A characteristic feature of nuclei far from stability is the close vicinity of the continuum. This presents new opportunities and new challenges, both to structure and reaction theory. The conventional methods for stable nuclei have been to use the Shell Model to describe the structure and coupled-channels calculations to describe reactions. Both methods were in fact pioneered and developed here at Argonne, by Maria Goeppert-Mayer, Dieter Kurath, Stan Cohen, and Bob Lawson (Shell Model), and by Malcolm MacFarlane and Steve Pieper (PTOLEMY), respectively. Both methods consider a finite number of basis of states. The close vicinity and strong influence of the continuum in unstable nuclei, however, makes it difficult or impracticable to use these methods.

Our theoretical efforts are currently directed towards RIA-type experiments that are or can be performed at existing low-energy, heavy-ion facilities, such as ATLAS at Argonne, Holifield at Oak Ridge, and at fragmentation facilities, such as Michigan State University. The aim has been not only to provide theoretical support for the analyses and interpretation of such experiments but also to test the structure models we have developed. Our activities can roughly be divided into the following categories:

*Ab Initio* calculations of light nuclei

Structure and reactions of halo nuclei

Structure of heavy drip-line nuclei

Reactions of interest to astrophysics

Reaction theory for nuclei far from stability

Hadronic models of nuclei

Nuclear structure in heavy and superheavy elements

Superdeformation

N-P pairing

We have been developing realistic two- and three-nucleon potentials and
the quantum many-body methods necessary to evaluate them in light nuclei.
The many-body methods we use are two quantum Monte Carlo (QMC) methods:
variational (VMC) and Green's Function (GFMC). To date they have been
successfully applied to all nuclei up to mass *A*=10 [2].
Some results for nuclear spectra are shown in the figure above, where
we compare calculated energies of ground and excited states with
experiment for a number of nuclei.
The left-most bars show the results for our realistic Argonne v_{18}
(AV18) *NN* potential [3] alone, while the middle bars show
the results with the Illinois-2 (IL2) three-nucleon potential [4] added.
This AV18/IL2 model currently reproduces 53 levels in *A*=3--10 nuclei
with an rms deviation of only 740 keV.

One of the interesting aspects for RIA-related physics is elucidating
the nature of the three-nucleon force in neutron-rich systems,
such as ^{6,8}He, or in neutron drops - collections
of neutrons artificially confined by an external potential well [5].
These studies can help to formulate more schematic models, like Skyrme
energy-density functionals, that can be used for much larger nuclei.
The *3N* force also plays an important role in the equation of state for
dense neutron matter and neutron stars [6].

Aside from calculating energies of nuclear states, the VMC and GFMC methods are being used to study a wide variety of other properties, such as elastic and transition form factors [7], spectroscopic factors [8], and weak decay rates [9]; additional applications specific to halo nuclei are discussed below.

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

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

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

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

[5] B. S. Pudliner, *et al.*,
Phys. Rev. Lett. **76**, 2416 (1996)

[6] R. B. Wiringa, V. Fiks, and A. Fabrocini,
Phys. Rev. C **38**, 1010 (1988)

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

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

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

However, complete many-body calculations of larger nuclei are difficult and
often impracticable, so it is useful to resort to much simpler descriptions
that grasp the essential physics of a given problem. One example is the
three-body model of two-neutron halo nuclei, which we developed
early on for ^{11}Li [3,4]. The model contained the basic
Borromean features, namely, that the ^{9}Li-neutron and the
neutron-neutron
subsystems are both unbound but the scattering lengths are fairly large
so that the combined ^{9}Li-n-n three-body system becomes bound.

Our early work was based on a density-dependent, contact interaction
between the two neutrons. The strength of this interaction was calibrated
to produce an infinite neutron-neutron scattering length at low density,
far from the ^{9}Li core.
Moreover, core recoil effects were ignored. These simplifications
made it possible to calculate the ground state [3] and the dipole
response [4] of ^{11}Li, effectively as a two-body problem,
using a two-body Greens function technique.

We have tested the model against numerous measurements, as, for example,
the production of ^{11}Li in pion-double-charge exchange reactions
on ^{11}B [5], fragmentation cross sections at high energy [6],
and fragment momentum distributions in Coulomb dissociation experiments
[7]. Although the model is simple and schematic, it reproduces many
essential features of the experiments. Of particular interest
is the effect of correlations between the two valence neutrons,
which is probed in the pion-double-charge exchange reaction [5],
and in the relative momentum distributions of the fragments [7].

