dc Magnetic Field Effects on Polarized Monochromatic Laser Radiation Absorption in Electronic Transitions: A Simple Model

Abstract

The hamiltonian Ĥ that describes the transition in an elementary atomic (or molecular) system is (+)

$$ \hat H = {\hat H_{ED}} + {\hat H_{MD}} + {\hat H_{EQ}} + {\hat H_{NL}} $$

((1))

$$ {\hat H_{ED}} = e\sum\limits_j {{{\vec r}_j}} \bullet {\vec E_T}(0) = e{\text{ }}\vec D \bullet {\vec E_T}(0) $$

((1.1))

$$ {\hat H_{MD}} = \frac{{e{\mu _o}}}{{2m}}\mathop H\limits^ \to \bullet \sum\limits_j {{{\vec r}_j}} x{\text{ }}{\vec P_j} = \frac{{e{\mu _o}}}{{2m}}\left( {{{\mathop H\limits^ \to }_T}(0){\text{ }} + {\text{ }}{{\mathop H\limits^ \to }_{DC}}} \right) \bullet \mathop M\limits^ \to $$

((1.2))

$$ {\hat H_{EQ}} = - \nabla Q{E_T}(0) $$

((1.3))

$$ {\hat H_{NL}} = \frac{{{e^2}{\mu ^2}o}}{{8m}}{\sum _j}(\vec H\;x\;{\vec r_j}) = \frac{{{e^2}{\mu ^2}o}}{{8m}}\;{\sum _j}\;\left[ {\left( {{{\vec H}_T}\left( o \right) + {{\vec H}_{DC}}} \right)\;x\;{{\vec r}_j}} \right] $$

((1.4))

The lack of H_DC (external d-c magnetic field) brings about negligible contribution of terms (1.2), (1.3) and (1.4) in respect of (1.1). On the contrary a d-c magnetic field of a few Tesla could be sufficient to make the term (1.2) comparable with (1.1).