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A constant of the 9S$_{1}$$_{/}$$_{2}$ state of 

This is in good agreement with the previous measure- ments of this transition, summarized with other data in Table II, and improves on the center-of-gravity frequency by two orders of magnitude. 

The center-of-gravity frequency, magnetic dipole, and electric quadrupole hyperfine coupling constants for the 7D$_{3}$$_{/}$$_{2}$ state were determined from the spectrum in Fig. 10. The filters used in collecting this spectrum were a 890 nm filter with a 10 nm passband for F1 and a 670 nm filter with a 30 nm passband for F2. This spectrum was taken by exciting Cs through the 6P$_{1}$$_{/}$$_{2}$ intermediate state. Use of the 6P$_{1}$$_{/}$$_{2}$ state eliminates possible transi- tions to the 7D$_{5}$$_{/}$$_{2}$ state due to angular momentum se- lection rules. The groups consist of six peaks, corre- sponding to the F → F ′ = 3 → F ′′ = 2 , 3 , 4 and F → F ′ = 4 → F ′′ = 3 , 4 , 5 transitions. The 18 peaks labeled a through r in Fig. 10 were used to extract the frequency and hyperfine coupling constants. 

The 7D state has J > 1 / 2 and, consequently, an elec- tric quadrupole coupling denoted by the hyperfine B con- stant. Minimizing the χ $^{2}$( ν, A, B ) function defined by Eq. (10) with respect to the center-of-gravity frequency and the hyperfine A and B constants, we find a value for the center of gravity of 780 894 762 . 250(28) MHz, a hyperfine A constant value of 7 . 386(6) MHz, and a hy- perfine B constant value of − 0 . 182(50). The χ 2 was 78 for 36 peaks. 

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## D. Results for the 7D 3 / 2 state 

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The systematic effects were studied by focusing on the six peaks labeled g , h , i , j , k , and l in Fig. 10, corre- sponding to transitions from the F = 3 ground state. The laser intensity on both stages of the transition was varied. For the 6S$_{1}$$_{/}$$_{2}$ → 6P$_{1}$$_{/}$$_{2}$ stage, the change in inten- sity ranged from ≈ 19W/cm 2 to ≈ 3W/cm $^{2}$, spread over ≈ 4000 optical modes within the 10 nm (3.8 THz) filter bandwidth. The slope of the center-of-gravity frequency as a function of light power yields a dependence of 22(27) kHz (Fig. 11), corresponding to an uncertainty of 49 kHz. We find uncertainties due to ac-Stark shifts of 14 kHz for the A constant and 17 kHz for the B constant. 

No effect of the external magnetic field was observed (Fig. 11), within the measurement uncertainties. Based on the scatter of the data, we assign uncertainties of 17 kHz, 3 kHz, and 17 kHz for the center-of-gravity fre- quency, the hyperfine A constant and the hyperfine B constant, respectively. 

Spectra were taken at four different temperatures of the vapor cell, corresponding to a Cs vapor pressure of 0.15, 0.2, 0.3, and 2.0 mPa. As with the 9S$_{1}$$_{/}$$_{2}$ state, there appears to be a small dependence of the center-of-gravity frequency as a function of the pressure in the cell, lead- ing to a 28 kHz shift when the pressure is increased by a factor of ≈ 10. However, since we fix the A and B constants, this serves as a maximal shift in the center-of- gravity frequency and we do not attempt to correct for this shift. We take the standard deviation as a conser- vative estimate of the error and assign an uncertainty of 12 kHz to the center-of-gravity frequency due to possi- 

