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Imput information for application of Shell Theory Automated for Rotational Structures, /STARS 2/ digital computer program - Vol. 2
Manual of engineering programming information for Shell Theory Automated for Rotational Structures /STARS 2/ - Vol. 3
The engineering programming information for the digital computer program for analyzing shell structures is presented. The program is designed to permit small changes such as altering the geometry or a table size to fit the specific requirements. Each major subroutine is discussed and the following subjects are included: (1) subroutine description, (2) pertinent engineering symbols and the FORTRAN coded counterparts, (3) subroutine flow chart, and (4) subroutine FORTRAN listing.
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We present in detail a theoretical model that provides absolute cross sections for simultaneous core-ionization core-excitation (K{sup −2}V ) and compare its predictions with experimental results obtained on the water molecule after photoionization by synchrotron radiation. Two resonances of different symmetries are assigned in the main K{sup −2}V peak and comparable contributions from monopolar (direct shake-up) and dipolar (conjugate shake-up) core-valence excitations are identified. The main peak is observed with a much greater width than the total experimental resolution. This broadening is the signature of nuclear dynamics.
The formalism developed in the companion Paper I is used here for the interpretation of spectra obtained recently on the nitrogen molecule. Double core-hole ionization K{sup −2} and core ionization-core excitation K{sup −2}V processes have been observed by coincidence electron spectroscopy after ionization by synchrotron radiation at different photon energies. Theoretical and experimental cross sections reported on an absolute scale are in satisfactory agreement. The evolution with photon energy of the relative contribution of shake-up and conjugate shake-up processes is discussed. The first main resonance in the K{sup −2}V spectrum is assigned to a K{sup −2}π{sup ∗} state mainly populated by the 1s→ lowest unoccupied molecular orbital dipolar excitation, as it is in the K{sup −1}V NEXAFS (Near-Edge X-ray Absorption Fine Structure) signals. Closer to the K{sup −2} threshold Rydberg resonances have been also identified, and among them a K{sup −2}σ{sup ∗} resonance characterized by a large amount of 2s/2p hybridization, and double K{sup −2}(2σ{sup ∗}/1π/3σ){sup −1}1π{sup ∗2} shake-up states. These resonances correspond in NEXAFS spectra to, respectively, the well-known σ{sup ∗} shape resonance and double excitation K{sup −1}(2σ{sup ∗}/1π/3σ){sup −1}1π{sup ∗2} resonances, all being positioned above the threshold.
We have used the relativistic multi-reference Møller-Plesset perturbation theory to calculate the positions of the dielectronic satellite transitions involving doubly excited 3ℓ3ℓ' configurations that are associated with the X-ray spectrum of Fe XVII. A comparison of these positions with the wavelengths employed in astrophysical modeling codes shows discrepancies of up to 36 mÅ. Inspection of the spectrum of Capella recorded with the high energy transmission grating on the Chandra X-Ray Observatory reveals several features enhanced by Fe XVI lines formed by dielectronic recombination, one of which may be of future diagnostic use as it is fairly well isolated and in large part formed by dielectronic recombination.
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We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of PSL(2,R) Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface Σ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form Σ×S 1 , where Σ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of n asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{M}$ g,n , which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces Σ. As a result, there is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.