Rotational Analysis of A2Πu-X2ΠgSystem ofCation

Jing Zhang,Yuan-yue Zhu,Lun-hua Deng,Yang-qin Chen

State Key Laboratory of Precision Spectroscopy,and Department of Physics,East China Normal University,Shanghai 200062,China

(Dated:Received on September 4,2013;Accepted on November 18,2013)

Rotational Analysis of A2Πu-X2ΠgSystem ofCation

Jing Zhang,Yuan-yue Zhu,Lun-hua Deng?,Yang-qin Chen

State Key Laboratory of Precision Spectroscopy,and Department of Physics,East China Normal University,Shanghai 200062,China

(Dated:Received on September 4,2013;Accepted on November 18,2013)

The Doppler-limited absorption spectrum ofcation was observed in the region of 11385-12100 cm-1by optical heterodyne velocity modulation absorption spectroscopy (OH-VMS).The transitions were assigned to the(2,19),(3,20),and(5,21)bands in the second negative system(A2Πu-X2Πg).All the available lines measured using OH-VMS were global f i tted in a nonlinear least-squares f i tting procedure,and precise molecular constants(Bv,Av,Dv,pv,qv,γv)were obtained for the involved levels.

Oxygen molecule cation,Second negative system,Rotational resolution

I.INTRODUCTION

The oxygen molecule and its ions()have been extensively studied.The singly ionized molecular ionhas four allowed electric dipole transitions in its low-lying electronic states:the f i rst negative(b4Σga4Σu)system,the second negative(A2Πu-X2Πg)system,the Hopeld(c4Πu-b4Πg)system,and the(B2Σg-A2Πu)system.

In this work,we mainly focused on the second negative system of16O2+.The earlier experimental observation of this system was carried out by Stark in 1914[1]and was identif i ed until the work of Stevens in 1931[2].After that,Albritton et al.obtained a series of molecular constants of the states involved in the system through performing a least-squares f i tting of 11 bands[3].Later,a summarization was made by Huber et al.[4].In 1984,Coxon and Haley[5]combined their data obtained from grating spectra with those of Colbourn and Douglas[6]performed a comprehensive least-squares analysis,merged constants were reported. Kong and Hepburn observed high vibrational levels (υ00=6-24)in the X2Πgstate ofusing a coherent extreme ultraviolet(XUV)[7].In 1997,Prasad et al. studied the second negative system using Fourier transform emission spectroscopy in the 15945-30210 cm-1region and a set of equilibrium constants was obtained [8].Using pulsed f i eld ionization photoelectron technique,Song et al.studied the spectrum ofin the 12.05-18.15 eV range and determined the Dunhamtype expansion coefficients for vibrational,rotational, and spin-orbit splitting constants[9].Thetransition has been the subject of several more recent spectroscopic studies.Zheng et al.observed high resolution spectrum of many bands in the16O2+second negative(A2Πu-X2Πg)system using optical heterodyne velocity modulation spectroscopy(OH-VMS)[10,11]. Li et al.measured the spectrum of two bands((8,0) and(8,1))in the A2Πu-X2Πgsystem using the laserinduced f l uorescence technique[12].Although the resolution is relatively lower(～0.2 cm-1),the lines are the only available ones related to the A2Πu(υ0=8)and the X2Πg(υ00=0,1)vibrational levels.

In this work,we study our new observation of the absorption spectrum ofin the 11385-12100 cm-1region.We performed a global f i tting of all the available rotational resolution lines of second negative system ofstudied by optical heterodyne velocity modulation spectroscopy.A total of 1045 lines were included in our global f i tting to determine 48 molecular constants.

