bcc Na, 298 K, r_c = 1.971 bohr from the liquid fit; speeds of long waves (m/s) and moduli (GPa)

simplest screening (Thomas-Fermi, point ions) - sodium.py
  [100]: L 1572  [110]: L 1790  [111]: L 1857
  C11 2.39  C12 2.30  C44 0.75  B 2.33  G(VRH) 0.29  anisotropy C44/C' 17.2;  polycrystal lengthwise 1674, sideways 543

Lindhard screening, point ions, no exchange-correlation
  [100]: L -2148  [110]: L -2553  [111]: L -2675
  C11 4.46  C12 2.10  C44 3.02  B 2.89  G(VRH) 2.07  anisotropy C44/C' 2.6;  polycrystal lengthwise 2418, sideways 1463

+ exchange-correlation hole (local field)
  [100]: L -3513  [110]: L -3901  [111]: L -4021
  C11 11.93  C12 8.81  C44 4.34  B 9.85  G(VRH) 2.88  anisotropy C44/C' 2.8;  polycrystal lengthwise 3763, sideways 1727

+ ion cores (empty core): the full improved model
  [100]: L 3681  [110]: L 4412  [111]: L 4630
  C11 13.10  C12 11.40  C44 6.57  B 11.96  G(VRH) 3.03  anisotropy C44/C' 7.7;  polycrystal lengthwise 4069, sideways 1771

measured, polycrystal at 20 C (B = 6.3 GPa, G = 3.3 GPa; CRC via Wikipedia): lengthwise 3323, sideways 1846 m/s

chain along [100]: plane spacing 0.6300; interplanar constants C_0..C_4 = +2.8361, -1.1989, -0.2466, +0.0198, +0.0130
chain pulse, improved model: timed lengthwise speed between planes 40 and 120: 3791 m/s (long-wave [100] value 3681 m/s)
