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Nuclear structure

Other working groups have outlined the key issues of nuclear structure far from stability and their experimental exploration with RIB facilities. Here we will focus on astrophysical aspects via mass and beta-decay measurements with RIB's involving neutron-rich and proton-rich nuclei [29]. Mass measurements reflect shell structure, deformation and pairing correlations. In $(n,\gamma)-(\gamma,n)$ or $(p,\gamma)-(\gamma,p)$ equilibrium conditions, as they are approached in the r- and rp-process, neutron or proton separation energies with a precision of about 100 keV are required for astrophysical applications and should be extended to lifetimes, preferably as small as ms. The properties of near proton drip-line isotopes are necessary to determine the rp-process reaction path in the mass range A$\ge$56. Of particular interest are measurements of masses, beta-decay half-lives and beta-delayed proton emission along the N=Z line, possibly extending up to Z=50. Such experiments can be performed at fragment separator facilities for radioactive beams like GANIL/LISE, GSI/ESR, NCSL/MSU or RIKEN. Regions where the r-process path comes closest to stability and causes three abundance maxima are located at the closed neutron shells N=50, 82, 126 for A$\sim$ 76-82, 128-132, 190-196. N=50 and 82 have been reached for A=79,80 and 129,130 by experiments at CERN-ISOLDE. The knowledge of beta-decay half-lives and delayed neutron emission were very helpful in interpreting the relation to solar abundances.
 
Figure: The rp-process path, including 2p-captures, for temperatures of 1.9 $\times 10^9$K and densities of 106g cm-3 [15]. Also shown are stable nuclei and the position of the proton-drip line.
\begin{figure}\epsfig{file=astro/fig8.eps,width=\columnwidth}\end{figure}
 

Characteristics of the shell structure further from stability are most influential, leading to questions whether for very neutron-rich nuclei the shell gap at N=82 is less pronounced (i.e. quenched) than predicted by global macroscopic-microscopic mass models like the Finite Range Droplet Model (FRDM) or the Extended Thomas Fermi approach with Strutinski Integral (ETFSI) [30]. This has an important effect on the r-process path and the resulting abundances below the A=130 peak. An experimental investigation of shell quenching along N=50 and 82 towards lower Z's (and reaching the r-process path at N=126 for the very first time) is a highly desirable goal. It will test the nuclear structure responsible for the abundances of heavy nuclei, improve the understanding how well microscopic-macroscopic models, self-consistent microscopic approaches or relativistic mean field theories can describe reality and lead to an extensive test of effective forces used for such calculations [31]. The theoretical studies of nuclear $\beta$-decay properties are based on the spectral distribution of the $\beta$-decay transition probability (the $\beta$-strength function). For the short-lived nuclides on the r- and rp-process paths, the approximation of allowed Gamov-Teller (GT) transitions is usually accurate enough. Microscopic models like the proton-neutron quasiparticle random phase approximation (QRPA) are generally used, based on empirical or self-consistent one-body single-particle potentials, a pairing interaction, and a spin-isospin effective NN-interaction [32]. Thus, this approach is based on single-particle spectra and their uncertainties. Therefore, beta-decay properties are another testing ground for self-consistent mean-field approaches which can be significantly improved if the form and parameters of the corresponding density functionals or effective forces are fitted not only to the nuclear ground state properties near the stability, but also to those of doubly-magic unstable nuclides. Further studies in the regions of 78Ni and 132Sn at RIB facilities and high-flux nuclear reactors will be extremely helpful.

 
Figure: The r-process path at a neutron separation energy Sn$\approx$3 MeV [32].
\begin{figure}\epsfig{file=astro/fig9.eps,width=\columnwidth}\end{figure}
 

Explosive nuclear burning also requires the ability to predict reaction cross sections with the aid of theoretical models. Especially for light nuclei, microscopic cluster models can be applied [33]. A high level density in the compound nucleus at the appropriate excitation energy allows to make use of the statistical model approach. For the majority of nuclei in astrophysical applications the necessary experimental information (on e.g. optical potentials for particle and alpha transmission coefficients, level densities, resonance energies and widths of giant resonances - to be implemented in predicting E1 and M1 gamma-transitions) is not available. The real challenge is thus to predict all these necessary ingredients [14]. Standard spectroscopic methods can be utilised in connection with RIB's to assess level densities and giant resonance properties, scattering experiments for determining optical potentials. 


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