The centrifugally decoupled exponential distorted wave (CDEDW) approximation for the calculation of rotationally inelastic molecular collision cross se

A new approximate method is presented for the rapid calculation of rotationally inelastic molecular collision cross sections. The method is called the centrifugally decoupled exponential distorted wave (CDEDW) approximation and involves the combination of two well known approximations. The first approximation is the neglect of the off-diagonal coupling terms which arise from the orbital angular momentum operator in the coupled differential equations in the body-fixed axis system. The second approximation is to treat the remaining coupling terms, which arise from the interaction potential, using a unitary perturbation approximation. The CDEDW method is applied to the calculation of total and partial rotationally inelastic cross sections in the ArN₂ system, and detailed comparisons are made with exact and several other types of approximate calculations. Agreement with exact calculations is good and often comparable with the coupled states and p-helicity decoupled approximations. The CDEDW method requires a similar amount of computational effort to the infinite order sudden (IOS) approximation, and we show that for the present system the CDEDW method gives more reliable results.     

Halfway house variational continuum distorted wave theory: high energy cross sections in the distorted wave perturbation approximation

The total cross section for charge transfer at high but non-relativistic energy is investigated within a new time-independent wave version of the halfway-house phase integral variational continuum distorted wave formalism, using simple first order perturbation theory. Following Crothers, Dubé and Brown this theory satisfies all known short and long range Coulomb boundary conditions which is essential if intermediate elastic divergences are to be avoided. The discussion is specialised to the particular case ofls →ls capture. Numerical results for this amplitude are obtained by a double numerical integration. Wave results derived for the capture process $$P^{Z_P^ + } + (T^{Z_T^ + } + e^ - ) \to (P^{Z_P^ + } + e^ - ) + T^{Z_T^ + } $$ in the caseZ _T = 1 =Z _P are compared with various theoretical impact parameter models and experimental data. Representative distributions of the total cross sections are presented as a function of the impact energy.     

Restriction on approximations of molecular integrals

The results of LCAO-MO-SCF calculations applied to molecules have to be invariant with respect to orthogonal transformations of the basis set of atomic orbitals. However, if the multicenter repulsion integrals needed for such a calculation are approximated, invariancy will in general not be retained. For two methods of approximation the behaviour of the multicenter integrals under such transformations has been investigated, along with the conditions which have to be fulfilled to ensure this invariancy.

---

Zusammenfassung Ergebnisse von LCAO-MO-SCF-Rechungen an Molekülen werden nichtinvariant gegen orthogonale Basistransformationen, wenn für die Mehrzentrenintegrale Näherungsausdrücke verwendet werden. Für zwei Näherungsmethoden wird der Einfluß der Transformationen auf die Mehrzentrenintegrale untersucht; Bedingungen für bestimmte Invarianzeigenschaften werden angegeben.

---

Résumé Les résultats d'un calcul LCAO-MO-SCF doivent être invariants par rapport aux transformations orthogonales de la base des orbitales atomiques. Cette invariance n'est en général pas respectée si les intégrales de répulsion multicentriques nécessaires pour un tel calcul sont évaluées d'une manière approchée. Le comportement des intégrales multicentriques lors de telles transformations a été étudié par deux méthodes d'approximation; on a envisagé les conditions à remplir pour satisfaire à l'invariance.

     

Tchebycheff-derivative approximations to photoabsorption cross sections in atoms and ions

Spectral moments and Tchebycheff's inequalities are employed in the construction of continuous, convergent approximations to photoabsorption and ionization cross sections in atoms and ions.     

Substantial velocity dependence of rotationally inelastic collision cross sections in Li2—Xe

A Doppler-based velocity selection technique has been used to measure the relative velocity dependence of the cross sections σ_ji,Δ(ν_r) for rotationally inelastic collisions from level j_i to j_i + Δν₁ = 8,22,42) in ⁷Li^*₂ A ¹Σ⁺_u)—Xe. The σ_jν^±2(ν_r) are strongly attenuated at a smaller ν_r by “torque averaging” due to molecular rotation; in contrast, for large |Δ|, σ_jiΔ = ν_r⁻ⁿ (1 n 2). An empirical intermolecular potential which reproduces these types of behavior for 3-D classical trajectories is exhibited.     

Elastic and inelastic cross sections for low-energy electron collisions with pyrimidine

We present theoretical elastic and electronic excitation cross sections and experimental electronic excitation cross sections for electron collisions with pyrimidine. We use the R-matrix method to determine elastic integral and differential cross sections and integral inelastic cross sections for energies up to 15 eV. The experimental inelastic cross sections have been determined in the 15-50 eV impact energy range. Typically, there is quite reasonable agreement between the theoretical and experimental integral inelastic cross sections. Calculated elastic cross sections agree very well with prior results.     

Rotational rainbows in inelastic atom—molecule differential cross sections

The existence of rotational raibows in atom-rigid rotor inelastic differential cross sections is shown by considering the classical limit of the centrifugal sudden-rotational sudden expression for the scattering amplitude.     

