The effect of detuning upon resonance fluorescence

The excitation spectrum of a two-level atom interacting with a strong laser field is considered as a function of the detuning. The spectral function of the system is calculated by making use of the Green's function formalism and includes a physical process which is neglected in many earlier treatments of the one photon problem. It is found that for zero and small detunings, the spectral function describes the well known three peak spectrum which evolves into a four line spectrum as the detuning is increased. Results of numerical calculations for a wide range of detuning are presented and analytic expressions are derived to describe the small and large detuning limits.     

Asymptotic expansions for distributions of latent roots in multivariate analysis

Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S₁(S₁ + S₂)^?1, where S₁ is $\text{W}{}_{\mathrm{<mtext>m</mtext>}}\text{(n}{}_1\text{, Σ, Ω)}$ and S₂ is W_m(n₂, Σ), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix Ω large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n^?1S, where S in W_m(n, Σ), for large n, and S₁S₂^?1, where S₁ is W_m(n₁, Σ) and S₂ is W_m(n₂, Σ), for large n₁ + n₂.     

Solid state polymerization of poly(lactic acid): Some fundamental parameters

Poly(lactic acid) (PLA) was submitted to solid state polymerization (SSP) in a fixed bed reactor under nitrogen flow, so as to examine technique efficiency for increasing the molecular weight and hence permitting the reduction of the melt polymerization residence times. In order to use a suitable starting material, SSP prepolymers of low and medium molecular weight were first prepared through solid state hydrolysis of commercial PLA grade under acidic and alkaline conditions. During these degradation runs, hydrolysis involved the random scission of ester groups in the polymer backbone, while the relevant kinetics and the resulting thermal properties were also examined. In a subsequent step, the prepolymers obtained were subjected to SSP at three temperatures, approximately 2.5–25.0 °C below their melting point. The process achieved an increase of up to 1.7 times the initial molecular weight, however, with different trends depending on the prepolymer characteristics, reaction temperature and time, as well as the pH of the hydrolysis medium. In addition to molecular weight build up, the effect of the SSP process on end product thermal properties was also investigated.     

Percolation of randomly distributed growing clusters: the low initial density regime

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, p. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low values of p we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a spanning cluster to occur, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.     

A note on minimum distance estimates

It is shown that minimum distance estimates enjoy the invariance property of maximum likelihood estimates. Supported under Grant No. 18-2773 of the American University of Beirut.     

Cooperative two-photon resonance fluorescence of a three-level atom

We have calculated the Green function describing the physical process where a three level atom interacts with a strong pump field as well as with a weak perturbing signal field in the limit of high photon densities. The theory is then used to describe the cooperative two-photon resonance fluorescence which occurs when the sum of the two atomic transition frequencies is nearly twice the frequency of the pump field. Our atomic system is equivalent to a two-level atom when the degeneracy of the ground state is removed by a Stark field. The excitation spectrum has been found to consist of new bands and sidebands which exist only in the presence of the Stark field. The resonance process which occurs when the Stark splitting is in the neighbourhood of the energy shift induced by the laser field has been discussed in detail.     

Unsolvability of binary forms

A property of a binary unit is obtained which is invariant in all number fields of fixed degree n, n ≥ 3. This property is then used to formulate a necessary condition for the solvability of a binary form.     

Resonance fluorescence spectrum of a three-level atom. II. Numerical results

Numerical computations are presented for the excitation spectra arising from the interaction between a three-level atom in the cascade configuration and a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered when the laser field is at resonance with the equally spaced levels of the atom as well as a function of the detunings. The physical process of optical amplification occurs without population inversion and it is more pronounced when the laser field is detuned than when it is at resonance. The shapes of the spectral lines for a number of side-bands are of the absorption-amplification type rather than that of the absorption one. In the presence of detunings as well as in the cooperative two-photon cascade process, the resulting spectra are far more complicated than those occuring at resonance. Results of numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically.     

Performance optimisation of a new-generation orthogonal-acceleration quadrupole-time-of-flight mass spectrometer

Orthogonal-acceleration quadrupole time-of-flight (oa-QTOF) mass spectrometers, employed for accurate mass measurement, have been commercially available for well over a decade. A limitation of the early instruments of this type was the narrow ion abundance range over which accurate mass measurements could be made with a high degree of certainty. Recently, a new generation of oa-QTOF mass spectrometers has been developed and these allow accurate mass measurements to be recorded over a much greater range of ion abundances. This development has resulted from new ion detection technology and improved electronic stability or by accurate control of the number of ions reaching the detector. In this report we describe the results from experiments performed to evaluate the mass measurement performance of the Bruker micrOTOF-Q, a member of the new-generation oa-QTOFs. The relationship between mass accuracy and ion abundance has been extensively evaluated and mass measurement accuracy remained stable (+/-1.5 m m/z units) over approximately 3-4 orders of magnitude of ion abundance. The second feature of the Bruker micrOTOF-Q that was evaluated was the SigmaFit function of the software. This isotope pattern-matching algorithm provides an exact numerical comparison of the theoretical and measured isotope patterns as an additional identification tool to accurate mass measurement. The smaller the value, the closer the match between theoretical and measured isotope patterns. This information is then employed to reduce the number of potential elemental formulae produced from the mass measurements. A relationship between the SigmaFit value and ion abundance has been established. The results from the study for both mass accuracy and SigmaFit were employed to define the performance criteria for the micrOTOF-Q. This provided increased confidence in the selection of elemental formulae resulting from accurate mass measurements.