[en] The Random Phase Approximation (RPA) treatment of nuclear small amplitude vibrations including particle-hole continua is handled in terms of previously developed techniques to treat single-particle resonances in a reaction theoretical framework. A hierachy of interpretable approximation is derived and a simple working approximation is proposed which involves a numerical effort no larger than that involved in standard, discrete RPA calculations. (author)

[en] The authors study fermionic dark matter in the random phase approximation and show that its statistical behavior is anomalous

No abstract available

[en] The static responseto a charge impurity near a metal surface is computed in RPA approximation for the case of a finite barrier. Particular attention is given to the problem of the correct infinite-volume limit and to the contribution of the one-particle states with energy higher than the potential barrier, which has been found to be not negligible. An integral equation for the self-consistent potential is derived and solved numerically. Results for Na and Zn are exhibited, showing remarkable difference with respect to the infinite-barrier case

[en] Background and purpose: To evaluate the efficacy of radiotherapy in patients with glioblastoma multiforme (GBM) with a limited prognosis and in patients older than 70 years. Patients and methods: Retrospective analysis of 202 patients with GBM treated between 1990 and 2000 in a single institution. Patients (including patients ≥70 years) were assigned to RPA groups and their survival was compared with RTOG data. Results: Median survival was 8.0 months for the total group and 13.9, 10.6, 3.8, 2.1 months for RPA group III (n=17), IV (n=87), V (n=60) and VI (n=38), respectively. Median survival for patients ≥70 years was 3.6 vs. 8.1 months for 50-70 years and 11.0 months for <50. In each separate RPA group, patients ≥70 years had a similar survival compared to patients of 50-70 years. Irradiated patients (66%) survived significantly longer than non-irradiated patients: 10.6 vs. 1.9 months (P<0.0001). In RPA group V the median survival for irradiated patients was 9.4 vs. 2.1 months for non-irradiated patients. In a multivariate analysis, RT remained the only prognostic factor for survival (HR 8.9, P<0.001). Conclusions: Prognosis for patients above 70 years of age is not different from younger patients, when analyzed for separate RPA groups. For patients with a poor prognosis (i.e. RPA group V), radiotherapy improves survival significantly

[en] An exact mathematical treatment of the random walk model in chromatography is given in this paper. Various factors which can cause broadening of peaks, such as equilibrium fluctuation, diffusion, size and structure of fixed phase particles, fluid velocity, flow around the particles, distribution ratio, column temperature and nonuniformity, etc., are all considered with a unified theory. Formulas of mean retention time and height of theoretical plate, containing all of the factors, are presented. (author) 9 refs

[en] Highlights: • The paper analyses the anomalies in the 1D Anderson model with weak disorder. • The Anderson model corresponds to a classical parametric oscillator, whose dynamics is studied with action-angle variables $\left(J,\theta \right)$. • The distribution of $\theta$ is flat for non-resonant values of the energy and modulated at the centre and at the edges of the band. • We show that for all other anomalies the modulation of the distribution of $\theta$ is significantly weaker (4th-order effect). • We conclude that Thouless formula for the localisation length is valid everywhere except at the centre and at the edges of the band. We consider the one-dimensional Anderson model with weak disorder. Using the Hamiltonian map approach, we analyse the validity of the random-phase approximation for resonant values of the energy, $E=2\cos \left(\pi r\right)$, with $r$ a rational number. We expand the invariant measure of the phase variable in powers of the disorder strength and we show that, contrary to what happens at the centre and at the edges of the band, for all other resonant energies the leading term of the invariant measure is uniform. When higher-order terms are taken into account, a modulation of the invariant measure appears for all resonant values of the energy. This implies that, when the localisation length is computed within the second-order approximation in the disorder strength, the Thouless formula is valid everywhere except at the band centre and at the band edges.

[en] The modified random-phase-approximation (RPA) method with the self-consistent separable residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in sodium clusters. The method allows one to study the coupling of different kinds of collective motion. As a particular case, the coupling of surface and volume modes is considered. The SRPA is applied to neutral and singly charged spherical sodium clusters in a wide size region (N_e=8,20,40,58,92,138,196,440,952) and good agreement with experimental data is achieved. This testifies to the applicability of the separable ansatz, which has the essential advantage of avoiding diagonalization of the RPA matrices and thus drastically simplifies the RPA calculations. The latter could be quite urgent for very large and deformed clusters where an extended configuration space and, consequently, high-rank RPA matrices are used. The predictions for E2 and E3 collective excitations are presented. The results obtained with the self-consistent Kohn-Sham and phenomenological Woods-Saxon single-particle schemes are exhibited and different parameters for the Woods-Saxon potential are proposed. copyright 1997 The American Physical Society

[en] A fully consistent relativistic RPA calculation is performed for the monopole compression mode in nuclei. The emphasis is put on the effects of Dirac sea states which are generally neglected in relativistic RPA calculations. It is found that these effects can be quite important. The main contributions from the pairs of Fermi and Dirac sea states are through the exchange of the scalar meson, while the vector mesons play a negligible role. Numerical results of relativistic RPA are checked with the constrained RMF model. A comparison of experimental and calculated energies gives a value of 230 MeV for the nuclear matter incompressibility. (author)

[en] A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained