The second random-phase approximation (SRPA) is an extension of the standard randomphase
approximation (RPA) where two particle-two hole (2p2h) configurations are included
together with the RPA one particle-one hole (1p1h) configurations. This beyond mean-field
model allows for reliable quantitative predictions to describe the widths and the
fragmentation of excited states, due to the coupling between 1p1h and 2p2h elementary
configurations.
I will present the formal developments and the practical applications that we have realized in
the last years. One important achievement was the development of a substantial
implementation of the SRPA model, based on a subtraction procedure. This subtraction
method was tailored to cure double-counting problems encountered when effective
interactions are used in beyond mean-field models, within energy-density functional theories.
At the same time, this procedure cures all the instabilities and divergences present in the
standard SRPA and produces renormalized single-particle excitation energies. The subtracted
SRPA (SSRPA) provides a well-defined theoretical framework for quantitative predictions on
nuclear excitation spectra.
Several recent applications will be shown, for instance, a systematic study on collective axial
compression modes in medium-mass and heavy nuclei. A related topic will be discussed,
namely the modification (enhancement) of the effective masses induced by beyond-meanfield
SSRPA effects. Low-lying compression excitations will also be described and a link with
the incompressibility modulus of asymmetric nuclear matter will be illustrated. Finally,
beyond-mean-field effects on the symmetry energy of infinite matter and its density
dependence will be deduced from the low-energy dipole response of the nucleus 68Ni.