.4. Improve the microscopic structure in cluster reaction models

Cluster models are useful tools used to describe collective behavior in
light nuclei, in particular alpha clustering, which most microscopic
models fail to produce. Microscopic cluster models treat Fermi
antisymmetrization and various nuclear symmetries exactly. They assume
the existence of cluster states described in a simple microscopic way
and determine quantum mechanically the wave functions of their relative
motion. The treatment of reactions occurs as a natural extension.
Applications of cluster models to astrophysical capture reactions at low
energies are particularly successful. The main limitation of the
microscopic cluster models is related to the simplified effective NN
interactions that allow the clusters to have reasonable energies and
radii. Improving the forces implies improving the internal description
of the clusters. Ultimately, in the age of advanced computation,
previous approximations should be lifted: the cluster model should
advance into an ab initio theory of reactions between light nuclei. For
instance, it is known that the effects of tensor and three-body forces
are required for a good description of the physical properties of the
clusters. Improved but tractable cluster wave functions consistent with
these forces must be derived.

Given the success of cluster models in nuclear astrophysics, improvement
on the accuracy of astrophysical S factors for transfer and capture
reactions previously studied should be obtained by combining ab initio
descriptions of bound and scattering states.

### III.B.5. Develop theoretical techniques to extract reaction rate information from indirect methods

The Coulomb barrier strongly hinders measurements of low-energy
astrophysical reaction rates. For this reason, researchers developed
indirect experimental techniques to extract rate information more
accurately. These techniques include the Coulomb Dissociation,
Asymptotic Normalization Coefficient (ANC), and Trojan horse methods. In
the Coulomb dissociation technique, a breakup reaction in the Coulomb
field of a heavy target is measured and then related to the inverse
capture reaction. In the ANC method, one uses transfer reactions to
extract the asymptotic normalization coefficient of the relevant ground
state wave function (the final state of the capture reaction), which, in
turn, determines the necessary astrophysical direct capture rate at zero
energy. Finally the trojan horse method relies on measurements of
cluster transfer reactions where a part of the incident nucleus act as a
spectator. These indirect methods are based on one-step simplifications
of the reaction amplitude. In the last few years, the effect of
Coulomb-nuclear interference, as well as continuum multi-step effects
and other higher-order processes, were shown to be relevant,
particularly in weakly bound nuclei, making the extraction of the
desired astrophysical information less transparent and precise. Optimal
observables that allow for a clean extraction of the astrophysical
information need to be identified.

Recent improvements of the accuracy of the direct capture measurements
have revealed a serious discrepancy between the direct and the indirect
methods. These discrepancies must be elucidated.

### III.B.6. Develop theoretical methods that describe fusion of heavy nuclei

![](media/image7.png){width="3.498031496062992in"
height="2.980708661417323in"}Fusion processes generate compound nuclei
which then decay by emission of gamma-rays and potentially by boiling
off neutrons. Complete fusion of light elements is responsible for
energy generation in stars, and is the experimental mechanism used to
generate super-heavy nuclei. Fusion is a dynamical process governed by
quantum mechanics and involves single- and multi-nucleon tunneling
through complicated barriers. Fusion is strongly affected by nuclear
shell effects and deformation. The actual theoretical description of
such processes is not satisfactory. Indeed, the different phenomena
participating in fusion, such as the coupling of different reaction
channels, polarization, reorientation, tunneling, and dissipation, make
the theoretical description problematic. Different avenues should be
followed to address this problem.

One approach involves the application of the coupled-channels technique,
which can take into account many open or virtual channels, possibly with
one or several particles in the continuum. This method should be further
developed to treat complex fusion processes. Also crucially important to
address are conceptual difficulties associated with differentiating
complete from incomplete fusion, as well as numerical issues in current
coupled-channels calculations including the continuum.

As discussed in Section III.C.2, a practical implementation of quantum
transport theory will benefit all reaction studies, including fusion,
where other descriptions are less successful. In particular, the
extension of time-dependent approaches that go beyond the mean-field
limit, and take into account nuclear correlations should be explored.

In the meantime, progress is expected from extensions of semi-classical
treatments such as the Langevin approaches by including more collective
degrees of freedom, and from partial studies targeting a specific aspect
of the fusion reaction such as the reorientation, the polarization, the
break-up, etc. Of particular interest is the role of the neutron haloes
and skins, and, in a more general context, the role of the isospin
dynamics in the fusion process.

## III.C. Nuclear matter equation of state

Isospin represents a fundamental quantity in nuclei and nuclear matter.
The third component of isospin measures the imbalance between neutrons
and protons in a given system. The liquid-gas phase transition in a
two-fluid asymmetric nuclear matter has some distinct new features
compared to that in the symmetric matter behaving as one fluid. For
example, the coexistence region shrinks with a reduced critical
temperature. Furthermore, the liquid and the gas phases present a
different asymmetry leading to an isospin fractionation or
"distillation\". The asymmetry term in the free energy drives both
phenomena. Studies of the isospin dependence of the nuclear phase
diagram thus enrich our understanding of the EOS of asymmetric matter.

