This work reviews foundations and applications of the complex-energy continuum shell model that provides a consistent many-body description of bound states, resonances, and scattering states. The model can be considered a quasi-stationary open quantum system extension of the standard configuration interaction approach for well-bound (closed) systems.

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum. PACS number(s): 25.70. Ef,23.50.+z,25.60+v,21.60.Cs Typeset using REVT E X 1 The prospect of reaching and measuring very unstable nuclei, as is materializing now, opens the possibility of studying spectroscopic processes occuring in the continuum part of nuclear spectra. Much work has already been done in this subject, particularly regarding halo nuclei [1]. Still, the role played by single-particle resonances and of the continuum itself upon particles moving in the continuum of a heavy nucleus is not fully understood. For instance, one may wonder whether two particles outside a core where the Fermi level is immersed in the continuum may produce a quasibound state and, in this case, whether that state is built upon narrow single-particle resonances or by an interplay between the two-particle interaction and the continuum, or by a combination of these mechanisms, as it happens in typical halo nuclei. To answer such questions is a difficult undertaking, particularly because the resonances on the real energy axis do not correspond to a definite state. A way of approaching this problem is by solving the Schrödinger equation with outgoing boundary conditions. One thus obtains the resonances as poles of the S-matrix in the complex energy plane. These poles (Gamow resonances) can be considered discrete states on the same footing as bound states (see Ref.[2] and references therein). However, in this case one finds that physical quantities, like energies and probabilities, become complex. One may attempt to give meaning to these complex quantities. Thus, it is usually assumed that the imaginary part of the energy of a decaying resonance is (except a minus sign) half the width. Other examples are the interpretation of complex cross sections done by Berggren [3] or the widely used radioactive decay width evaluated by Thomas as the residues of the S-matrix [4]. All these interpretations are valid only if the resonances are isolated and, therefore, narrow. In this case the residues of the S-matrix becomes real. One may thus apply this theory and evaluate all resonances, giving physical meaning to the narrow ones only. To achieve this goal a representation consisting of bound states, Gamow resonances and the proper continuum was proposed some years ago [2] (Berggren representation). One chooses the proper continuum as a given contour in th...

The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the nonrelativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A −1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10 6 . The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.