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Each <strong>of</strong> these extensions will open the possibilities <strong>of</strong><br />

new phase transitions.<br />

New results are also expected from the microscopic<br />

approaches based on EDF methods. These should allow<br />

a deeper understand<strong>in</strong>g <strong>of</strong> the orig<strong>in</strong> and the nature <strong>of</strong><br />

the nuclear shape phase transitions. In particular, the<br />

richer scenario <strong>of</strong>fered by these microscopic approaches<br />

with respect to more schematic boson models will lead<br />

to more realistic predictions for the position <strong>of</strong> the critical<br />

nuclei <strong>in</strong> the mass table<br />

Reactions<br />

The availability <strong>of</strong> low- and high-energy radioactive<br />

beams and, <strong>in</strong> particular the discovery <strong>of</strong> halo-nuclei,<br />

has brought out a renewed <strong>in</strong>terest <strong>in</strong> the model<strong>in</strong>g <strong>of</strong><br />

nuclear reactions. To take <strong>in</strong>to account the complexity<br />

<strong>of</strong> the many-body problem, current approaches to<br />

reaction theory <strong>in</strong>volve different approximations whose<br />

validity needs to be checked, <strong>in</strong> particular when applied<br />

to exotic light nuclei.<br />

In the last few years important advances <strong>in</strong>clude:<br />

(a) the description <strong>of</strong> very-low energy subbarrier fusion<br />

processes that should provide <strong>in</strong>formation on the<br />

<strong>in</strong>ner part <strong>of</strong> the ion-ion potential;<br />

(b) general parameterizations <strong>of</strong> the ion-ion optical<br />

potentials aimed at the description <strong>of</strong> both fusion<br />

and quasielastic processes for stable and unstable<br />

systems;<br />

(c) a consistent coupled-channel microscopic formalism<br />

for the description <strong>of</strong> mult<strong>in</strong>ucleon transfer reactions,<br />

with the <strong>in</strong>tent <strong>of</strong> clarify<strong>in</strong>g the smooth transition from<br />

graz<strong>in</strong>g to deep-<strong>in</strong>elastic processes;<br />

(d) massive calculations <strong>of</strong> elastic and break-up<br />

processes <strong>in</strong>volv<strong>in</strong>g exotic halo nuclei, exploit<strong>in</strong>g<br />

coupled-channels approaches based on cont<strong>in</strong>uum<br />

discretization;<br />

(e) novel approaches based on the ab <strong>in</strong>itio <strong>in</strong>clusion <strong>of</strong><br />

the halo few-body nature <strong>in</strong>to the reaction formalism;<br />

(f) extensions to the explicit treatment <strong>of</strong> four-body channels<br />

(as <strong>in</strong> break-up reactions <strong>in</strong>volv<strong>in</strong>g two-neutron<br />

halo nuclei).<br />

<strong>Perspectives</strong><br />

There are two major issues <strong>in</strong> any reaction approach:<br />

first, to ensure that sufficiently detailed microscopic<br />

structure <strong>in</strong>formation <strong>of</strong> the <strong>in</strong>teract<strong>in</strong>g nuclei is <strong>in</strong>corporated<br />

(via optical potentials, form-factors, spectroscopic<br />

factors, etc.) and, second, a proper treatment <strong>of</strong> the<br />

relevant dynamics. These two aspects are <strong>of</strong>ten <strong>in</strong>tertw<strong>in</strong>ed<br />

and need to be carefully addressed.<br />

With<strong>in</strong> this general framework several topics can be<br />

s<strong>in</strong>gled out for future work. In particular:<br />

(a) a more extended use <strong>of</strong> microscopic models for the<br />

excitation (via different probes as Coulomb, <strong>in</strong>elastic,<br />

charge-exchange, transfer, etc) <strong>of</strong> different collective<br />

and non-collective modes (e.g. dipole pigmy<br />

states).<br />

(b) a consistent description <strong>of</strong> the <strong>in</strong>terplay between<br />

cont<strong>in</strong>uum and many-body correlations, for systems<br />

with unbound ground states and above threshold for<br />

weakly-bound systems<br />

(c) a further clarification <strong>of</strong> the reaction mechanism for<br />

two- and multiparticle transfer reactions, <strong>in</strong> relation<br />

with the role <strong>of</strong> pair<strong>in</strong>g-like <strong>in</strong>teractions (<strong>in</strong> both isosp<strong>in</strong><br />

T=0 and T=1 channels)<br />

(d) a systematic comparison between different scatter<strong>in</strong>g<br />

approaches with similar structure and dynamical<br />

<strong>in</strong>puts, <strong>in</strong> order to clarify the validity <strong>of</strong> different<br />

approximation schemes<br />

(e) the development <strong>of</strong> a reliable framework for the study<br />

<strong>of</strong> quasi-free breakup, that will yield <strong>in</strong>formation on<br />

the wave function <strong>of</strong> the struck particle, <strong>in</strong> particular<br />

at high energies at which the scatter<strong>in</strong>g framework<br />

is expected to become simpler.<br />

In addition to developments with<strong>in</strong> the conventional<br />

models, promis<strong>in</strong>g results have been obta<strong>in</strong>ed employ<strong>in</strong>g<br />

other approaches, <strong>in</strong> some cases novel, and <strong>in</strong> other<br />

cases revitalized after decades <strong>of</strong> obsolescence (such<br />

as TDHF mean-field calculations for reactions). In the<br />

case <strong>of</strong> reactions <strong>in</strong>volv<strong>in</strong>g light ions, <strong>in</strong> particular, much<br />

is expected from the extension <strong>of</strong> ab <strong>in</strong>itio shell-model<br />

calculations to reactions, as well as from structure models<br />

based on the cluster approach.<br />

Toward a unified description<br />

<strong>of</strong> nuclear structure and reactions<br />

<strong>Nuclear</strong> theory is rapidly evolv<strong>in</strong>g from studies <strong>of</strong> nuclei<br />

close to the valley <strong>of</strong> beta-stability towards a description<br />

<strong>of</strong> vast regions <strong>of</strong> short-lived and exotic nuclei far from<br />

stability and at the nucleon drip-l<strong>in</strong>es. Such an expansion<br />

imposes str<strong>in</strong>gent constra<strong>in</strong>ts on microscopic structure<br />

and reaction models that are be<strong>in</strong>g developed. These<br />

ma<strong>in</strong>ly concern the model space that must take <strong>in</strong>to<br />

account the coupl<strong>in</strong>g between bound states and the<br />

cont<strong>in</strong>uum, and the construction <strong>of</strong> effective <strong>in</strong>teractions<br />

that can be used all over the nuclear chart. This<br />

overview <strong>of</strong> the various aspects <strong>of</strong> modern nuclear theory<br />

has focused on the current status and perspectives <strong>of</strong><br />

our understand<strong>in</strong>g and modell<strong>in</strong>g <strong>of</strong> low-energy nuclear<br />

physics.<br />

<strong>Perspectives</strong> <strong>of</strong> <strong>Nuclear</strong> <strong>Physics</strong> <strong>in</strong> <strong>Europe</strong> – NuPECC Long Range Plan 2010 | 109

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