### III.C.1. Develop statistical approaches to phase transitions and cluster formation in asymmetric nuclear matter

Most features and results of the liquid-gas phase transition can be
successfully described by statistical approaches. Only a few global
variables in reactions leading to the liquid-gas phase transition have
to be described dynamically, as demonstrated by molecular dynamics and
transport model simulations.

To extend existing statistical and thermodynamic approaches to the
liquid-gas phase transition and to cluster formation in asymmetric
matter, theoretical efforts in several directions must be explored. From
the conceptual point of view, development of a statistical description
of transient, finite, and open unbound systems based on information
theory and the characterization of phase transitions should be pursued
focusing on two-fluid systems. The role of the long-range non-saturating
Coulomb force must be investigated. From the nuclear physics point of
view, statistical multi-fragmentation models need to include more
information from nuclear structure studies on the masses and binding
energies of nuclei near neutron and proton drip lines. Furthermore,
critically important is better knowledge of the isospin dependence of
level density parameters for hot nuclei. With these improvements,
statistical approaches to be developed for the liquid-gas phase
transitions in asymmetric matter should be also useful for describing
phase transitions and cluster formation in some astrophysical
situations.

### III.C.2. Develop a quantum transport theory for complex reactions

In energetic central reactions of heavy nuclei, the nuclear medium
becomes excited and its density increases relative to that of normal
nuclei. Under these circumstances, the de Broglie wavelength of the
nucleons becomes comparable to the nucleon mean-free path, signifying
the quantum nature of nucleon transport across the reaction zone. The
importance of the quantum nature of the nucleon dynamics is reinforced
by the uncertainty principle which imposes a strong delocalization of
the nucleons. The role of the isospin degree of freedom needs to be
investigated within the framework of quantum transport theories
including sufficient many-body correlations and dynamical fluctuations.
Such theories would enable us to accurately study the origin of
measurable isospin effects and directly relate them to the properties of
underlying nuclear interactions. The challenge is to implement practical
quantum transport theories that reduce to an ab initio theory in the
limit of sufficient computing power and/or few-body systems.

One avenue of future research utilizes a non-equilibrium Green's
function approach at the 2-body level. This approach yields a
practically viable time-dependent density matrix. A further important
task involves the incorporation of the impressive developments in
electronic quantum transport applied to nanostructures in
semi-conducting devices.

Quantum transport theories may also be developed by improving existing
semi-classical transport theories that are very successful in studying
many aspects of heavy-ion reactions. One possibility would be to follow
a stochastic extension of mean-field theories in which the one-body
distribution experiences a stochastic evolution in response to the
action of a fluctuation term. The amplitude of this term is related to
the stochastic nature of the nucleon-nucleon and also incorporates
thermal effects. Another approach is by further developing the
antisymmetrized quantum molecular dynamics (AMD) model to include
collective dynamics associated with its matching to mean-field theory.

### III.C.3. Identify the role of isospin degree of freedom in the dynamics from peripheral to central reactions

The isospin degree of freedom plays an essential role in nuclear
reactions via both the initial state and the reaction dynamics. Besides
those reaction observables sensitive to the asymmetry term of the EOS,
it is particularly important to identify the role of isospin degree of
freedom in specific processes which we specify below.

![](media/image8.jpeg){width="4.5in"
height="3.119291338582677in"}Competition between various reaction
mechanisms occurs in central collisions. We need to identify the
interplay of low-energy dissipative mechanisms, e.g. fusion (incomplete)
vs. deep-inelastic vs. neck fragmentation. A stiff symmetry term in the
EOS leads to a dynamics characterized by more repulsion between nuclei.
Also, we need to model fusion dynamics in the presence of a large charge
asymmetry in the entrance channel. A dynamical prompt dipole radiation
is expected (and observed even in stable ion collisions) to be of great
interest as a cooling mechanism along the fusion path.

In addition, fragmentation in semi-peripheral reactions at the Fermi
energies needs to be studied. An interesting neutron enrichment of the
overlap ("neck") region is expected, due to the migration of
neu\\(spectator regions) to lower (neck) density regions. This effect is
sensitive to the density dependence of the symmetry energy.

The early stage of the reaction dynamics between neutron-rich nuclei
needs to be understood. Pre-equilibrium particle emissions and
collective flows appear particularly sensitive not only to the density
but also to the momentum dependence of the interaction. In asymmetric
matter the splitting of neutron and proton effective masses due to the
non-locality and/or relativistic structure of isovector interactions is
expected. The sign of the splitting is quite controversial. Hence, it is
very important to extract information on this fundamental question from
nuclear collisions. One can use probes, such as pre-equilibrium
particles, that are particularly sensitive to the high-density phase.

