Physics Commons^™

Analytically Reduced Form For The Class Of Integrals Containing Multicenter Products Of 1s Hydrogenic Orbitals, Coulomb Or Yukawa Potentials, And Plane Waves, Jack C. Straton

Physics Faculty Publications and Presentations

The class of integrals containing the product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials with m plane waves is investigated analytically. The results obtained by Straton (1989) are extended and generalized. It is shown that the dimensionality of the entire class can be reduced from 3m to M+N-1.

Fourier Transform Of The Multicenter Product Of 1s Hydrogenic Orbitals And Coulomb Or Yukawa Potentials And The Analytically Reduced Form For Subsequent Integrals That Include Plane Waves, Jack C. Straton

Physics Faculty Publications and Presentations

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.

Application Of The Linear Muffin-Tin-Orbital Band-Structure Method To Calculate Optical Properties Of Solids, R. Zemach, J. Ashkenazi, E. Ehrenfreund

Physics Articles and Papers

Optical matrix elements have been derived for crystals by applying the theory of optical transitions within the formalism of the linear muffin-tin-orbital band-structure method and using Racah algebra. A Brillouin-zone integration by the tetrahedron method allows straightforward numerical computation of the optical function ε₂(ω) [or σ(ω)]. Other optical functions may be derived by using a Kramers-Kronig analysis.

Calculation Of Optical Properties Of Trans-Polyacetylene By The Linear Muffin-Tin-Orbital Method, R. Zemach, J. Ashkenazi, E. Ehrenfreund

Physics Articles and Papers

The basic optical properties of trans-(CH)_x in the P2₁/n and the P2₁/a space groups are derived from first principles. The relevant optical matrix elements are calculated within the self-consistent linear muffin-tin-orbital band-structure method. The derived optical response functions are compared with the results from a variety of optical as well as electron-energy-loss experimental studies. It is shown that the measured optical constants are consistent with the P2₁/n structure.

Ground State Of Trans-Polyacetylene And The Peierls Mechanism - Ashkenazi Et Al. Reply, J. Ashkenazi, W. E. Pickett, H. Krakauer, C. S. Wang, B. M. Klein, S. R. Chubb

Physics Articles and Papers

Ashkenazi et al. reply to Original Article: J. Ashkenazi, W. E. Pickett, H. Krakauer, C. S. Wang, B. M. Klein, and S. R. Chubb, Ground state of trans-polyacetylene and the Peierls mechanism, Physical Review Letters 62, 2016 (1989).

Ground State Of Trans-Polyacetylene And The Peierls Mechanism - Errata, J. Ashkenazi, W. E. Pickett, H. Krakauer, C. S. Wang, B. M. Klein, S. R. Chubb

Physics Articles and Papers

Errata to Original Article: J. Ashkenazi, W. E. Pickett, H. Krakauer, C. S. Wang, B. M. Klein, and S. R. Chubb, Ground state of trans-polyacetylene and the Peierls mechanism, Physical Review Letters, 62, 2016 (1989).

Ground State Of Trans-Polyacetylene And The Peierls Mechanism, J. Ashkenazi, W. E. Pickett, H. Krakauer, C. S. Wang, B. M. Klein, S. R. Chubb

Physics Articles and Papers

It is shown formally that the Peierls expression is inadequate for studying the instabilities of a physically realizable one-dimensional chain of atoms, due to the long-range nature of the Coulomb interaction. Detailed total-energy studies of trans-polyacetylene, for both suggested crystal structures (P2₁/n,P2₁/a) and for the one-dimensional chain, establish that no appreciable total-energy minimum occurs for nonzero dimerization amplitude within the local-density approximation. The measured dimerization is discussed within the context of recent models of electron correlation.

Excitations In A Nearly Half-Filled Hubbard Model With U=∞, S. E. Barnes

Physics Articles and Papers

It is shown that, even near half filling, the elementary excitations of the large-U Hubbard model form wide bands of width ∼t, the intersite hopping integral, and that the slave-boson-based mean-field approximation is qualitatively wrong in the relevant limit. This large-U limit has no Kondo-type divergences.

