Energy dependence

The volume of defects is calculated using intensity evaluation. Considering the polychromatic radiation of microfocus X-ray tubes the X-ray beam is represented by an energy dependent intensity distribution Io(E). The intensity Ip behind a sample of thickness s is given by integrating the absorption law over all energies ... 

Fig. 2 shows the response of a C2 film system on a step wedge (wall thickness range 2. .. 18 mm) exposed with a X-ray tube at 160 kV. For the exposure withy-rays (Irl92 or Co60) corresponding linear relationships are obtained. From this linear relationship it is followed, that the influence of the scattered radiation and the energy dependence of the absorption coefficient can be considered by an effective absorption coefficientPcff in equation (1). 

For the interaction between a nonlinear molecule and an atom, one can place the coordinate system at the centre of mass of the molecule so that the PES is a fiinction of tlie three spherical polar coordinates needed to specify the location of the atom. If the molecule is linear, V does not depend on <() and the PES is a fiinction of only two variables. In the general case of two nonlinear molecules, the interaction energy depends on the distance between the centres of mass, and five of the six Euler angles needed to specify the relative orientation of the molecular axes with respect to the global or space-fixed coordinate axes. 

The details of the second-order energy depend on the fonn of exchange perturbation tiieory used. Most known results are numerical. However, there are some connnon features that can be described qualitatively. The short-range mduction and dispersion energies appear in a non-expanded fonn and the differences between these and their multipole expansion counterparts are called penetration tenns. 

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. 

Lavrich D J, Buntine M A, Serxner D and Johnson M A 1993 Excess energy-dependent photodissociation probabilities for Ot in water clusters O, I 1i Chem. Rhys. 99 5910-16... 

Su T 1985 Kinetic energy dependences of ion poiar moiecuie coiiision rate constants by tra]ectory caicuiations J. Chem. Phys. 82 2164-6... 

Variational RRKM calculations, as described above, show that a imimolecular dissociation reaction may have two variational transition states [32, 31, 34, 31 and 36], i.e. one that is a tight vibrator type and another that is a loose rotator type. Wliether a particular reaction has both of these variational transition states, at a particular energy, depends on the properties of the reaction s potential energy surface [33, 34 and 31]- For many dissociation reactions there is only one variational transition state, which smoothly changes from a loose rotator type to a tight vibrator type as the energy is increased [26],... 

Bailey C G, Dessent C E FI, Johnson M A and Bowen K FI 1996 Vibronic effects in the photon energy-dependent photoelectron spectra of the CFIjCN dipole-bound anion J. Chem. Phys. 104 6976-83... 

Figure Bl.7.13. A schematic diagram of an ion-guide mass spectrometer. (Ervin K M and Annentrout P B 1985 Translational energy dependence of Ar + XY —> ArX + Y from thennal to 30 eV c.m. J. Chem. Phys. 83 166-89. Copyright American Institute of Physics Publishing. Reproduced with pemiission.)...

Using a guided ion beam instrument the translational energy dependent reaction cross sections of endothemiic fragmentation processes can be detemiined [32]. Modelling these cross sections ultimately yields their energy tln-esholds and a great deal of valuable themiochemical infomiation has been derived with this teclmique. Precision of 0.2 eV can be obtained for reaction tln-esholds. Bimolecular reactions can also be studied and reaction enthalpies derived from the analysis of the cross section data. 

Sekiguchi S, Kobori Y, Akiyama K and Tero-Kubota S 1998 Marcus free energy dependence of the sign of exchange interactions in radical ion pairs generated by photoinduced electron transfer reactions J. Am. Chem. Soc. 120 1325-6... 

A more accurate calculation will account for differences in the energy dependent mean free paths of the elements and for the transmission characteristics of the electron analyser (see [7]). 

These electronic energies dependence on the positions of the atomic centres cause them to be referred to as electronic energy surfaces such as that depicted below in figure B3.T1 for a diatomic molecule. For nonlinear polyatomic molecules having atoms, the energy surfaces depend on 3N - 6 internal coordinates and thus can be very difficult to visualize. In figure B3.T2, a slice tln-oiigh such a surface is shown as a fimction of two of the 3N - 6 internal coordinates. 

Jensen J A, Yan C and Kummel A C 1995 Energy dependence of abstractive versus dissociative chemisorption of fluorine molecules on the silicon (111)-(7 7) surface Science 267 493-6... 

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

Chou J Z and Fiynn G W 1990 Energy dependence of the reiaxation of highiy excited NO2 donors under singie coiiision conditions vibrationai and rotationai state dependence and transiationai recoii of CO2 quencher moiecuies J. Chem. Rhys. 93 6099-101... 

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

For sueh a trial wavefunetion, the energy depends quadratieally on the linear variational Cj eoeffieients ... 

Hamiltonian contains (fe2/2me r ) 32/3y2 whereas the potential energy part is independent of Y, the energies of the moleeular orbitals depend on the square of the m quantum number. Thus, pairs of orbitals with m= 1 are energetieally degenerate pairs with m= 2 are degenerate, and so on. The absolute value of m, whieh is what the energy depends on, is ealled the X quantum number. Moleeular orbitals with = 0 are ealled a orbitals those with = 1 are 7i orbitals and those with = 2 are 5 orbitals. 

The so-called peak power delivered by a pulsed laser is often far greater than that for a continuous one. Whereas many substances absorb radiation in the ultraviolet and infrared regions of the electromagnetic spectrum, relatively few substances are colored. Therefore, a laser that emits only visible light will not be as generally useful as one that emits in the ultraviolet or infrared ends of the spectrum. Further, witli a visible-band laser, colored substances absorb more or less energy depending on the color. Thus two identical polymer samples, one dyed red and one blue, would desorb and ionize with very different efficiencies. 

The dopamine is then concentrated in storage vesicles via an ATP-dependent process. Here the rate-limiting step appears not to be precursor uptake, under normal conditions, but tyrosine hydroxylase activity. This is regulated by protein phosphorylation and by de novo enzyme synthesis. The enzyme requites oxygen, ferrous iron, and tetrahydrobiopterin (BH. The enzymatic conversion of the precursor to the active agent and its subsequent storage in a vesicle are energy-dependent processes. 

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