Transition probabilities uniform

The dipole interaction depends on the distance between the ions (6.4). Therefore, the transition probability increases with increasing concentration of magnetic ions. Studies of the concentration dependence of the relaxation can be conveniently performed on samples of amorphous frozen solutions with a uniform distribution... 

We assume that the absorbing gas is of a uniform composition and in thermal equilibrium. The absorption coefficient, which is defined by Lambert s law, Eq. 3.1, is expressed in terms of the probabilities of transitions between the stationary states of the supermolecular system, in response to the incident radiation. Assuming the interaction of radiation and matter may be approximated by electric dipole interaction, i.e., assuming the wavelengths of the radiation are large compared with the dimensions of molecular complexes, the transition probability between the initial and... 

For an oriented sample with a uniform director orientation the 23Na NMR spectrum at a weak radiofrequency field thus consists of three equally spaced peaks. The relative magnitude of the three resonance lines is governed by the transition probabilities between the different energy levels. It turns out (9) that the central line contributes 40% of the total intensity while each of the satellites contributes 30%. The deuteron NMR spectrum consists of two equally intense peaks. 

Fig. 5. A qualitative sketch of the classical (upper) and uniform semiclassical (lower) transition probability as a continuous function of n2 (with n, fixed). and " indicate the extrema of the function n2(ql,nl) as a function of qx (as seen in Fig. 1, for example).

The calculating machine generates the chain of configurations, again using periodic boundary conditions, subject to the transition probabilities satisfying Eqs. (37) and (38), by moving successively one of tlxe N molecules selected at random, but uniformly, by a random but uniform amount The pressure is obtained by... 

A further, rough approximation of the uniform distribution of the s character between v levels, aj, = 1/JV, Pyi = I — l/N, gives the order of magnitude of the total (or radiative) width of v levels and the 0> v> transition probability ... 

In some works (see, e.g.. Ref. 34), the resonance dependence of Wif on A/ is assumed to be smoothed due to the uncertainty in the A/ values caused by the interaction between the reactants and the medium. Starting from this assumption, averaging of the transition probability over some interval of A/ values around an average value A/ is performed. The distribution of A/ values in this interval is assumed to be uniform. " ... 

Note The real collision-induced line profile depends on the interaction potential between A and B. In most cases it is no longer Lorentzian, but has an asymmetric profile because the transition probability depends on the intemu-clear distance and because the energy difference A (/ ) = Ei R) — Ek(R) is generally not a uniformly rising or falling function but may have extrema. 

B. Potential Profile with Uniform Transition Probabilities... 

One of these methods is the vibrational spectroscopy which has its roots in the late 1920 s and early 1930 s. One of them was the fundamental understanding of molecular vibrations on the basis of quantum mechanics it was first put in evidence by the absorption of infrared radiation and later also found in the modulations of scattered visible light in the Raman effect. The two methods complement each other dramatically because of their different response to the selection rules which control the transition probabilities between different vibrational states of a molecular framework. The other root was a gradual and substantial improvement of the experimental techniques, such as stronger and more uniform sources of the primary radiations, higher resolution in the spectroscopic part of the equipment, and, perhaps most of all, more sensitive and reliable receivers. 

We now consider a beam of radiation, intensity I(o)), uniformly filling the solid angle do. The power absorbed from this beam by one atom is given by the energy of one photon multiplied by the transition probability ... 

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