The relationship between the nuclear mean field and nucleon-nucleon
cross sections needs to be made more explicit. In reactions above the
Fermi energies, the isospin degree of freedom influences the dynamics
through the symmetry potential, isospin-dependent nucleon-nucleon cross
sections, and the Pauli blocking. The isospin dependence of in-medium
nucleon-nucleon cross sections is predicted to be weaker than that in
free-space. Since both the time scale and magnitude of isospin transport
are affected by the in-medium nucleon-nucleon cross sections, some
observables, such as the isospin diffusion and neutron-proton
differential flow, can also be used to extract information about the
isospin-dependence of in-medium nucleon-nucleon cross sections. A
crucial theoretical challenge is to calculate consistently all
isospin-related ingredients used in describing the reaction dynamics
from the same nuclear effective interactions.

Finally, all these phenomena require a strong simulation effort in order
to assess their sensitivity to the effective force, EOS, and transport
properties.

### III.C.4. Determine observables constraining the equation of state and phases of asymmetric matter from sub- to supra-normal nuclear densities

> RIA provides a unique opportunity to pin down the isospin-dependent
> part of the EOS of asymmetric matter, specifically, the density
> dependence of the symmetry energy. A set of observables has been
> promising as EOS probes and should be studied thoroughly.

Thus, the n-to-p ratio at large energies and probably also spectra and
yields of hard photons from the (n,p) bremstrahlung in central
reactions, are sensitive to the density and momentum dependence of the
symmetry potential. The energetic particles are expected to stem from
the high-density zone formed early on in a reaction. The symmetry
potential is expected to affect relative emission times for neutrons and
protons accessible through the n-p correlation functions. The neutron
and proton scattering from nuclei with widely varying n-p imbalance,
studied as a function of energy, and possibly the charge-exchange
reactions, can constrain the potential at subnormal and normal
densities.

Isotopic yields of Intermediate Mass Fragments (IMF) in central
collisions satisfy an approximate scaling relationship, with an
exponential coefficient constraining the symmetry energy at the time of
fragment emission. Correspondingly, from the scaling, one leans both on
the symmetry energy and on the conditions at emission. The
characteristics of midrapidity IMF from semicentral collisions have been
further suggested for probing the symmetry energy, and among those, the
correlations between different fragment N/Z ratios, masses, and
alignment.

Transport of isospin across a reacting system is sensitive to both the
density and momentum dependence of the symmetry potential, with the
potential providing a driving force. A particularly promising probe for
the features of the potential at high density and excitation is the
differential n-p flow quantifying the different accelerations that
neutrons and protons are subjected to. Finally, ratios of charged pions,
produced in NN collisions, can reveal features of the symmetry energy at
high densities. A stiff symmetry energy, larger at high ρ, will lead to
fewer π ^--^, relative to π^+^, than a soft symmetry energy. Studies of
effects for mesons with smaller rescattering effects, such as
subthreshold kaons, would be desired.

## 

## III.D. Nuclear astrophysics

We identify six astrophysical sites where close collaboration between
nuclear physics and astrophysics will maximize the impact of RIA
science. These are stars in general, core-collapse supernovae, white
dwarf supernovae, compact stellar objects together with their associated
explosive surface layer phenomena such as X-ray bursts and novae, and
the s-process in low-mass giant stars.

Nuclear theory is needed to transform the data from RIA into a
comprehensive theoretical understanding of the physics of unstable
nuclei. The experimental results of RIA must be interpreted in terms of
nuclear theory and then be incorporated into astrophysical simulations
to be translated into astrophysical observables. This requires that new
experimental and theoretical nuclear physics data are merged with
existing data into an evaluated and documented data archive for nuclear
astrophysics. This path will maximize the scientific impact of RIA on
astrophysics as it allows one to go far beyond the straightforward
implementation of directly measured data into astrophysical models. For
example, using theoretical models, one can derive astrophysically
important quantities such as reaction rates from indirect measurements
in the many instances where a direct experiment is not possible.
Furthermore, this approach will enable us to reliably predict the subset
of relevant nuclear properties that cannot be measured - either because
they are beyond the capabilities of even RIA, or because they come only
into play at the extreme temperatures and densities in the astrophysical
environment. This includes charged-particle-induced reaction rates,
which have to be extrapolated to the low astrophysical energies using
theoretical reaction models. For most astrophysical applications,
nuclear theory is required that leads to the development of accurate
global models that can be applied efficiently to all nuclei instead of
attempting to understand the physics of just a particular nucleus or
reaction. We identify here the nuclear theory efforts that are necessary
to maximize the impact of RIA experiments on progress in nuclear
astrophysics.