II.EXPERIMENTS

The experimental setup has been detailedly described in our previous work[13].A mixture of16O2(3 Pa) and He(560 Pa)f l owed continuously in the absorption cell.The gas was discharged at the current of 300 mA (peak to peak)at 23 kHz.The incident laser beam was frequency-modulated with an electro optical modulator (EOM)driven at 480 MHz.The acquired signal from a detector was f i rst demodulated by a double-balance mixer at a frequency of 480 MHz and further demodulated by a lock-in amplif i er at 23 kHz.The wavelength of the laser beam was determined by an attached wavemeter of the laser system and further calibrated by the iodine spectrum[14]using an additional iodine reference absorption cell.

III.SPECTRAL ANALYSIS AND RESULT

The involved two electronic states X2Πgand A2Πuin the second negative system ofbelong to Hund’s case(a)and Hund’s case(b),respectively.The same2Π case(a)matrix elements for the two states were employed in Refs.[5,8,10-12].The ADand γυcannot be determined simultaneously without isotopic parameters.Generally one of them was f i xed to zero and the other was f i tted.Prasad et al.f i xed γυat zero to f i t AD[8]while Coxon et al.f i xed ADto f i t γυ[5].We f i t γυin this work.For each vibrational level,the constants of Tυ,Aυ,Bυ,Dυ,pυ,qυ,and γυare f i tted.Using OH-magnetic rotational(MR)-VMS,Zheng et al.recorded the(2,18),(4,20),(6,20),(3,18),(3,19),and(4,19)bands in the16O2+second negative(A2Πu-X2Πg) system[10,11].In this work,the(2,19),(3,20),and (5,21)bands are newly measured and the(4,20)band was re-measured.The wavenumbers of rotational lines in these bands are shown in Tables I-IV.All the above bands except(5,21)are included in a global f i tting using the PGOPHER[15].

TABLE I Wavenumbers(in cm-1)of rotational lines in the(4,20)band of the second negative system for16O2+.Numbers in the parentheses indicate(νcal.-νobs.)×104cm-1.

TABLE II Wavenumbers(in cm-1)of rotational lines in the(2,19)band of the second negative system for16O2+.

Figure 1 shows the interconnections of the vibrational levels.The new measured bands make the vibrational levels have good interconnection and make the global fi t reasonable.The(5,21)is individual fi tted since υ0=5 and υ00=21 levels do not have good interconnection with the other levels.

TABLE III Wavenumbers(in cm-1)of rotational lines in the(5,21)band of the second negative system for16O2+.

What should be mentioned is that when υ0≤6,the branches’names are dif f erent from those exported from PGOPHER and the subscript lable i of Pijand Rijbands should be changed.For example,the P22band in PGOPHER corresponds to the actual P12band.All the lines are f i tted with the same weight and the standard deviation of the global f i tting is 0.0043 cm-1,which is less than the experimental uncertainty of 0.007 cm-1. The estimated constants along with one standard deviation errors are listed in Table V for the X2Πustate and in Table VI for the A2Πustate,respectively.In Table V,the constants for υ00=18,19,20 came from the global f i tting with Tυ00=18f i xed at the value in Ref.[8]. In the previous analysis[10,11],the line positions areweighted according to(νcal.-νobs.).Since the experimental uncertainties are the same for all the lines,the line positions were not weighted in this work.The precision is almost the same as the previous result and the constants are consistent with the previous ones(in 3σ).The(4,20)band is corrected and the(3,20)band was added and thus the constants for υ00=20 should be more reliable.In Table VI,the constants for υ0=2,3, 4,6 come from the global fi tting.We fi t γυand fi xed ADat zero as Coxon et al.did[5].The precision of our constants is better than Coxon et al’s.Prasad et al.[8] fi tted the constants for υ0=2,3,4,5 using Coxon et al’s line positions,they fi tted ADand fi xed γυat zero for these levels.Though our line positions are obtained at higher resolution,our precision is close to Prasad et al.’s [8].The reason is that Prasad et al.’s line positions have bigger rotational numbers(＞30.5)than ours(≈22.5). The(5,21)band including 106 lines is fi tted and the reported standard deviation is 0.0058 cm-1.The constants of υ00=21 are newly reported and the constants of υ0=5 are consistent with those in Refs.[5,8].

