Angular correlations

Coulomb repulsion by occupying different r giom of space in the SCF picture Is 2s, both electrons reside in the same 2s region of space. In this particular example, the electrons undergo angular correlation to avoid one another. 

Functions with higher / values and with sizes like those of lower-/ valence orbitals are also used to introduce additional angular correlation by pemiitting angularly polarized orbital pairs to be fomied. Optunal polarization functions for first- and second-row atoms have been tabulated and are included in the PNNL Gaussian orbital web site data base [45]. 

In the Be atom, the two valence electrons occupy a 2s, 2p valence shell, the 2s and 2p Atomic Orbitals (AO) having an important "differential overlap" (ie a good coincidence of their spatial extension). The contribution of the 2p AO to the angular correlation of the... 

From (4.56) and Table 4.3, we derive the relative intensity ratios 3 2 1 1 2 3 for the hyperfine components of a Zeeman pattern of a powder sample. The transition probability for the case of the polar angle 6 = Oq can readly be calculated by integrating (4.56) only over the azimuthal angle (j). One obtains a factor (1 + cos 0o)/2 and sin 0o for m = 1 and m = 0, respectively, which are multiplied by the square of the Clebsch-Gordan coefficients. As a consequence of the angular correlation of the transition probabilities the second and fifth hyperfine components (Fig. 4.17) disappear if the direction k of the y-rays and the magnetic field H are parallel (0q = 0). 

By using NFS, information on both rotational and translational dynamics can be extracted. In many cases, it would be favorable to obtain separate information about either rotational or translational mobility of the sensor molecule. In this respect, two other nuclear scattering techniques using synchrotron radiation are of advantage. Synchrotron radiation-based perturbed angular correlations (SRPAC) yields direct and quantitative evidence for rotational dynamics (see Sect. 9.8). NIS monitors the relative influence of intra- and inter-molecular forces via the vibrational density of states (DOS) which can be influenced by the onset of molecular rotation (see Sect. 9.9.5). 

Synchrotron Radiation Based Perturbed Angular Correlation, SRPAC (Example Whole-Molecule Rotation of FC)... 

SRPAC is a scattering variant of time-differential perturbed angular correlation (TDPAC). In TDPAC, an intermediate nuclear level is populated from above after the decay of a radioactive parent. If this nuclear level exhibits hyperfine... 

Synchrotron Radiation Based Perturbed Angular Correlation, SRPAC... 

Nuclear inelastic scattering (NIS), nuclear forward scattering (NFS), nuclear lighthouse effect (NLE), synchrotron radiation-based perturbed angular correlation (SRPAC)... 

Kobayasi, T. (1994) Fourier inversion formalism for the calculation of angular correlation of positron annihilation radiation of semiconductors, Bull. Coll. Med. Sci. Tohoku Univ., 3, 11-22. 

Several experimental techniques such as Compton scattering, positron annihilation, angular correlation, etc., are used for measuring momentum densities. One of the most popular techniques involved in measuring momentum densities is termed as electron momentum spectroscopy (EMS) [29]. This involves directing an electron beam at the surface of the metal under study. Hence EMS techniques fall under what is classified as coincidence spectroscopy. 

Schwartz, C. Importance of angular correlations between atomic electrons. Phys. Rev. 1962, 126, 1015-19. 

Figure 5. Angular correlation function versus time. Note the decrease in the large peak near the tetrahedral angle. 

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