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Posted: **Tue Jul 05, 2022 8:54 am**

: A To Obtain Realistic Results We Need To Use The Screened Coulomb Or Yukawa Potential For The Ionic Potential Va See 1 (71.79 KiB) Viewed 12 times

: A To Obtain Realistic Results We Need To Use The Screened Coulomb Or Yukawa Potential For The Ionic Potential Va See 2 (49.59 KiB) Viewed 12 times

(a) To obtain realistic results we need to use the screened Coulomb or Yukawa potential for the ionic potential Va (see Eq. (3.42) and Exercise 1.5). The electrons redistribute in an attempt to neutralize the ionic potential. As we shall see in Chap. 13 they succeed to do so for distances further away than 1/k, from the ion. Show by dimensional analysis involving the Fourier component e²/(ek²), the Fermi energy F, and the electron density n that k² kr/ao. S
9g = i 9q Ze² 9 €o q²+k² Nh 2Mwq (3.42)
Exercise 1.5 The Yukawa potential is defined as Vk² (r) constant with the dimensions of a wavevector. = e-kar, with ks being some real positive Prove that the Fourier transform is Vks = 4meo Relate the result to the Coulomb potential. Hints: work in polar coordinates q²+ks²