Spectrum of One-Dimensional Anharmonic Oscillators

We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.Comment: 11 pages, 5 figures, 4 tables; there are changes to match the version published in Can. J. Phy

Density Matrix Renormalisation Group Approach to the Massive Schwinger Model

The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field theta = pi is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.Comment: 38 pages, 18 figures, submitted to PR

Determination of long-lived fission products and actinides in Savannah River site HLW sludge and glass for waste acceptance

Savannah River Site (SRS) is currently immobilizing the radioactive, caustic, high-level waste sludge in Tank 51 into a borosilicate glass for disposal in a geologic repository. A requirement for repository acceptance is that SRS report the concentrations of certain fission product and actinide radionuclides in the glass. This paper presents measurements of many of these concentrations in both Tank 51 sludge and the final glass. The radionuclides were measured by inductively coupled plasma - mass spectrometry and {alpha}, {beta}, and {gamma} counting methods. Examples of the radionuclides are Sr-90, Cs-137, U-238, Pu-239, and Cm-244. Concentrations in the glass are 3.1 times lower due to dilution of the sludge with a nonradioactive glass forming frit in the vitrification process. Results also indicated that in both the sludge and glass the relative concentrations of the long lived fission products insoluble in caustic area in proportion to their yields from the fission of U-235 in the SRS reactors. This allowed the calculation of a fission yield scaling factor. This factor in addition to the sludge dilution factor can be used to estimate concentrations of waste acceptance radionuclides that cannot be measured in the glass

A New Finite-lattice study of the Massive Schwinger Model

A new finite lattice calculation of the low lying bound state energies in the massive Schwinger model is presented, using a Hamiltonian lattice formulation. The results are compared with recent analytic series calculations in the low mass limit, and with a new higher order non-relativistic series which we calculate for the high mass limit. The results are generally in good agreement with these series predictions, and also with recent calculations by light cone and related techniques

An Application of Feynman-Kleinert Approximants to the Massive Schwinger Model on a Lattice

A trial application of the method of Feynman-Kleinert approximants is made to perturbation series arising in connection with the lattice Schwinger model. In extrapolating the lattice strong-coupling series to the weak-coupling continuum limit, the approximants do not converge well. In interpolating between the continuum perturbation series at large fermion mass and small fermion mass, however, the approximants do give good results. In the course of the calculations, we picked up and rectified an error in an earlier derivation of the continuum series coefficients.Comment: 16 pages, 4 figures, 5 table

Structural modulation of the photophysical and electronic properties of pyrene-based 3D metal-organic frameworks derived from s-block metals

Materials in which charge delocalization and migration can be tuned are critical for electronic applications. Crystalline framework materials containing π-rich polycyclic aromatic moieties, such as pyrene, can provide a pathway for fast anisotropic charge transport. The extent of interchromophore interaction for structurally distinct assemblies of the π-conjugated aromatic ligand 4,4′,4′′,4′′′-(1,3,6,8-pyrenetetrayl) tetrabenzoic acid (H4TBAPy) was studied within two novel metal–organic frameworks (MOFs), Na(TBAPy)(DMF) and K(TBAPy)(DMF), via steady-state and time-resolved spectroscopic techniques. Single-crystal X-ray diffraction was used to determine the structures of K(TBAPy)(DMF) and Na(TBAPy)(DMF), which both form 3D MOFs comprising 1D rod-like SBUs surrounded by columnar stacks of TBAPy that are aligned in an eclipsed and x-shaped (staggered) geometry, respectively. Spectroscopic and computational results indicate significant chromophore interactions and potentially fast charge transport. Furthermore, distinct transient emission decay profiles are observed and are attributed to significant differences in the stacking orientation of the organic ligands in the two MOFs. Lastly, the study identifies design principles that may be exploited in the rational construction of s-block based MOFs for microelectronic and sensing applications.Christopher N. Coleman, Patrick C. Tapping, Michael T. Huxley, Tak W. Kee, David M. Huang, Christian J. Doonan and Christopher J. Sumb

Conformations of closed DNA

We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structure. The stability of the distorted configurations is assessed, along with the effects of fluctuations on the free energy of the various configurations.Comment: 39 pages in REVTEX with 14 eps figures. Submitted to Phys. Rev. E. This manuscript updates, expands and revises, to a considerable extent, a previously posted manuscript, entitled "Conformations of Circular DNA," which appeared as cond-mat/970104

Constraints, Histones, and the 30 Nanometer Spiral

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin.Comment: ReVTeX, 15 pages, 18 figure

Phase transition in the transverse Ising model using the extended coupled-cluster method

The phase transition present in the linear-chain and square-lattice cases of the transverse Ising model is examined. The extended coupled cluster method (ECCM) can describe both sides of the phase transition with a unified approach. The correlation length and the excitation energy are determined. We demonstrate the ability of the ECCM to use both the weak- and the strong-coupling starting state in a unified approach for the study of critical behavior.Comment: 10 pages, 7 eps-figure

Ab initio calculation of the neutron-proton mass difference

The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14\% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of $300$ kilo-electron volts, which is greater than $0$ by $5$ standard deviations. We also determine the splittings in the $\Sigma$, $\Xi$, $D$ and $\Xi_{cc}$ isospin multiplets, exceeding in some cases the precision of experimental measurements.Comment: 57 pages, 15 figures, 6 tables, revised versio