Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

Z1 and Z2 variations in the stopping powers of Z1=10 to 18 ions deduced from Dsam lifetime measurements

From lifetime measurements of the ²²Ne(3.26 MeV), ¹³P(2.23 MeV) levels and published data, deviations from theory of the stopping powers for Ne and other ions in many materials have been deduced; they correlate strongly with electron densities deduced from positron lifetimes. The data also indicate that Z₁ deviations for s-d shell nuclei are Z₂ dependent.     

Characteristic and quasimolecular X-rays from collision systems with Z1 + Z2 = 133, 134 under single and multiple collision conditions

Measurements with Hg-vapor targets bombarded with 18 MeV to 150 MeV xenon ions show that M-Mo X-rays are excited in a single collision, and target L-lines are suppressed in gas targets compared to solids, furthermore, projectile L-lines show a pressure dependent energy shift of 50 eV between 10^?3 and 1 Torr.     

Spectra in Standard-like Z3 Orbifold Models

General features of the spectra of matter states in all 175 models found in a previous work by the author are discussed. Only 20 patterns of representations are found to occur. Accomodation of the minimal supersymmetric standard model (MSSM) spectrum is addressed. States beyond those contained in the MSSM and nonstandard hypercharge normalization are shown to be generic, though some models do allow for the usual hypercharge normalization found in SU(5) embeddings of the standard model gauge group. The minimum value of the hypercharge normalization consistent with accommodation of the MSSM is determined for each model. In some cases, the normalization can be smaller than that corresponding to an SU(5) embedding of the standard model gauge group, similar to what has been found in free fermionic models. Bizarre hypercharges typically occur for exotic states, allowing for matter which does not occur in the decomposition of SU(5) representations—a result which has been noted many times before in four-dimensional string models. Only one of the 20 patterns of representations, comprising seven of the 175 models, is found to be without an anomalous U(1). The sizes of nonvanishing vacuum expectation values induced by the anomalous U(1) are studied. It is found that large radius moduli stabilization may lead to the breakdown of σ-model perturbativity. Various quantities of interest in effective supergravity model building are tabulated for the set of 175 models. In particular, it is found that string moduli masses appear to be generically quite near the gravitino mass. String scale gauge coupling unification is shown to be possible, albeit contrived, in an example model. The intermediate scales of exotic particles are estimated and the degree of fine-tuning is studied.     

The ν2, 2ν2, 3ν2, ν4, and ν2 + ν4 bands of 15NH3

The ir absorption of gaseous ¹⁵NH₃ between 510 and 3040 cm^?1 was recorded with a resolution of 0.06 cm^?1. The ν₂, 2ν₂, 3ν₂, ν₄, and ν₂ + ν₄ bands were measured and analyzed on the basis of the vibration-rotation Hamiltonian developed by V. ?pirko, J. M. R. Stone, and D. Papou?ek (J. Mol. Spectrosc.60, 159–178 (1976)). A set of effective molecular parameters for the ν₂ = 1, 2, 3 states was derived, which reproduced the transition frequencies within the accuracy of the experimental measurements. For ν₄ and ν₂ + ν₄ bands the standard deviation of the calculated spectrum is about four times larger than the measurements accuracy: a similar result was found for ν₄ in ¹⁴NH₃ by ?. Urban et al. (J. Mol. Spectrosc.79, 455–495 (1980)). This result suggests that the present treatment takes into account only the most significant part of the rovibration interaction in the doubly degenerate vibrational states of ammonia.     

Fourier transform spectroscopy on the 3ν2, 2ν2 + ν6 and ν3 + ν5 bands of H2CO

Fourier transform spectra covering the range from 1500 to 5400 cm^?1 with 0.02-cm^?1 resolution have been obtained for formaldehyde. A study of the region above 4000 cm^?1 has yielded rotational constants and other asymmetric rotor parameters for three bands: 3ν₂ (ν₀ = 5177.7611 ± 0.0005 cm^?1)2ν₂ + ν₆ (ν₀ = 4734.193 ± 0.004 cm^?1), and ν₃ + ν₅ (ν₀ = 4335.102 ± 0.001 cm^?1). An analysis of the A-type Coriolis interaction between the 2ν₂ + ν₆ state and the unobserved 2ν₂ + ν₄ state has yielded partially deperturbed rotational constants for the 2ν₂ + ν₆ state. Vibration-rotation interaction constants have been obtained for the ν₂ and ν₆ normal modes by combining the present results with those of previous workers.     

The vibration-rotation spectrum of methinophosphide: The overtone bands 2ν1 and 2ν3, the summation bands ν1 + ν2 and ν2 + ν3, and the difference band ν1 - ν2

The vibration-rotation bands 2ν₁, 2ν₃, ν₁ + ν₂, ν₂ + ν₃, and ν₁ - ν₂ of H¹²CP were recorded and analyzed. These data were combined with previously reported results for this molecule to obtain an improved and extended set of vibrational and rotational constants. All x_ij and γ_ij were calculated except those that require data from a summation band involving ν₁ and ν₃.     

