Existence of a multiplicative basis for a finitely spaced module over an aggregate

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable representations admits a multiplicative basis. In Sections 4.10-4.12 of [P. Gabriel, A. V. Roiter, Representations of finite-dimensional algebras. Encyclopaedia of Math. Sci., vol. 73, Algebra 8, Springer-Verlag, 1992] an analogous hypothesis was formulated for finitely spaced modules over an aggregate. We prove this conjecture.Comment: 17 page

Radiation Damping in the Photoionization of Fe^{14+}

A theoretical investigation of photoabsorption and photoionization of Fe^{14+} extending beyond an earlier frame transformation R-matrix implementation is performed using a fully-correlated, Breit-Pauli R-matrix formulation including both fine-structure splitting of strongly-bound resonances and radiation damping. The radiation damping of $2p\rightarrow nd$ resonances gives rise to a resonant photoionization cross section that is significantly lower than the total photoabsorption cross section. Furthermore, the radiation-damped photoionization cross section is found to be in good agreement with recent experimental results once a global shift in energy of $\approx -3.5$ eV is applied. These findings have important implications. Firstly, the presently available synchrotron experimental data are applicable only to photoionization processes and not to photoabsorption; the latter is required in opacity calculations. Secondly, our computed cross section, for which the L-shell ionization threshold is aligned with the NIST value, shows a series of $2p \rightarrow nd$ Rydberg resonances that are uniformly 3-4 eV higher in energy than the corresponding experimental profiles, indicating that the L-shell threshold energy values currently recommended by NIST are likely in error.Comment: 4 pages, 1 figures, and 2 table

Radiative transition rates and collision strengths for Si II

Aims. This work reports radiative transition rates and electron impact excitation collision strengths for levels of the 3s23p, 3s3p2, 3s24s, and 3s23d configurations of Siii. Methods. The radiative data were computed using the Thomas-Fermi-Dirac-Amaldi central potential, but with the modifications introduced by Bautista (2008) that account for the effects of electron-electron interactions. We also introduce new schemes for the optimization of the variational parameters of the potential. Additional calculations were carried out with the Relativistic Hartree-Fock and the multiconfiguration Dirac-Fock methods. Collision strengths in LS-coupling were calculated in the close coupling approximation with the R-matrix method. Then, fine structure collision strengths were obtained by means of the intermediate-coupling frame transformation (ICFT) method which accounts for spin-orbit coupling effects. Results. We present extensive comparisons between the results of different approximations and with the most recent calculations and experiment available in the literature. From these comparisons we derive a recommended set of gf- values and radiative transition rates with their corresponding estimated uncertainties. We also study the effects of different approximations in the representation of the target ion on the electron-impact collision strengths. Our most accurate set of collision strengths were integrated over a Maxwellian distribution of electron energies and the resulting effective collision strengths are given for a wide range of temperatures. Our results present significant differences from recent calculations with the B-spline non-orthogonal R-matrix method. We discuss the sources of the differences.Comment: 6 figures, 5 tables within text, 2 electronic table

Atomic Processes in Planetary Nebulae and H II Regions

Spectroscopic studies of Planetary Nebulae (PNe) and H {\sc ii} regions have driven much development in atomic physics. In the last few years the combination of a generation of powerful observatories, the development of ever more sophisticated spectral modeling codes, and large efforts on mass production of high quality atomic data have led to important progress in our understanding of the atomic spectra of such astronomical objects. In this paper I review such progress, including evaluations of atomic data by comparisons with nebular spectra, detection of spectral lines from most iron-peak elements and n-capture elements, observations of hyperfine emission lines and analysis of isotopic abundances, fluorescent processes, and new techniques for diagnosing physical conditions based on recombination spectra. The review is directed toward atomic physicists and spectroscopists trying to establish the current status of the atomic data and models and to know the main standing issues.Comment: 9 pages, 1 figur

Atomic data for the K-vacancy states of Fe XXIV

As part of a project to compute improved atomic data for the spectral modeling of iron K lines, we report extensive calculations and comparisons of atomic data for K-vacancy states in Fe XXIV. The data sets include: (i) energy levels, line wavelengths, radiative and Auger rates; (ii) inner-shell electron impact excitation rates and (iii) fine structure inner-shell photoionization cross sections. The calculations of energy levels and radiative and Auger rates have involved a detailed study of orbital representations, core relaxation, configuration interaction, relativistic corrections, cancellation effects and semi-empirical corrections. It is shown that a formal treatment of the Breit interaction is essential to render the important magnetic correlations that take part in the decay pathways of this ion. As a result, the accuracy of the present A-values is firmly ranked at better than 10% while that of the Auger rates at only 15%. The calculations of collisional excitation and photoionization cross sections take into account the effects of radiation and spectator Auger dampings. In the former, these effects cause significant attenuation of resonances leading to a good agreement with a simpler method where resonances are excluded. In the latter, resonances converging to the K threshold display symmetric profiles of constant width that causes edge smearing.Comment: 18 pages, 8 figures, submitted to Astronomy & Astrophysics 200

Decay Properties of K-Vacancy States in Fe X-Fe XVII

We report extensive calculations of the decay properties of fine-structure K-vacancy levels in Fe X-Fe XVII. A large set of level energies, wavelengths, radiative and Auger rates, and fluorescence yields has been computed using three different standard atomic codes, namely Cowan's HFR, AUTOSTRUCTURE and the Breit-Pauli R-matrix package. This multi-code approach is used to the study the effects of core relaxation, configuration interaction and the Breit interaction, and enables the estimate of statistical accuracy ratings. The K-alpha and KLL Auger widths have been found to be nearly independent of both the outer-electron configuration and electron occupancy keeping a constant ratio of 1.53+/-0.06. By comparing with previous theoretical and measured wavelengths, the accuracy of the present set is determined to be within 2 mA. Also, the good agreement found between the different radiative and Auger data sets that have been computed allow us to propose with confidence an accuracy rating of 20% for the line fluorescence yields greater than 0.01. Emission and absorption spectral features are predicted finding good correlation with measurements in both laboratory and astrophysical plasmas.Comment: 13 pages, 4 figures. Submitted to A&A. Electronic Table 3-4 available at http://lheawww.gsfc.nasa.gov/users/palmeri/patrick.htm

Radiative and Auger decay data for modelling nickel K lines

Radiative and Auger decay data have been calculated for modelling the K lines in ions of the nickel isonuclear sequence, from Ni$^+$ up to Ni$^{27+}$. Level energies, transition wavelengths, radiative transition probabilities, and radiative and Auger widths have been determined using Cowan's Hartree--Fock with Relativistic corrections (HFR) method. Auger widths for the third-row ions (Ni$^+$--Ni$^{10+}$) have been computed using single-configuration average (SCA) compact formulae. Results are compared with data sets computed with the AUTOSTRUCTURE and MCDF atomic structure codes and with available experimental and theoretical values, mainly in highly ionized ions and in the solid state.Comment: submitted to ApJS. 42 pages. 12 figure

Loop Quantization of the Supersymmetric Two-Dimensional BF Model

In this paper we consider the quantization of the 2d BF model coupled to topological matter. Guided by the rigid supersymmetry this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of Loop Quantum Gravity methods.Comment: 17 pages, Late