Determination of Fluorescence Polarization and Absorption Anisotropy in Molecular Complexes Having Threefold Rotational Symmetry

The current work concerns investigation of the polarization properties of complex molecular ensembles exhibiting threefold (C3) rotational symmetry, particularly with regard to the interplay between their structure and dynamics of internal energy transfer. We assume that the molecules or chromophores in such complexes possess strongly overlapped spectra both for absorption and fluorescence. Such trimeric structures are widely found in biological preparations, as for example the trimer of C-phycocyanin (C-PC). Higher order aggregates, e.g. hex-amers and three-hexamer rods, are also investigated and compared with the trimer case. The theory addresses both steady-state and 8-pulse excitation and establishes some links between them. Monochromophoric, bichro-mophoric and trichromophoric molecular complexes are individually examined. For steady-state excitation, analytical formulas are reported for the degree of fluorescence polarization and absorption anisotropy. It is shown that the polarization is dependent on the chromophore inclination relative to the symmetry axis, the relative efficiencies of absorption and fluorescence by chromophores of different spectral types, and the rates of energy equilibration. To assess the validity of the theory, it has been applied to C-PC aggregates. Here it was found that different C-PC aggregates provide practically identical polarization response. For S-pulse excitation we give analytical formulas for determination of the fluorescence depolarization, and also the depolarization associated with absorption recovery, both for a monochromophoric trimer and some particular cases of bichromophoric trimer. More complicated systems are analyzed by computer modeling. Thus it transpires that the initial polarization anisotropy r(t = 0) takes the value 0.4 for all considered aggregates; the long-time limit r(t →∞) has about the same value as is associated with steady-state excitation. We also show that with steady-state excitation the degree of fluorescence polarization is practically equal for various C3 aggregates of C-PC, and that the major factor determining the polarization is the chromophore orientation relative to the symmetry axis

Calculation of francium hyperfine anomaly

The Dirac-Hartree-Fock plus many-body perturbation theory (DHF+MBPT) method has been used to calculate hyperfine structure constants for Fr. Calculated hyperfine structure anomaly for hydrogen-like ion has been shown to be in good agreement with analytical expressions. It has been shown that the ratio of the anomalies for $s$ and $p_{1/2}$ states is weakly dependent on the principal quantum number. Finally, we estimate Bohr--Weisskopf corrections for several Fr isotopes. Our results may be used to improve experimental accuracy for the nuclear $g$ factors of short-lived isotopes.Comment: 5 pages, 3 tables, 2 figures. arXiv admin note: text overlap with arXiv:1703.1004

Gauge theory solitons on noncommutative cylinder

We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra of the cylinder, and an isomorphism between the free module and its direct sum with the Fock module on the cylinder. We construct explicitly the gauge theory soliton and evaluate the spectrum of perturbations about this soliton.Comment: References added; to appear in Theor.Math.Phy