NOTE ON THE USE OF NON-ORTHOGONAL WAVE FUNCTIONS IN PERTURBATION CALCULATIONS

1955 ◽  
Vol 33 (12) ◽  
pp. 709-712 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Interaction Energy ◽  
Energy Function ◽  
Wave Functions ◽  
First Approximation ◽  
Ionic Change

A method of first approximation is proposed for handling collision problems involving a chemical or ionic change, so that the interaction energy function is different at the beginning and end of the collision.

scholarly journals The effect of a nuclear spin on the optical spectra.—III

1930 ◽  
Vol 127 (805) ◽  
pp. 407-416 ◽  
Keyword(s):  
Interaction Energy ◽  
Nuclear Spin ◽  
Energy Levels ◽  
Optical Spectra ◽  
Wave Functions ◽  
Orbital Momentum ◽  
Multiplet Structure ◽  
Multiple Wave ◽  
First Approximation ◽  
Intensity Ratios

In two recent papers the author has discussed the effect of a nuclear spin on the optical spectra by the method of multiple wave-functions. In these papers the interaction energy of the nuclear and electron spins was not taken into account, as has been pointed out by Hill. By its omission the equations were simplified considerably, without affecting the intensity ratios of the lines of the multiplet. The problem of finding the relative intensities is a purely kinematical one, depending as it does, to the first approximation, on the un­perturbed wave-functions. In the papers cited we used the interaction energy of the nuclear spin and orbital momentum to find the 4 i n + 2 wave-functions ( i n being the number of quanta of nuclear spin) which must replace the two wave-functions necessary to describe the electron spin fine structure. In order to describe the multiple energy levels correctly we must calculate the interaction energy of the two spins in addition to the energy increments already calculated in I and II. This is the first purpose of the present paper, and the work is carried out for the cases i n = ½, 1, 1½, 4½. It is found that in the case of the p ½ levels the interaction energy of the two spins is equal to that of the nuclear spin and orbital momentum, while for the p 3/2 levels the ratio is — ⅕. It is further found that the energy levels of the S terms are correctly given in I and II. As regards comparison with Jackson’s results in the case of cæsium, it would seen that, the separation of the p -levels being very small in comparison with that of the S-level, he has been able to observe the multiplet structure of the lines due to the separation of the S-level only. If we make this assumption it will be seen on reference to I that our results agree quite well with his observations.

scholarly journals Assessment of Solvated Interaction Energy Function for Ranking Antibody–Antigen Binding Affinities

2016 ◽  
Vol 56 (7) ◽  
pp. 1292-1303 ◽  
Author(s):  
Traian Sulea ◽  
Victor Vivcharuk ◽  
Christopher R. Corbeil ◽  
Christophe Deprez ◽  
Enrico O. Purisima
Keyword(s):  
Interaction Energy ◽  
Energy Function ◽  
Antigen Binding ◽  
Binding Affinities ◽  
Solvated Interaction Energy

INTERBARYONIC FORCE AS A SOLITON-SOLITON INTERACTION IN SKYRME MODEL

1988 ◽  
Vol 03 (11) ◽  
pp. 2681-2706 ◽  
Author(s):  
ZVONIMIR HLOUSEK
Keyword(s):  
Interaction Energy ◽  
Real World ◽  
Nuclear Force ◽  
Effective Interaction ◽  
Skyrme Model ◽  
Soliton Interaction ◽  
Quantization Method ◽  
First Approximation ◽  
Collective Coordinate ◽  
General Method

We present a general method for calculating the interaction energy of two solitons using the semiclassical, collective coordinate quantization method. The result also has a simple geometrical interpretation. We apply our result in several models, and obtain the expressions for the interaction energy. In particular, we use our method to derive the effective interaction energy of two solitons of Skyrme model. Because the solitons of the Skyrme model can be used to model (in the first approximation) the real world baryons, the interaction energy of two solitons can then be interpreted as an approximation to a two-body nuclear force.