The consequences of such a new understanding of element production and
the required nuclear physics output must then be explored in
astrophysical models and theories. We identify those aspects of
astrophysical theories that are intimately related to the RIA
experiments, and we also identify those parts that simply comprise the
larger astrophysical context. For example, multi-dimensional
core-collapse supernovae simulations form the larger context, while
r-process post-processing calculations of such supernova models will
maximize RIA science return. Astrophysics theory is also needed to help
prioritize and plan RIA nuclear astrophysics experiments. For example,
sensitivity studies can identify the critical nuclear physics in
astrophysical models. Such studies require estimates of uncertainties
for experimental and theoretical nuclear data.

### III.D.1. Understand nucleosynthesis in the first generation of stars

Although stars have been unambiguously identified as the cauldrons of
the nuclides with mass numbers of 12 or larger, many questions about the
origin of the elements in the Universe remain still unanswered. During
their hydrostatic burning stages, stars generate their energies from
nuclear reactions producing new elements up to the zinc mass range.

Of particular current importance is the question of the nucleosynthesis
in the first generation of stars. The formation and evolution of these
stars is closely linked with the properties of the first cosmological
structures that emerged after the Big Bang, and with the onset of
reionization of the Universe. Most valuable information about the many
unknown processes that played a role in that era is contained in the
spectroscopic abundance data of the most metal-poor stars. Such stars
are now being discovered and many more will be found in future, much
more powerful spectroscopic surveys. An example is SEGUE, part of the
Sloan Digital Sky Survey (SDSS) extension, that will identify 35,000
candidate stars with ultra-low metallicity (UMP stars). Nuclear
astrophysics is needed to decipher the unique information contained in
the abundance patterns of these stars, which serve as probes for the
properties and evolution of the first stars and their cosmological
environment. Abundances determined in UMP stars are particularly
important, as they provide nucleosynthesis information on a single
supernova event or a superposition of very few nuclear production sites,
possibly also including intermediate mass stars. This is in contrast to
the solar system abundance distribution, which is a convolution of
numerous nucleosynthesis sites that are sometimes difficult to
disentangle.

![](media/image9.jpeg){width="3.1251968503937007in"
height="3.1251968503937007in"}Integrated simulations taking into account
both structure formation and nuclear production in the early universe
will lead to predictions of abundance patterns of the most metal-poor
stars that can be compared with spectroscopic data. These studies will
also clarify the nuclear physics needed to understand the underlying
nucleosynthesis processes peculiar to the first generation of stars.
However, the modeling of stellar evolution and the associated
nucleosynthesis requires the knowledge of many reaction cross sections
which, at stellar conditions, usually cannot be directly measured in the
laboratory and hence require some extrapolation procedure of data. The
theoretical models used for these extrapolations have to be improved,
advancing them to tools based on a microscopic description of the
reaction partners and dynamics.

### III.D.2. Develop quantitative nuclear microphysics for core-collapse supernova to understand the explosion mechanism and the origin of the heavy elements 

![](media/image10.png){width="3.3751968503937007in"
height="3.3437007874015747in"}The nuclides produced inside of massive
stars are ejected into the interstellar medium by cataclysmic events
involving the collapse of the stellar inner core and the subsequent
ejection of the outer stellar shells. The general picture of such
core-collapse supernovae is well accepted; however, current models are
still sensitive to the details, and slight variations in the codes
change a successful explosion to a fizzle. To obtain quantitative
supernova models, theorists must explore multidimensional effects,
detailed transport effects, and adequately incorporate all relevant
physics. Simultaneously, the underlying nuclear physics needs to be
understood. While gravity is the energy source for supernovae, neutrinos
mediate this energy, and nuclear physics will play a major role in
transforming the core collapse into an explosion. Challenges for nuclear
theory include the calculation of electron captures on nuclei at extreme
conditions, neutrino-nucleus interactions, the neutrino opacity of
nuclear matter, and the equation of state at finite temperatures and
high density.

During supernova explosions, the abundances of the nuclides produced in
the hydrostatic burning stages are modified and new elements are
produced. It is one eminent goal to simulate nucleosynthesis
consistently following all phases of hydrostatic burning and explosion.
Besides improved stellar models and the development of successful
supernova models that take into account the observed asymmetries of the
explosion, this requires the coupling of a large nuclear network to the
supernova models involving numerous reaction rates, many of which have
to be predicted by theory.

A particular important case of explosive nucleosynthesis is the
p-process, which is responsible for the origin of the most proton-rich
stable isotopes in nature in the mass range from selenium to mercury. A
likely site for the p-process is the supernova shock front passing
through the envelope of a dying star triggering (g,n), (g,p), and (g,a)
photodisintegration reactions on stable and unstable nuclei. P-process
model calculations rely heavily on reaction rate calculations using
statistical models, in particular for reaction rates on unstable nuclei.
These models require accurate descriptions of level densities and
nuclear potentials.

![](media/image11.jpeg){width="4.625196850393701in"
height="3.4925196850393703in"}Neutrinos play a crucial role for the
supernova dynamics and nucleosynthesis. The neutrino spectra have to be
reliably calculated as a function of space-time, including their
generation by weak-interaction processes on nuclei (electron captures,
beta-decays), and their transport through the hot and dense matter, and
potentially invoking neutrino flavor oscillations. The emitted supernova
neutrino spectra are predicted to exhibit a characteristic energy
hierarchy between the various neutrino types. It is the goal to observe
these differences with dedicated detectors from a future galactic
supernova.

