Relaxation Of A Two-Level System: Non-Negativity Of Density Matrix And Possibility For Anomalously Long T2

Density matrix equations for the relaxation of a two-level system are studied. Standard dogma, Γik ≥ (γi + γk)/2, about the relaxation constant for the off-diagonal (Γik) and diagonal (γi) matrix elements is verified for the case of up- and down-transitions with high rates w21 and w12. Non-negativity of the density matrix imposes much weaker limitation, Γ21 ≥ (1/2)[(w21)1/2 -(w12)1/2]2. An almost \u27physical\u27 system is suggested, which describes to a certain approximation such decrease of transverse relaxation constant Γ