Singularities in ion trap nonlinear coherent states

We present a theoretical analysis of the k-boson nonlinear coherent states of a two-level trapped ion interacting with two laser fields. Such states are both the zero-energy state of the interaction Hamiltonian and the eigenstates of a deformed annihilation operator. For the single-boson case, we show that the structure of the states and their coherence and minimum-uncertainty properties can be compromised whenever the Lamb-Dicke parameter is one of the roots of certain Laguerre polynomials. We investigate these problems, which are strictly related to the non-analyticity of the deformation function in the annihilation operator.     

KaonB parameter with static cavity QCD corrections

The kaonB parameter is computed in a framework in which static cavity QCD loop corrections to the weak interactions of hadrons are included by extending the Fock state wavefunction to includeO(g) bremsstrahlung and vacuum fluctuation states. Since the QCD corrections are inherent in the calculation of the matrix elements of the bare effective weak ΔS=2 Hamiltonian between hadronic states the scale matching problem of the standard short distance analysis is alleviated. The modified static cavity model used is characterised by four parameters; the effective quarkgluon coupling constant, the confinement pressure, the zero-point energy and a parameter governing the centre-of-mass corrections. These parameters are fitted to the π and ? masses and the charge radii of π andK. Results are given for the ultra-relativistic (m _u=m _d=0) sector and for a region (m _u=m _d≈140 MeV) where the ΔI=1/2 rule is uniquely reproduced. For the parameter set which describes the ΔI=1/2 rule we findB _K=0.58 at a basis size ofN _B=6.     

Photoproduction of neutral pions to discrete nuclear states

We study the photoproduction of neutral pions on nuclei to discrete final states at intermediate energies. Both photoproduction and distortion of the π⁰ are dominated by Δ-excitation, which requires a careful treatment of the Δ-nucleus dynamics. We use the Δ-hole approach, which has been used to describe a variety of pion- and photon-induced nuclear reactions. It is shown that π⁰ photoproduction is very sensitive to medium effects of Δ-propagation and can therefore be used to investigate the Δ-nucleus interaction. The validity of the distorted-wave impulse approximation for this reaction is examined. Results for low-lying excitations in ¹²C are compared with the available data.     

Rotational selection rules for doublet-quartet transitions in asymmetric top molecules

Selection rules on the rotational structure of doublet-quartet transitions in asymmetric top molecules are discussed on the basis of the spin-orbit coupling mechanism, rather than by symmetry arguments, and some additional rules are found with respect to a previous work. In the case that the combining doublet and quartet states are appreciably mixed only with levels directly connected to them by the spin-orbit operator, it turns out that, except for the very low values of the rotational quantum numbers, branches with |ΔN ? ΔJ| > 1 are essentially forbidden. Thus, branches with ΔN = ± 3 (T and N branches) are not expected to be observable. In this case, it is found also that in a high magnetic field transitions with ΔM_s = ±2 are forbidden, and only ΔM_s = 0, ±1 bands are expected to occur. All these restrictions are removed if the combining states are also appreciably contaminated by states indirectly connected to them by the spin-orbit operator, through intermediate levels.     

The Zeeman effect in doublet-quartet transitions in orthorhombic rotating molecules

Theoretical predictions on the effect of magnetic fields of variable strength on the rotational structure of doublet-quartet transitions in orthorhombic near symmetric top molecules are reported, with the assistance of computer simulations of line profiles. Low-field profiles are discussed, and it is shown that low-field linewidths are approximately equal to 2gβH|ΔJ ? ΔN| for transitions between states of any spin multiplicity. In a high field, transitions allowed by direct spin-orbit contamination of the combining states give rise to three lines with ΔM_s = 0, ±1, whereas two additional lines, with ΔM_s = ±2, are found if the combining states are appreciably contaminated also by indirect coupling to the active states, through intermediate levels. Computed Zeeman profiles are reported and discussed for several typical cases, with emphasis on the effects of different light polarizations. Prospectives of applicability are briefly outlined.     

A study of the effective line width in lithium ferrites using magneto microwave Kerr effect

A new technique to determine the effective line width ΔH_eff using the dimensional resonance phenomenon observed in magneto-microwave Kerr-effect experiment is discussed. This effect depends on the Permeability tensor components and the damping parameter α. The components of permeability tensor μ have been calculated theoritically and the damping parameter α is determined from experimental data. The measurements have been made at 24 GHz on three samples of lithium ferrite and their effective line widths have been obtained both in the partially magnetised and the saturated states of magnetisation. It has been found that ΔH_eff for two states of magnetisation are different. Further, the value of ΔH_eff obtained are higher than expected at this frequency. This suggests the possibility of additional relaxation mechanisms at dimensional resonance.     