Upon leaving the star, neutrinos can also leave fingerprints by
producing certain elements via neutrino-induced nucleon spallation off
nuclides in the outer stellar shells. The abundance of specific elements
can serve as neutrino thermometers and put constraints on oscillation
parameters once the physics of neutrino-nucleus interactions is well
understood.

The rapid neutron capture process (r-process) is responsible for the
synthesis of about half of the stable nuclei heavier than iron. As it
requires extremely high neutron densities, it is most likely connected
to explosive astrophysical sites. Currently, the r-process site or sites
are unknown, and different scenarios related to supernova explosions and
neutron star mergers are discussed and actively investigated. New,
accurate observations of r-process elements in stars expected from
ongoing and planned astronomical campaigns, as well as the solar
r-process abundance pattern, are the only way to directly constrain the
conditions at the r-process site and might hold the key to the solution
of the r-process problem. The interpretation of abundance observations
in terms of r-process conditions requires the understanding of the
underlying nuclear physics of extremely unstable neutron-rich nuclei.
RIA represents a major step in this quest, making a significant fraction
of the nuclei in the r-process accessible to experiments for the first
time. However, even with RIA, there are r-process nuclei that remain out
of reach, and even for the ones that are accessible, not all relevant
properties can be measured in all cases. This includes neutron capture
rates on unstable nuclei that can only be measured indirectly, for
example, using (d,p) transfer reactions or Coulomb breakup. For the
interpretation of such measurements, reaction models that can be applied
to heavy r-process nuclei need to be developed. In addition, theoretical
corrections for the extreme astrophysical environments during the
r-process are needed, such as theoretical predictions of capture and
decay rates on thermally populated excited states. Therefore, progress
in the understanding of the nuclear physics of the r-process requires a
concerted effort in experiment and theory. The challenge is to develop
global models that capture nuclear structure changes far from stability
and therefore have predictive power for heavy nuclei towards the neutron
drip line. What needs to be calculated are neutron separation energies,
half lives, neutron capture cross sections, beta-delayed neutron
emissions, beta-delayed and neutron-induced fission probabilities and
fragment distributions. As the r-process might occur at sites with
extreme neutrino fluxes, neutrino-induced total and partial spallation
and fission cross sections have to be calculated. It will be important
to find ways to characterize the possible theoretical uncertainties so
as to be able to judge the significance of possible differences between
r-process models and observations.

Developing realistic multi-dimensional hydrodynamic models of
core-collapse supernovae comprises the larger astrophysical context
which addresses open questions such as the explosion mechanism and
asymmetries. What is specifically needed to enhance the RIA science
output is to develop core collapse simulations, explosive
nucleosynthesis calculations, and r-process post-processing calculations
of the multi-dimensional thermodynamic trajectories of the supernova
simulation that incorporate all relevant nuclear physics. This will
transform the results from RIA into astrophysical predictions that can
be compared with observables. Besides core-collapse supernovae,
alternative sites for the r-process, in particular for secondary weaker
r-processes, need to be explored astrophysically. This is a prerequisite
for determining the nuclear physics that is relevant for such scenarios
and needs to be identified in time to guide the RIA experimental effort.

### III.D.3. Understand the nucleosynthesis of thermonuclear supernovae

![](media/image12.png){width="2.3854330708661418in"
height="2.8751968503937007in"}Thermonuclear supernovae, observationally
classified as Type Ia, are of key importance to astrophysics and
cosmology. They represent extremely bright standard candles used to
probe cosmological distances and the acceleration of the universe. They
are also an important source for nucleosynthesis, mainly elements around
iron. Type Ia supernovae are powered by the thermonuclear explosion of a
white dwarf that accretes matter from a companion star, thereby growing
in mass until it approaches the Chandrasekhar mass limit. Important open
questions are the nature of the progenitor system and the nuclear
processes that lead to the thermonuclear runaway. These questions need
to be answered before the problem of the nature of the actual ignition
can be addressed in a self-consistent way.

Weak interaction rates during the explosions significantly affect the
dynamics of the explosion and the composition of the ejected ashes.
Reliable theoretical predictions for electron capture rates, as well as
experimental constraints from RIA experiments, are needed to make
nucleosynthesis a powerful constraint for Type Ia supernova models. In
addition, nuclear burning of the outermost layers in Type Ia supernovae
needs to be investigated to clarify whether these events contribute to
the synthesis of proton-rich heavy p-nuclei found in nature (see Section
II).

