\sqrt{v_{1c}^2-1} \approx v_2 + 2k_{\textrm{AB}}p_D
</math><br>
This occurs when <math>k_{\textrm{AB}}p_D</math> tends to zero, and so <math>v_2=v_3</math>.<br>Setting <math>k_{\textrm{AB}}p_D</math> to zero, amounts to neglecting magnetisation that starts on the ground state ensemble and end on the excited state ensemble and vice versa. <br>This will be a good approximation when <math>p_AG \gg p_B</math>.