Matrix Zeeman

Pauwels J, Hofmann C, Vandbcasteele C (1994) Calibration of solid sampling Zeeman atomic absorption spectrometry by extrapolation to zero matrix. Fresenius J Anal Chem 348 418-421. 

The influence of matrix concomitants often cannot be recognised or quantified. Progress in background correction techniques (e.g. direct Zeeman-AAS [218]), furnace techniques, microweighing, and electronic signal processing have gradually made possible the elimination... 

In eqn (4.1), g and A-t are 3x3 matrices representing the anisotropic Zeeman and nuclear hyperfine interactions. In general, a coordinate system can be found - the g-matrix principal axes - in which g is diagonal. If g and A, are diagonal in the same coordinate system, we say that their principal axes are coincident. 

We now notice that we could write a Hamiltonian operator that would give the same matrix elements we have here, but as a first-order result. Including the electron Zeeman interaction term, we have the resulting spin Hamiltonian ... 

Table 16. Zeeman Matrix Elements and Magnetic Moments fordx Systems in Coov Symmetry3).

We use these relations to write out the energy matrix initially in zero field (i.e., ignoring the Zeeman interaction) ... 

To find out what the X-band spectrum of such a system will look like, let us now complete the energy matrix with the Zeeman interaction using all the spin-operations written out in Equations 7.48a to 7.48m ... 

Pruszkowska et al. [135] described a simple and direct method for the determination of cadmium in coastal water utilizing a platform graphite furnace and Zeeman background correction. The furnace conditions are summarised in Table 5.1. These workers obtained a detection limit of 0.013 pg/1 in 12 pi samples, or about 0.16 pg cadmium in the coastal seawater sample. The characteristic integrated amount was 0.35 pg cadmium per 0.0044 A s. A matrix modifier containing di-ammonium hydrogen phosphate and nitric acid was used. Concentrations of cadmium in coastal seawater were calculated directly from a calibration curve. Standards contained sodium chloride and the same matrix modifier as the samples. No interference from the matrix was observed. 

Lum and Callaghan [ 140 ] did not use matrix modification in the electother-mal atomic absorption spectrophotometric determination of cadmium in seawater. The undiluted seawater was analysed directly with the aid of Zeeman effect background correction. The limit of detection was 2 ng/1. 

Electrothermal atomic absorption spectrophotometry with Zeeman background correction was used by Zhang et al. [141] for the determination of cadmium in seawater. Citric acid was used as an organic matrix modifier and was found to be more effective than EDTA or ascorbic acid. The organic matrix modifier reduced the interferences from salts and other trace metals and gave a linear calibration curve for cadmium at concentrations < 1.6 pg/1. The method has a limit of detection of 0.019 pg/1 of cadmium and recoveries of 95-105% at the 0.2 pg of cadmium level. 

Maximum power heating, the L vov platform, gas stop, the smallest possible temperature step between thermal pretreatment and atomisation, peak area integration, and matrix modification have been applied in order to eliminate or at least reduce interferences in graphite furnace AAS. With Zeeman effect background correction, much better correction is achieved, making method development and trace metal determinations in samples containing high salt concentrations much simpler or even possible at all. 

To understand clearly the origin of the disagreement between Eq. (62) and Anderson and Hartmann s result, let us reformulate the problem in terms of the Zeeman temperature Tz and the dipole-dipole temperature TD. At time zero, the density matrix is... 

In the following, we pay special attention to the connections among the spherical, Stark and Zeeman basis. Since in momentum space the orbitals are simply related to hyperspherical harmonics, these connections are given by orthogonal matrix elements similar (when not identical) to the elements of angular momentum algebra. 

Conventional EPR techniques have been successfully used to measure the D and E values of matrix-isolated carbenes in the ground triplet state because the steady-state concentration of triplet species is sufficiently high in the system. The technique cannot be used, however, for excited species having triplet hfetimes of the order of 10-100 ns, since their steady-state concentration is too low. The D parameters are estimated from the external magnetic field effect on the T—T fluorescence decay in a hydrocarbon matrix at low temperamre. The method is based on the effect of the Zeeman mixing on the radiative and nonradiative decay rates of the T -Tq transition in the presence of a weak field. The D values are estimated by fitting the decay curve with that calculated for different D values. The D T ) values estimated for nonplanar DPC (ci symmetry) is 0.20... 

The stabilized temperature platform furnace (STPF) concept was first devised by Slavin et al. It is a collection of recommendations to be followed to enable determinations to be as free from interferences as possible. These recommendations include (i) isothermal operation (ii) the use of a matrix modifier (iii) an integrated absorbance signal rather than peak height measurements (iv) a rapid heating rate during atomization (v) fast electronic circuits to follow the transient signal and (vi) the use of a powerful background correction system such as the Zeeman effect. Most or all of these recommendations are incorporated into virtually all analytical protocols nowadays and this, in conjunction with the transversely heated tubes, has decreased the interference effects observed considerably. 

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