Dipole strength functions

Role of Discrete Levels in Deriving Absolute Dipole Strength Functions... 

Figure 8. 175Lu(n,y) excitation function, calculated using our original dipole strength function sys-tematics, compared with experimental data from [MAC78,BEE80]. 

Figure 10 Recently derived absolute dipole strength functions for 176Lu (solid curves), compared with those predicted by our original sys-tematics (dashed curves). The arrows indicate the value assigned to the one free parameter, Ex. In our recent derivation, Ex = 11 MeV, and in our original systematics, Ex = 5 MeV.

The time-dependent Kohn-Sham equations can now be propagated in real time. This approach is still less common than the linear-response scheme that will be described in the next section. After performing the propagation in some finite time the dipole-strength function can be evaluated as described in section 2.3.2. 

The dipole-strength function. Next, we want to express the dipole-... 

The dipole-strength function S(co) may, thus, be written in terms of the polarizability as... 

In the following we are going to relate the dipole-strength function given in eqn (55) to the photoabsorption cross section photoabsorption cross section is derived in ref. 23 for a monochromatic electric field. If the calculational method contains all frequencies, e.g. as in refs. 13, 24 and 25, we have to sum over all excited states n. Furthermore, in experiments the molecules are randomly oriented. Therefore, we take the sum of all directions of the matrix elements ... 

From eqn (57) we see, that the dipole-strength function is directly proportional to the photoabsorption cross section. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

Figure 1. Photoabsorption cross section for the dipole plasmon in axially deformed sodium clusters, normalized to the number of valence electrons N - The parameters of quadrupole and hexadecapole deformations are given in boxes. The experimental data [39] (triangles) are compared with SRPA results given as bars for RPA states and as the strength function (49) smoothed by the Lorentz weight with A = 0.25 eV. Contribntions to the strength function from p =0 and 1 dipole modes (the latter has twice larger strength) are exhibited by dashed curves. The bars are given in eVA. ...

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

The three coefficients in angular brackets are given in Table 4.8. It was previously found that for j, f = 0...4, higher-order terms in j(j + 1), /(/ + 1) are not needed. The coefficients are functions of separation, R, and can readily be fitted to an analytical expression of the form Eq. 4.39, with BXL = (00 al 10), 0 I lI l), (o AXL T, respectively. These coefficients are given in the lower part of Table 4.8. The results show that the j, j corrections amount to 10 or 15% for j, / = 1...3 for the main components, XL = 01 and 23, and even more for the lesser components. Since the associated spectral intensities vary as the squares of dipole strength, these variations are clearly significant for the spectra. 

This expression may be viewed as a sum of two terms. The first one, the integral over the squared derivative of the dipole function, p R), models those contributions which arise from the variation of the dipole strength with the separation R. The second models the contributions due to the variation of direction, p, as the rather natural separation of the kinetic energy operator into a radial and angular part suggests [314]. 

An explanation was offered by van Kranendonk many years after the experimental discovery. Van Kranendonk argued that anticorrelations exist between the dipoles induced in subsequent collisions [404], Fig. 3.4. If one assumed that the induced dipole function is proportional to the intermolecular force - an assumption that is certainly correct for the directions of the isotropic dipole component and the force, and it was then thought, perhaps even for the dipole strength - an interference is to be expected. The force pulses on individual molecules are correlated in... 

The dipole response in real time gives access to the response in frequency domain by Fourier transfrom D (a)), from which one can extract the strength function S(n>) = cA b yf and the power spectrum P( ) = I)(a/) 2. The strength function is the more suited quantity in the linear regime, where it can be related to the photoabsorption cross section [31], while the power spectrum better applies for spectral analysis in the non linear regime [24],... 

The transition dipole moment functions are — like the potentials — functions of Q. Their magnitudes determine the overall strength of the electronic transition ki —> kf. If the symmetry of the electronic wavefunc-tions demands likfki to be exactly zero, the transition is called electric-dipole forbidden. The calculation of transition dipole functions belongs, like the calculation of the potential energy surfaces, to the field of quantum chemistry. However, in most cases the fikfkt are unknown, especially their coordinate dependence, which almost always forces us to replace them by arbitrary constants. 

Figure 3. (a) The electric potential and (b) the average polarization of a water molecule between two surfaces with a — 5 x 10 4 C/m2, separated by a distance 2d = 40 A, as a function of the position from the middle distance. The average polarization of the water molecules from interface, mt, was calculated using eq 20b, for pic = 0 and pie = - 0.1 D, and A =100 A2, (c, d) The interaction force calculated, at various electrolyte concentrations, from eqs 12a,b with the boundary conditions (19b) and(20b), versus separation distance, compared to the DLVO predictions, (e) The interaction force for An = 3 A and dipole strengths (0 < pie <3D,A= 100 A2). The repulsion initially decreases and then increases with the increasing strength of the surface dipoles. 

The analysis of cometary data requires knowing the vibrational transition band strengths in the state of CN. Two very different values for the Einstein coefficient (A) of the fundamental 1-0 vibrational band have been reported one based on analysis of cometary data and the other from measurements in a King furnace.Using the CASSCF/MRCI dipole moment function, the computed /fjo value was in excellent agreement with the value measured in the King furnace. The small uncertainty in the computed value suggests that some of the assumptions in the model used to analyze the cometary data are in error. 

---