XXZ chain with a boundary

The XXZ spin chain with a boundary magnetic field h is considered, using the vertex operator approach to diagonalize the hamiltonian. We find explicit bosonic formulas for the two vacuum vectors with zero particle content. There are three distinct regions when h ⩾ 0, in which the structure of the vacuum states is different. Excited states are given by the action of vertex operators on the vacuum states. We derive the boundary S-matrix and present an integral formula for the correlation functions. The boundary magnetization exhibits boundary hysteresis. We also discuss the rational limit, the XXX model.     

Resonant fluorescence of gaseous bromine excited by the 5145 Å radiation of a single longitudinal mode argon ion laser

The resonant fluorescent spectra of gaseous bromine excited by the single longitudinal mode 5145 Å radiation of an argon ion laser were reinvestigated. Three new transitions were found in addition to the five previously reported. The excitation frequency and the fluorescent line positions from Δv = 1 to Δv = 9 were carefully measured for each of the eight transitions. The fluorescent lines of Δv = 5 and Δv = 10 are too weak to be detected. The isotopic molecules and the vibration-rotation states involved were assigned. All the fluorescent line positions up to Δv = 10 were calculated, and they agreed with the observed values to within 0.2 cm^?1. The relative intensities in each progression also agreed with the known Franck-Condon factors.     

Raman E 1 and E 1 + Δ1 resonances in a system of unstrained germanium quantum dots

The positions and shapes of the Raman E ₁ and E ₁ + Δ₁ resonances of optical phonons are studied as functions of the size of unstrained germanium quantum dots. The quantum dots are grown by molecular-beam epitaxy in GaAs/ZnSe/Ge/ZnSe structures on GaAs(111) wafers. The positions of the E ₁ and E ₁ + Δ₁ resonances are found to shift by at most 0.3 eV. This shift is shown to be well described in terms of a cylindrical model using the quantization of the spectrum of bulk electron-hole states in germanium that form an exciton in a two-dimensional critical point. The fact that the peaks of the E ₁ and E ₁ + Δ₁ resonances appear separately has been detected for the first time, and it is related to the transformation of the interband density of states into a delta function because of spectrum quantization. An increase in the resonance amplitudes in quantum dots as compared to the bulk case is related to the degeneracy multiplicity of the exciton state in the (111) direction.     

The Rotational Spectrum of ClClO2 in Its v4=1 and v6=1 Vibrationally Excited States: An Example of Strong Coriolis Interaction

The two lowest vibrational states of ³⁵Cl³⁵ClO₂, v₄=1 (A′) and v₆=1 (A″), were investigated between 223 and 500 GHz. More than 250 rotational transitions were recorded with J and K_a up to 71 and 34, respectively. The spectra are heavily perturbed by strong c-type and weaker a-type Coriolis interactions. Near degeneracies of rotational levels of the two vibrational states having ΔJ=0, ΔK_a=5 to 1, and ΔK_a+ΔK_c= odd cause moderate to severe perturbations in the rotational structure, preventing the states from being fit as isolated ones. Distortions in the hyperfine structure facilitated the assignment of rotational quantum numbers. Several resonantly interacting levels with ΔK_a=5 to 2 were accessed, and a number of transitions between the states were observed. While resonant Coriolis interaction with ΔK_a=1 occurs only at K_a>40, the effects of this interaction are so severe that nonresonant interaction considerably perturbs the highest K_aQ-branches observed. The observed transitions could be fit to within experimental uncertainties employing the first-order Coriolis coupling constants fixed to those from the harmonic force field, sextic distortion constants fixed to those of the ground state, and some higher order Coriolis terms. The energy difference calculated from the fit agrees well with that obtained from the matrix-isolation infrared spectrum. Quadrupole coupling constants were determined for both Cl nuclei and both vibrational states.     

Determination of fine structure intervals in a series of excited sodium D states using doppler free two-photon spectroscopy

Using Doppler free two-photon spectroscopy technique, we have measured the absolute values of fine-structure (fs) intervals in a series of excited sodium n²D states (n = 3,6,7, and 8). We have shown the structures are inverted and our measured values for these states are: Δ_fs(3²D) = -1523 ± 8 MHz, Δ_fs(6²D) = -385 ± 5 MHz, Δ_fs(7²D) = -253 ± MHz, and Δ_fs(8²D) = -173 ± 10 MHz.     

States on Symmetric Logics: Conditional Probability and Independence. II

We study the notions of conditional probabilities, independence and ε-independence for states on symmetric logics. We prove that a non-atomic state on the logic with the Lyapunov’s property is determined by its specification of independent events. We present the examples of (1) Δ-subadditive but is not subadditive and (2) two-valued non Δ-subadditive states on symmetric logic. We investigate the independence relation transitivity for a Δ-subadditive state. We also study continuity properties of conditional probabilities and ε-independence relation with respect to natural pseudometric for Δ-subadditive state. Finally, we pose two open problems.     

