Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

with the theoretical value of the radiative lifetime for the F1 L state, s L 1 = 13.3ns, calculated for a 12-A˚ nanocrystal using Eq. (45).In a magnetic field, the angle-dependent decay rates [G 1 (h H , H ), G 2 (h H ,H )] are determined from Eq. (46). The field-dependent decay was thencalculated, averaging over all angles to account for the random orientationof the crystallite ‘‘c’’ axes. The calculation at 10 T (Fig. 8c) used a bulk value ofg e = 0.68 [25] and the calculated value for D (19.4 meV) and g (10.3 meV) for12-A˚ -radius dots. The hole g factor was treated as a fitting parameter becauseits reliable value is not available. This procedure allowed an excellentagreement with the experiment for g h = 1.00. However, the most recentmeasurements of the electron g factor yield g e c 1.4 for NCs of 12 A˚ radius[26], implying that the hole g factors may require a reevaluation.E. Magnetic Circular Dichroism of CdSe NanocrystalsThe splitting of the exciton levels in a magnetic field is usually much smallerthan the inhomogeneous width of optical transitions and it cannot be seendirectly in absorption spectra. However this splitting can be observed inmagnetocircular dichroism (MCD) experiments in which the differencebetween the absorption coefficients, a F , for right and left circular polarizedlight (r F ), respectively, in the presence of a magnetic field can be measuredwith high accuracy. Assuming that the inhomogeneous exciton line has aGaussian shape, one finds for exciton states with identical Zeeman splitting(see e.g., Ref. 40):a MCD ðe; e 0 Þ ¼ a þ ðe; HÞ a ðe; HÞ¼ 2CDe e e 0 1p ffiffiffiffiffir 2 exp2p rðe e 0 Þ 22r 2 !ð52Þwhere C is a constant related to the oscillator strength of the state, De is thefield-dependent Zeeman splitting of the state, r is the inhomogeneous linewidthof the state, and e 0 is the position of the maximum of the transition atzero magnetic field. The MCD signal for a single line should have a typicalderivative shape with extrema separated by 2r. Its intensity is proportionalto the Zeeman splitting of the levels De and grows linearly with magneticfield. To extract the absolute value of the splitting, one can normalize theMCD signal by a SUM = a + + a (this procedure eliminates the unknownconstant C).Equation (52) can also be used for an ensemble of randomly orientedquantum dots. In this case, however, De characterizes the effective averagesplitting of the exciton states in a magnetic field because the Zeeman splittingin each CdSe NC depends on the angle (h H ) between the magnetic field and theCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.