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Hyperfine quantum beat spectroscopy of a polyatomic molecule in a weak magnetic field with polarized light
Voolumr 1 II. number
CHEMICAL
3
2 Novcmbcr
PHYSICS LEl-l-ERS
HYPERFINE QUANTUM BEAT SPECTROSCOPY OF A POLYATOMIC IN A WEAK MAGNETIC FIELD WITH POLARIZED LIGHT J. MiiHLBACH,
M. DUBS, H. BITT0
Pll~si~aliscil-Cftentiscf~cs Received
Institur
1983
MOLECULE
and J. Robert HUBER
der Universitr?t Ziin~cit, Wintcrtlmrcrstrasse
190. CH-SO37 Zurich,
Switrerland
I6 July 1981
Resolved Zeemnn splirtings in molecular quantum beats arc used for the lirst time to ass@ hypertine components of n rriplet sublevel of a polyatomic molecule. I’rom linear Zeeman splittings and level anti-crossing, Land6 factors and spinorbit coupling clemcnts arc determined for propynal. Specitic Zeeman components are identified by changing the laser polarizalion.
2. Theory
l_ Introduction Quantum
is a powerful tool to the highest spectral resolution [l]. Combined with molecular beam techniques, it allows detailed investigation of the perturbation among single rovibronic levels in poiyatomic molecules (2-71. The present discussion is restricted to quantum beats in molecules due to spin-orbit coupling. Previous quantum beat experiments on molecules by applying a magnetic field were mainly performed to prove the spin-orbit nature of the coupling [3]. A more detailed magnetic study on pyrazine [4] showed line broadenings and shifts of the beat frequencies in the Fourier spectrum at low fields. These effects were attributed to first- and second-order Zeeman interacstudy
tions.
beat spectroscopy
atoms
For
the triplet
and niolecules
at
nwthylglyoxal
[S],
llypertine
levels was resolved,
(hf)
the Zeenlan
splitting
of
but no as-
signnwits
of the levels were given. In the present communication, we report the magnetic field dependence of quantum beats in the fluorescence decay of a single rovibronic level of propynal (HCXCtIO) [7]. The Zeeman-split hf components were clearly resolved and assigned to the four hf components
of the triplet
sublevel
involved.
Level anti-
crossing was observed, which provides direct information on the coupling strength of the interacting levels. Furthermore, within the Zceman multiplets, specific components were identified by changing the laser polarization.
In describing quantum beats in molecules like propynal, we consider molecular eigenstates obtained from zeroth-order Born-Oppenheimer (BO) states by diagonalizing the molecular Hamiltonian which includes spin-orbit coupling us0 _If the coupling is restricted to two zeroth-order BO states, separated in energy by u, the eigenstates are of the form
la)=als)-Pit),
Ib)=/3ls)+cXlt)
(1)
with a spacing k&,6)
= [(A$
+ 4L&]?
(2)
c? and f12 give the singlet and triplet character of the eigenstates, respectively [S] . The laser pulse produces coherences in the excited state when two or more states such as la> and lb) are connected to a common ground state lg) by allowed transitions that fall within the coherent laser bandwidth. These coherences are related to the off-diagonal matrix elements of the excited-state density matrix, which is expressed in the basis of molecular eigenstates. Within the spectral resolution provided by the present experiment, the hyperfine structure of the levels becomes important. For a qualitative discussion, attention is now focused on a single hf component_ It is characterized by the total angular momentum F (including nuclear spin) and its projection ill onto the di-
0 009-26 14/S4/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B-V.
Volume
I1 1. number
rcction of the generate states the discussion rwtic sublcvcls
CIII:LlICAI.
3
PHYSICS
magnetic field B. The field splits the dcIi) (i =o.b; for simplifying the notation, is limited to two levels) into 2E‘+ I magwith a Zceman energy
AEz = gF(i)p,$lM
= fioL(i)r2f.
2 Nuvcmbcr
1.EI-TERS
EII
e
1984
r1e
(3)
This expression is valid at low magnetic fields when the spins arc not decoupled from the molecular rotation and the Zecman splitting is small compared to the scparation &,b) given in eq. (2). wL(i) denotes the Armor frequency of state Ii>. The Land6 factorsgEas well as the transition probabilities arc calculated by firstardcr perturbation theory from the corresponding values of the zcroth-order BO sta~cs and the mixing cocfficicnts of the wavcfunctions (set below). For laser polarization parallel to B. only transitions with Mf = 0 arc allow4 and consequently only beats between Icvels with AM = 0 arc observed. No beats will be defected when only state la) is present. The beats bctwecn states 10) and lb), obeying the selection rule M = 0, will split into 2/= + 1 components (2F - I for I*‘+ F - 1 laser transitions) with a splitting given by
-lq,Fq =l>
-_ lq&=l>
Fig. 1. Schematic level di3pam for quantum beats in 3 magnctic field. 13~1 csciration from 3 sin_elcgxound-srarc Zccmar component to two hf ciecnstatcs is shown (-). together with the rcsultin~ fluorcsccncc (- -). The left side rcfcrs to pi~~allcl rhc right side to pcrpendicuhr hccr cscitition. Quantum bat! arc produced by cohcrcnces between lcvcls with cqu4 AI mlucs (...).a~ WA CISby Zcernan cohcrenccs with ltiY I = 3 ( ‘- -).
A4 = Is,.&) -+@)MBB/fi.
