Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance (ISGMR) in nuclei is studied in the framework of a fully consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function technique. The negative energy states in the Dirac sea are also included in the single particle Green's function in the no-sea approximation. The single particle Green's function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energy-weighted sum rule m(-1) and the centroid energy of the ISGMR in Sn-120 and Pb-208 are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.

Importance of self-consistency in relativistic continuum random-phase approximation calculations

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between the misachieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.

Relativistic Continuum Random Phase Approximation and Applications I. Formalism

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function, which includes also the negative states in the Dirac sea in the nose aapproximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green's function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented.

Miscibility and phase behavior in blends containing random copolymers of poly(ether ether ketone) and phenolphthalein poly(ether ether ketone)

The miscibility and phase behavior of polysulfone (PSF) and poly(hydroxyether of bisphenol A) (phenoxy) with a series of copoly(ether ether ketone) (COPEEK), a random copolymer of poly(ether ether ketone) (PEEK), and phenolphthalein poly(ether ether ketone) (PEK-C) was studied using differential scanning calorimetry. A COPEEK copolymer containing 6 mol % ether ether ketone (EEK) repeat units is miscible with PSF, whereas copolymers containing 12 mol % EEK and more are not. COPEEK copolymers containing 6 and 12 mol % EEK are completely miscible with phenoxy, but those containing 24 mol % EEK and more are immiscible with phenoxy. Moreover, a copolymer containing 17 mol % EEK is partially miscible with phenoxy; the blends show two transitions in the midcomposition region and single transitions at either extreme. Two T(g)s were observed for the 50/50 blend of phenoxy with the copolymer containing 17 mol % EEK, whereas a single composition-dependent T-g appeared for all the other compositions. An FTIR study revealed that there exist hydrogen-bonding interactions between phenoxy and the copolymers. The strengths of the hydrogen-bonding interactions in the blends of the COPEEK copolymers containing 6 and 12 mol % EEK are the same as that in the phenoxy/PEK-C blend. However, for the blends of copolymers containing 17, 24, and 28 mol % EEK, the hydrogen-bonding interactions become increasingly unfavorable and the self-association of the hydroxyl groups of phenoxy is preferable as the content of EEK units in the copolymer increases. The observed miscibility was interpreted qualitatively in terms of the mean-field approach. (C) 1996 John Wiley & Sons, Inc.