For the case of a no-inside-gain particle, i.e. no energy is emitted by the particle internally ( σ σ abs > 0 ), we have a particular case of the Optical theorem 1 4 π π ε ε ε ε 0 ℑ ℑ ( α α e ) + 1 4 π π μ μ μ μ 0 ℑ ℑ ( α α m ) ≥ ≥ 2 k 3 3 [ | α α e | 2 ( 4 π π ε ε ε ε 0 ) 2 + | α α m | 2 ( 4 π π μ μ μ μ 0 ) 2 ] Equality occurs for non-absorbing particles, i.e. for ℑ ℑ ( ε ε ) = ℑ ℑ ( μ μ ) = 0 .