Alternative Feynman-Diagram Method For The General-Spin Kondo Problem, S. E. Barnes

Physics Articles and Papers

We introduce a new method of replacing spin operators with pseudofermions. For a spin value S there are 2S pseudofermions each of which can have spin ‘‘up’’ or ‘‘down’’. In contrast to the standard Abrikosov method which has 2S+1 inequivalent fermions, i.e., one for each S_z value, the present pairs are all equivalent. It follows that the general spin expression is obtained by multiplying the S=(1/2 result by a ceratin combinational factor. This aids in the construction of rotationally invariant solutions for the general-spin Kondo problem for the case when n≤2S, where n is the number of conduction-electron scattering …

Erratum: Determination Of Dissociation Energies And Thermal Functions Of Hydrogen Bond Formation Using High Resolution Ftir Spectroscopy [J. Chem. Phys. 8 7, 5674 (1987)], B. A. Wofford, M. E. Eliades, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

Erratum

The Spectroscopy And Molecular Dynamics Of The High Frequency Ν1 6 Intermolecular Vibrations In Hcn‐‐‐Hf And Dcn‐‐‐Df, B. A. Wofford, M. W. Jackson, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

Gas phase rovibrational analysis of the high frequency intermolecular hydrogen bonded bending overtone 2ν⁰ ₆ [ν₀=1132.4783(2) cm^{− 1}] in HCN‐‐‐HF and its corresponding perdeuterated fundamental ν¹ ₆ [ν₀=409.1660(2) cm^{− 1}] are reported. Evaluated rovibrational parameters provide the basis for quantitative modeling of the molecular dynamics associated with this vibration. A quantum mechanical calculation permits determination of the quadratic and quartic force constants K _{6 6}=537(17) and K _{6 6 6 6}=4.98(12) cm^{− 1} which in turn are used to estimate the pertinent cubic band stretching interaction constants …

Spin-Exchange Cross Section For Electron Excitation Of Na 3s 3p Determined By A Novel Spectroscopic Technique, Xianming Han, G. W. Schwinn, A. Gallagher

Scholarship and Professional Work - LAS

An experimental technique is described which enables determination of the partial cross sections for electron excitation of atoms as a function of changes in spin and orbital angular momentum. This method provides a good signal-to-noise ratio in the energy region near threshold, and could be used to study long- or short-lived excited states of many atomic systems. Measurements for Na 3S−3P, near-threshold excitation are reported here. The results are generally in good agreement with the close-coupling calculations of D. L. Moores and D. W. Norcross [J. Phys. B 5, 1482 (1972)] for the largest ΔmS and ΔmL components of …

Reduced-Mass Fock-Tani Representations For A+ + (B+C-) --> (A+C-) + B+ And First-Order Results For {Abc} = {Ppe, Epe, Μpμ, Μdμ, And Μtμ}, Jack C. Straton

Physics Faculty Publications and Presentations

The Fock-Tani transformation in the Jacobi three ⟶ two-body reduced-mass system is carried out and the first-order T matrix is found to be identical to that for the full three-body transformation. The Fock-Tani transformation in the reduced-mass system in which particle b is fixed at the origin is found to give a first-order T matrix with an error of m_c /m_b in the initial momentum wave function. First-order differential and total cross sections are calculated for a⁺ + (b⁺c^-)⟶(a⁺c^-) + b⁺ where |abc|= { …

Fourier Transform Of The Product Of N One-Center Hydrogenic Orbitals, Jack C. Straton

Physics Faculty Publications and Presentations

Integrating the radial part of the Fourier transform of the product of N hydrogenic orbitals results in an associated Legendre function that can be reduced to a finite series of elementary functions. This transform is found to depend on a polynomial in the wave vector k divided by a binomial in k² raised to a power that is the sum of principle quantum numbers. This form facilitates the analytical reduction of integrals arising from orthogonalization corrections in atomic processes. Transforms for the product of orbital pairs (1s,1s) through (1s,3d) are given …

Electron Paramagnetic Resonance Of Gd3+ Ions In The Superconductor Gdba2Cu3OX, F. Mehran, S. E. Barnes, C. C. Tsuei, T. R. Mcguire

Physics Articles and Papers

EPR from Gd³⁺ ions in the high-T_c≃90 K superconductor GdBa₂Cu₃O_x is reported. The temperature dependence of the linewidth and intensity of the Gd³⁺ ions in the vicinity of T_c are related to the corresponding characteristics of the Cu²⁺ ions.

