Standard RPA Research Articles

Self consistent RPA for superfluid Fermi systems

Self consistent RPA, a formalism generalizing usual RPA such as to incorporate fully RPA groundstate correlations, is extended to superfluid or superconducting Fermi systems. An application to the seniority model demonstrates strong improvement over the standard mean-field RPA scheme.

VARIATIONAL DESCRIPTION OF THE ROTATING NUCLEI

Pairing vibrations in strongly rotating nuclei are treated using the variational approach. The residual interaction is assumed to be due to monopole pairing. A simple generalization of the standard BCS plus RPA enables us to obtain the set of mutually dependent equations describing the quasi-particles and the pairing vibrational phonons.

Nuclear response in an extended RPA formalism; an application to 48Ca 0103

An extension of the standard (1p1h) RPA is derived, by considering the Feynman diagram expansion of the polarization propagator and the relationship between the self-energy and the particle-hole interaction that must be fulfilled in order to obey conservation laws. The resulting Extended RPA (ERPA) equations include the dynamic coupling of 1p1h states to 2p2h states, which leads to a fragmentation of single-particle and single-hole strength and screening of the interaction by the medium. The method has been applied to 48Ca using a realistic G-matrix interaction based on meson-exchange. The results show an improved description of the response over the whole energy range upto 100 MeV. Remaining discrepancies point in the direction of further strength reduction due to short-range correlations as well as a stronger coupling to 2p2h states at low energy.

A modified RPA for open-shell nuclei

A modified RPA suitable for open-shell nuclei is constructed using the Green function method. Unlike the standard RPA, this modification makes allowance for the spread of bound single-particle and single-hole states over more complex configurations which is done due to a more realistic approximation of single-particle Green functions. The calculations of the nucleon-nucleus S-matrix and of the probability amplitudes for the single-particle transitions of the nucleus from the ground state into scattering states are examined. For the separable effective forces these quantities are expressed in closed form.

Generalized Tamm–Dancoff approximation (GTDA) and random-phase approximation (GRPA) calculations on LiH, Be, and Li2

The theory for polarization propagator calculations based on a correlated reference state in the form of a spin singlet restricted antisymmetrized geminal power (AGP) is discussed. Particular attention is paid to the calculation of excitation energies and transition moments for the molecules over all internuclear separations, i.e., not just single point vertical energies, which is done in standard RPA or in higher-order treatments using perturbation methods. Simple applications to the Be atom, and the LiH and Li2 molecules are used to illustrate how this simple correlated state, which is completely determined by the choice of orbital basis (i.e., no choice of configurations is necessary), can cure the notorious consistency problems and the instabilities against the breaking of symmetry, which plague standard RPA based on a Hartree–Fock (HF) single determinantal reference state.

A microscopic theory of the alkali overlayer plasmons on metal surfaces

By applying the standard RPA to a tight-binding model for N-layer slabs, we obtained the response function of the electronic system microscopically. The method is first used to elucidate the plasmons in the thin slab geometry. Deviations from the classical theories are found for very thin slabs. The method is then used to study the overlayer plasmon of alkali monolayers on metal surfaces. The orbital hybridization effect between the substrate and the overlayer is found to reduce the intensity of the intraband overlayer plasmon significantly, while it does not seriously affect the interband mode. The obtained behavior of the intra- and inter-surface-band overlayer plasmon explains fairly well the characteristics of those observed by the angle resolved electron energy loss spectroscopy (AREELS).

Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained. This new scheme is applied to 56Ni ( 56Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2 + eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.

Crystal field effect in planar ferromagnets

Correlated effective field theory which includes fluctuations semiempirically has been used here to study the crystal field effect on the magnetic behaviour in planar ferromagnets. An attempt has been made to reproduce the experimentally observed magnetic order parameter of a planar ferromagnet (Rb 2CrCl 4) with a suitable choice of crystal field and exchange parameters. An alternative model Hamiltonian with anisotropic exchange and no crystal field effect has been considered to reproduce the same experimental results. Both calculations have been compared with the standard RPA results and the existing theoretical results.

The competition between different degrees of freedom in the structure of the quintet states of negative parity of some even-even Sn isotopes

Levels 2 +, 3 −, 1 −, 2 −, 3 −1, 5 − are interpreted as eigenvalues of a boson expanded Hamiltonian containing a shell model term, pairing, and quadrupole-quadrupole and octupole-octupole interaction. The expansion is performed in terms of standard RPA noncollective phonons and the so-called correlated phonons which are related to the RPA collective phonons by a canonical transformation whose parameters are determined so that the energy of the ground state is minimum. The noncollective degrees of freedom are included via an effective Hamiltonian depending on energy. Formalism is applied to 114Sn, 116Sn, and 118Sn. Also, transition probabilities and quadrupole moments are calculated. Results are compared with experimental data as well as with the previous theoretical calculations.

On the validity of the random phase approximation for a solvable nuclear model

The validity of the RPA for a slight variation of the well-known Lipkin model is investigated. Contrary to previous conclusions, it is found that the standard RPA may yield good results even for higher excited states, whilw perturbation theory and the renormalized RPA yield poorer results.

Corrections to electromagnetic transition rates due to ground-state correlations

With the assumption that the two-particle-two-hole correlation structure of the nuclear ground state is given by the RPA result, some corrections to transition rates are calculated. These corrections decrease significantly the theoretical values for the transition strength of the dipole states in 16O and are therefore in the direction of improving the agreement between theory and experiment. It is also found that appreciable transition strength may be obtained above the giant resonance region. Two mechanisms are considered in the later case, 1. (i) the direct excitation of high-energy two-particle-two-hole states proceeding via the ground-state correlations of the RPA theory and 2. (ii) the shifting of transition strength to higher energies via the mixing of the dipole states into two-phonon states at higher energies. In addition, corrections to the calculation of the form factors for two J = 2 − ( T = 1) states of 16O are considered. The corrections arising from an analysis of the ground-state correlations are found to improve the agreement between theory and experiment when comparison is made to standard RPA calculations.