THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Ab initio study of AmCl(+): f-f spectroscopy and chemical binding

A valence full configuration interaction study with a polarized double-zeta quality basis set has been carried out for the lowest 49 electronic states of AmCl(+). The calculations use a pseudopotential treatment for the core electrons and incorporate a one-electron spin-orbit interaction operator. Electrons in the valence s, p, d, and f subshells were included in the active space. The resulting electronic potential energy curves are largely repulsive. The chemical bonding is ionic in character with negligible participation of 5f electrons. The molecular f-f spectroscopy of AmCl(+) arises essentially from an in situ Am(2+) core with states slightly redshifted by the presence of chloride ion. Am(+)+Cl asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the f-f spectroscopy of isolated Am(+) and Am(2+). The attractive curves have substantial binding energies, on the order of 75-80 kcal/mol, and are noticeably lower than recent indirect measurements on the isovalent EuCl(+). An independent empirical correlation supports the predicted reduction in AmCl(+) binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while the energies of the attractive curves do not display this sensitivity. The calculations were carried out using our recently developed parallel spin-orbit configuration interaction software.