Observation Of Al2O3: Cr3+ Magnetic Resonance Via Solitons In Long Josephson Junctions, F. Mehran, S. E. Barnes, C. C. Chi, R. L. Sandstrom, C. P. Umbach

Physics Articles and Papers

We have detected the zero-field electron-spin resonance signal of Al₂O₃ with ∼1000 ppm Cr³⁺ using an edge Josephson junction. The sample comprises the substrate upon which the junction was fabricated and the coupling to the electron-spin resonance is via the solitons which exist in these "long" devices.

Temporary Anion States Of Polyatomic Hydrocarbons, Kenneth D. Jordan, Paul Burrow

Paul Burrow Publications

Contents

I. Introduction

II. Electron Transmission Spectroscopy

A. Background

B. Interpretation of Transmission Data

III. Alkenes, Dienes, and Polyenes

A. Ethylene and Alkyl-Substituted Ethylenes

B. Butadiene, Hexatriene, and Octatetraene

C. Other Conjugated Dienes

D. Cyclooctatetraene

E. Nonconjugated Dienes

IV. Alkynes

A. Acetylene and Alkyl-Substituted Acetylenes

B. Cyclic Acetylenes

C. Butadiyne and 2,4-Hexadiyne

V. Aromatic Systems

A. Benzene and Alkyl-Substituted Benzenes

B. Naphthalene, Anthracene, and Tetracene

C. Styrene and cis- and trans-Stilbene

D. Biphenyls

E. Triptycene, Dibenzonorbornadiene, and Related Compounds

VI. Halogen-Containing Compounds

A. Saturated Compounds

B. Unsaturated Compounds

VII. Conclusions

VIII. Acknowledgment

IX. References

X. Bibliography of Studies …

Molecular Dynamics In Hydrogen‐Bonded Interactions: A Preliminary Experimentally Determined Harmonic Stretching Force Field For Hcn‐‐‐Hf, B. A. Wofford, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

Observation of the 2ν₁ overtone band in the hydrogen‐bonded complex HCN‐‐‐HF permits evaluation of the anharmonicity constant X _{1 1}=−116.9(1) cm^{− 1} and determination of the anharmonicity corrected fundamental frequency ω₁. This information, and available data from previous rovibrational analyses in the common and perdeuterated isotopic species of HCN‐‐‐HF, offer an opportunity for calculation of an approximate stretching harmonic force field. With the assumptions f _{1 2}=f _{2 4}=0.0, the remaining force constants (in mdyn/Å) are evaluated as: f _{1 1}=8.600(20), f _{2 2}=6.228(9), f _{3 3}=19.115(40), f _{4 …}

Comment On "Orientation, Alignment, And Hyperfine Effects On Dissociation Of Diatomic Molecules To Open Shell Atoms", Mark D. Havey, Linda L. Vahala

Electrical & Computer Engineering Faculty Publications

A recent paper in this journal [Y. B. Band e t a l., J. Chem. Phys. 8 4, 3762 (1986)] reported parameters describing orientation and alignment produced, in an axial recoil limit, by one photondissociation of diatomic molecules. Reported also were values, applicable to the resonance transitions of the alkali atoms, for orientation and alignment depolarization coefficients. Most of the numerical values reported for the coefficients were incorrect, in some cases by as much as a factor of 2. We report a tabulation of correct depolarization coefficients applicable to the resonance transitions of common alkali isotopes. Further, the coefficients …

