Bose-Einstein factor

This is the net Bose-Einstein factor. It will be used in the following to form Bayesian estimators (see, e.g., Frieden, 1983) of the object nm. ... 

The main external parameter influencing data, and thus the quality of the final results, is the temperature which is introduced in eq2 via the Bose-Einstein factor. For a temperature change from 25 up to 50 °C, the variation of intensity for peaks lying around 1000 cm is expected to be 0.3%/°C for NOs" and 0.2%/°C for S04. These changes in intensity can be close to these induced by a very small variation of the salt concentration. The temperature influence can thus reduce the sensitivity of the method and sensor, when required by the detection of very small amounts. Therefore it should be more convenient to use reduced intensity by dividing I by the Bose-Einstein factor in order to discard any influence of the temperature. If not, the changes of I (and Jp) due to the variation of the temperature can induce erroneous interpretation, and /or large uncertainty in the exploitation of data. 

Here, / is the intensity and n is the Bose-Einstein factor. The values d D = 0.53, d = 1.3, and a = 1 lead to the observed exponent - 0.36.25 That the bending fracton dimension is the proper one to use in (4) is consistent with the fact that it is the bending modes that depolarize the scattered light. 

In his derivation, Frieden uses the concept of a number-count set nm, each member representing the number of photons counted in a spectral interval. The total number of photons m= x nm is taken as known to be N. In terms of frequencies vm, the values of the object spectrum are given by om = nmhvm, where h is Planck s constant. The number of normal modes or degrees of freedom available for occupation by photons of frequency vw is labeled zm. The Bose-Einstein degeneracy factor... 

Principle (17) now consists of just the Bose-Einstein degeneracy factor, exactly Kikuchi and Soffer s form (1977). Also, as these authors showed (see also Section IX.B), in the case (11a) of sparsely occupied df it becomes Jaynes s maximum-entropy form (39) (Jaynes, 1968). Hence, both the Kikuchi-Soffer and Jaynes estimators are special cases of the ML approach, corresponding to the prior knowledge that the unknown spectrum is equal-energy white with the highest conviction. 

For a gas containing N molecules of the same chemical species, the molecules would all be indistinguishable from one another. The factor W has to be divided by Nl in this case. The proper explanation can only be understood through a detailed discussion of quantum mechanics and Bose-Einstein statistics. This explanation is beyond the realm of interest here, and we simply state the proper weighting for a collection of N indistinguishable molecules as... 

Unfortunately, the density of Hi is limited by a three body recombination process of the form Hi+Hi - H2+hT. The highest density achieved under controlled conditions is 4.5 x 1018atoms-cm 3, at a temperature of 0.4 K. This is a factor of twenty too low for Bose-Einstein condensation. 

Bednorz-Muller theory Beer-Lambert law Bose-Einstein statistics Debye-Huckel theory Diels-Alder reaction Fermi-Dirac statistics Fischer-Tropsch effect Fisher-lohns hypothesis Flory-Huggins interaction Franck-Condon factor Friedel-Crafts reaction Geiger-Miiller effect... 

Bednorz—Muller theory Beer—Lambert law Bose—Einstein statistics Debye-Hiickel theory Diels—Alder reaction Fermi—Dirac statistics Fischer—Tropsch effect Fisher—Johns hypothesis Flory—Huggins interaction Franck—Condon factor Friedel—Crafts reaction Geiger-Miiller effect... 

Bose-Einstein occupation factors, 276 Bovine pancreatic trypsin inhibitor (BPTI), 122-123, 125, 368 Bovine rhodopsin, 133... 

Bose-Einstein occupation factors, 276 energy dissipation rate, 275 equations of motion, 275-276 Fourier-space Langevin equation, 276 Hamiltonian and harmonic modes, 274 memory kernel, 275 molecule-bath coupling constants, 274 transmission coefficient, 276... 

N(y, T) Bose-Einstein population factor Ar, thermal shock resistance... 

Conductivity can be deduced from vibrational spectra in IR spectroscopy, the absorption coefficient a(co) is related to tr(co) a(o)) = 4no(o))/nc, n being the refractive index and c the velocity of light. In Raman spectroscopy, the scattered intensity /(m) is related to conductivity by a(o ) oc o)I (o)/n(a)) + 1, n(co) being the Bose-Einstein population factor . Finally, the inelastic incoherent neutron scattering function P(o)) is proportional to the Fourier transform of the current correlation function of the mobile ions. P co) is homogeneous with a) /(cu) formalism. However, since P(co) reflects mainly single particle motions, its comparison with ff(co) could provide a method for the evaluation of correlation effects. (For further discussion, see also Chapter 9 and p. 333.)... 

---