2 - WIEN 2k

Dirac equation in a spherical potentialFor a spherical potential V(r):The resulting equations for the radial functions (g and f nκ nκ ) are simplifiedif we define:2ε ' −Vε ' = ε − m ec( )( r)Energy:Radially varying mass: Mer = me+22cThen the coupled equations can be written in the form of the radial eq.:−h1ddrdg⎡ h l +22( l 1) ⎤ h dV dg h dV ( 1+κ )22⎛ 2 nκ⎞nκr Vg2⎜ ⎟ + ⎢ +2 ⎥ nκ−−2 22 22Mer ⎝ dr ⎠ 2Mer 4Mdr drec4Mec⎣⎦drrgnκ= ε ' gnκMass-velocity effectDarwintermSpin-orbitcouplingNote that:κ( κ + 1 ) = l( l +1)