Fundamentals of Inelastic Electron Scattering by P. Schattschneider

By P. Schattschneider

Electron power loss spectroscopy (ELS) is an enormous topic with a protracted and honorable background. the matter of preventing energy for top strength debris the earliest pioneers of quantum mechanics comparable to Bohr and Bethe, who laid the theoretical foun­ dations of the topic. The experimental origins may possibly possibly be traced to the unique Franck-Hertz test. the trendy box comprises issues as varied as low power mirrored image electron strength loss stories of floor vibrational modes, the spectroscopy of gases and the fashionable idea of plasmon excitation in crystals. For the research of ELS in electron microscopy, a number of traditionally detailed components of physics are correct, together with the speculation of the Debye­ Waller issue for digital inelastic scattering, using advanced optical potentials, lattice dynamics for crystalline specimens and the speculation of atomic ionisation for remoted atoms. but the box of electron strength loss spectroscopy includes few necessary texts which might be instructed for college students. With the new visual appeal of Raether's and Egerton's hooks (see textual content for references), now we have for the 1st time either a entire assessment text-due to Raether-and a lucid introductory textual content which emphasizes experimental aspects-due to Egerton. Raether's textual content has a tendency to stress the hot paintings on floor plasmons, whereas the power of Egerton's e-book is its therapy of internal shell excitations for microanalysis, in line with using atomic wavefunctions for crystal electrons.

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At velocity Vo, we have 80 = 31r. Use of Eq. 39) then shows that UT ~ o. early identical with the incoming one which means that the atom is transparent for the electron beam. Inspection of Eq. ) vanishes under these circumstances, too. 2 en II III 1 IL. rev) Electron Velocity Fig. 11. a) Phase shifts 1/0,1/1,1/2,1/3,1/4 calculated theoretically for argon as a function of electron velocity. b) Comparison of the cross-section calculated using these phase shifts with those observed. 4]. 40 In Fig.

Eventually, GOS decreases due to destructive interference of the overlapping oscillatory functions Fnl, F n'l' ,j>... 11. 11]. In order to obtain the total cross section, integrate If{ {}) 12 with respect to 0: ! If{{})1 11' at = 21T 2 sin{}d{} o = :; I)21 + 1)(21' + 1) l,l' (e 2i6 / 1)( e-2i6/~ - = :; I)21 - 1) . 39a) 1)1 2 l 00 = ~ L)21 + 1) ·12isin8l ei6 /1 2 1=0 = ~; f sin 2 Dl (21 + 1) l=O where we have used the orthogonality of p" and the identity e2i6 - 1 = 2i sin f)ei6. 39b) From Eq. 38)' it is seen that the problem of calculating the scattering amplitude f( {}) is equivalent to determination of Dl, 35 which are the phase shifts of the partial waves Ji (kr) in the expansion Eq.

E. 11]. 9) ka, kb designating free states, cp, cp' are the eigenfunctions of the electrons bound to the target nucleus,-before and after the collision. In general, cp is, in r:space: cp( rl, ... TN) for an N-electron atom. Hence, < blV la > is obtained in r:representation by insertmg 1= f rfrl ... d3rNIr > ®Irl ... rN >< rl ... rNI® < rld3r. 5). 5) < blV la >= J d3rl ... d3rNCP'· (rl ... TN )CP(TI ... 11) V is the interaction potential between probe electron at position r and one atom (since the target is an arrangement of non-interacting atoms, as long as inner shell excitations are considered): V= -Ne2 r e2 +2: 1r-" N 1 -"I.

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