Mean energy

Viehland L A and Robson R E 1989 Mean energies of ion swarms drifting and diffusing through neutral gases Int. J. Mass Spectrom. Ion Processes 90 167-86... 

The variance p<7centa of the mean energy ia shown as a subscript to the variance value recorded for the BBK scheme. 

Camp and Stein (1943) originally proposed for flocculation that the mean fluid shear rate is proportional to the square root of the mean energy dissipation... 

For radiation in equilibrium with electromagnetic oscillators consisting of the charges on material ions we can combine the formula for the mean energy of a resonator (Planck, Wcirme-strahluny, p. 124) ... 

The increase in the electron energy may have several consequences. It may lead to dissociative or nondissociative electron attachment (54, 61). This would give rise to a step enhancement as in N20 (8). The most important possibility is electronic excitation of the molecular species, which should manifest itself by an increased yield of all products arising from excited intermediates as the mean energy of the electron swarm rises with field strength. 

Figure 5.3. The classical picture the energies of dipoles varies continuously from parallel alignment with the applied magnetic field (-m-B) to antiparallel (+m-B). On the right is shown the distribution of molecules that results and the lower mean energy of the ensemble relative to the field-free environment.

Recall the splitting of the d orbitals in octahedral environments. The energies of the t2g and g subsets are shown in Fig. 8-4 with respect to their mean energy. We have used the conventional barycentre formalism. In effect, we express the energy of an electron in the t2g or orbitals with respect to the total energy possessed by a set of five electrons equally distributed amongst the five d functions. Alternatively, we say that our reference energy is that of 2l d electron within the equivalent spherical mean field. 

According to current turbulence measurements in stirred tanks, there is a very considerable difference between the maximum energy density and the mean energy dissipation. Various authors (see e.g. [24] -[26] conclude that the... 

A survey of the published literature indicates that the ratio of the maximum to mean energy dissipation rate in the vessel, Smax/ m can vary substantially but typically in the range 10 to 100 [85]. Recent measurements [100] of the turbulent flow properties with a range of impellers and vessel configurations indicate that the differences between the reported ratios of Smax/Cm re partly due to differences in the geometrical variables. For example, detailed factorial designs of experiments showed significant effects of impeller diameter to tank diameter ratio and off-bottom clearance to impeller diameter ratio on the value of emax/Cm-... 

For the present purpose, the quantities A and F of Eq. (35) are considered as independent of temperature and pressure. If Eq. (35) is applied to measurements at two different pressures p and po particular temperature T, the unknown change of mean energy AE can be eliminated. The resulting equation may be written as ... 

As a result, the energy E of photons emitted by an ensemble of identical nuclei, rigidly fixed in space, upon transition from their excited states (e) to their ground states (g), scatters around the mean energy Eq = E. Eg. The intensity distribution of the radiation as a function of the energy E, the emission line, is a Lorentzian curve as given by the Breit-Wigner equation [1] ... 

The emission line is centered at the mean energy Eq of the transition (Fig. 2.2). One can immediately see that I E) = 1/2 I Eq) for E = Eq E/2, which renders r the full width of the spectral line at half maximum. F is called the natural width of the nuclear excited state. The emission line is normalized so that the integral is one f l(E)dE = 1. The probability distribution for the corresponding absorption process, the absorption line, has the same shape as the emission line for reasons of time-reversal invariance. 

The ratio F/Eq of width F and the mean energy of the transition Eo defines the precision necessary in nuclear y-absorption for tuning emission and absorption into resonance. Lifetimes of excited nuclear states suitable for Mossbauer spectroscopy range from 10 s to s. Lifetimes longer than 10 s produce too... 

In the description of nuclear y-resonance, we assume that the photon emitted by a nucleus of mean energy Eq = E —Eg carries the entire energy, Ey = Eq. This is not true for nuclei located in free atoms or molecules, because the photon has... 

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