Observation of the 171 , 173 YbOH spectra

Chapter V: Spectroscopy of Odd Isotopologues, 171 , 173 YbOH

5.4 Observation of the 171 , 173 YbOH spectra

red (^𝑂𝑃₁₂ and^𝑂𝑃_1𝐺) and blue (^𝑅𝑅₁₁ and^𝑅𝑅_1𝐺) of the band head. As discussed in the previous section, the small isotope shifts result in the even isotoplologue^𝑃𝑃₁₁,

𝑃𝑄₁₂, ^𝑄𝑄₁₁, and ^𝑄𝑅₁₂, and odd isotopologue ^𝑃𝑃_1𝐺 +^𝑃 𝑄_1𝐺, and ^𝑄𝑄_1𝐺 +^𝑄 𝑅_1𝐺 branches to be severely overlapped (Fig. 5.3).

21.05 21.10 21.15 21.20 21.25 21.30 21.35 21.40 21.45 21.50

* *

LIF signal

Laser Wavenumber (cm ) -17300 -1

170YbOH

171YbOH

172YbOH

173YbOH

176YbOH

174YbOH

All

G=0 G= 1

G=2 G=3 Obs.

Figure 5.5: Observed molecular beam LIF spectra and calculated predictions of the^𝑂𝑃₁₂(3) even isotopologue and^𝑂𝑃_1𝐺 odd isotopologue branch features of the 𝐴˜²Π_1/2(0,0,0) −𝑋˜²Σ⁺(0,0,0)band of YbOH. The even isotopologue spectrum was predicted using the optimized parameters (or isotopically scaled values) given in Ref. [116]. The predicted^171,173YbOH spectra were calculated using the optimized parameters determined in this study and given in Table 5.1. A temperature of 15 K and Lorentzian full width at half maximum (FWHM) of 30 MHz was used for all predictions. The lines marked with * are unidentified. This figure was reproduced from Ref. [129] with permission from AIP.

The molecular beam LIF data and calculated spectrum in the region of the even

𝑂𝑃₁₂(3) and odd^𝑂𝑃_1𝐺(3) lines is shown in Fig. 5.5. The calculated spectrum for the even^172,174YbOH isotopologues were obtained using the optimized parameters given in Ref. [116], while for the even^170,176YbOH isotopologes these parameters were scaled by their expected isotopic dependence. The calculated spectrum for the

odd isotopologues was obtained using the optimized parameters determined in this study and given in Table 5.1. For all calculated spectra, a rotational temperature of 15 K and a Lorentzian line shape with a full width at half maximum (FWHM) of 30 MHz was used.

For a Hund’s case (b𝛽𝑆) state, the Fermi contact hyperfine interaction has only diagonal matrix elements which are given by [140]

⟨(𝑆 𝐼_{𝑌 𝑏})𝐺 ,(𝐺 𝑁)𝐹|𝑏_𝐹I·S| (𝑆 𝐼_{𝑌 𝑏})𝐺 ,(𝐺 𝑁)𝐹⟩

= 𝑏_𝐹

2 [𝐺(𝐺+1) −𝐼(𝐼+1) −𝑆(𝑆+1)],

(5.1)

where here we have neglected the effects of the proton nuclear spin as they are unresolved in the spectrum. For a²Σ⁺state (the ground state of the odd isotopologues of YbOH) the quantum number𝐺 takes two values,𝐺₁=𝐼+𝑆and𝐺₂= 𝐼−𝑆, and the Fermi contact interaction splits these two states by ^𝑏₂^𝐹[𝐺₁(𝐺₁+1) −𝐺₂(𝐺₂+1)]. This splitting results in the separation of the^𝑂𝑃₁₀(3)and^𝑂𝑃₁₁(3)lines of¹⁷¹YbOH by∼ 𝑏_𝐹 ∼+6750 MHz and the^𝑂𝑃₁₂(3)and^𝑂𝑃₁₃(3)lines of¹⁷³YbOH by∼ 3𝑏_𝐹 ∼ -5660 MHz. Additionally, the ordering of the energy levels of different𝐺 values is opposite in¹⁷³YbOH compared to¹⁷¹YbOH, with the lower𝐺 states (𝐺 =0) lower in energy in¹⁷¹YbOH while the higher𝐺states (𝐺 =3) lower in energy in¹⁷³YbOH.