One uncertainty in the model is the ^{9}Li-neutron interaction which
was poorly know in the early 90's. A better empirical knowledge
was obtained in the mid-90's. We used this opportunity to improve
our calculations [8] by using more realistic ^{9}Li-neutron and
neutron-neutron interactions, and also to treat recoil effects in the
three-body system correctly. The new model was used to analyze high-energy
nuclear induced breakup reactions [9]. The analysis showed that equal
amounts of *s* and *p* waves in the ^{11}Li halo were
favored by the data.

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

[2] K. Varga, S. C. Pieper, Y. Suzuki, and R. B. Wiringa,
Phys. Rev. C **66**, 034611 (2002)

[3] G. F. Bertsch and H. Esbensen, Annals of Physics 209, 327 (1991)

[4] H. Esbensen and G. F. Bertsch,
Nucl. Phys. **A542**, 310 (1992)

[5] H. Esbensen, D. Kurath and T.-S. H. Lee, Phys. Lett. B287, 289 (1992).

[6] H. Esbensen and G. F. Bertsch,
Phys. Rev. C **46**, 1552 (1992)

[7] H. Esbensen, G. F. Bertsch, and K. Ieki,
Phys. Rev. C **48**, 326 (1993)

[8] H. Esbensen, G. F. Bertsch, and K. Hencken,
Phys. Rev. C **56**, 3054 (1997)

[9] G. F. Bertsch, K. Hencken, and H. Esbensen,
Phys. Rev. C **57**, 1366 (1998)

We have developed a coupled-channels description of a proton interacting with a deformed core, a so-called particle-rotor model [1]. The model has been applied to analyze the data for the proton decay of nuclei that are known or expected to be deformed, and a fairly consistent picture has emerged. Thus it appears that the spectroscopic factors we extract are in good agreement with estimates based on BCS pairing.

A numerical problem we faced was to calculated extremely narrow widths,
of the order of 10^{-20} MeV associated with life-times in the range
of milliseconds to seconds. This would be very difficult in ordinary
scattering theory, or by treating the decaying state as a Gamow state
with a complex energy. We adopted and developed a different technique,
which is based on the Gell-Mann Goldberger transformation [2].

We have also developed a description of the proton decay from near-spherical nuclei which includes couplings to vibrational excitations of the core, i.e., a particle-vibration model [3].

[1] H. Esbensen and C. N. Davids,
Phys. Rev. C **63**, 014315 (2001)

[2] C. N. Davids and H. Esbensen,
Phys. Rev. C **61**, 054302 (2000)

[3] C. N. Davids and H. Esbensen,
Phys. Rev. C **64**, 034317 (2001)

One possibility is to calculate reaction rates from the most accurate
and reliable nuclear structure models on the market. This can be done
for lighter nuclei where the QMC calculations provide an accurate
description of nuclei. First calculations of radiative captures to
^{6}Li [1], ^{7}Li, and ^{7}Be [2] have been
made; these reactions with stable nuclei are important for big bang
nucleosynthesis. In the case of ^{6}Li the cross section is so
small at the relevant energies that experiments are extremely difficult,
while the experimental situation for capture to ^{7}Be is very
uncertain, as shown in the above figure. The calculation's accurate
reproduction of the ^{7}Li S-factor suggests that lower data
for the ^{7}Be S-factor may well be the most reliable.
We plan to extend these studies in future to other nuclei amenable to
QMC calculations, such as ^{8}B.

Another possibility is to measure the Coulomb dissociation of
unstable nuclei, and use detailed balance to infer the rate of the
inverse radiative capture reactions. This avenue is possible at a RIA
facility where beams of unstable nuclei can be produced with sufficient
intensity. This is already possible for lighter nuclei at the existing
fragmentation facilities. Thus we have taken part in the analysis of the
^{8}B Coulomb dissociation experiments, which have been performed
at Michigan State University [3,4]. The analysis showed that the
Coulomb dissociation technique can be made into a reliable tool for
inferring radiative capture rates.

