Calculation of Siegert eigenvalues for molecular systems: results for He(21,3S)+ H

The variational calculation of Siegert eigenvalues has previously been shown to provide reliable positions and widths for atomic resonances. This approach is herein extended to molecular problems, and the first such calculations for a molecular autoionizing system, He(2^1,3S)+H→ He+H⁺+e^?, are reported.     

Vibrational partition functions for H2O derived from perturbation-theory energy levels

Purely vibrational energy levels and partition functions are calculated using three different potential energy surfaces for the H₂O molecule. Results obtained with perturbation-theory, independent-normal-mode (INM), and harmonic approximations are compared with accurate values. For the cases considered here, the expected improvement that perturbation theory provides over the corresponding harmonic treatment is found to be substantial, while the INM approximation leads to results which are worse than the corresponding harmonic ones. In fact, we show that reliable partition functions for these potential surfaces can be obtained when resonance contributions are removed from the perturbation-theory treatment, and we propose a theoretical criterion for deciding when a particular interaction should be treated as resonant.     

The ground state energy per particle for infinite particle quantum systems

We give a simple proof that the ground state energy per particle for several interacting particle systems is monotone and bounded as the number of particles increases. Some of the systems for which the proof holds are anharmonic oscillator approximations to || _d ^/4 quantum fields, many body Schrödinger operators with nearest and next to nearest neighbor couplings, and systems whose energy is given by operators which are not restricted to being differential operators.Research partially supported by the National Science Foundation under grant No. MCS-77-03568     

Symmetric cubical sets

We introduce a new cubical model for homotopy types. More precisely, we will define a category Q_Σ with the following features: Q_Σ is a prop containing the classical box category as a subcategory; the category of presheaves of sets on Q_Σ models the homotopy category; and combinatorial symmetric monoidal model categories with cofibrant unit have homotopically well-behaved enrichments.