Developing multi-dimensional hydrodynamic models of Type Ia supernovae
comprises the larger astrophysical context which addresses open
questions such as nature of the progenitors, ignition processes, flame
propagation, and ejected nickel mass. Running such simulations with
updated strong and weak rates ties directly to RIA experiments. In
addition, nucleosynthesis post-processing calculations of the
multi-dimensional thermodynamic trajectories will determine the effect
of RIA experimental results on observable isotopic yields.

### III.D.4. Understand nova nucleosynthesis

The nova problem is related to the Type Ia supernova progenitor
question. Novae are stellar explosions powered by explosive hydrogen
burning on the surface of accreting white dwarfs. The explosions repeat
with periods ranging from decades to 100,000 years, each time ejecting
the entire accreted envelope together with some of the underlying
white-dwarf material. The occurrence of novae in an accreting white
dwarf system therefore prevents the growth of the white dwarf needed to
initiate a Type Ia supernova. Novae are important probes for the
structure and evolution of accreting white dwarfs, and it is important
to explore the borderline between binary systems that go supernovae and
novae. Novae themselves are important contributors to galactic
nucleosynthesis possibly responsible for the origin of ^13^C, ^15^N, and
^17^O in nature, and likely contributors to the galactic inventory of
radioactive ^26^Al. Key questions are how novae can accumulate the
massive envelopes that they are observed to eject, and related to that,
how white dwarf material is mixed into the burning envelope. Again,
nucleosynthesis and observed abundances of ejecta, including the
possible future detection of γ-ray emission from radioactive decay for
example of ^22^Na, could provide powerful constraints. This requires
that the nuclear physics of the proton-rich unstable nuclei
participating in explosive hydrogen burning is well understood. Some of
these reactions will be measured directly at RIA, but some are out of
reach for experimental study and need to be calculated theoretically, or
at least be derived from indirect measurements with the help of
theoretical reaction models. As direct reaction rate experiments are
difficult and take a long time, theoretical calculations are also
important to guide experimental efforts, especially at a facility like
RIA where beam time will be highly competitive.

![](media/image13.wmf){width="3.7811023622047246in"
height="2.6145669291338582in"}In the broad astrophysical context, fully
self-consistent nova models need to be developed that take into account
the evolution of the white dwarf prior to ignition and also include a
realistic treatment of multidimenional effects such as mixing and
convection. Implementing accurate reaction rates in such calculations
and using them for sensitivity studies with realistic nuclear physics
uncertainty will directly enhance the scientific return of RIA.

[]{#__RefHeading___Toc99943723 .anchor}**III.D.5. Use X-ray binaries to
understand neutron star structure**

The final outcome of the death of a massive star is either a neutron
star a black hole. Neutron stars provide a unique laboratory for
studying the properties of matter under extreme conditions. Open
questions include the nuclear equation of state at high densities, in
particular the density dependence of the neutron proton symmetry energy,
as well as the conditions needed for superfluidity and the formation of
exotic phases such as meson or quark condensates. Neutron stars might
even be made entirely of strange matter, so called strange stars.
Nuclear theory needs to address these fundamental questions directly,
and also in terms of experimental observables in heavy-ion collisions
that can be studied for stable nuclei at RHIC and for extreme isospins
at RIA.

![](media/image14.png){width="3.5in" height="2.561811023622047in"}X-ray
binaries that contain a neutron star that accretes matter from a
companion are a particularly rich source of information on neutron
stars. These systems provide a wide range of observables, ranging from
thermal radiation, ms oscillations, and absorption lines to bright X-ray
bursts and superbursts. These observables are directly powered by a
variety of nuclear processes. Understanding the nuclear physics of these
processes is a pre-requisite for using them as powerful probes to
extract neutron star properties such as mass, radius, magnetic field
strengths, spin frequencies, and core cooling rates. Among the most
important nuclear processes is the explosive hydrogen and helium burning
that powers X-ray bursts and determines the composition of the neutron
star crust. The reaction sequence during an X-ray burst proceeds through
nuclei at or close to the proton drip line mainly by (p,γ) and (p,α)
reactions and beta-decays (rp-process). A statistical description of the
proton-induced reactions for nuclei close to the proton drip line is
inadequate due to the insufficient density of states. Hence, nuclear
reaction models incorporating appropriate nuclear structure have to be
developed for extrapolation or prediction of low-energy reaction cross
sections and for the extraction of crucial information for such cross
sections from indirect experimental measurements. Improved nuclear
structure models for the description of beta-decays at finite
temperature are also needed.