Determination Of Dissociation Energies And Thermal Functions Of Hydrogen‐Bond Formation Using High Resolution Ftir Spectroscopy, B. A. Wofford, M. E. Eliades, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

A technique which employs high resolution Fourier transform infrared spectroscopy is demonstrated for evaluation of hydrogen bonddissociation energiesD ₀ and D _e . Results for HCN‐‐HF give a D ₀=20.77(22) and D _e =28.77(45) kJ/mol which are compared with previously determined values obtained from microwave absolute intensity measurements and a b i n i t i o molecular orbital calculations. Rovibrational band information available for HCN‐‐HF also permits evaluation of thermal functions of dimer formation in kJ/mol: ΔU ^○ _298.2 =20.1(2), ΔH ^○ _298.2 =22.6(2), ΔG ^○ _298.2 =59.4(2), ΔS ^○ _298.2 =−0.1235.

Photorefraction In Batio3, Stephen Ducharme

Stephen Ducharme Publications

This thesis summarizes the results of experimental investigations of the photorefractive properties of melt-grown BaTiO₃ single crystals. Three basic photorefractive material properties are studied: (1) the effective density of photorefractive charges, (2) the photoconductivity of the photorefractive charges, and (3) the relative contributions of electron and hole photoconduction. Volume holographic measurement techniques are used: two-beam energy coupling, four-wave mixing, and erasure of volume holograms. The photorefractive properties were altered experimentally by chemically reducing or oxidizing a BaTiO₃ crystal. I have extended the “hopping conduction” model of photorefractive transport to include simultaneous electron and hole photoconduction. The extension of …

Fock-Tani Transformation And A First-Order Theory Of Charge Transfer, P. C. Ojha, M. D. Girardeau, J. D. Gilbert, Jack C. Straton

Physics Faculty Publications and Presentations

A unitary (Fock-Tani) transformation of the second-quantized Hamiltonian breaks the interaction into its component parts, e.g., elastic scattering, inelastic scattering, rearrangement interaction, etc. The interaction for a particular process is ‘‘weaker’’ than the overall interaction; this is reflected in certain orthogonality corrections which appear in a perturbation expansion of the T-matrix element. As a result, the internuclear potential makes a negligible contribution of order m_e/m_p to the first-order amplitude for charge transfer. We find very good agreement with experimental and the best available theoretical results for the total cross section for the reaction p+H(1s)→H(1s)+p for …

Nonadiabatic Theory Of Fine-Structure Branching Cross Sections For Na-He, Na-Ne, And Na-Ar Optical Collisions, Linda L. Vahala, P. S. Julienne, Mark D. Havey

Electrical & Computer Engineering Faculty Publications

The nonadiabatic close-coupled theory of atomic collisions in a radiation field is generalized to include electron spin and is used to consider the weak-field Na–rare-gas (RG) optical collision Na(²S_1/2)+RG+nhν μNa(²P_j)+RG+(n-1)hν. The effects of detuning and incident energy on the branching into the atomic Na 3p²P_3/2 and 3p²P_1/2 states are examined. The cross sections σ(j) are found to have a strong asymmetry between red and blue detuning as well as a complex threshold and resonance structure dependence on energy. A partial cross-section analysis …

Safety Evaluation Report Related To The Renewal Of The Operating License For The Triga Training And Research Reactor At The University Of Utah, United States Nuclear Regulatory Commission, Office Of Nuclear Reactor Regulations

Radioactive Materials

This Safety Evaluation Report for the application filed by the University of Utah (UU) for a renewal of operating license R-126 to continue to operate a training and research reactor facility has been prepared by the Office of Nuclear Reactor Regulation of the U.S. Nuclear Regulatory Commission. The facility is owned and operated by the University of Utah and is located on its campus in Salt Lake City, Salt Lake County, Utah. The staff concludes that this training reactor facility can continue to be operated by UU without endangering the health and safety of the public.

