DeBroglie wavelength

Approximations have been reviewed in the case of short deBroglie wavelengths for the nuclei to derive coupled quantal-semiclassical computational procedures, by choosing different types of many-electron wavefunctions. Time-dependent Hartree-Fock and time-dependent multiconfiguration Hartree-Fock formulations are possible, and lead to the Eik/TDHF and Eik/TDMCHF approximations, respectively. More generally, these can be considered special cases of an Eik/TDDM approach, in terms of a general density matrix for many-electron systems. 

In a classical Bohr orbit, the electron makes a complete journey in 0.15 fs. In reactions, the chemical transformation involves the separation of nuclei at velocities much slower than that of the electron. For a velocity 105 cm/s and a distance change of 10 8 cm (1 A), the time scale is 100 fs. This is a key concept in the ability of femtochemistry to expose the elementary motions as they actually occur. The classical picture has been verified by quantum calculations. Furthermore, as the deBroglie wavelength is on the atomic scale, we can speak of the coherent motion of a single-molecule trajectory and not of an ensemble-averaged phenomenon. Unlike kinetics, studies of dynamics require such coherence, a concept we have been involved with for some time. 

Election motion Nuclear motion DeBroglie wavelength... 

Electrons of 150 eV and neutrons of 0.1 eV possess a DeBroglie wavelength of about 1 A, which matches the elementary lattice dimensions in crystals. The appreciable scattering cross sections for electrons causes them to be strongly absorbed and thus... 

Example Problem What is the deBroglie wavelength of a neutron moving with the average Fenni energy in a 208Pb nucleus You can assume that the neutron is nonrelativistic and use r0 = 1.2 fm. 

Figure 19. Photon energy dependence of the photoionization cross section intensity of photoelectron peak varies depending upon input photon energy, due to the variation in the deBroglie wavelength of outgoing electron. These wavelengths are compared to the radial wavefunctions of Cu 3d and Cl 3p orbitals. Reproduced from Ref. 28. Copyright 1985, American Chemical Society.

The deBroglie wavelengths, A, of electrons traveling with kinetic energies, KE, in the range from 20 to 200 eV are slightly smaller than typical interatomic distances and thus appropriate for diffraction from surfaces... 

Thermal neutrons have energies comparable to the excitation energies of molecular solids and because of their mass they carry momentum. This momentum or wave-vector, k, is conventionally represented through the characteristic deBroglie wavelength, X and hence, k = 2n/X. Typical neutron wavelengths match the interatomic distances in solids, ca. 2 A and, unlike the... 

Phonon dispersion expresses the phase relationship between different molecules in the lattice as they participate in the same mode. The repeat distance between molecules which vibrate totally in-phase is the phonon (deBroglie) wavelength, it is written in terms of the crystalline unit-cell dimensions and defines the characteristic momentum of the phonon, q. The... 

This has been designated the p temperature region. The activation energy for thermal electron attachment and the pre-exponential term for the rate constant for thermal electron attachment are obtained. At that time neither of these two quantities had been measured so comparisons could not be made, ko was estimated from the electron concentration measured as a function of reaction time. The maximum value of k was determined by the DeBroglie wavelength of the electron and stabilization to the ultimate ions by collisions at high pressures. 

Maximum value of A calculated from the DeBroglie wavelength of the electron. The value of ln(DeBA) is about 36 at 400 K. Electron. 

A.7.17 First calculate the deBroglie wavelength of the electron at the accelerat-1.23 nm 1.23x10- ... 

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