Vacuum graph

The form of the third diagram is determined by the factor in I hc factors 3, 6, and I follow from the symmetry character of the system. The first term is obtained as a result of connecting two line pairs of the third term in all the possible ways (namely, three). The second term is obtained by connecting any two lines of the third term, there are six such ways. These numerical factors axe called symmetry factors. The first term with two closed loops is referred to as a vacuum graph since it has no external lines. The term with one closed loop has two external lines (two factors J), while the last one has four such lines (four factors J). 

An algebraic expression not depending on the external coordinates corresponds to the vacuum graph. All the graphs corresponding to the terms in N, have this structure. 

It also contains a vacuum graph, and therefore cancels out. 

Cancellation of the vacuum graphs happens just as before, since Af has not been altered. It follows that only h and i of the graphs in Figure 2.59 are cancelled. 

The graph only ever goes through the origin at zero pressure. We have discovered that the only way to have a completely clean substrate (one with no adsorbate on it, with 9 = 0) is to subject the surface to an extremely low pressure - in effect, we have subjected the substrate to a strong vacuum. Effectively, the vacuum sucks the adsorbate away from the substrate surface. We give the name desorption to the removal of adsorbate. 

A mass spectrometer ionizes molecules in a high vacuum, sorts the ions according to their masses, and records the abundance of ions of each mass. A mass spectrum is the graph plotted by the mass spectrometer, with the masses plotted as the x axis and the relative number of ions of each mass on the y axis. Several methods are used to ionize samples and then to separate ions according to their masses. We will emphasize the most common techniques, electron impact ionization for forming the ions, and magnetic deflection for separating the ions. 

Amass spectrometer is a device for separating atoms and molecules according to their mass. A substance is first heated in a vacuum and then ionized. The ions produced are accelerated through a magnetic field that separates ions of different masses. The graph below was produced when a certain element (element X) was analyzed in a mass spectrometer. Use the graph to answer the questions below. 

During the year 2000, at Deluxe Vacuum Co., the East and West divisions had equal sales and the North sold the most. Which graph could be the graph of Deluxe s yearly sales for 2000 ... 

Figures 2a and 2b allow to observe pressure effect on the total permeation. It is possible to see as higher as vacuum better the total permeation, but separation capability is reduced as shown in Figure 2b and confirmed by selectivity profile in Figure 3a. A recovery (%) is presented in Figure 3b, concentration increases of the target compound in feed provides lower recovery results. This is an interesting graph for process set up definitions.

Fig. 14. Graph of At the first derivative of the thermogravimetric curve dw/dt, and o, the weight of reactant Wr as a function of reciprocal absolute temperature for the degradation of polythene in vacuum [27],...

A somewhat similar approach can also be used for the mixed self energy - vacuum polarization diagrams of Fig. 13. The detailed evaluation of these graphs is presented by Lindgren et al. [59] and we report only the result of their calculation here, which for the lsi/2-state of uranium yields 1.12 eV in the Uehling approximation (no Wichmann-Kroll vacuum polarization potential included in the Dirac equation) and 1.14 eV by taking into account the Wichmann-Kroll potential also [7]. 

Fig. 13. QED diagrams of order (two photon lines) contributing to the Lamb shift in hydrogenlike systems. SE implies self energy , VP vacuum polarization . The nomenclature of the single graphs is therefore evident.

---