Wavelength modulation absorption spectrometry from optically pumped collision broadened atoms and molecules

A theoretical investigation of the influence of optical pumping on wavelength modulation absorption spectrometry (WMAS) signals from collision broadened atoms and molecules is presented. General expressions for the nf-WMAS signal from atomic and molecular systems, modeled as three-level systems that can accommodate both optical saturation and optical pumping, are derived by the use of a previously developed Fourier series-based formalism in combination with rate equations solved under steady-state conditions. The expressions are similar to those describing the nf-WMAS signal from two-level systems that can accommodate optical saturation [Schmidt FM, Foltynowicz A, Gustafsson J, Axner O, WMAS from optically saturated collision-broadened transitions. JQSRT 2005;94:225-54], the difference being the value of the saturation flux, wherefore the general parametric dependence of WMAS signals from optically pumped systems is the same as that from optically saturated systems. The additional effect of optical pumping on the WMAS signal is investigated for three typical cases: molecules or atoms in an ordinary atmosphere, atoms in an inert atmosphere, and atoms or molecules possessing metastable states. The possibility to describe any of these systems with a two-level model is investigated.     

Wavelength modulation diode laser absorption spectroscopy for high-pressure gas sensing

A general model for 1f-normalized wavelength modulation absorption spectroscopy with nf detection (i.e., WMS-nf) is presented that considers the performance of injection-current-tuned diode lasers and the reflective interference produced by other optical components on the line-of-sight (LOS) transmission intensity. This model explores the optimization of sensitive detection of optical absorption by species with structured spectra at elevated pressures. Predictions have been validated by comparison with measurements of the 1f-normalized WMS-nf (for n = 2–6) lineshape of the R(11) transition in the 1st overtone band of CO near 2.3 μm at four different pressures ranging from 5 to 20 atm, all at room temperature. The CO mole fractions measured by 1f-normalized WMS-2f, 3f, and 4f techniques agree with calibrated mixtures within 2.0 %. At conditions where absorption features are significantly broadened and large modulation depths are required, uncertainties in the WMS background signals due to reflective interference in the optical path can produce significant error in gas mole fraction measurements by 1f-normalized WMS-2f. However, such potential errors can be greatly reduced by using the higher harmonics, i.e., 1f-normalized WMS-nf with n > 2. In addition, less interference from pressure-broadened neighboring transitions has been observed for WMS with higher harmonics than for WMS-2f.     

Analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function

Modulated spectroscopic detection techniques that rely on dispersion, e.g. Faraday modulation/rotation spectroscopy and wavelength-modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy, are often described in terms of Fourier coefficients of a modulated dispersion lineshape function. This work derives a non-complex analytical expression for the nth Fourier coefficient of a modulated Lorentzian dispersion lineshape function. The expression is easier to implement, and orders of magnitude faster to execute, than previous approaches involving numerical calculations of integrals. The first six Fourier coefficients are explicitly given and illustrated for their optimum modulation amplitudes, which are also given.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

Fine-structure splittings of 2F states of singly ionized strontium

We have studied the 4d?nf and 5d?nf (n = 4?8) transitions of singly ionized strontium using high-resolution optical spectroscopy. The ²F fine structure is inverted in all the states observed and decreases from ?1.06cm^?1 in 4f to ?0.26 cm^?1 in 8f.     

Nonfactorizable contributions to hadronic decays of charm mesons in the Cabibbo-suppressed modes

We investigate nonfactorizable contributions to charm meson decays into D → ππ/K K?/K K?*/K? K*/D → K*K?* modes. Obtaining the contributions from spectatorquark diagrams for N _c = 3, we determine the nonfactorizable isospin amplitudes required to explain the data for these modes. For these decays, we observe that ππ, πρ, decay modes favor a nonfactorizable-isospin-amplitudes ratio A ₀ ^nf /A ₂ ^nf equal to (1.123±0.158) and for K K?, K K?*, K? K* and K*K?* modes, the ratio of nonfactorizable amplitudes A ₀ ^nf and A ₁ ^nf turns out to be unity.     

Opto-mechanical estimation of micro-trap with cold atoms via nonlinear stimulated Raman scattering spectrum

In this paper a method for identifying the wavelength range of a tunable vertical cavity surface-emitting laser (VCSEL) is introduced. The measuring technology is wavelength modulation spectroscopy (WMS). The laser is tuned over its wavelength by applying a temperature ramp using the onboard Peltier element. During this ramp the 2f absorption lines are recorded. After finishing the temperature ramp and collecting the lines, a ratio-compare algorithm calculates the theoretical amplitudes of selected predefined lines. Then it compares the measured 2f line amplitudes iteratively with the theoretical ones. If the error of the ratios of the calculated and the measured lines is below a predefined limit, the searched lines and hence the emission wavelength are identified.     