Relation of the field-theoretical method for molecular scattering to the distorted wave formalism

The results of the field-theoretical method for molecular scattering are obtained without the formalism of field theory. Given the Feshbach optical potential the exact transition potential is obtained on the basis of the distorted wave method. A series of approximations to these two operators is presented which allow one to get the results obtained previously by successive approximations in the field-theoretical method.     

Partial differential cross sections for inelastic He++Ne collisions at low energy

We report differential cross section measurements with high angular resolution for different channels of the inelastic processes He⁺+Ne→He⁺+Ne* and He⁺+Ne→He*+Ne⁺, for collision energies between 100 and 200 eV. For the Ne states (2p ⁵3s)^1,3 P ₁, which decay optically, we determined the fraction with the alignment at right angles to the scattering plane. The results are used to discuss the mechanism of the processes and the influence of the spin-orbit interaction upon the collision.     

Range of validity of distorted wave Born and impulse approximations for (e, 2e)

The formulation of approximations for the calculation of the (e, 2e) reaction on atoms is considered. The range of validity of the two common working approximations, the distorted wave Born and impulse approximations, is illustrated. A feasible approximation that treats the reaction in more detail is derived.     

Velocity dependence of collision broadening cross sections in NH3

The velocity dependence of collision broadening cross sections for both self-broadening and Xe broadening of an infrared transition in NH₃ has been studied by measuring laser saturation resonance linewidths for molecules with specified velocities along the laser propagation direction. For self-broadening, the velocity dependence is in accord with inelastic collisions due to a predominantly dipole-dipole interaction potential, with smaller contributions due to shorter range forces, whereas for Xe broadening, the magnitude and velocity dependence of the collision broadening cross section is in better agreement with velocity changing collisions in the pressure range studied.     

A program for calculating partial molecular photoionization cross sections

Physicomechanics Research Institute, Far East University. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 5, pp. 139–140, September–October, 1991.     

Partial photoionization cross sections of molecular oxygen

Measurements of partial photoionization cross sections of O₂ for excitation energies between 20 and 45 eV are reported and compared to a calculation using the Stieltjes-Tchebycheff moment theory. Positive evidence is obtained for a predicted σ-type shape resonance between 1 and 2 eV above threshold in certain ionic-state cross sections. Implications for angular distribution of photoelectrons from an oriented O₂ are discussed.     

On the estimation of cross sections for the formation of triatomic collision complexes

The traditional procedure of associating the formation of a collision complex with the passage over a centrifugal potential barrier is reinvestigated. It is argued that the complex is better defined in terms of a spatially localized critical surface (or separation), such that the complex is strongly coupled, while the system is weakly elsewhere. Weak coupling implies that the rotational and vibrational energies of the diatomic fragment are, to a good approximation, conserved. Strong coupling implies that only total energy and angular momentum is conserved. Graphical methods are used to obtain upper bounds for the cross section within weak or strong coupling dynamics by optimizing the attraction within the given constraints. Results for a K + NaCl system and a O(¹D)+H₂ system are presented and compared with results of molecular dynamic simulations available in the literature. The weak coupling constraints are found to give a useful representation of the simulation data. Discontinuities in the optimal orientation of approach indicate the presence of orientational barriers.     

Sudden approximation relations between tensorial cross sections for the collision of two diatomic molecules

We demonstrate relations between tensorial cross sections for the collision between two diatomic molecules, one of which does not rotate during the collision. The demonstration relies on a factorisation of the S matrix. A numerical example is presented for the rotational excitation problem of CO by H₂ (j = 1) molecules     

Predicting ion mobility collision cross sections directly from standard quantum chemistry software

A method is proposed to predict ions' collision cross‐sectional area from properties that are already evaluated in standard quantum chemistry software. Computed molecular isodensity surface areas recover the predictions of existing projection approximations. Computed solvent cavity areas give comparable accuracy. This provides a simplified workflow for assigning ion‐mobility mass spectra.     

Total dissociative electron attachment cross sections for molecular constituents of DNA

Total cross sections for the dissociative electron attachment process are presented for the DNA bases thymine, cytosine, and adenine and for three compounds used as surrogates for the ribose and phosphate groups, tetrahydrofuran, 3-hydroxytetrahydrofuran, and trimethylphosphate, respectively. Cross section magnitudes are obtained by observation of positive ion production and normalization to ionization cross sections calculated elsewhere using the binary-encounter-Bethe method. The average cross section of the three bases is 3-10 times smaller than the effective cross section per nucleotide reported for single strand breaks in surface-bound supercoiled DNA. Consequently, damage to the bases alone does not appear to account for the major portion of the strand breaks. The presence of an OH group on the ribose surrogate considerably enhances its cross section. Model compounds in which protonation or OH groups are used to terminate bonds may therefore display larger cross sections than in DNA itself.     

Regge pole analysis of differential cross sections for elastic molecular scattering

The angle and energy dependence of differential cross sections σ(E, θ) that exhibit diffraction oscillations is analyzed by a Regge representation. It is shown that: (1) the Regge poles can be estimated directly from the measured σ(E, θ); (2) a fixed-energy Regge pole calculation can reproduce the E-dependence of σ(E, θ).