Perturbation theory for excited states. IV

Two of the perturbation methods developed in Paper I (CIPT and SCPT) are extended for use with uncoupled Hartree-Fock perturbation theory. Corrections to the uncoupled results are discussed and it is found that it is possible to correct using functions which when applied to ground state calculations are equivalent to the geometric approximation. It is also shown that CIPT and SCPT can be applied to ground state calculations and that when coupled perturbed orbitals are used CIPT and SCPT are equivalent to the usual coupled perturbation theory.     

Exact solutions for spherically confined hydrogen‐like atoms

We present exact analytical solutions for the much‐studied problem of a hydrogen‐like atom confined in a spherical box of radius R. These solutions, which are obtained for all states and all R, are expressed directly in terms of the Kummer M‐functions whose analytical and numerical properties are well known, and may be calculated using standard computing packages. The solutions are illustrated by precise calculations that yield accurate energies E for any given radius R, or for R when E is known. In the special case where E = 0, it is shown that the solution may be expressed in terms of Bessel functions. Finally, the physical assumptions made in applying this model to describe atomic confinement are discussed critically. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Why the constituent interchange model does not predict the dimensional counting rule to any finite order in QCD

We demonstrate that the constitutent interchange diagram for nucleon nucleon elastic scattering contains a pinch singularity. This means that it predicts that \(\frac{{d\sigma }}{{dt}} \sim s^{ - 9} f\left( \theta \right)\) for high energy elastic scattering, at least to any finite order in QCD. We also show how the dimensional counting rule may perhaps be recovered by summing a suitable infinite series of graphs.     

Studies under Continuous Irradiation of Photochromic Spiro[fluorenopyran‐thioxanthenes]

New indeno‐fused spiro[benzopyran‐thioxanthenes] were synthesized (see 3a – d in Scheme 3) and their photochromic properties evaluated under continuous irradiation (Table 1). When submitted to irradiation for several minutes with a Xe lamp, the system behaved as one constituted by two open colored forms with different thermal bleaching rates and different susceptibilities to degradation. An increase in irradiation time led to significant degradation and to the apparent predominance of the open colored form with the faster bleaching rate.     

Photochemical Degradation of the Plant Growth Regulator 2‐(1‐Naphthyl) acetamide in Aqueous Solution Upon UV Irradiation

The photochemical degradation of 2‐(1‐naphthyl) acetamide (NAD) in aqueous solution using simulated sunlight excitation as well as UV light within the 254–300 nm range was investigated to obtain an insight into the transformation mechanism that could occur under environmental conditions. Several photoproducts were identified using HPLC/MS/MS techniques. The degradation quantum yield was found to be independent of the excitation wavelength, but showed a dependence of oxygen concentration. This increased by a factor of approximately 3 from aerated to oxygen‐free solutions. There is a clear involvement of both triplet and singlet excited states in NAD photoreactivity. The participation of singlet oxygen as a significant route in NAD degradation was ruled out by comparison with the behavior using Rose Bengal as a photosensitizer. A mechanistic pathway implying hydroxylation process through NAD radical cation species as well as an oxidation reaction by molecular oxygen is proposed. The photochemical behavior of NAD appears to mainly involve the aromatic moieties without any participation of the amide side chain. Toxicity tests clearly show that the generated primary photoproducts are responsible for a significant increase in the toxicity. However, upon prolonged irradiation this toxicity tends to decrease.     

Coupled N-dimensional harmonic oscillator systems

A general decoupling procedure is described for systems of N interacting harmonic oscillators coupled by some bilinear perturbing potentials, and explicit conditions are derived which must be fulfilled in order to obtain physical bound states. Illustrative examples include a general treatment of the 2-oscillator system, some particular extensions to systems containing 3 oscillators, and a class of N-oscillator models.