Long-range dispersion coefficients for like centrosymmetric linear molecules and an application to H2-H2

The real spherical tensor theory of long-range intermolecular coefficients developed in previous papers is applied to derive explicit formulae for the first three dispersion coefficients for like centrosymmetric linear molecules. The expansion of angle-dependent coefficients in associated Legendre polynomials allows one to identify the isotropic and anisotropic components of the dispersion interaction in terms of London dispersion constants, the treatment of higher coefficients being simplified by the coupling of the elementary (l, l′)-polarizations to resultant angular momenta L_A and L_B onto each molecule. The contributions from all coupling schemes are given explicitly for C₆, C₈, C₁₀, and numerical results are presented for H₂-H₂ using two-term reduced spectra values from the Kaiserlautern group.     

On the angular shape of van der Waals dimers of small polar molecules

Ab initio calculations on twenty van der Waals dimers of small polar molecules at the experimentally observed intermolecular separation R, using Hartree-Fock molecular moments, show that the minima in the electrostatic interaction expanded up to R⁻⁶ converges to angular structures which are close to those observed experimentally for such complexes.     

A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials

We consider the Schrödinger operator with zero-range potentials onN points of three-dimensional space, independently chosen according to a common distributionV(x). Under some assumptions we prove that, whenN goes to infinity, the sequence converges to a Schrödinger operator with an effective potential. The fluctuations around the limit operator are explicitly characterized.     

On the evaluation of the anisotropic-isotropic transition volume fraction for a semirigid polymer

It has been found that a method allowing the calculation of an anisotropic-isotropic transition volume fraction for a given semirigid polymer can be derived from the equations recently proposed by Blonski and coworkers to evaluate the equilibrium compositions of isotropic and anisotropic phases coexisting within ternary systems semirigid polymer/flexible polymer/solvent. By using the term anisotropic-isotropic transition volume fraction of a semirigid polymer we will refer to its smallest volume fraction giving an anisotropic character to liquid ternary phases also including a flexible polymer and a solvent. Its evaluation simplifies the construction of the corresponding ternary diagram and can also be seen as a fast and quantitative way of estimating the influence exerted by the semirigid polymer, through its intrinsic anisotropy, on ternary phases.     

On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

We consider a non-relativistic quantum system consisting of K heavy and N light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential α V. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming α sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K = 1 the result is extended to arbitrary α. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schrödinger group. Exploiting the asymptotic formula, an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones is also outlined.     

The laplacian in regions with many small obstacles: Fluctuations around the limit operator

We consider the Laplacian _m in ³ (or in a bounded region of ³) with Dirichlet boundary conditions on the surfaces of some identical (small) neighborhoods ofm randomly distributed points, in the limit whenm goes to infinity and their linear size decreases as 1/m. We give here a stronger form of the result showing the convergence of the above operator to – C(x), whereC(x) is the limit density of electrostatic capacity of the obstacles. In particular results on the rate of convergence and on the fluctuations of _m around the limit operator are given.     

Linear response theory of the dipole–dipole dispersion interaction between H(1s) atoms

A self-consistent theory of the linear response previously developed by one of us is applied to the dipole–dipole dispersion interaction of two ground state H atoms in the united atom (He) limit, using a Sellmeier representation of the polarizability in terms of pseudostates. Numerical calculations show that a truncated 12-term expansion out of the N = 22 H(1s) dipole pseudospectrum built from STOs with orbital exponent c = 0.985 gives a result exceeding by no more than 5% the variational result for the He dispersion energy.     

Ionization for Three Dimensional Time-Dependent Point Interactions

We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the strength of the interaction (t) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (t), we prove that there is complete ionization as t, starting from a bound state at time t=0. Moreover we prove also that, under the same conditions, all the states of the system are scattering states.On leave from Dipartimento di Matematica, Università di Roma, La Sapienza, Italy.