 Physics Help Forum Susceptibility of a simple metal (Problem 31.6 in Ashcroft's
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 Atomic and Solid State Physics Atomic and Solid State Physics Help Forum May 14th 2017, 07:49 AM #1 Junior Member   Join Date: Aug 2009 Posts: 9 Susceptibility of a simple metal (Problem 31.6 in Ashcroft's 1. The problem statement, all variables and given/known data The susceptibility of a simple metal has a contribution ##\chi_{c.c}## from the conduction electrons and a contribution ##\chi_{ion}## from the diamagnetic response of the closed-shell core electrons. Taking the conduction electron susceptibility to be given by the free electron values of the Pauli paramagnetic and Landau diamagnetic susceptibilities, show that: $$\frac{\chi_{ion}}{\chi_{c.c}} = -\frac{1}{3} \frac{Z_c}{Z_v}\langle (k_F r)^2 \rangle$$ where ##Z_v## is the valence, ##Z_c## is the number of core electrons, and #### is the mean square ionic radius defined in (31.26). 2. Relevant equations $$(31.26) = \frac{1}{Z_i} \sum <0|r_i^2 |0>$$ $$\chi^{molar} = -Z_i (e^2/(\hbar c))^2 \frac{N_A a_0^3}{6}\langle (r/a_0)^2 \rangle$$ $$\chi_{pauli} = \bigg(\frac{\alpha}{2\pi}\bigg)^2 (a_0k_F)$$ $$\chi_{Landau} = -1/3 \chi_{Pauli}$$ 3. The attempt at a solution I thought that ##\chi_{molar}=\chi_{ion}## and that ##\chi_{c.c} = \chi_{Landau}+\chi_{Pauli} = 2/3 \chi_{Pauli}##. But when I divide between the two susceptibilities I don't get the right factors, has someone already done this exercise from Ashcroft and Mermin? I tried searching google for a solution but to a veil.  Tags 316, ashcroft, metal, problem, simple, susceptibility Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post stevie281 Electricity and Magnetism 4 Nov 1st 2016 11:58 PM pranimaboity2050 Advanced Electricity and Magnetism 0 Dec 10th 2014 11:21 PM ling233 Quantum Physics 0 Oct 4th 2014 08:57 AM eloiamb Kinematics and Dynamics 4 Jul 29th 2010 12:19 PM Morgan82 Kinematics and Dynamics 2 Oct 29th 2008 02:14 AM 