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

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

[3] B. Davids *et al.*,
Phys. Rev. Lett. **86**, 2750 (2001)

[4] B. Davids *et al.*,
Phys. Rev. C **63**, 065806 (2001)

We have also investigated the Coulomb dissociation of halo nuclei.
Early on we applied first-order perturbation theory, which is a
fairly reasonable approximation for neutron halo nuclei [4].
For proton halo nuclei [5], on the other hand, the first-order
approximation becomes unreliable at low beam energies.
The reason is a dynamic polarization effect, which is of order Z^{3}
in the target charge Z. It is caused by an interplay of higher-order
E1 and E2 transitions [6,7].
This mechanism does not play any role in the Coulomb dissociation
of a neutron halo nucleus because the E2 strength is strongly
suppressed compared to what it is in a proton halo nucleus.

Another complication of the dissociation of proton halo nuclei
is that the Coulomb form factors are sensitive to close collisions,
where the proton-core distance is larger than the projectile target
distance [6,7]. The combined effect of dynamic polarization and
close collisions explains nicely the strong reduction that has been
observed in the dissociation cross section of ^{8}B at low
energy [7].

[1] G. F. Bertsch, H. Esbensen, and A. Sustich,
Phys. Rev. C **42**, 758 (1990)

[2] K. Hencken, G. Bertsch, and H. Esbensen,
Phys. Rev. C **54**, 3043 (1996)

[3] H. Esbensen and G. F. Bertsch,
Phys. Rev. C **64**, 014608 (2001)

[4] H. Esbensen, G. F. Bertsch, and C. A. Bertulani,
Nucl. Phys. **A581**, 107 (1995)

[5] H. Esbensen and G. F. Bertsch,
Nucl. Phys. **A600**, 37 (1996)

[6] H. Esbensen and G. F. Bertsch,
Nucl. Phys. **A706**, 383 (2002)

[7] H. Esbensen and G. F. Bertsch,
Phys. Rev. C 66, 044609 (2002)

A major goal of pursuing a broad approach of this kind is to investigate the
influence of hadronic interactions on a range of observables including the
properties of nuclei and neutron stars [5]. In the RIA facility, by approaching
the neutron dripline, especially the isospin effects in hadronic physics will
become important. For theory this entails the need to extrapolate the nuclear
forces to large isospins, which can only be controlled by studying the impact
of varying isospin-dependent interactions for a wide range of observables. In
this spirit we varied several isospin-dependent chirally invariant interaction
terms in our model [8] and studied the influence of those terms on the neutron
skin of heavy nuclei and on the radii of neutron stars as shown in the Figure.
The graph shows the correlation of the neutron skin Δ r_{np} of ^{208}Pb
and the radius of a neutron star with a typical mass of 1.4 solar masses. The
strengths of isospin interactions are varied. The shaded band denotes the
expected accuracy of an upcoming experiment measuring the neutron distribution
in Pb.

As extension of our studies we also investigate isospin-dependent flow and fragment production patterns in heavy-ion collisions at RIA-relevant energies. In the same framework we have already successfully reproduced experimental particle production yields at very high beam energies [7].

[1] P. Papazoglou, J. Schaffner, S. Schramm, D. Zschiesche, H. Stöcker and W.
Geiner, Phys. Rev C **55**,
1499 (1997)

[2] P. Papazoglou, S. Schramm, J. Schaffner, H. Stöcker and W. Greiner,
Phys. Rev. C **57**, 2576 (1998)

[3] P. Papazoglou, D. Zschiesche, S. Schramm, J. Schaffner-Bielich, H. Stöcker
and W. Greiner, Phys. Rev. C **59**,
411 (1999)

[4] Ch. Beckmann, P. Papazoglou, S. Schramm, D. Zschiesche, H. Stöcker, W.
Greiner, Phys. Rev. C **65**,
024301 (2002)

[5] S. Schramm, Phys.
Rev. C **66**, 064310 (2002)

[6] M. Hanauske, D. Zschiesche, S. Pal, S. Schramm, H. Stöcker, W. Greiner,
Ap. J. **537**, 958 (2000)

[7] D. Zschiesche, S. Schramm, J. Schaffner-Bielich, H. Stöcker, W. Greiner,
Phys. Lett. B **547**, 7 (2002)

[8] S. Schramm, preprint
nucl-th/0210053, submitted to Phys. Lett. B

We have been engaged in a long term collaboration with experimentalists in the study of heavy elements and have used these data to make predictions about the stability of superheavy elements. An early result of such extrapolations was the realization that there is a strong [1] spherical neutron shell stabilization starting at roughly 178 neutrons rather than at the 184 neutron closed shell. From our studies of the heaviest elements, we found that there is a large gap [2] in the level spacings of deformed actinides at N=162 and N=164, suggesting exta stabilization for nuclei with such neutron numbers.

