Shake processes

A.G. Kochur, D. Petrini, E.P. da Silva, 2s-photoionisation of atomic magnesium Shake processes and Coster-Kronig radiationless decay, A A 365 (2001) 248. 

Arndt et al. [30] proposed another reason for smaller Kj3/Ka ratios by EC, i.e. larger shakeoff probability in PI. They demonstrated that if the number of 3d electrons in PI is assumed to be by two less than that in EC, the experimental results of Paic and Pecar and their own data for Mn can be explained. Smaller shake probabilities for EC than for PI have already lieen pointed out by Crasemann et al [44]. It is important to compare the effect of the shake process on the K /Ka ratios by EC and by PI for V and Cr atoms. 

The calculated shakeup-plus-shakeoff probabilities for V and Cr following PI and EC are listed in Table 13. It is clear that the probabilities for EC are negligibly small and those for PI are about 5% for 3p electrons and about 10% for 3d electrons. Using the values of Table 13, we obtained the effective numbers of 3p, 3d, and 4s electrons after EC and PI and calculated the Kjd/Ka ratios for atoms. There is no influence of the shake process on the Kf3/Ka... 

It should be noted, however, that in actual situations the final states of the shakeup process are molecular Rydberg states and should be described by the MO wave functions. We estimated the contributions from the shakeup probabilities for atoms accompanying A -shell PI to the total (shakeup-plus-shakeoff) probabilities. The shakeup probabilities were calculated with the HS wave functions as the overlap integrals by the method used in our previous work [47]. The shakeup probabilities in PI were found to be about 30 40% of the total probabilities for 3p electrons and about 40 50% for 3d electrons. These large shakeup probabilities suggest that the chemical effect on the shakeup process would be large if the shakeup probabilities are calculated with the MO wave functions and the contributions of the shake process in PI to the Kf3/Ka ratios for 3d elements would be appreciable. 

The chemical effect on the K jKa ratios for 3d elements have been calculated for compounds with Td and Oh symmetry and are in qualitative agreement with the experimental data. It is found that the ratios for compounds with Td symmetry are larger than those with Oh symmetry. The excitation mode dependence on the KfilKo. ratios for 3d elements was studied. For the same chemical compounds the KfdfKa ratios by EC are smaller than those by PI due to the excess 3d electron in EC, but the difference is too small to explain the experimental results. It was pointed out that the large experimental values may be due to the sum of the effect of the excess 3d electron and the chemical effect. The larger shake process in PI plays a minor role for the excitation mode dependence. 

On the other hand, fluorescence yields for the XI lines in the case of the ion impacts were assumed to be Yxi only for k L K L through the shake process. Here Yxi was determined from the photon induced X-ray spectra. However, for the K L state produced through the direct Coulomb interaction, Y=0.013 was adopted because the direct Coulomb ionization is not accompanied with the orbital reairangeinent. These considerations give the total X-ray production cross sections for the XO and XI lines, ctxo and Oxi,... 

Fig. 3. Schematic KX-ray spectra induced by 1.4 MeV /amu He". Here white lines indicate observed spectra [9] and black lines calculated, where the direct Coulomb interaction and the shake process for multiple ionization have been taken into account.

Using the total shake (shakeoff plus shakeup) probabilities in Table IV, we modified the the number of 2>p, 3d, and 4s electrons and calculated the K/3IKa ratios after PI. Comparing the K(3IKa ratios for PI with and without the shake processes, the increase in the IKa ratio due to the shake processes is found to be less than 0.5% for V and less than 0.4% for Cr. This fact indicates that the shakeoff and shakeup processes increase the K/3 IK a ratios for PI, but play a minor role in the difference between EC and PI. 

We have calculated the K/3/Ka x-ray intensity ratios for several chemical compounds of 3d elements by PI and EC with the DV-Xo method. The results indicate that the ratio depends on the excitation mode as well as the chemical state and both effects should be considered to compare with the experimental data. For similar chemical environments, the ratio by PI is larger than that by EC. This can be ascribed to the presence of an excess 3d electron in the latter case and partially to difference in the shake process between two excitation modes. However, the dependence on the excitation modes is very small and easily masked by the chemical effect. 

Now we use the treatment in the preceding section to give a physical picture of the SHAKE process of resetting the coordinates to satisfy bond-stretch constraints. If the bond-stretch constraint Eq. [95] had been formulated, instead, in terms of the bond-stretch internal coordinated (i.e., magnitude of the distance between the two atoms), the following bond-stretch SHAKE displacements would have been found from Eq. [77] ... 

We consider stabihty of the interface between two incompressible fluids A and B, as illustrated in Figure 5.1. When the upper fluid is the denser of the two, a gravitationally produced instability arises. It is the prototype of various instabilities that are produced by acceleration of fluids in contact and which are employed in forming emulsions, aerosols, and foams by various shaking processes and ultrasonic vibration. While important in its own right, it also serves here as a vehicle for introducing the techniques of linear stabihty analysis which will be employed throughout this chapter and the next. 

Allow the undissolved portion of the powder to settle in the vial. A cloudy suspension may remain even after 5 minutes or more. You should wait only until it is obvious that the larger particles have settled completely. Using a filter-tip pipette (Technique 8, Figure 8.9), transfer the liquid phase to a centrifuge tube. Add a second 2-mL portion of methanol to the conical vial and repeat the shaking process described previously. After the solid has settled, transfer the liquid phase to the centrifuge tube containing the first extract. 

Shaking Separatory Fuimels. A separatory funnel and its contents should be shaken to mix the immiscible liquids as intimately as possible (Fig. 2.61b). The shaking process increases the surface area of contact between the immiscible liquids so that the equilibrium distribution of the solute between the two layers will be attained quickly however, overly vigorous or lengthy shaking may produce emulsions (discussed below). 

---