Additions and Corrections
6460 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
where Nj, is the density of centers within a homogeneous line width of the laser frequency in wavenumbers (cm-I), IYo, ( ~ ( 5 is ~ )the absorption coefficient at the laser frequency, T2is the homogeneous transverse relaxation time given by the usual formula Tz.= 2/ PAY^^^^,^^^^), c is the speed of light, NtOt is the (total) density of absorbers producing the integrated absorption for the vibronic transition Sbt, n is the index of refraction, L = [(n2 + 2)/312, and ii is the dipole moment for the vibronic transition under consideration. (This relation may be easily generalized for nonisotropic hosts.) Since the dipole moment is independent of temperature, this equation is stating the fundamental fact that all the temperature dependence in n is in T2. Equation 2 may be written in the following useful forms if either the oscillator strength or the integrated extinction coefficient is known: u =
-( -$= ?Se(?) 2ae2T2 L cme
4606cTz d?
(3)
wherefis the oscillator strength, e is the electron charge, me is the electron mass, e is the room-temperature extinction coefficient in L/(mol cm), and the integral is performed over the entire (vibronic) line for the transition. (If the vibronic structure cannot be resolved, this formula must be generalized.) The last equality from the integrated is the result of computing the value of Stot/Ntot extinction coefficient. We note that calculation of u from eq 3 differs from the formula for the room-temperature cross section by a factor on the order of the ratio of the inhomogeneous width to the homogeneous width, a factor which may be as large as lo3 or larger in some systems.
To illustrate, these formulas may now be applied to the data for quinizarin in boric acid at 1.4 K in Figure 1. The initial growth rate of the sample transmission is dT/dt = 0.015/s. Using a measured, low-power hole width of 835 MHz and measurements of the integrated absorption coefficient, T2 = 7.6 X s and therefore u = 6.4 X cm2. Thus, using eq 1, the efficiency 7 may be computed to be 2 X 10". If a room-temperature value for n had been used, the value for the quantum efficiency would have been on the order of unity, which is unphysical for this system. In a similar fashion, we have found that for 1,4-diaminoanthraquinone in boric acid the fwhm hole width extrapolated to zero whereas burning intensity at 1.4 K is 2.0 GHz, and 7 = 4 X for resorufin in poly(viny1 alcohol) at the same temperature the fwhm hole width is 2.4 GHz and 7 = 8 X lom6. It is hoped that with the publication of standard methods for the computation of 7 presented in this paper, future measurements of 7 will be able to be consistently compared with previous determinations of this important parameter. Acknowledgment. This work was supported in part by the Office of Naval Research. Registry No. Quinizarin, 81-64-1; boric acid, 11 113-50-1; 1,4-diaminoanthraquinone,128-95-0;resorufin, 635-78-9;poly(viny1 alcohol), 9002-89-5. 'IBM World Trade Visiting Scientist on leave from The Institut fur Physikalische Chemie der Universitat Miinchen, West Germany. IBM Postdoctoral Fellow.
*
ZBM Research Laboratory San Jose, California 95193
Received: August 9, 1984
ADDITIONS AND CORRECTIONS 1984, Volume 88
R. Lu, J. B. Halpern,* and W. M. Jackson: Photodissociation of C2N2,ClCN, and BrCN in a Pulsed Molecular Beam. Page 3423. In Figures 8 and 9 the dimensions of the impact parameter were misstated as nanometers, rather than the correct cm or lo-" m. The abscissas of Figures 8 and 9 should be changed to read the following: Impact Parameter X lo-" m. Page 3424. Paragraph 2. The units of the values of the impact parameter quoted in this paragraph should be changed to read as lo-" m. Note that this error does not affect the value of sin cy calculated from eq 11 and the discussion which follows.
W. E. Moerner* M. Gehrtzt A. L. Hustont
