Widths Stark effect

Mark s contributions while at the I. G. were not limited to the emerging field of polymer science. In those five years, he also took part in studies of X-ray optics and continued his study of the X-ray structure of metals and metal salts. Other seemingly unrelated paper were published on the width of X-ray emission lines (12), Schlenk isomerism (13), the structure of aromatic compounds (14), and a special "hobby" the optical Stark Effect (15, 16). Regarding this latter work, Mark relates that his supervisors tolerated the research commenting that "as long as they are doing something decent and important" it was okay "as sport doesn t cost much money". 

The reason that I am elaborating in such detail on these c.t.s. s is that they are practically the only states in region 3, and also I believe that if we can only get a clear understanding of these states, the question of optical transition will sort itself out automatically. There are also many other effects in molecular complexesjyhere the c.t.s. s enter. I have already mentioned the cases of the quadratic Stark effect and of tfie asymmetric crystal field, where the c.t.s. s must be allowed to play an equally important and indeed analogous role. A further effect relates to the width of the charge transfer bands. The main cause of the breadth is essentially the same as that for the width of the crystal-field spectrum, except that it is much... 

We have calculated exactly the Zeeman effect for the levels IS, 3S and 3P. Indeed it is necessary to know the shift for all the hyperfine levels very well. These calculations are very classical and we just present the results in a Zeeman diagram (see Fig. 5). The most important part in the diagram is the crossing between the 38 2 (F=l, mp=-l) and 3P1/2(F=1, mj =0) levels, because the quadratic Stark effect is proportional to the square of the induced electric field and inversely proportional to the difference of energy between the two considered levels. Moreover the selection rules for the quadratic Stark effect in our case (E perpendicular to B) impose Am.F= l. So it is near this crossing that the motional Stark shift is large enough to be measured. In our calculations the Stark effect is introduced by the formalism of the density matrix [4] where the width of the levels are taken into account. The result of the calculation presented on... 

Owing to the special form of the eigenwave functions for t] f=0, and in accordance with the absence of first-order Zeeman effect, it may be shown that the magnetic dipolar contribution to nitrogen resonance line width is very small33,34). Lines are consequently narrow for many of the compounds studied, a very convenient feature when weak effects, like the Stark effect, are to be studied35). 

In the present chapter we shall start from the results obtained in Chapter 3 and treat the Stark effect of a hydrogenic atom or ion with the use of the phase-integral approximation generated from an unspecified base function developed by the present authors and briefly described in Chapter 4 of this book. Phase-integral formulas for profiles, energies and half-widths of Stark levels are obtained. The profile has a Lorentzian shape when the level is narrow but a non-Lorentzian shape when the level is broad. A formula for the half-width is derived on the assumption that the level is not too broad. 

Extensive theoretical studies of donor and acceptor spectra have shown that in semiconductors with a concentration of neutral impurities No and a concentration of ionized centres N, the increase of the line widths is proportional to (Ni/No)2 3 when linear Stark effect is present, to (Ni/No)4 3 when the quadratic Stark effect dominates, and to Nj/Nq when the quadrupole effect dominates [70,90]. 

In Fig. 3 the apparatus is shown with which Stolte (1972) has performed measurements of this type NO molecules were selected with the help of electrostatic sixpole fields, in accordance with their linear Stark effect in strong fields. The source slit of 0 05 mm width has an image formed by the selected NO molecules in the plane of the detector slit which has an experimental width of 1-4 mm f.w.h.m. this width includes all disturbing effects like the magnification factor (about 18), the imperfect linear Stark effect of the NO molecules in the selected state, the finite width of the transmission of the velocity selector (Av/v = 7% f.w.h.m.) in combination with the chromatic lens errors and the directional dependence of the maximum transmitted velocity of the velocity selector. The j = nij = Q = 3/2 state was selected where 1 is the projection of the electronic angular momentum on the molecular axis. The hyperfine structure of NO influences the situation only slightly. 

Though I do not wish to reiterate the well known history of polymer science, it is worthwhile emphasizing that these two industrial scientists made important contributions to pure science, as they had intended. They investigated fundamental questions concerning the constitution of polymers, without envisaging any immediate use of their work in industry. Moreover, Mark and his collaborators had the opportunity to do scientific work that was not connected with polymers and metals. They published papers on the width of x-ray emission lines, the optical Stark effect, molecular structure... 

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