Advancing X-ray burst calculations, for example, to take into account
more physics such as multi dimensional effects, rotation, or diffusion,
comprises the larger astrophysical context which addresses open
questions such as flame propagation across the surface, oscillations
modes, transition from unstable to stable burning, and super-bursts. To
enhance the scientific impact of RIA, these calculations need to be used
to explore the underlying nuclear processes by incorporating all
relevant nuclear physics. Astrophysical X-ray burst models that give
light curves are intimately related to the RIA experiments. The light
curves are sensitive to the nuclear physics input and place the relevant
RIA experimental results into the astrophysical context. In addition,
these light curves can be directly compared to observations from
high-energy satellite missions. Astrophysical models also need to
explore whether some of the synthesized elements in X-ray bursts can be
ejected from the neutron star and either can contribute to the element
abundances in the Universe or are at least observable spectroscopically.
Due to continuous accretion, the ashes of X-ray bursts become
incorporated into the crust of the neutron star where it undergoes
electron captures, neutron drips, and potentially pycnonuclear fusion
reactions. These reactions generate energy, which changes the properties
of the neutron star and are observable as residual luminosity in soft
X-ray transients during periods without accretion. Calculations of these
crust processes that incorporate RIA nuclear physics are needed to
explore the sensitivity of observables to neutron star properties such
as crust conductivities, compactness, and the state of matter in the
interior. Together with such calculations, results from RIA will allow
one to use observations of X-ray binaries to constrain the properties of
neutron stars.

### III.D.6. Understand low-mass giants and the s-process

In the final, advanced phase of evolution, low- and intermediate-mass
stars inflate to giant dimension, fueled by nuclear burning of H and He
in shells surrounding the electron-degenerate core. These Asymptotic
Giant Branch (AGB) stars are the nuclear production site of the slow
neutron capture process (s-process). About half of all elements heavier
than iron are made by this sequence of neutron capture processes,
interrupted by β-decays. In the past, much of the s-process nuclear
physics involving experimental work with stable beams and targets has
been completed. Simultaneously, a better theoretical understanding of
the thermodynamic evolution of AGB stars has been developed. However,
the main uncertainties are still the mixing processes, in particular at
convective boundaries, and those induced by rotation and magnetic
fields. These uncertainties impede accurate chemical yield predictions
for stars of all masses, as well as the initial models for supernova
explosions.

![](media/image15.png){width="4.75748031496063in"
height="1.7007874015748032in"}Branching points in the s-process in AGB
stars provide a method to better understand the physics of mixing in
stars. Branchings are radioactive nuclides where stellar β-decay and
neutron capture times are comparable. The branching ratio depends then
on the thermodynamic conditions and on the uncertain mixing processes.
The branchings determine isotopic as well as some elemental ratios in
the stellar ejecta. These are observable in stellar spectra or can be
measured in presolar grains. Comparison of these astrophysical
observables with model predictions directly tests the model assumptions
including mixing mechanisms. This method of using the s-process on
radioactive nuclides as a diagnostic tool can significantly improve our
understanding of the conditions at the nuclear production sites in stars
in general. However, accurate capture cross sections and β-decay
half-lives of the involved unstable nuclides are absolutely necessary
for this approach. Some of the potent cases in this context can only be
measured with a neutron facility in conjunction with radioactive target
production at RIA. Nuclear theory is needed to complement the
experimental data to provide accurate cross sections over the entire
relevant energy range. Nuclear theory is also needed to calculate
corrections to neutron capture rates and beta decay half-lives due to
the stellar environment.

# IV. Summary: Challenges and Opportunities

RIA theory covers a range of activities from nuclear structure and
reactions, to nuclear equation-of-state issues. Furthermore, many
nuclear issues are relevant to processes in astrophysical environments.
Since all nuclei heavier than carbon are made in stars, this synergy is,
in fact, natural. Understanding both the basic nature of the nuclear
many-body problem and understanding the effects of nuclear physics on
stellar evolution and nucleosynthesis constitutes major intellectual
efforts. Furthermore, low-energy nuclear science remains important in
matters of national safety and security.

The previous chapter describes a number of theoretical challenges that
must be met during the next decade in order to facilitate the success of
an experimental program focused on short-lived isotopes. These efforts
include:

-   Development of ab initio approaches to medium mass nuclei.

-   Development of self-consistent nuclear DFT methods for static and
    dynamic problems.

-   Development of reaction theory that incorporates relevant degrees of
    freedom for weakly bound nuclei.

-   Exploration of the isospin degrees of freedom of the
    density-dependent nuclear force.

-   Development and synthesis of nuclear theory, and its consequent
    predictions, into various astrophysical models to determine the
    nucleosynthesis in stars.

Present research facilities and projected upgrades to them, and the
future RIA experimental facility, are measuring, or will measure,
nuclear structure and reactions for nuclei that have very short
half-lives and live close to the neutron (or proton) drip line. Many of
these experiments will be relevant to astrophysics and will enable a
comparison of theoretical predictions to experimental data. There will
be numerous (in fact, many) nuclei and nuclear properties that we cannot
measure. For an understanding of those systems, a robust
nuclear-theoretical capability is required.

Certain critical investments in nuclear theory research over the last 10
years are yielding significant knowledge and understanding of properties
of nuclei. Continued success will require investments in the following
areas.

-   Several approaches to the nuclear many-body problem have enabled
    both few- and many-body calculations to proceed in an ab initio way,
    starting from the basic two- and three-nucleon interactions.
    Critical investments for nuclear theory will include extensions of
    ab initio techniques to heavier nuclei and drip-line systems.