The opposite ordering is due to the opposite sign of the nuclear magnetic moments of the ¹⁷¹Yb and ¹⁷³Yb nuclei. This is reflected in the opposite ordering of the

𝑂𝑃_1𝐺(3)lines in Fig. 5.5 (states lower in energy result in higher energy transitions).

The splitting between the ^𝑂𝑃_1𝐺(𝑁^′′) (and also the ^𝑅𝑅_1𝐺(𝑁^′′)) branches remains constant for different values of𝑁^′′since the energy splitting from the Fermi contact interaction remains constant over all rotational states.

As discussed in Section 5.3 and shown in Fig. 5.3, the bandhead region of the YbOH spectrum is dominated by the^𝑃𝑃₁₁,^𝑄𝑄₁₁,^𝑃𝑄₁₂, and^𝑄𝑅₁₂even isotopologue branch features. The dominance of the even isotopologues makes the observation and as- signment of the odd isotopologue^𝑃𝑃_1𝐺 +^𝑃𝑄_1𝐺 and^𝑄𝑄_1𝐺 +^𝑄 𝑅_1𝐺 branch features nearly impossible. Therefore, utilizing the chemical enhancement technique, de- scribed in Section 5.3, proved critical in the measurement of the odd isotopologue branch features in the band head region. The observed and predicted high-resolution absorption spectrum of the cryogenic buffer gas cooled (CBGC) sample in the band- head region is presented in Fig. 5.6. Fig. 5.6ais the spectrum with no enhancement light (same as Fig. 5.3), while Fig. 5.6b is the spectrum with the enhancement light applied and on resonance with the atomic¹⁷³Yb transition. The enhanced pro-

duction due to the atomic excitation provides approximately a factor of 4 increase in the¹⁷³YbOH signals. The difference between the enhanced and non-enhanced spectra (b-a) is presented in Fig. 5.6c and is the spectrum of only the ¹⁷³YbOH isotopologue. The prediction of the¹⁷³YbOH spectrum in this region is presented in Fig. 5.6d. The prediction was made using the optimized parameters determined in this study (Table 5.1), a rotational temperature of 5 K, and a 90 MHz FWHM lineshape. A comparison of Fig. 5.6aandcshows that the chemical enhancement technique developed here provides a significant simplification of the observed spec- trum as well as an improvement in the signal to noise ratio. While the chemical enhancement technique allowed the isolation of the¹⁷³YbOH spectrum, the spectral features presented in Fig. 5.6care still a blend of many lines. The feature marked

"A" in Fig. 5.6 is primarily a blend of the ^𝑃𝑃₁₂ +^𝑃𝑄₁₂(1) (𝐹^′′

1 = 3 → 𝐹^′

1 = 3) and^𝑃𝑃₁₂+^𝑃𝑄₁₂(2) (𝐹^′′

1 =4 → 𝐹^′

1 =4) ¹⁷³YbOH transitions. The feature marked

"B" in Fig. 5.6 is primarily a blend of the ^𝑃𝑃₁₂ +^𝑃𝑄₁₂(3) (𝐹^′′

1 = 5 → 𝐹^′

1 = 5),

𝑃𝑃₁₂ +^𝑃 𝑄₁₂(1) (𝐹^′′

1 = 2 → 𝐹^′

1 = 3), and ^𝑃𝑃₁₂ +^𝑃 𝑄₁₂(3) (𝐹^′′

1 = 4 → 𝐹^′

1 = 4)

173YbOH transitions.