As experimental spectroscopic studies go to higher mass actinides, we continue [3-7] to utilize such data to make more accurate extapolations of the properties of superheavy elements. The figure shows our estimate of shell stabilization energies based on studies of the heaviest elements. We find large stabilization effects for all elements from Z=112 to Z=120.

[1] R. R. Chasman, in *Proceedings of the International Symposium on
Superheavy Elements, Lubbock, Texas, 1978*, edited by M. A. K. Lodhi

[2] R. R. Chasman, I. Ahmad, A. M. Friedman, and J. R. Erskine,
Rev. Mod. Phys. **49**, 833 (1977)

[3] R. R. Chasman and I. Ahmad, Phys. Lett. B **392**, 255 (1997)

[4] I. Ahmad, A. M. Friedman, R. R. Chasman, and S. W. Yates,
Phys. Rev. Lett. **39**, 12 (1977)

[5] I. Ahmad, R. R. Chasman, A. M. Friedman, and S. W. Yates,
Phys. Lett. B **251**, 338 (1990)

[6] I. Ahmad, et al.,
Nucl. Phys. **A646**, 175 (1999)

[7] I. Ahmad, R. R. Chasman and P. R. Fields,
Phys. Rev. C **61**, 044301 (2000)

Experimental searches for superdeformed shapes are difficult and
theoretical guidance [1-3] is necessary. For a theoretical calculation to be
useful, it must describe many shape possibilities. In addition to
describing the shapes in superdeformed minima, a useful theoretical
treatment must also give an accurate description of the fission
barrier and the barriers between normal and superdeformed shapes. If
either barrier is too low, the superdeformed minimum will not
accommodate any states. We have developed a four-dimensional [4-8]
description of nuclear shapes that includes an explicit description of
necking in. This approach gives an accurate treatment of fission
barriers in addition to an accurate treatment of deformed,
superdeformed and hyperdeformed nuclear shapes. Our calculations [9]
include nuclei that have too large a neutron excess to be accessible
with today's accelerators. By accessible we mean that these nuclides
can be produced at sufficiently high spins to populate very deformed
shapes. In the figure, we display the calculated energy surface of
^{108}Cd at an anglular momentum of I=60 hbar. At this angular
momentum, the minimum in the energy surface corresponds to a very
extended shape with major to minor axis ratios of 2.3:1. With present
day accelerators, such angular momenta are not accessible.

[1] R. R. Chasman, Phys. Lett. B **187**, 219 (1987)

[2] R. R. Chasman, Phys. Lett. B **219**, 227 (1989)

[3] E. F. Moore, et al.,
Phys. Rev. Lett. **63**, 360 (1989)

[4] R. R. Chasman, Phys. Lett. B **302**, 134 (1993)

[5] J. L. Egido, L. M. Robledo, and R. R. Chasman,
Phys. Lett. B **322**, 22 (1994)

[6] R. R. Chasman, Phys. Lett. B **364**, 137 (1995)

[7] J. L. Egido, L. M. Robledo, and R. R. Chasman,
Phys. Lett. B **393**, 13 (1997)

[8] R. R. Chasman,
Phys. Rev. Lett. **80**, 4610 (1998)

[9] R. R. Chasman,
Phys. Rev. C **64**, 024311, (2001)

We are developing a treatment of n-p pairing that goes far beyond the quasi-particle approach. We have developed [1,2] a triple projection method that gives a more accurate treatment of the pairing Hamiltonian and corresponds roughly to isospin projection. In the figure, we display low-lying states calculated for several odd-odd nuclei using constant pairing matrix elements. In the upper part of the figure, we show calculated spectra for equally spaced single-particle levels and in the lower part of the figure, we show results for a system in which some single particle levels are bunched in the vicinity of the Fermi level.

[1] R. R. Chasman,
Phys. Lett. B **524**, 81 (2002)

[2] R. R. Chasman,
Phys. Lett. B **553**, 204 (2003)