Calculation of the fine-structure parameters for np 5 n′f configurations of rare-gas atoms

In the single-configuration approximation, fine-structure parameters are calculated semiempirically in the intermediate coupling scheme for the configurations 2_p ⁵ nf(n=4–6) of NeI, 3p ⁵ nf(n=4–7) of ArI, and 4p ⁵4f of KrI. With the fine-structure parameters obtained, the coefficients of expansion of the wave functions in basis functions of the LS-coupling scheme and the gyromagnetic ratios are calculated. To the authors’ knowledge, analogous data are absent in the literature. The correctness of the fine-structure parameters obtained is confirmed by values of the fine-splitting constant, which is well known for other configurations of rare-gas atoms with an almost filled p shell.     

Global and heliolatitude indices of solar activity and cosmic ray modulation

The time variation of the galactic cosmic rays (GCR) (1958–2006) is described using solar activity indices in the form Z^α, Z^α exp[?(φ/φ₀)^β], where Z and φ are one of the solar activity indices and the heliolatitude of sunspots; α, β, and φ₀ are the optimum parameters found by the least-squares method. The time variation of the GCR flux is satisfactorily described, the role of the active region heliolatitude in the index in relation to the cosmic ray modulation is revealed.     

Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n

A study has been made of the influence of the phase-difference of two ultrasonic beams, a fundamental and its nth harmonic, on the intensities or amplitudes of diffracted lightwaves. After showing the similarity between superposed and adjacent ultrasound in the Raman-Nath region ρ ? 1, simplified expressions for the intensities have been set up to draw conclusions concerning the symmetry of the diffracted pattern, the amplitude modulation, and the numerical calculation of the factor α_n, from the intensities in which α_n represents the ratio of the ultrasonic pressures. All results are illustrated in the case of a fundamental and its second or third harmonic.     

Application of microwave amplitude modulation technique to measure spin-lattice and spin-spin relaxation times accurately with a continuous-wave EPR spectrometer: Solution of Bloch’s equations by a matrix technique and least-squares fitting

A matrix technique to calculate signals recorded using the microwave amplitude-modulation technique is described. The calculations are carried out for spin packets, on and off resonance, to take into account inhomogeneous broadening. Both, the transverse component of magnetization representing the continuous-wave signal in a resonator, such as a cross-looped resonator, as well as the signal (electromotive force) induced in a pickup coil oriented parallel to the external magnetic field, are calculated for an arbitrary value of the coefficient of modulation. This is accomplished by solving the relevant Bloch equations in the rotating frame for the case when the amplitude of the microwave field is modulated by a sinusoidal wave, using Fourier expansions of the longitudinal and transverse components of the magnetization in Bloch equations. This results in a series of coupled equations inM _α(n) (α=y,zz), the magnetic moments of vaarious orders, leading to a penta-diagonal matrix of infinite dimension. These equations are then truncated and solved by a fast matrix technique to calculateM _α(n), required to calculate the modulation signals as functions of the amplitudemodulation frequency Ω. It is outlined how to exploit the expressions for the modulation signals to estimate the spin-lattice relaxation timesT ₁ and spin-spin relaxation timesT ₂ accurately by the leastsquares procedure, fitting simultaneously all signals obtained for spin packets, on and off resonance, at various modulation frequencies. Illustrative examples are provided.     

Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.     

Measurements of relative transition probabilities of ns-4p,nd-4p,and nf-3d transitions in neutral potassium

Relative transition probability (A-value) measurements are reported for the ns-4p (n = 6–15), nd-4p (n = 5–13), and nf-3d (n = 7–14) series transitions in neutral potassium (KI). The results are based on intensity measurements of optically-thin KI spectral lines from a steady-state potassium emission source. The source employed was a radially-symmetric potassium-seeded argon plasmajet containing ? 5 mole per cent K-atoms. Local emission coefficients were obtained by means of the Abel transform. For the prevailing free-stream conditions (P ～ 11 torr, T ～ 3200 K, n_e ～ 10¹⁴ cm^-3), the potassium excited state populations are described by a Boltzmann distribution down to and including the ground state.The reported A-values are normalized to that of the 580.2 nm line (7s-4p_{$\text{3}\text{2}$} transition). The relative accuracy is estimated to be 5–20% for the ns-4p series and 15–25% for the nf-3d transitions. With the exception of the data for the 6s-4p and all nf-3d transitions, the measurements agree to within estimated experimental uncertainties with the values given in the NBS tabulation [Wiese et al. (1969)], although systematic differences are observed. For the exceptions noted, the measurements lie 25–50% below the relative NBS values. Comparison is also made to recent calculations of Lindgard and Nielson, and Ormonde.     

Phenomenology of the ψ (3105) and the hypothesis of charm

We estimate the effective coupling strengths of the ψ(3105) to ordinary hadrons and examine possibility that this resonance is the uncharmed vector meson φ_c composed predominantly of charmed quarks. Distinctive decay modes of φ_c are pointed out.     

