Calculation of energies and widths

C. A. Nicolaides, Theoretical approach to the calculation of energies and widths of resonant (Autoionizing) states in many-electron atoms, Phys Rev. A 6 (1972) 2078. 

C.A. Nicolaides, D.R. Beck, A Variational Method for Calculating the Energies and Widths of Resonances, Phys. Lett. 60A (1977) 92 C.A. Nicolaides, D.R. Beck, The Variational Calculation of Energies and Widths of Resonances, Phys. Lett. 65A (1978) 11. 

M.F. Fels, A.U. Hazi, Calculation of energies and widths of resonances in inelastic scattering Stabilization method, Phys. Rev. A 5 (1972) 1236. 

C.A. Nicolaides, D.R. Beck, The variational calculation of energies and widths of resonances, Phys. Lett. 65A (1978) 11. 

The calculation of energies and widths of the resonances of HOCl was done using the complex method outlined in the previous section. In our particular implementation we used an efficient truncation/recoupling procedure (10,11) to obtain eigenvalues and eigenfunctions of the real Hamiltonian. The Hamiltonian for the HOCl dissociation is given in standard body-fixed Jacobi coordinates. For zero total angular momentum, J, it is ... 

While the detailed calculations gave energies and widths in reasonable agreement with the observed experimental results, they did not provide a simple physical picture of why the He spectrum was the way it was. To address this issue Macek described the He atom using hyperspherical coordinates. In this approach, the two electrons, each described by three coordinates, are replaced by an equivalent single particle in six dimensions.8,9 In Fig. 23.3 we show the He atom in which rt and r2 are the vectors from He2+ to each of the two electrons. The hyperradius Rh is defined by... 

On the theoretical side, both quantal and semlclasslcal methods have been used to calculate resonance energies and widths, principally for colllnear reactions, although there are a few studies of 3D reactions. In quantal studies of 3D reactions, some close-coupling calculations on H+H2 have been reported (If), (li), but the large number of channels has necessitated approaches based upon the J -conserving (3),... 

Deconvolution of spectra (energy distribution of orbitals and widths of bands) accomplished by comparison of variable energy photoelectron spectra and SCF-Jfct -SW ground state calculation. 

Fig. 1. Atomic cascade in antiprotonic hydrogen. The hadronic interaction is observed by a level shift and a broadening of the low-lying atomic levels as compared to the calculated binding energies and radiative decay widths assuming a pure electromagnetic interaction...

Table 1. Calculated electromagnetic energies and line widths of the antiprotonic transitions measured with the crystal spectrometer. The energy resolution AEexp of the Bragg spectrometer was determined from narrow transitions of antiprotonic noble gases. Ob stands for the Bragg angle...

Table I. Energy and Width of the 2P Resonance in the e-Be Scattering from Various Calculations.

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