Energy curves relativistic density

Relativistic Density Functional Calculations for Potential Energy Curves of Uranyl Nitrate Hydrate... 

Fig 1. Potential energy curve of the Au2- Circles represent the relativistic density functional theory (RDFT) results, full line represents the fitted empirical pair potential energy function (PEF). 

Let us consider how independent /i(i ) 2 effects contribute to the v E) for the hydrogen halides, HX (X = I, Br, and Cl). The curves shown on Fig. 7.6 correspond to relativistic adiabatic potential energy curves (respectively 0 dotted, 0+ dashed, 1 and 2 solid) for HI obtained after diagonalization of the electronic plus spin-orbit Hamiltonians (see Section 3.1.2.2). The strong R-dependence of the electronic transition moment reflects the independence of the relative contributions of the case(a) A-S-Q basis states to each relativistic adiabatic II state. The independent experimental photodissociation cross sections are plotted as solid curves in Fig. 7.7 for HI and HBr. Note that, in addition to the independent variations in the A — S characters of each fl-state caused by All = 0 spin-orbit interactions, all transitions from the X1E+ state to states that dissociate to the X(2P) + H(2S) limit are forbidden in the separated atom limit because they are at best (2Pi/2 <— 2P3/2) parity forbidden electric dipole transitions on the X atom. In the case of the continuum region of an attractive potential, the energy dependence of the dissociation cross section exhibits continuity in the Franck-Condon factor density (see Fig. 7.18 Allison and Dalgarno, 1971 Smith, 1971 Allison and Stwalley, 1973). 

The maximum energy of radiation can be determined by plotting an absorption curve as shown in Fig. 6.7, or, more accurately, by use of a magnetic spectrometer, as in the case of a particles, but at much lower flux density B, because of the higher e/m values. At the same energy, the velocity v of electrons is much higher than that of a particles which makes relativistic correction necessary ... 

Figure 7. Short-range behaviour of nuclear electrostatic potentials V r) (in atomic units) for different finite nuclear charge density distributions in the case of mercury, Z = 80, A = 200 (dashed curve PNC, solid curves FNCs). The FNC curves may be identified from their labels at the origin, see also Eq. (109). The corresponding charge density distributions are standardized to a common value of the rms radius, a 5.4590 fin, determined from Eq. (54). The ground state energies for Hg and Hg /i" (only PNC) are indicated, together with the lower continuum threshold for the relativistic one-electron states (horizontal dashed lines). In the present scale, the full spectrmn of bound electronic states practically coincides with the horizontal axis. The conversion factor from atomic units of length to femtometer is la.u. = 52917.7249frn, and the myon-electron mass ratio is = 206.768262 [1].

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