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Spin-orbit Interaction





SPIN ORBIT INTERACTION

The energy of a magnetic moment in a magnetic field is given by:

:\Delta H=-\boldsymbol{\mu}\cdot\boldsymbol{B}

Where \mu is the Magnetic Moment of the particle and B is the Magnetic Field it experiences.


Magnetic Field


We shall deal with the Magnetic Field first. For simplicity in many-electron systems we shall assume the nucleus to be stationary and not use the Biot-Savart Law . To calculate the magnetic field

:\boldsymbol{B} = - {\boldsymbol{v} imes \boldsymbol{E}\over c^2}

  :<math>\boldsymbol{B} {\boldsymbol{r} imes\boldsymbol{p}\over m_ec^2} \left {E\over r} ight </math>
  :<math>\left E Ight {\partial V \over \partial r}={1\over e}{\partial U(r) \over \partial r}</math>
  :<math>\Delta E \left\langle\Psi ight \Delta H \left \Psi ight angle</math>