Intensity statistical weight

Equation 29.20 applies only to a one-line spectrum, and the sensitivity decreases when the radical sample exhibits HFS. As a simple case, reconsider the H3C spectrum, with its four lines one of the outside lines represents only one-eighth of the total number of radicals in the sample because the 1 3 3 1 intensity ratios reflect the statistical weights of the various nuclear spin configurations. Thus the detection sensitivity falls off rapidly with progressive HFS. 

For spectra corresponding to transitions from excited levels, line intensities depend on the mode of production of the spectra, therefore, in such cases the general expressions for moments cannot be found. These moments become purely atomic quantities if the excited states of the electronic configuration considered are equally populated (level populations are proportional to their statistical weights). This is close to physical conditions in high temperature plasmas, in arcs and sparks, also when levels are populated by the cascade of elementary processes or even by one process obeying non-strict selection rules. The distribution of oscillator strengths is also excitation-independent. In all these cases spectral moments become purely atomic quantities. If, for local thermodynamic equilibrium, the Boltzmann factor can be expanded in a series of powers (AE/kT)n (this means the condition AE < kT), then the spectral moments are also expanded in a series of purely atomic moments. 

Figure 5. Experimental s-weighted intensity function (a) compared with calculated si(s) curves for (b) random chain according to conditional probabilities derived from the statistical weights of Abe, Jernigan, and Flory ( i) with near-neighbor dependence of rotation angles, and (c) an assemblage of randomly packed spheres with average segments placed at their centroids (see text)...

Nuclear spin statistical weights were discussed in Section 5.3.4 and the effects on the populations of the rotational levels in the v = 0 states of H2, 19F2, 2H2, 14N2 and 1602 illustrated as examples in Figure 5.18. The effect of these statistical weights in the vibration-rotation Raman spectra is to cause a J" even odd intensity alternation of 1 3 for H2 and 19F2 and 6 3 for 2H2 and 14N2 for 1602, all transitions with J" even are absent. It is for the... 

The differences between the eigenvalues of both equations will furnish the relative locations of the torsional bands, whereas the Franck-Condon factors (120) will give the relative intensities. Notice, that the nuclear statistical weights have to be taken into account to compare the intensities of transitions belonging to different degrees of degeneracy. 

Intensities and Statistical Weights. The absolute absorption intensity of a vibrational-rotational transition is proportional to the square of the transition moment Py times the population in the lower state. Py varies only slightly for different rotational levels, so the principal factors determining the relative intensity are the degeneracy and the Boltzmann weight for the lower level,... 

The size of the resonance lines is different from that of the absorption lines for example, the Mjy absorption of lanthanum is laiger than the My absorption, whereas the Mjy resonance line is less intense than the My line 18). For heavy rare earths, only My resonance lines have been observed up to now however, the total intensities of the Mjy and My emission spectra remain in the ratio of the statistical weights because Mj3 is much more intense than Ma (79). Spin relaxation effects different for 3 d i2 or 3 d /2 excited electrons could be invoked to explain these measurements. 

Here L0 and Lv are the effective absorption path lengths at line frequencies vQ and vv, respectively g is a statistical weight factor m//I is the dipole matrix element of the rotational transition r+/, and Ap is the halfwidth of the line at half intensity. 

The relative intensity of the 5s l5p l ionization compared with 5p 2 ionization is about 1/20, at both wavelengths. Within the groups of lines of the p4 configuration the relative intensities in complete photoionization spectra seem to agree roughly with the statistical weights of 5 3 1 5 1 for 3P2,i,o> XD2, and S0, with minor deviations. The relative contributions of direct and indirect photoionization can sometimes be separated [65], and where this is done the continuum (direct) part approximately follows the statistical weights at the... 

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