Ben Chen(陳犇), Yi-Ni Chen(陳旖旎), Jia-Nuan Pan(潘佳煖),

Jian-Ping Yin(印建平), and Hai-Ling Wang(汪海玲)?

State Key Laboratory of Precision Spectroscopy,East China Normal University,Shanghai 200241,China

Keywords: spectroscopic parameters,Franck-Condon factors,an eEDM candidate,lifetime

1. Introduction

Heavy polar diatomic molecule, PbF, with a single unpaired electron and a larger internal electric field (Eeff), is a valuable and sensitive candidate for measuring the electron electric dipole moment(eEDM)accurately.[1-3]Spectroscopic experimental study of open shell state of PbF is required for implementing the precise eEDM measurement.

The preliminary study of the B-X1emission spectrum of PbF was first conducted by Rochester in a carbon tube furnace in 1938.[4]Reddy and Rao have photographed the B-X2subsystem in the 2ndorder of a 21-ft(1 ft=3.048×10-1cm-1)concave grating spectrogram,but in their spectra the fine structure is not well-resolved.[5]Later,Singh and Singh determined the rotational constants of the upper and lower states,B and X2states.[6]In 1977, Lumley and Barrow studied the rotational transitions of the B-X1system of PbF in a King furnace by the spectrograph method and gave the rotational constants for the B and X1states.[7]In 1985,Balasubramanian used the relativistic configuration interaction approach to calculate the lowlying states of PbF and gave the associated potential curves.[8]In 1992, Chen and Dagdigian produced PbF by reacting Pb atoms with F2molecules, detected the B-X spectrum of PbF by laser-induced fluorescence method,and made a rough estimate of the lifetime of the B state.[9]Ziebarthet al.studied the high-resolution emission spectra of PbF in X22 Π3/2-X21 Π1/2transition.[10]In addition, the radiative lifetime of the B state of PbF and the average transition dipole moment of B-X1transition were given by McRavenet al.[11]In 2010,McRavenet al.used resonance enhanced multi-photon ionization(REMPI)technique to measure the rotational spectra of the B,D,E,and F states of208PbF,and determined spectroscopic constants for these states and for the isotopologues206PbF and207PbF[12]as well. In a recent study, Baturoet al.reported the electricfield-dependentgfactor of207,208PbF’s lowest rotational energy level through experimental measurements and theoretical calculations, and gave the optimal electric field of eEDM measurement.[13]However, the reported spectral data of BX1transition of PbF are still meager. Only partial parameters of PbF in B state were given by above studies,the rovibronic spectra and structures of the PbF B-X1transition still need studying further.

In this work, the spectra of (0, 0) and (1, 0) bands of PbF in B-X1transition are recorded and analyzed to obtain the rovibronic structure and spectral constants of the B state and X1state. Also,the FCFs of the transitions between the vibrational levels of the B-X1transition and the potential energy curves of B and X1states are calculated by the Morse potential method[14]and RKR/LEVEL[15-20]methods.

2. Experiment setup

In the present work, the laser ablation and laser induced fluorescence techniques were used for generating PbF radical and measuring the spectrum of PbF in the range of 260 nm-285 nm. The details of the experimental setup are described in the following.

The PbF molecular beam was produced by the reaction of Pb plasma with CF4gas. The ablation laser with a wavelength of 1064 nm and the laser output energy of～1 mJ was focused on～0.5 cm above the rotating and translating Pb metal rod through a lens with a focal length of 30 cm to generate Pb plasma. The reaction gases(10%CF4gas mixing with argon carrier gas in volume)were ejected into the reaction chamber from the pulse valve and reacted with the Pb plasma at a distance of 1 cm from the pulse valve to generate PbF molecular beam.

The fluorescence spectrum of B2Σ+-X21 Π1/2transition of the PbF molecules was excited by an excitation laser at a distance of 30 cm from the ablation point. The excitation laser was an Nd:YAG laser pumped dye laser with a typical linewidth of 0.04 cm-1for the fundamental beam. The diameter of the excitation laser beam in the detection chamber was～1 mm. Typical laser pulse energy for detecting the B2Σ+-X21 Π1/2transition of PbF was～0.5 mJ.Typically,the static pressure and the dynamic pressure of the reaction chamber were 3.5×10-6Pa and 5.0×10-3Pa,respectively. The static pressure and the dynamic pressure of the detection chamber were 2.0×10-6Pa and 2.0×10-4Pa,respectively.

The laser excited fluorescence signal was collected with a lens telescope system onto a photomultiplier. The signal from the photomultiplier was directed to a gated integrator. A 1-GHz digital oscilloscope was used to measure the radiative lifetime of thev＇=0 level and thev＇=1 level of PbF B2Σ+state.

The wavenumbers of the spectral lines were calibrated by a calibrated wavemeter.

3. Results and discussion

The B-X1transition of PbF is expected to be the2Σ+-2Π1/2transition,each band has six branches. Figure 1 shows the schematic diagram of energy level transitions between the2Σ+state and2Π1/2state. These six branches are denoted as Q21,Q1,P21,R1,P1,and R21.

As shown in Fig.1,the allowed transitions are those with ΔJ=0,±1. Transitions for which ΔJ=J＇-J＇＇=-1 belongs to the P-branch, ΔJ=J＇-J＇＇= 0 the Q-branch, and ΔJ=J＇-J＇＇=+1 the R-branch.

Fig.1. Schematic diagram of energy levels of B-X1 transition of 208PbF.