High-resolution study of some doubly excited vibrational states of PH2D: the ν1+ν2, ν2+ν5, ν2+ν3, and ν2+ν6 bands

The absorption bands ν₁+ν₂, ν₂+ν₃, and ν₂+ν₆ of PH₂D have been recorded for the first time using a high-resolution Bruker 120 HR interferometer, and rotationally analyzed. Some transitions belonging to the very weak band ν₂+ν₅ and enhanced in intensity by strong interactions with the ν₁+ν₂ band were also assigned. Sets of parameters obtained from the fit reproduce experimental line position of the bands ν₁+ν₂ and ν₂+ν₃ with about the experimental accuracy. The residuals of the ro-vibrational energies of the ν₂+ν₆ band are about 10 times larger. Reasons for the poorer reproduction of the latter data are given.     

A theoretical model for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in methane

The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane are reviewed, and the major vibration-rotation interactions (H₃₀, $\text{H}\text{?}{}_{40}$, $\text{H}\text{?}{}_{21}$, $\text{H}{}_{31}$, $\text{H}\text{?}{}_{22}$) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2ν₄ isotropic Raman spectrum of ¹²CH₄, leading to a very good agreement between the experimental and calculated spectra.     

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

The Fourier-transform spectrum of CH₃F from 2800 to 3100 cm^?1, obtained by Guelachvili in Orsay at a resolution of about 0.003 cm^?1, was analyzed. The effective Hamiltonian used contained all symmetry allowed interactions up to second order in the Amat-Nielsen classification, together with selected third-order terms, amongst the set of nine vibrational basis functions represented by the states ν₁(A₁), ν₄(E), 2ν₂(A₁), ν₂ + ν₅(E), 2ν₅⁰(A₁), and 2ν₅^±2(E). A number of strong Fermi and Coriolis resonances are involved. The vibrational Hamiltonian matrix was not factorized beyond the requirements of symmetry. A total of 59 molecular parameters were refined in a simultaneous least-squares analysis to over 1500 upper-state energy levels for J ≤ 20 with a standard deviation of 0.013 cm^?1. Although the standard deviation remains an order of magnitude greater than the precision of the measurements, this work breaks new ground in the simultaneous analysis of interacting symmetric top vibrational levels, in terms of the number of interacting vibrational states and the number of parameters in the Hamiltonian.     

High-resolution infrared spectrum of the ν3 and ν2 + ν3 − ν2 bands of 14N16O2

The infrared absorption spectrum of the ν₃ band of ¹⁴NO₂ has been recorded with a resolution and a frequency accuracy much improved over the previous investigations. The K- and N-line assignments have been greatly extended and a more accurate set of spectroscopic constants derived. Several lines in the subbands with K_a ≥ 3 have been observed to be doubled by spin-rotation interaction and spin-rotation interaction constants have been obtained. Several weak series of lines in the spectrum (K_a = 0, 1, 2, and 3) have been unambiguously assigned to the “hot band” ν₂ + ν₃ ? ν₂. Lines of the K_a = 3, 4, 5, and 6 sub-bands of ν₃ have been found to be perturbed by a Coriolis interaction with the K_a = 4, 5, 6, and 7 levels of 2ν₂.     

Molecular constants for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in 12CH4

In a previous paper (J.-E. Lolck and A. G. Robiette, J. Mol. Spectrosc.88, 14 (1981)) a theoretical model for the interacting upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane was described. The present paper summarizes the results obtained, using this model, in a comprehensive analysis of the five bands of ¹²CH₄ through J′ = 12. Values of 80 molecular constants, of which 17 correspond to vibrationally off-diagonal operators, are reported. In addition the computed energy levels of the v₃ = 1 state are compared to the experimental ones and to the result of the previous isolated band approach.     

The ν2 + ν4 and 2ν2 isotropic Raman bands of 12CH4

The purely isotropic Raman spectrum of the ν₁ band, the ν₂ + ν₄ band (enhanced through interaction with ν₁), and the 2ν₂ band of ¹²CH₄ was obtained with a spectral resolution of 0.30–0.35 cm^?1 from exposures with different orientations of the linearly polarized exciting light. The ν₂ + ν₄ and 2ν₂ bands show partially resolved rotational structure. The spectra are interpreted in terms of a model which takes explicitly into account vibrational and rovibrational interactions with other vibrational states, using molecular constants determined primarily from infrared spectra. The computed contours are in excellent agreement with the experimental ones and the observed and calculated peak wavenumbers agree within one tenth of the spectral resolution limit, except for a small region near the ν₁ band. The good overall agreement represents an independent check on the overall correctness of the previously reported molecular constants. A detailed discussion is given of the contributions to the intensities of individual transitions from the three transition moment matrix elements, which in an isolated-band model are the intensity parameters of the ν₁, 2ν₄, and 2ν₂ isotropic bands, respectively.     

