QRPA

QRPA, or Quasiparticle Random Phase Approximation, is a linear response method used in quantum many-body physics to describe small-amplitude excitations around a superconducting ground state. It extends the standard Random Phase Approximation by incorporating pairing correlations through quasiparticles, typically obtained from a Bogoliubov transformation applied to a BCS or Hartree–Fock–Bogoliubov ground state. QRPA is especially important in nuclear structure, where it is used to model collective excitations such as giant resonances and to compute transition strengths, beta-decay rates, and nuclear matrix elements relevant for double beta decay and astrophysical processes.

Conceptually, QRPA builds a basis of two-quasiparticle configurations and solves an eigenvalue problem for the excitation energies and amplitudes. The forward and backward amplitudes, X and Y, couple through matrices A and B that encode quasiparticle energies and the residual interaction in particle-hole and, in some formulations, particle-particle channels. The resulting equations yield excited-state energies ω and their corresponding QRPA amplitudes, describing the structure of the states and their transition properties.

Variants of QRPA include proton-neutron QRPA (pn-QRPA) for beta-decay and charge-exchange transitions, deformed QRPA for axially or triaxially deformed nuclei, and relativistic QRPA (RQRPA) based on covariant energy density functionals. Practical implementations increasingly employ improvements such as renormalized QRPA, finite-amplitude methods (FAM-QRPA) for efficiency, and extensions to better handle correlations beyond the small-amplitude regime.

Limitations of QRPA include its reliance on a mean-field plus pairing starting point, sensitivity to the chosen effective interaction, and potential breakdowns for strongly correlated systems. Despite these, QRPA remains a central tool for studying nuclear excitations and related weak-interaction processes.