A generalized RPA theory of the nuclear response function

Takayanagi, Kazuo; Shimizu, Kiyotaka; Arima, A.

doi:10.1016/0375-9474(88)90319-3

Cited by 95 publications

(55 citation statements)

References 41 publications

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“…[6], [11], [20] and [21]). In the same line, a step further in difficulty is the SRPA [7], [24], which opens decay channels beyond one particle-one hole (1p1h) states and the Extended RPA (ERPA) ( [8], [19] and [22]), adding more complex ground state correlations than in the RPA. Others approaches are the Correlated Basis Function (CBF) [9], the Green function method [10] and the one Boson Loop Expansion (BLE) [29], [30].…”

Section: Introductionmentioning

confidence: 99%

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

Bauer

2003

Nuclear Physics A

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We have performed a many-body calculation of the longitudinal nuclear (e, e ′ ) reaction employing a Second RPA (SRPA) formalism which contains the ∆(1232). More explicitly, our scheme contains RPA correlations as well as Hartree-Fock and second order self-energies, where an accurate evaluation of exchange terms is achieved. Using this formalism we have evaluated the longitudinal response function for 40 Ca. We give final results at momentum transfers ranging from 300 up to 500 MeV/c, obtaining a good agreement with data.PACS number: 21.65+f, 25.30.Fj, 21.60.Jz.

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Section: Introductionmentioning

confidence: 99%

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

Bauer

2003

Nuclear Physics A

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“…As complex many-body correlations are very important for the formation of giant resonances and for their low-energy fine features, a variety of self-consistent approaches beyond random phase approximation (RPA) were developed and applied to Calcium. Nuclear field theory [39][40][41][42][43], quasiparticle-phonon model [44] second RPA (SRPA) [45][46][47][48][49], mode coupling model [50] and method of chronological decoupling of diagrams (later renamed to time-blocking approximation) [51][52][53][54][55][56][57] account for two-particle-two-hole excitations with various coupling schemes, which are responsible for damping effects of both giant resonance and low-energy strength. Continuum effects are known to contribute to the damping of giant resonances and to cause an additional broadening [54,[58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Electric dipole response of neutron-rich calcium isotopes in relativistic quasiparticle time blocking approximation

Егорова

Литвинова

2016

Phys. Rev. C

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New results for electric dipole strength in the chain of even-even Calcium isotopes with the mass numbers A = 40 -54 are presented. Starting from the covariant Lagrangian of Quantum Hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for J ≤ 6 and natural parity were computed in a self-consistent relativistic quasiparticle random phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations (2q⊗phonon) formed the model space for the calculations of the dipole response function in the relativistic quasiparticle time blocking approximation (RQTBA). The calculations in the latter approach were performed for the giant dipole resonance (GDR) and compared to those obtained in RQRPA and to available data. Evolution of the dipole strength with neutron number is investigated for both high-frequency GDR and low-lying strength. The development of a pygmy resonant structure on the low-energy shoulder of GDR is traced and analyzed in terms of transition densities. A dependence of the pygmy dipole strength on the isospin asymmetry parameter is extracted.

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“…The extension of the RPA to include also the 2p-2h excitations, so called the second RPA, has been investigated and used by many authors [10][11][12][13][14][15][16][17][18][19][20]. Currently the frontier of this approach is the self-consistent second RPA [20], which is still used only for schematic models (their equation is solved only approximately).…”

Section: Introductionmentioning

confidence: 99%

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

Terasaki

Smetana

Šimkovic

et al. 2017

Int. J. Mod. Phys. E

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It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and, numerically, for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

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A generalized RPA theory of the nuclear response function

Cited by 95 publications

References 41 publications

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

Electric dipole response of neutron-rich calcium isotopes in relativistic quasiparticle time blocking approximation

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

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