High resolution infrared spectrum of the ν2 + ν3 and ν1 + ν2 bands of ozone

The vibration-rotation bands ν₁ + ν₂ and ν₂ + ν₃ of ozone appearing in the 5.7 μm region have been recorded at a resolution of 0.019 cm^?1 with a SISAM spectrometer. The rotational levels of the (110) and (011) vibrational states have been fitted using a Hamiltonian which takes into account the Coriolis interaction between these two states. The rotational and coupling constants deduced from this study have been used to calculate a list of the vibration-rotation lines which is of interest for high resolution studies of atmospheric spectra in the 1670–1890 cm^?1 region.     

The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Line positions and intensities for the ν1 + ν2 and ν2 + ν3 bands of H218O

The intensities of about 90 lines of the ν₁ + ν₂ and ν₂ + ν₃ bands of H₂¹⁸O have been measured using a Fourier transform spectrum of natural water vapor. The constants involved in the rotational expansion of the transformed transition moment operators corresponding to these bands have been determined through a fit of these line intensities. The constants obtained are used to compute the whole spectrum of the ν₁ + ν₂ and ν₂ + ν₃ bands of H₂¹⁸O providing reliable line positions and intensities. For lines involving perturbed levels a comparison is given with the results obtained for H₂¹⁶O and it is shown that the results for one isotopic species cannot be transferred directly to another one.     

Theoretical integrated intensities for the 2ν2 and 2ν2-ν2 bands of HCN and DCN

Dipole moment functions, both perpendicular and parallel to the molecular axis, are calculated from the SCF and MRD-CI results of a previous study for the normal ν₂ bending vibrations of HCN and DCN. Vibrationally averaged dipole moments and the infrared transition matrix elements are then obtained from the dipole moment functions and vibrational wave functions. MRD-CI results, with known experimental values in parentheses, for HCN are 〈0|μ|0〉 = ?2.954(?2.985) D, 〈1|μ|1〉 = ?2.915(±2.942) D, 〈0|μ|1〉 = 0.148(0.147) D, 〈0|μ|2〉 = ?0.027 D, 〈1|μ|2〉 = 0.210 D. Calculated absolute intensities at 1 atm and 0°C for the (02⁰0) ← (000), (02⁰0) ← (010), and (02²0) ← (010) bands of HCN are 25 (40 ± 10 as estimated from spectra), 8.5, and 17.0 atm^?1 cm^?2, respectively. Results for DCN are also reported.     

The ν2 and ν4 bands of AsH3

The infrared absorption of arsine, AsH₃, between 750 and 1200 cm^?1 has been recorded at a resolution of 0.006 cm^?1. Altogether 2419 transitions, including nearly 700 “perturbation allowed” transitions with Δ∥k ? l∥ = ±3, ±6, and ±9, have been assigned to the ν₂(A₁) and ν₄(E) bands. Splitting of the transitions for K″ = 3, 6, and 9 was also observed. To fit the rotational pattern of the v₂ = 1 and v₄ = 1 vibrational states up to J = 21, all the experimental data were analyzed simultaneously on the basis of a rovibrational Hamiltonian which took into account the Coriolis interaction between ν₂ and ν₄ and also included several essential resonances within them. The derived set of 38 significant spectroscopic parameters reproduced the 2328 transition wavenumbers retained in the final fit within the accuracy of the experimental measurements.     

Lifetime of the Z1 centre in KC1:Sr

Data on the radiative lifetime τ(Z₁) of the relaxed excited state of the Z₁ centre in KC1:Sr in the 63–135 K range are reported for the first time [τ(Z₁)= 194 ± 10 nsec at 63 K]. The activation energy of deexcitation (ΔE = 0.132 ± 0.008 eV) for the luminescence process is in agreement with the value obtained by Paus from a quantum yield analysis.The results are discussed on the basis of an analogy with the F-centre behaviour.     

The ν9 + ν11 − ν11, ν10 + ν11 − ν11 hot band system in allene-d4

The hot band system ν₉ + ν₁₁ ? ν₁₁, ν₁₀ + ν₁₁ ? ν₁₁ in allene-d₄ was studied at a resolution near 0.010 cm^?1. About 1500 partly overlapped hot band rotational lines were assigned and fitted to a model taking into account z-Coriolis resonance between the combination levels ν₉ + ν₁₁ and ν₁₀ + ν₁₁ as well as vibrational l-type resonances within these levels. Upperstate constants have been derived from an analysis in which the constants for the ν₁₁ level were constrained. A detailed study of rotational as well as vibrational l-type doublings occurring in the KΔK = ?1 subband is presented, and the sign of vibrational l-type doubling constants for the ν₁₀ + ν₁₁ level is determined. A localized (x, y)-Coriolis resonance between ν₁₀ + ν₁₁ and ν₄(B₁) + ν₁₁ is discussed and the interaction parameter is obtained as well as some constants for ν₄ + ν₁₁.