Systematic Estimate Of Binding Energies Of Weakly Bound Diatomic Molecules, Linda L. Vahala, Mark D. Havey

Electrical & Computer Engineering Faculty Publications

There is often insufficient spectroscopic data for a full RKR inversion to yield a potential for weakly bound diatomic molecules. In these cases, parametrized functions such as the Morse or Thakkar potentials may be used to obtain estimates of the binding energy. The Thakkar potential is more flexible, and has been used successfully on some weakly bound systems. In the more usual case, the Thakkar parameter p, which determines long range behavior R^-p, is chosen by p=-a₁-1, where a₁ is the first Dunham coefficient; p is usually noninteger. The authors present …

Preliminary Rovibrational Analysis Of The Nν6+Ν1−Nν6 Vibration In Hcn⋅⋅⋅Hf, E. Kyrö, K. Mcmillan, M. Eliades, D. Danzeiser, P. Shoja-Chaghervand, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

A preliminary rotation‐vibration analysis of the n=0 and n=1 subbands associated with the nν₆+ν₁−nν₆ hydrogen‐bonded vibration in HCN⋅⋅⋅HF has been completed. The following excited staterotational constantsB′ and band origin frequencies ν₀ have been determined for the complex. The results are consistent with a rotation‐vibration interaction constant α₁=−68.3±1 MHz which correlates with an excited stater(N⋅⋅⋅F) internuclear distance of 2.762 Å, a decrease of 0.034 Å relative to the ground state.Excited state lifetimes associated with assigned transitions are demonstrated to be …

Travelling-Wave Sub-Doppler Excited Molecule Energy Transfer Spectroscopy, Khalid Iqbal, Shannon G. Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

A general formulation of traveling‐wave sub‐Doppler excited molecule energy transferspectroscopy is presented. The line profile analysis is applied to that determined experimentally for the R(22) ν3 HCN transition. Pn the noise equivalent power of the detector is demonstrated to be ⩽10−12 W. Finally, the technique is applied to resolve the KsR(7) ν1 transition head in NH3.

Forbidden Lines Of Np^Q Ions. I. Detailed Balance And Line Intensity Ratios, Menas Kafatos, J. P. Lynch

Mathematics, Physics, and Computer Science Faculty Articles and Research

Ground state forbidden transitions of np^q ions of C, N, 0, Ne, Mg, Si, S, and Fe can provide important information on the state of cosmic ionized gases. Wavelengths of these lines are in the far- and near-UV visible and near-- and far-IR regions of the spectrum. The line intensity ratios of particular transitions in q = 2, 4 ions can provide information on the temperature of the gas and in q = 3 ions information on the density of the gas. In the present work we have tabulated the line intensities of 95 transitions of these ions, which include …

Studies Of The Temporary Anion States Of Unsaturated Hydrocarbons By Electron Transmission Spectroscopy, Kenneth D. Jordan, Paul Burrow

Paul Burrow Publications

The concept of occupied and unoccupied orbitals has provided a useful means for visualizing many of the most important properties of molecular systems. Yet, there is a curious imbalance in our experimental knowledge of the energies of occupied and unoccupied orbitals. Whereas photoelectron spectroscopy has provided a wealth of data on positive ion states and has established that they can be associated, within the context of Koopmans’ theorem, with the occupied orbitals of the neutral molecule, the corresponding information for the negative ion states, associated with the normally unoccupied orbitals, is sparse. In part this reflects the experimental difficulties connected …

A Study Of He+ + Ar Collisions At Energies Between 600 Ev & 1500 Ev, Alton Dull Jr.

Masters Theses & Specialist Projects

This investigation was undertaken in order to confirm and to extend earlier studies of processes whereby energy and angular momentum are transferred from external to internal degrees of freedom in low velocity collisions between ions and atoms. Specifically, this investigation sought to verify the proper functioning of a device designed to study low velocity atomic and molecular collisions, to confirm results obtained in an earlier study of spectra produced by collisions of He⁺ions with argon atoms, and to extend the energy and wavelength ranges of this study to 1500 eV and 6200 Å, respectively.

The data was in …