X-ray scattering factors for O2− and N3−

1978 ◽  
Vol 34 (6) ◽  
pp. 994-999 ◽  
Author(s):  
K. Schwarz ◽  
H. Schulz
Keyword(s):  
Neutral Atom ◽  
Form Factors ◽  
Theoretical Models ◽  
Wave Functions ◽  
Radial Variation ◽  
Sphere Model ◽  
X Ray ◽  
X Ray Scattering ◽  
First Approximation ◽  
Ray Scattering

Form factors calculated from several theoretical models show that the Xα method is accurate to about 1%. With the latter scheme and the Watson-sphere model the atomic form factors for O2- and N3- are computed for varying sphere radii. To a first approximation this radial variation accounts for the different environments of such ions. Deviations of up to 25% in the scattering factors occur when compared with the results obtained from the wave functions of the corresponding neutral atom.

scholarly journals Franck-Condon factors and r-centroids for the diatomic fluorides of germanium and silicon

2008 ◽  
Vol 73 (5) ◽  
pp. 555-560
Author(s):  
S. Kanagaprabha ◽  
Rajeswara Palanichamy ◽  
V. Sathiyabama
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Close Agreement ◽  
Band System ◽  
Potential Energy Function ◽  
Wave Functions ◽  
Integration Technique ◽  
Condon Factors ◽  
Franck Condon ◽  
Suitable Potential

A suitable potential energy function was found by analysing the potential functions proposed by Morse, Mohammad and Rafi et al. for the A2?+-X2?3/2 and B2?+-X2?3/2 band systems of GeF and the 1?-1? band system of SiF. It was found that the potential proposed by Rafi et al. is in close agreement with the Rydberg-Klein-Rees (R-K-R) potential. Using this potential, the wave functions were evaluated by the Wentzel-Kramer-Brillouin (W-K-B) method. The Franck-Condon factors and r-centroids were computed by a numerical integration technique. The results are compared with available theoretical values. The intensities of the various bands were investigated.

On a Unified Potential Energy Function for Ionic and Non-ionic Bonds and the Question of Chemical Bonding

1982 ◽  
Vol 37 (7) ◽  
pp. 710-715 ◽  
Author(s):  
G. Van Hooydonk
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Anomalous Behaviour ◽  
Bond Type ◽  
First Approximation ◽  
Spectral Behaviour ◽  
Ionic Bonds ◽  
Sutherland Parameter ◽  
First Time

Abstract For 39 diatomic ionic and non-ionic molecules, the anomalous behaviour of the spectral para-meters αe and ωχxe with respect to the bond type is reviewed. It is shown that on using a "uni-versal" Sutherland parameter defined as ⊿ = ½kere2/Dion, the anomalous behaviour disappears. Hard spectroscopic evidence is thus presented, for the first time to the author's knowledge, that just one bond type, in fact an ionic one, can account, in first approximation, for the spectral behaviour of both non-ionic and ionic bonds, H2 included.

Coefficients of radial integral in the electrostatic interaction and their applications

2004 ◽  
Vol 82 (7) ◽  
pp. 517-522
Author(s):  
Z Chen ◽  
A Z Msezane
Keyword(s):  
Interaction Energy ◽  
Cross Sections ◽  
Electrostatic Interaction ◽  
Atomic State ◽  
Wave Functions ◽  
Radial Integral ◽  
Open Shells ◽  
Two Open Shells

We have derived the equations to calculate the electrostatic interaction energy and the coefficients of radial integrals between electrons ln or l1m and l′ of the atomic state |ln[S1L1]l1m[S2L2][ScLc]l′ SL >, where ln[S1L1], l1m[S2L2], and l′ are three open shells. The expressions have been checked against the formulas in the literature by reducing them to those for the case of atoms having two open shells. We demonstrate our formulas by evaluating the coefficients of the radial integrals in the interaction between the 2s or 2p4 and 3p electrons of the 2s2p4(2,4P)3p(3S,3P,3D) state of oxygen. Using these coefficients the wave functions and photoionization cross sections of oxygen 2s has been evaluated and compared with previous results. PACS Nos.: 31.15.Ne, 31.10.+z, 32.80.Fb

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