Second random-phase approximation, Thouless' theorem and the stability condition reexamined and clarified

Abstract

It has been revealed through numerical calculations that the Second Random Phase Approximation (SRPA) with the Hartree-Fock solution as its reference state results in 1) spurious states at genuinely finite energy, contrary to common expectation, and 2) unstable solutions, which within the first-order Random Phase Approximation correspond to real low-energy collective vibrations. In the present work, these shortcomings of SRPA are shown to not contradict Thouless' theorem about the energy-weighted sum rule, and their origin is traced to the violation of the stability condition. A more general theorem is proven. Formal arguments are elucidated through numerical examples. Implications for the validity of SRPA are discussed.

11 pages, incl. 5 figures; to appear in Phys. Rev. C

References in corpus (13)

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• Subtraction method and stability condition in the extended RPA theories
• Second RPA and correlated realistic interactions
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Cited by in corpus (14)

• Subtraction method in the second random--phase approximation: first applications with a Skyrme energy functional
• Effective density functionals beyond mean field
• Electric dipole strength and dipole polarizability in ${}^{48}$Ca within a fully self-consistent second random-phase approximation
• Complex-energy approach to sum rules within nuclear density functional theory
• Damping of the isovector giant dipole resonance in ${}^{40,48}$Ca
• Nuclear excitations as coupled one and two random--phase--approximation modes
• Estimation of 2p2h effect on Gamow-Teller transition with Second Tamm-Dancoff-Approximation
• Comparative analysis of formalisms and performances of three different beyond mean-field approaches
• Soft breathing modes in neutron--rich nuclei with the subtracted second random--phase approximation
• Energy-weighted sum rule for nuclear density functional theory
• Multipole responses in fissioning nuclei and their uncertainties
• Giant Resonances based on Unitarily Transformed Two-Nucleon plus Phenomenological Three-Nucleon Interactions
• Self-Consistent Random Phase Approximation from Projective Truncation Approximation Formalism
• Recent applications of the subtracted second RPA method