TABLE IV Wavenumbers(in cm-1)of rotational lines in the(3,20)band of the second negative system for16O2+.

TABLE V Molecular constants(in cm-1)forstate of

TABLE V Molecular constants(in cm-1)forstate of

aConstants for υ00=18,19,20 based on the global f i tting and constants for υ00=21 based on the individual band f i t.bValue was f i xed.cNumbers in parentheses denote one standard deviation in unit of the last quoted digit.

Constantsaυ00=18υ00=19υ00=20υ00=21 Tv29659.556b30940.53921(72)c32187.4863(12)33399.4523(13) Bv1.3166795(100)1.29491084(973)1.2728851(127)1.2506177(508) Av182.54985(72)180.89079(55)179.11935(81)177.2018(14) γv×1023.527(22)4.036(16)4.537(34)5.176(67) pv×1021.6250(90)1.6118(74)1.5826(86)1.492(34) qv×1040.857(95)0.736(74)0.30(17)2.24(54) Dv×1066.3610(119)6.4737(114)6.594(21)6.9781(853)

FIG.1 Interconnections of the vibrational levels.Solid lines show the bands adopted from the Refs.[10,11]and the dashed lines show the bands measured in this work.The (5,21)band was not included in the global f i tting.

IV.CONCLUSION

V.ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China(No.11004062).

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TABLE VI Molecular constants(in cm-1)for A2Πustate of

TABLE VI Molecular constants(in cm-1)for A2Πustate of

aNumbers in parentheses denote one standard deviation in unit of the last quoted digit.bValue was f i xed at the one of Ref.[8].

Constantsυ0=2υ0=3υ0=4υ0=5υ0=6 TvFitted42734.83370(76)a43551.85147(59)44341.59584(91)45103.6477b45839.3691(18) Ref.[8]42734.4552(40)43551.5277(40)44341.2006(29)45103.6477(53) Ref.[5]42733.92(13)43550.92(13)44340.57(13)45103.03(13)45838.27(12) BvFitted1.0122870(103)0.99206396(936)0.9716480(104)0.9510106(486)0.9301201(203) Ref.[8]1.012328(14)0.992107(22)0.971653(18)0.951083(19) Ref.[5]1.01226(3)0.99203(3)0.97155(4)0.95094(4)0.93005(6) AvFitted-2.7715(25)-2.2912(19)-1.7031(32)-0.9933(50)-0.175(13) Ref.[8]-2.7782(53)-2.3054(89)-1.6913(77)-0.9407(96) Ref.[5]-2.780(15)-2.277(13)-1.689(24)-0.994(25)-0.22(6) γv×102Fitted-0.0222(48)0.0935(30)0.2662(47)0.479(11)0.837(10) Ref.[5]0.018(22)0.097(17)0.285(28)0.511(28)0.91(4) pv×102Fitted-2.572(12)-2.7993(91)-3.075(11)-3.620(49)-4.105(17) Ref.[8]-2.649(22)-2.816(32)-3.065(25)-3.466(34) Ref.[5]-2.61(5)-2.80(4)-3.07(6)-3.50(6)-4.09(8) qv×104Fitted-0.048(21)-0.205(12)-0.425(19)-0.827(55)-1.227(42) Ref.[8]-0.285(42)-0.464(31)-0.871(68) Ref.[5]-0.09(8)-0.24(6)-0.38(10)-0.68(11)-1.08(15) Dv×106Fitted6.245(12)6.3758(103)6.543(13)6.8311(786)6.863(45) Ref.[8]6.254(12)6.463(21)6.566(18)6.741(25) Ref.[5]6.28(3)6.43(2)6.53(3)6.68(3)6.92(6)

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[15]C.M.Western,PGOPHER,a Program for Simulating Rotational Structure,University of Bristol, http://pgopher.chm.bris.ac.uk

?Author to whom correspondence should be addressed.E-mail：lhdeng@phy.ecnu.edu.cn