-   Self-consistent mean-field theories offer a robust and global
    approach to a wide range of nuclei and nuclear properties. Critical
    to the success of this endeavor will be a full description of the
    energy density functional, and the development of methods to treat
    excited states and giant resonances on the same footing.

-   The treatment of the continuum in both structure and reaction
    theories has been, and will continue to be, a critical area that
    requires both new ideas and potentially new computational techniques
    in order to be successfully applied to nuclear scattering of
    near-drip-line nuclei.

-   An understanding of the isospin dependence of the nuclear equation
    of state will be an important outcome of the medium-energy collision
    work performed at RIA. Theorists also need to develop methods to
    extract from experimental data relevant quantities that will enable
    a description of the nuclear equation of state.

-   The interplay of astrophysics and low-energy nuclear theory requires
    some level of coordination. This is taking place through two
    supernova SciDAC efforts for nuclear physics relevant to supernova
    production. We identified several other astrophysically interesting
    sites that would benefit from nuclear theory input.

While significant progress on the basic theoretical underpinnings of the
nuclear many-body problem will require an enhanced workforce development
and research effort, one challenge will be to export the knowledge
gained from these research activities to the broader nuclear physics and
nuclear astrophysics communities. One component of future research will
be to assess the validity of models used in nuclear science applications
(for example, in nuclear astrophysics), and that assessment hinges on
our ability to perform calculations in ever larger nuclei and in nuclei
far from stability.

We also identified several important areas and elements of theoretical
nuclear astrophysics that should be actively supported. Each scientific
area involves interdisciplinary challenges for both nuclear theory and
astrophysics theory. Progress requires mutually beneficial and
coordinated research in theoretical astrophysics and nuclear physics.
This will allow us to combine leading-edge nuclear physics with the
latest astrophysical models to answer the major open questions in
nuclear astrophysics.

# Appendix: development of this report and its authors

The RIA Theory Bluebook was generated by the RIA Theory Group at the
direction of the RIA Theory Group Executive Committee. Executive
committee members are:

-   David J. Dean, Chair (ORNL)

-   Jacek Dobaczewski (Warsaw)

-   Karlheinz Langanke (GSI)

-   Filomena Nunes (MSU)

-   Erich Ormand (LLNL)

A meeting of the full RIA Theory Group was held in Chicago on October
31, 2004 to begin the process of writing. At that meeting, summary talks
of the current status and future directions were given by Witek
Nazarewicz (nuclear structure), Phillip Chomaz (nuclear reactions), and
Yong Qian (nuclear astrophysics). A writing team was also established at
the Chicago meeting. Dean served as editor of the Bluebook. The members
of these teams are:

-   Nuclear Structure

    -   George Bertsch (University of Washington)

    -   Dick Furnstahl (Ohio State University)

    -   Witek Nazarewicz (University of Tennessee/ORNL)

    -   Erich Ormand (LLNL) (Coordinator)

-   Nuclear Reactions

    -   Philippe Chomaz (GANIL)

    -   Pawel Danielewicz (Michigan State University)

    -   Bao-An Li (Arkansas State University)

    -   Filomena Nunes (Michigan State University) (Coordinator)

    -   Ian Thompson (Surrey)

    -   Daniel Baye (Brussels)

-   Nuclear Astrophysics

    -   Karlheinz Langanke (GSI, Darmstadt)

    -   Hendrik Schatz (Michigan State University) (Coordinator)

    -   Chris Fryer, Alexander Heger, Falk Herwig, and Frank Timmes
        (LANL)

-   Interdisciplinary Science

    -   Alex Brown (Michigan State University) (Coordinator)

    -   Vladimir Zelevinsky (Michigan State University)

    -   David Dean (ORNL)

Chairs of the various writing sections held regular teleconferences
during the course of the writing of the document.

Once written, the report was posted on the web for a period of 3 weeks
for open comment from the RIA Theory Group. The writing group
incorporated comments from the community into the document. Final
publication occurred in May 2005. The bluebook will reside on the RIA
Theory Group web page at
[www.orau.org/RIATG/](http://www.orau.org/RIATG/).

# FIGURE CREDITS

-   Figure 1: Courtesy of Steven Pieper and the GFMC collaboration,
    Argonne National Laboratory

-   Figure 2: "Shape coexistence and triaxiality in the superheavy
    nuclei", S. Cwiok, P.H. Heenen, and W. Nazarewicz, Nature 433, 705
    (2005).

-   Figure 3: Courtesy W. Nazarewicz, University of Tennessee

-   Figure 4:

-   Figure 5:

-   Figure 6:

-   Figure 7:

-   Figure 8: from B. O\'Shea, priv. comm. 2005.

-   Figure 9:

-   Figure 10:

-   Figure 11:

-   Figure 12:

-   Figure 13: