11 ble temperature-dependent effects. The hyperfine A con- stant shows no such dependence and the scatter is less than the uncertainty on the mean. We therefore use the uncertainty on the weighted mean of the data taken at different temperatures to arrive at an uncertainty of 1 kHz for the hyperfine A constant. For the hyperfine B constant we find an 11 kHz uncertainty (from the scatter of the data). A theoretical analysis of the frequency dependence on misalignment similar to that described for the 8S$_{1}$$_{/}$$_{2}$ state analysis yielded a 48 kHz uncertainty for the center-of- gravity frequency and uncertainties of 12 kHz for the hy- perfine A constant and 143 kHz for the B constant. In addition, the effects of misalignment were investigated experimentally. Spectra of the six peaks labeled g , h , i , j , k , and l in Fig. 10 were taken at three different beam alignments. The degree of misalignment was char- acterized by the peak amplitude. Misalignment of the beams so that the peak amplitudes decreased by more than a factor of two resulted in no detectable change in the center-of-gravity, A constant, or B constant. The uncertainties to the center-of-gravity frequency and the hyperfine A constant are summarized in Table I. With the uncertainties from Table I we find the fluorescence spectrum. We superposed that cal- culated spectrum on the experimental spectrum and adjusted the peak intensities to match the isolated 7D$_{3}$$_{/}$$_{2}$ peaks. In this way we accounted for and removed the 7D$_{3}$$_{/}$$_{2}$ parameters. To quantify the influence of the 7D$_{3}$$_{/}$$_{2}$ state and estimate the uncertainty resulting from the overlapped spectra, we fit the spectra with and with- out subtracting the spectrum from the 7D$_{3}$$_{/}$$_{2}$ state. We found a maximum deviation of 10 kHz in the center-of- gravity frequency of the 7D$_{5}$$_{/}$$_{2}$ state, 1 kHz in the hyper- fine A constant, and 30 kHz in the hyperfine B constant which we take to be the uncertainties due to this overlap. The contributions from the two transitions are separated in Fig. 13. For a given ground state hyperfine component F , there are nine distinct transitions due to the manifold of in- termediate states and upper states. The five groups of peaks labeled in Fig. 12 were used to extract values for the center-of-gravity and hyperfine A and B con- stants. In group one, only three peaks were of sufficient amplitude to be fit. All nine peaks were fit in groups three and five. Seven peaks were used in group two and six peaks in group four. From the fit to these 34 peaks we determined the center-of-gravity frequency to be 781 522 153 . 682(25) MHz and the hyperfine A and B constants were − 1 . 717(4) MHz and − 0 . 182(86) MHz, re- spectively. To improve the precision of the fits, we use scans with increasing frequency and decreasing frequency simultaneously. The minimum χ 2 was 90 for 34 peaks prior to normalization. Figure 12 shows the experimental fluorescence spec- tra for excitation of the 7D$_{3}$$_{/}$$_{2}$ and 7D$_{5}$$_{/}$$_{2}$ states through the 6P$_{3}$$_{/}$$_{2}$ state along with the calculated spectra for exci- tation to the 7D$_{3}$$_{/}$$_{2}$ and 7D$_{5}$$_{/}$$_{2}$ states. The spectrum was collected using a 850 nm filter with a 10 nm passband for F1 and a 700 nm filter with a 25 nm passband for F2. The close energy spacing of the 7D$_{3}$$_{/}$$_{2}$ and 7D$_{5}$$_{/}$$_{2}$ states did not allow for a selection of only one of the states when ex- cited through the 6P$_{3}$$_{/}$$_{2}$ state. However, because we were able to determine the 7D$_{3}$$_{/}$$_{2}$ state energy and hyperfine splitting as described in Section IV D, we were able to fix the frequency of the 7D$_{3}$$_{/}$$_{2}$ state from these measure- ments and use the spectrum shown in Fig. 12 to extract information about the 7D$_{5}$$_{/}$$_{2}$ state. In addition, angular momentum considerations result in much stronger tran- sition probabilities for the 6P$_{3}$$_{/}$$_{2}$ → 7D$_{5}$$_{/}$$_{2}$ transition com- pared to the 6P$_{3}$$_{/}$$_{2}$ → 7D$_{3}$$_{/}$$_{2}$ transition. To remove the effect of the overlap, we calculated the 7D$_{3}$$_{/}$$_{2}$ spectrum through the 6P$_{3}$$_{/}$$_{2}$ state using the values determined by the 6S$_{1}$$_{/}$$_{2}$ → 6P$_{1}$$_{/}$$_{2}$ → 7D$_{3}$$_{/}$$_{2}$ excitation. Figure 13 shows the contribution of the transitions to the 7D$_{3}$$_{/}$$_{2}$ to The systematics were studied in the same way as with the previous states. We focused on group four of Fig. 13 due to its size and also the fact that there is very little contribution from the 7D$_{3}$$_{/}$$_{2}$ state for this group. The optical intensity was varied for both stages of the These numbers are in good agreement with previous mea- surements, shown in Table II and lead to a significant improvement in the knowledge of the center-of-gravity frequency. E. Results for the 7D 5 / 2 state A$_{7D}$$_{3}$$_{/}$$_{2}$ = 7 . 386(15) MHz B$_{7D}$$_{3}$$_{/}$$_{2}$ = − 0 . 18(16) MHz . ν$_{6S}$$_{1}$$_{/}$$_{2}$$_{:7D}$$_{3}$$_{/}$$_{2}$ = 780 894 762 . 250(77) MHz FIG. 12: The calculated spectrum (upper trace) of the 7P → 6S fluorescence when the Cs atoms are excited to the 7D 3 / 2 , 5 / 2 state. The experimental signal (lower trace) shows the 7P → 6S fluorescence when the Cs atoms are excited to the both the 7D 3 / 2 , 5 / 2 states through the 6P 3 / 2 state. In the experimental spectrum data are shown for only those regions where there was a signal. 0.774 0.773 0.772 f$_{rep}$ - 1000 MHz [MHz] 7  2 P$^{✍}$ 6  2 S 1/2 Fluorescence from  6  2 S 1 /2 ✎ 6  2 P 3/2 ✏ 7  2 D 3/2, 5/2 Excitation Experiment Calculation Group1 Group2 Group3 Group4 Group5 3 – F'' 3 – F'' 4 – F' ' 4 – F''