Influence of the minimal supersymmetric standard model extended by an additional Higgs singlet on the anomalous magnetic moment of the muon

We present the results of the influence of the minimal supersymmetric standard model with an additional Higgs singletN, with vacuum expectation valuev _N, on the anomalous magnetic moment of the muon. This gives different mass matrices for the charginos and neutralinos, which are taken into account within the relevant penguin diagrams leading to a contribution Δa _μ to the anomalous magnetic moment of the muon. We show that a large vacuum expectation value for the Higgs singlet leads to a suppression of the supersymmetric contribution making it difficult to see in an experiment in the near future.     

Ultraviolet photoemission study of LiF

Photoemission from evaporated films of LiF were measured at photon energies of 10-27 eV. The photoelectron spectra exhibit features that can be identified as density-of-states structures in the valence and conduction bands of LiF. Regions of high density of states can be seen at ca. 3.3 and 7.8 eV above the vacuum level. The valence-band spectrum shows a doublet structure similar to the calculated density of states for the F^?2p band of LiF. The base width of this structure is found to be 4.6 ± 0.3 eV. The photoelectron spectra for photon energies > 15 eV indicate that the highest occupied states of the F^?2p band are located at 11.8 ± 0.3 eV below the vacuum level. The photoelectron spectra in the exciton region, however, show photo-emission from higher occupied states.     

Phase properties of the nonlinear squeezed vacuum states

Using properties of the inverses of annihilation and creation operators of f-oscillator we construct the f-analogues of squeezed vacuum states. If used to describe the motion of a trapped ion, the phase probability distributions of these states for large η are very different from those of the usual squeezed vacuum state.     

Thermoreflectance of Mo from 0.5 to 35 eV

The thermoderivative spectrum, ΔR/R, is presented for Mo from 0.5 to 35 eV. Much of the observed structure is interpreted in terms of transitions involving states at the Fermi level. Spin—orbit splitting of the Δ₅ band is observed and is estimated to be 0.24 eV. Structures at 10.3 and 24.2 eV are identified as thermally modulated volume plasmons. A large feature at 11.5 eV corresponds to transitions from the occupied d bands to high lying bands. Structure is observed at 33.7 eV which can be related to modulation of core state transitions.     

Low energy photoelectron spectroscopy of solids. Aspects of experimental methodology concerning metals and insulators

Both He(I) and He(II) ultraviolet photoelectron spectra (UPS) for metals (Ag, Au) and thin solid films of organic (anthracene) and inorganic compounds (LiF, LiCl, LiBr, LiI, NaF, NACl, Li₂SO₄, NaOH) are presented. The results of measurements on two different spectrometers have shown that both the bias voltage, V_b, applied to the solid sample, and the angle of incidence, Ø, of the photon beam with the sample are crucial to the accurate determination of the work function (metals) and binding energies (insulators). The true binding energy of a band in the UPS with respect to the vacuum level, E_b^vac, is defined as the minimum value of (hv - ΔE), where ΔE is the energy difference between the threshold of the SEED, E_T, and the band maximum. ΔE is maximized at low values of ø and of V_b. The intensity of photoelectron emission (signal) increases with both ø (2–30°) and V_b (5–20 V). It is recommended that the variation of ΔE with both ø and V_b should be observed in any determination of E_B^vac.     

Dielectronic recombination rate coefficients for Fe23+ ion

The dielectronic recombination rate coefficients are explicitly calculated for the Li-like ion Fe²³⁺, which recombines with the continuum electron to form Fe²²⁺. Both 1s²2s and 1s²2p initial states are treated for the temperature range 1～8 keV. The rate coefficients are obtained from a direct evaluation of the Auger and radiative transition probabilities which are calculated from nonrelativistic Hartree-Fock wave functions. The L-shell electron excitation with Δn≠0 is found to be the dominant transition, while the 2s→2p excitation with Δn = 0 contributes approx. 10–25% of the Δn≠0 value. The K-shell excitation effect is about 1～30% in the temperature range considered, and the cascade effect is estimated to be a reduction in the rate of about 14%.     

Electronic structure of adsorbed alkali atoms for comparison with UPS data

We have generalised our earlier work calculating the induced density of states in alkali chemisorption to include the valence np level in addition to the s level. This allows the theory to take account of the possibility of sp hybridization. Hybridization is said to be weak is the sp level separation ΔE_sP exceeds twice the width of the s or p_z resonance. In the converse case hybridization is strong and the induced density of states no longer reflects distinguishable s and p_z resonances. We argue that ΔE_sP for the chemisorbed alkali exceeds considerably that for the free alkali atom. In the case of Na on r_s = 2 jellium (considered typical of the smaller alkali on r_s = 2?3 substrates) hybridization is strong for the atomic value of ΔE_sp but weak when a somewhat larger value is taken, making the conclusions a little indefinite. For Cs on Cu(111), we find a clear situation of weak hybridization with the atomic ΔE_sP and a fortiori with a more realistic value. There should thus be a well defined 6s resonance in this system. Our estimate of the width of the 6s resonance is in good agreement with photoemission data.