The heavy-metal nature of Pb is reflected clearly in the large spin-orbit splitting in the ground electronic state. The predominant electronic configuration of the X state is found to beσ2π4π?. The large spin-orbit splitting in the X state arises from electron occupation in theπ?orbital. The Hamiltonian of the ground state,X21 Π1/2,can be expressed as

wherevJ＇＇p＇＇,J＇p＇is the transition frequency between the upper stateJ＇p＇and the lower stateJ＇＇p＇＇, and given in Eq. (6);Sis the relative transition dipole moment between the upper state and the lower state,symbol＇＇and symbol＇represent the upper state and lower state,respectively.

From Eqs.(4)and(5),the calculated relative intensity of Q21branch is around twice stronger than that of the P1branch and the R21branch, and the intensity of the P1branch and R21branch are almost similar to each other.

The B2Σ+-X21 Π1/2transition of the PbF molecule is a perpendicular transition as deduced by Lumley and Barrow.[7]Figure 2 gives the recorded experimental and simulated spectra of the PbF B2Σ+-X21 Π1/2(1,0)and(0,0)bands,respectively.

As shown in Fig. 2, the simulated spectra of (0, 0) and(1, 0) are in good agreement with the experimental ones.The recorded experimental spectra of the (0, 0) and (1, 0)bands of the B-X1system are both double-headed. The spectra features have a sharp cut-off in intensity at the lowest transition frequency, and a gradual loss. The spectra are blue-degraded, thus the rotational constants are inequal:B＇(B2Σ+)＞B＇＇(X 21 Π1/2).

The relatively weak spectra on the left-side of(0, 0)and(1, 0) bands belong to the P1branches, the ones in the middle are mainly for the Q branch and Q21branch,and the ones on the right side are for the R branch and R21branch. However, under our present experimental conditions only three branches,P1,Q21,and R21,are resolvable. From the recorded spectra (Fig. 2), the intensity of experimentally measured P1branch and R21branch are weaker,the intensity of Q21branch is approximately twice stronger than that of the P1branch and the R21branch. These are consistent with our calculated values from Eq.(5).

Fig. 2. Experimental (red) and simulated (black) LIF excitation spectra of PbF B2Σ+-X 21 Π1/2 transition for(a)(0,0)band and(b)(1,0)band.

The rovibronic spectra of these two bands, (0,0) and(1,0) (in Fig. 2), are simulated using Pgopher program.[23]The rotational and fine structure constants are determined by directly fitting the experimental data of each band. The derived spectral parameters of the B and X1states are given in Table 1.

Table 1. Spectral parameters of B2Σ+ states and X 21 Π1/2 states of 208PbF(in units of cm-1).

In Herzberger’s book, it is mentioned that the B state of PbCl and PbBr is easy to predissociate and assigned as a diffuse band.[24]According to our measurement, the B state of PbF has a short lifetime. It may also be caused by predissociation similar to the case for the B state of PbCl and PbBr. In the present work,we also find that we can excite PbF from its X1state to B state by using much lower laser energy than from its X1state to A state. It is because the oscillator strengths of the corresponding band systems are relatively great.[9]

Fig.3.Decay profile for excitation of(a)v＇=0 level and(b)v＇=1 level of the B state of PbF,with black dots denoting measured experimental decay data,and red solid lines referring to fitting curves.

Figure 3 displays a typical decay profile for excited B state of PbF molecule. The contributions due to the laser scattered light from the excitation laser and the ablation laser are eliminated in the decay profile which is shown in Fig.3. The fluctuation of the decay profile results from the fluctuation of the laser output power.

The best fits yielded lifetimes for the B statev＇=0 andllevels are 11.90 ns and 10.51 ns, respectively. The duration of the probe laser pulse and the response time of the photomultiplier in the present experiment are both～10 ns. It was shown in Ref.[9]that the lifetime for thev＇=0 level and thev＇=1 level are 3.6±0.4 ns and 6.6±0.4 ns, respectively. It was estimated in Ref.[11]that the lifetime of the B state is less than 2 ns.To accurately measure the lifetime of the vibrational level of the B state,a laser with a narrow band width or a CW laser,and a rapid response detector are needed.

The potential energy curve of B state is calculated by the Morse potential and RKR/LEVEL methods,and the obtained results are shown in Fig.4. The calculated FCFs of the B-X1transition are shown in Table 2.The calculated FCFs by Morse potential and RKR/LEVEL methods are consistent with each other. The calculated results show that the intensity of the(0,0)band and the(1,0)band are similar.The transition intensity of(2,0)is around half that of the(0,0)and the(1,0).

Fig.4. Calculated potential energy curves of PbF X1 state and B state by Morse potential(red line)and RKR/LEVEL(black line)methods.

Table 2. Calculated Franck-Condon factors of PbF B2Σ+-X 21 Π1/2 transition.

4. Conclusions

In this work,the laser ablation technique combining with the chemical reaction method is used to produce PbF radicals.The rovibronic spectra of(0,0)and(1,0)bands of PbF B2Σ+-X21 Π1/2transition in a range of 260 nm-285 nm is detected by the laser induced fluorescence method. The rovibronic molecular parameters of the X1state and B state are derived by analyzing the recorded spectra of the(0,0)and(1,0)bands of PbF B2Σ+-X21 Π1/2transition. Also,the lifetimes of B(v＇=0,1)state are discussed from the fluorescence decay spectra. Finally, based on the obtained results in the present work, the Franck-Condon factors of B-X1transition of PbF are calculated and compared with that obtained by the Morse potential and RKR/LEVEL methods.

Acknowledgement

Project supported by the National Natural Science Foundation of China(Grant Nos.11674096 and 11874151).