High excitation energy structures in208Pb

Level-crossing signals of impact radiation of He I have been analyzed with regard to the determination of excitation matrices. The signals have been registered at various electricfield strengths by sweeping a magnetic field strength ?_z through the positions ofΔm=2 crossings of Zeeman substates ofn ³ D ₂ andn ³ D ₃ levels (n=4 and 5) of He I excited by 35keV-He⁺-He collisions. We analyzed the signal amplitudes and signal shapes with regard to a spin-dependence of the excitation matrix usually discarded by theoretical arguments. To this end a parametrization of spin-dependent excitation matrices has been performed, and the dependence of the level-crossing amplitudes on the 19 parameters obtained have been studied. It turned out that the observed relative signal amplitudes can satisfactorily be explained by only two parameters, the two multipole components of orderk=2 andk=4 of the alignment of the orbital angular momentum. Thus in agreement with theoretical estimations no spin-dependence must be taken into account.     

Porphyrin free base phosphorescence

The wavelength for heavy atom enhanced phosphorescence is unambiguously established by time resolved excitation spectra in 50% EPA and 50% ethyl iodide at 77 K for protoporphyrin (795 nm), mesoporphyrin (773 nm), octaethylporphin (768 nm), and porphin (785 nm). Excitation spectra also establish the phosphorescence wavelength of brominated protoporphyrin in EPA at 77 K to be 783 nm, with a quantum yield φ_p ～ 9 × 10^?4. Using laser excitation the phosphorescence quantum yields in EPA were found for protoporphyrin (φ_p ～ 5 × 10^?5), mesoporphyrin (φ_p < 6 × 10^?5), and tetraphenylprophin (φ_p ～ 2 × 10^?5). Tetraphenylporphin phosphorescence shows no heavy atom enhancement. Natural radiative lifetimes for phosphorescence of the various free bases are found to be 70 sec and higher.     

Spin-dependent Kondo effect induced by Rashba spin-orbit interaction in parallel coupled double quantum dots

Electronic transport through parallel coupled double quantum dots (DQD) with Rashba spin-orbit (RSO) interaction is investigated in Kondo regime by means of the slave-boson mean field approximation at zero temperature. By the co-action of the phase factor deduced by RSO interaction and the magnetic flux penetrating the parallel DQD, an interesting spin-dependent Kondo effect emerges. The molecular state representation theory is used to obtain a detailed understanding of the spin-dependent Kondo effect. It is shown that Quantum interference between the bonding Kondo state and antibonding state, which is modulated by the RSO interaction, plays a crucial role to the density of states and the linear conductance. The magnitude of each spin component conductance can be modulated by the RSO interaction strength. The conductance of each spin component exhibits 4π-periodic function with respect to φR. Moreover, the swap operation in the parallel DQD system can be implemented by tuning the RSO interaction.     

Heat transfer over a stretching surface with variable heat flux in micropolar fluids

Heat transfer over a stretching surface with uniform or variable heat flux in micropolar fluids is investigated in this Letter. The boundary layer equations are transformed into ordinary differential equations, and then they are solved numerically by a finite-difference method. The effects of the material parameter K, Prandtl number Pr, velocity exponent parameter m, and heat flux exponent parameter n on the heat transfer characteristics are studied. It is found that the local Nusselt number is higher for micropolar fluids compared to Newtonian fluids.     

Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems

The exp S formalism for the ground state of a many-body system is derived from a variational principle. An energy functional is constructed using certain n-body linked-cluster amplitudes with respect to which the functional is required to be stationary. By using two different sets of amplitudes one either recovers the normal exp S method or obtains a new scheme called the extended exp S method. The same functional can be used also to obtain the average values of any operators as well as the linear response to static perturbations. The theory is extended to treat dynamical phenomena by introducing time dependence to the cluster amplitudes. This allows the calculation of both nonlinear dynamical behaviour and of dynamical linear response and Green's functions. Practical approximation schemes are considered. In a SUB n approximation the m-body amplitudes are restricted to the order $\text{m ? n}$ and the energy functional is a finite-order multinomial in the amplitudes to be variationally determined. It is shown that the solution corresponds to summing well-defined subsets of Goldstone diagrams. These subsets are conveniently specificed in terms of tree structures, the normal or extended generalized time ordering g.t.o. trees. The extended exp S method is in the SUB n approximation able to sum, in addition to the normal SUB n diagrams, a set which contains m-body cluster amplitudes of arbitrarily high order (m > n) in the ordinary sense. The article also discusses how the SUB n truncation schemes must be modified to be able to treat a system with a strong repulsive core in the two-body interaction. The method is formulated for the general cases of Bose and Fermi systems which may or may not conserve total particle number. It is shown that the simplest approximation, SUB 1, in the extended exp S method agrees with the mean field theory, which is the coherent-state approximation in the boson case or the Hartree-Fock approximation in the fermion case. It is argued that the extended exp S method already in low-order approximations can realistically treat a great variety of diverse many-body problems, even including systems which may undergo ground-state phase transitions. A few applications are described in more detail. The Bose liquid is treated in the extended SUB 2 approximation. It is shown that the ground-state results in the uniform limit are exact and agree with the hypernetted-chain approximation. The modifications due to hard-core interactions and the non-linear equations of motion are also discussed in this case. For Fermi systems it is shown that the supercondictive phase transition of the BCS model Hamiltonian and the deformation phase transition of the Lipkin model are properly obtained by the extended exp S method in a low-order approximation.