The high-resolution absorption spectrum in the bandhead region is also presented in Fig. 5.7. Fig. 5.7ais again the spectrum without chemical enhancement but now Fig. 5.7bis the spectrum with chemical enhancement of¹⁷¹YbOH via the excitation of the 𝐹^′′ =1/2 → 𝐹^′ =1/2 ³𝑃₁−¹𝑆₀ ¹⁷¹Yb transition. The difference between the enhanced¹⁷¹YbOH and unenhanced spectrum (a-b) is shown in Fig. 5.7c, this is the spectrum from only the¹⁷¹YbOH isotopologue. A prediction of the¹⁷¹YbOH spectrum in the bandhead region is presented in Fig. 5.7d. Here, the prediction was also made using the optimized parameters given in Table 5.1, a rotational temperature of 5 K, and a 90 MHz FWHM lineshape. The¹⁷¹YbOH bandhead at 17323.55 cm⁻¹ is an unresolved blend of the^𝑃𝑃₁₁+^𝑃𝑄₁₁(1),^𝑃𝑃₁₁+^𝑃𝑄₁₁(2), and^𝑃𝑃₁₁+^𝑃𝑄₁₁(3) features. In contrast to the¹⁷³YbOH spectrum (shown in Fig. 5.6c), the¹⁷¹YbOH spectrum has several unblended features in the bandhead region. For example the feature labeled "A" in Fig. 5.7 is the^𝑄𝑄₁₁+^𝑄 𝑅₁₁(1) (𝐹^′′

1 =1→ 𝐹^′

1=1)transition, the feature labeled "B" is the^𝑃𝑃₁₁+^𝑃𝑄₁₁(5) (𝐹^′′

1 =5→ 𝐹^′

1 =5)transition and the feature marked "C" is the^𝑄𝑄₁₁+^𝑄 𝑅₁₁(2) (𝐹^′′

1 =2→ 𝐹^′

1=2)transition.

Though the odd isotopologue^𝑅𝑅_1𝐺branch features are relatively isolated (similar to the^𝑂𝑃_1𝐺features shown in Fig. 5.5), recording the chemically enhanced absorption spectrum proved critical for the disentanglement and assignment of the branch features in this region as well. The disentangling of the¹⁷¹YbOH ^𝑅𝑅₁₁(2) lines is

demonstrated in Fig. 5.8. The left side of Fig. 5.8 presents the molecular beam LIF in the region of the even isotopologue^𝑅𝑅₁₁(2) and odd isotopologue^𝑅𝑅_1𝐺(2) lines. The right side of Fig. 5.8 presents the CBGC absorption spectrum in this same region. The predicted spectrum presented in Fig. 5.8 used the optimized YbOH parameters, rotational temperatures of 15 K and 5 K, and FWHM linewidths of 30 MHz and 90 MHz for the molecular beam LIF and CBGC absorption spectra respectively. Fig. 5.8a is the CBGC absorption spectrum with no enhancment light, while Fig. 5.8b,c, anddare the absorption spectra with¹⁷⁶YbOH,¹⁷⁴YbOH, and¹⁷¹YbOH enhancement respectively. Each isotopologue is enhanced by driving the³𝑃₁−¹𝑆₀ transition of each respective Yb isotope (¹⁷⁶Yb, ¹⁷⁴Yb, and¹⁷¹Yb).

The pure ¹⁷¹YbOH spectrum is shown in Fig. 5.8e and was obtained by taking the difference of the enhanced and unenhanced spectra, d-a. The pure ¹⁷¹YbOH spectrum in Fig. 5.8ereveals a small¹⁷¹YbOH feature that was obscured in the high- resolution LIF data by the much stronger¹⁷⁴YbOH^𝑅𝑅₁₁(2)line. This illustrates the power and ability of the novel chemical enhancement based spectroscopic technique to produce model-independent isolation of the¹⁷¹YbOH spectrum.

A total of 94 spectral features of the ˜𝐴²Π_1/2(0,0,0)−𝑋˜²Σ⁺(0,0,0)band of¹⁷³YbOH were measured and assigned to 128 transitions. The measured transition wavenum- bers, assignments, associated quantum numbers, and the difference between the observed and calculated transition wavenumbers are given in Table A.2 in Appendix A. A total of 65 spectral features of the ˜𝐴²Π_1/2(0,0,0) − 𝑋˜²Σ⁺(0,0,0) band of

171YbOH were measured and assigned to 70 transitions. The measured transition wavenumbers, assignments, associated quantum numbers, and the difference be- tween the observed and calculated transition wavenumbers are given in Table A.3 in Appendix A.