liquid Na (927 kg/m^3): r_s = 4.05, v_F = 1.0371e+06 m/s, k_TF = 1.4682e+10 1/m, ion plasma frequency 4.2943e+13 rad/s (hbar w = 28.3 meV)
  Bohm-Staver speed sqrt(m_e/3M) v_F = 2925 m/s;  w_pi/k_TF = 2925 m/s
  measured: 2531 m/s at 373 K, 2520 m/s at 383 K (CRC, via knowledgedoor); ratio 1.156
  without the electrons following (rigid background): no sound at all; the ions just ring at 6.83 THz

solid bcc Na (298 K): density 967 kg/m^3, k_TF d = 5.035, Bohm-Staver 2966 m/s
  [100]: screened ions: lengthwise 1572 m/s, sideways 883, 883 m/s;  rigid background: lengthwise frequency 6.98 THz (no sound)
  [110]: screened ions: lengthwise 1790 m/s, sideways 213, 883 m/s;  rigid background: lengthwise frequency 6.98 THz (no sound)
  [111]: screened ions: lengthwise 1857 m/s, sideways 539, 539 m/s;  rigid background: lengthwise frequency 6.98 THz (no sound)
  measured, polycrystal at 20 C (B = 6.3 GPa, G = 3.3 GPa, 968.8 kg/m^3; CRC via Wikipedia): lengthwise 3323 m/s, sideways 1846 m/s
  Bohm-Staver in lattice units: v = sqrt(4 pi)/kappa = 2966 m/s

chain pulse, screened ions: timed lengthwise speed 1554 m/s (normal mode 1572 m/s)
chain pulse, screened: largest displacement at planes 40 and 120, relative to the antenna plane: 9.72e-01, 9.13e-01
chain pulse, rigid: largest displacement at planes 40 and 120, relative to the antenna plane: 1.63e-04, 1.13e-04
