RQRPA

RQRPA stands for Relativistic Quasiparticle Random-Phase Approximation. It is a theoretical framework used in nuclear structure physics to describe small-amplitude collective excitations of atomic nuclei. Built on relativistic mean-field theory, RQRPA extends the quasiparticle random-phase approximation by incorporating pairing correlations in a relativistic setting. The approach starts from a relativistic mean-field ground state produced by a Lagrangian with nucleon-meson interactions (or density-dependent couplings), and uses Bardeen–Cooper–Schrieffer or Bogoliubov pairing to form quasiparticles. The RQRPA then treats small oscillations around this ground state by linearizing the equations of motion, yielding a matrix eigenvalue problem in which the eigenvalues give excitation energies and the eigenvectors provide transition amplitudes. The residual interaction is derived consistently from the same effective Lagrangian, guaranteeing self-consistency and the approximate fulfillment of energy-weighted sum rules in ideal cases.

Applications of RQRPA include the description of giant resonances and spin-isospin excitations such as Gamow-Teller and spin-dipole modes, as well as calculations of beta-decay rates and strength distributions in both stable and neutron-rich nuclei. The framework is applicable to spherical and deformed systems and can be extended to include the coupling to the continuum or more sophisticated pairing schemes. In some contexts, the acronym RQRPA is also used for Renormalized QRPA, a related variant that introduces additional renormalization to address Pauli-principle corrections and improve stability of the description.

Overall, RQRPA provides a self-consistent, relativistic, microscopic method for studying nuclear excited states, complementing nonrelativistic QRPA approaches and contributing to global surveys of nuclear structure properties across the chart of nuclides.