In view of the great demand for travel services in North America at the time of the Congress it is strongly recommended that Congress participants make immediate arrangements for their transportation. Living Accommodation Provisional reservation of rooms in Montreal has already been made. These will be allotted in the order of receipt of the registration forms which accompany the general information booklet. Because accommodation in Montreal hotels and motels is much in demand during the summer months it is strongly recommended that these forms be sent to the nearest American Express office or correspondent as early as possible, and not later than 15 February 1957, to ensure the accommodation desired. Excursions An excursion of general interest to an important section of the St. Lawrence Seaway Development is being arranged for the afternoon of Saturday, 13 July 1957, and a day's outing by steamer on the St. Lawrence River is being organized for Sunday, 14 July 1957. Three trips of mineralogical and geological interest will be available for the period following the Congress. Further details are given in the general information booklet. Exhibition It is planned to arrange an exhibition of apparatus and books of crystallographic interest at the Congress tteadquarters. Manufacturers and publishers wishing to receive detailed information should write to Dr A
The semiclassical Franck-Condon principle is shown to be related to the more rigorous (``exact'') quantum-mechanical perturbation formula in the following ways: (1) the Franck-Condon formula can be derived from the ``exact'' formula by using a mean value approximation or by neglecting certain commutators; (2) if the electric dipole moments are treated as approximately independent of position, the Franck-Condon and the ``exact'' absorption (or emission) spectrum have the same zeroth, first, and second moments, i.e., the same integrated spectrum, mean absorption frequency, and breadth; (3) the errors in higher moments than the second become relatively unimportant at high temperatures. If the electron-nuclear interaction is sufficiently strong the errors are unimportant even at absolute zero.
The use of a quasi-molecular description in a many particle problem is found to be possible only if the masses or stiffnesses are allowed to be temperature dependent.
A detailed analysis is made of the case in which the energy difference between the two electronic states is a linear function of the vibrational coordinates—and the latter are describable by normal modes. ``Exact'' formulas for the absorption and emission spectrum are obtained.
A new approximate method is presented for calculating the density of states and one-electron Green's function in the low-energy tail of a high-density impurity band. Such states occur in regions of large attractive potential produced by unusually high (random) concentrations of attractive centers and/or unusually low concentrations of repulsive centers. These well-separated deep wells each have one bound state of lowest energy. The distribution of these lowest levels yields the low-energy tail. For any one well, a bound-state energy E(x 0 ) is estimated variationally using ^(x) = /(x -x 0 ), where /(x) has any fixed form. The best energy for any well is obtained by minimizing £(x 0 ) with respect to x 0 in the vicinity of that well. The number of wells that contribute to the density of states at energy E is given by the number of local minima in E(xo) that occur at the level E. In the high-density limit, Gaussian statistics are adequate for treating the potential fluctuations and the expectation value for the density of states is easily calculated. At low energies the best choice for the function / is that which maximizes the expected density of states. Application to an exactly soluble one-dimensional model, a Gaussian "white noise" potential, yields the correct asymptotic form p(E) = const \E | exp[-(f) | IE | 3 / 2 ]. In three dimensions, the density of states in the Gaussian approximation is found to have the form p(E) = [_A CE)/£ 2 ]exp[ -23(£)/(2£)], where £ is proportional to the concentration of impurities and to the square of the strength of the impurity potential. For screened, charged impurities,where E Q = h 2 Q 2 /(2m*), (1/Q) is the screening radius, and v= (EQ-E)/EQ is the energy below the mean potential Eo in units of Eg. Computer-calculated curves are provided for the "universal" dimensionless functions a(v) and b(v). The exponent b(v) behaves like v m when v is small (strong screening) and behaves like v 1 when v is large (weak screening).
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