(1)
On the other hand, with the laser polarized pcrpcndicular to B, transitions with 4M = +1 arc allowed to both states lo) and 16) (cf. fig. 1). Under these conditions, three different types of cohercncc arc possible among sublevels of excited states: (i) Cohcrences between levels Ia) and lb) with &If = 0. These occur at the same frequencies as with parallel polarization but show diffcrcnt relative intensities among the magnetic sublevc)s. The intensities arc given by the Hijnl-London factors, or may be cxprcsscd by the 3j-symbol I Al 0:
1.;
f’
1
-H-q
Iv
q
(
2
).
(5)
r/ = 0 for parallel and y = f 1 for pcrpcndicular polarizition. f:K denotes the total angular momentum of the ground state. (A small influcnu? of detector gcomctry and polarization has been r~glcctcd in this quiditativc trcatmcnt.) (ii) Zeeman beats 191 within state Ii) obeying IAMI -5 7. Thcsc beats arc observed at twice the Armor frcquency wL(i). With the weak field employed here. these beats arc not prominent for the following reawhere
sons. If the coupling is weak between sindct and triple states, either the intensity or the beat frequency is low With stronger coupling or at a hi&er field, the level spacing no longer remains constant and the Zeeman beats are split into 2F - 1 lines which are all located a the low-frequency side of the spectrum. Properly iden. tified, these beats permit direct determination of the land6 factors of the eigenstatcs Ii). (iii) Eecman beats between states 10) and lb) with l&VI = 2 at frequencies
(6) =
lw(u.b)+
[wL(u)-uL(b)]nl+[oL(u)toL(t,)]I.
Analogous to the ordinary Zeeman beats, these oscilla. tions are observed only when neither the laser cxcitation nor the detection have cylindrical symmetry with icspcct to the field. Ntliough the transition moments of thcsc beats arc similar in magnitude to those with AM = 0, the beat amplitudes have different signs for tmnsitions F + F and F + F + 1 in emission. ‘Ihcrcfore, they partially cancel each other due to the fact that we detect the total fluorescence to all final levels. 289
\'dulllr
3
I ll.llunlbcr
CllEhtlCAL PIIYSICS LISTTERS
‘flw dcwctcd amplitude is expected IO be reduced by roughly a11 order of magnitude. depending on the transitim cscitcd.
.-.--_ 2 Novcmbcr 1984
f.3
K'.l
3. Expcrimrntnl
I %-oi propyml
sccdcd
in I bar of xenon
was ex-
tmdcd through a putscd nozzle in a supersonic frecjet apprrrtitus dcscribcd previously 16.71. The only addltion 10 Illis :Ipprcr;llus was 3 Iiclrnll0ltZ Coil (5 Cm X 5 CIII Jiamcrcr) riiounrctl in ltic vacuuni chamber with IIIC rictd direction parattct to the jet propagation. The csci[alion. mgncric field and dcicclion axes were ~uu~ually pcrpcndicular. No compensation was made for the horizonttit co~llpo~lcnt of the earth magnetic licld. A pair of prisms was used to rolalc the laser potarim;ltion. TIE temporal laser pulse width of 5 ns providcd 3 col~crc~l~ bandwidrll of ==ZOOMHz. Ttic fluorcsccncc decays wcrc f’ouricr rransfomcd according IO WIIIIIIOII
proccdurcs
including
a phase-shift
correction.
4. Results 3nd discu.ssion Fig. 2 stiows tlie I-ouricr transforiu of the tluoresccncc drc:~y of propynal in a magnetic field, obtained for excitation of ItlcJ’,K’= 3,l ..-J”,K” = 2.0 rotational transition of’ the GA (St + SO) band (for spccrral details. cf. rcf’. [Cl). It is important 10 IIOW that a si/r_& rotational transition is cxcitcd. which is coupled IO 3 nearby triplet rovibrational slate of appropriate synuuctry md angular IW~ICII~~III. The two proton nuctcm spirls 1, and J? ',I propyml give rise IO a ~t~tilling into four III COII~~~IWIIIS with I*’ = J + I, f 12 :’ 1 _ .3.3,4 for the rransition under study. The largest ~cmlribution 10 tl~c splitting is due to rhc inkractions of /, rrntl fz wiIh ltic clcciroii spin S. We assume Ilund's
rouplirlg
c3sc bp 181.
A wcdc magnetic ficld splils cacti hf conlponent into ZJ.‘+ I ZCCIIUII conlponcn[s. As depicted in fig. 2, al a fictd of I (_i Iwo hf bca1 signals arc co~nplc~cty resolved illro 5 3110 7 tints. corresponding to I:= :! and 3, rcspcclively. Two 3ddilioilat componcnis with simltcr splittings ccnlerctl al %:30 MHz arc resolved at higher iictds iuro 7 and 9 lines. in perfcc( agreement with J = .i. t’ur~hcr cvidcnm rhat the observed beats belong IO
Fig. 2. I:ouricr-lransformcd fluorcsccncc decay of propyml withour applied magnetic ficld (lop), with hscr polarization parallel IO n rnapnctic field of 1 G (center) and with larcr poIsri;r;rtion pcrpcndicubr IO the ticId (bottom). ‘1%~splitting in the top 1:ouricr spectrum is rauscd by rhc uncompcnwtcd cmh magnetic field.
I~IC four hf components of one triplet sublcvcl is provided by the mcasurcd L.andC factors. The observed splittings in the magnetic field arc dcpcndent on the singlet .triplct state mixing. TIlc coupling strength us0 which is needed to calculate the nixing coefficients was determined from lcvcl anti-crossing (LAC).
CtiF.hllCAL
Volume II I, number 3
PHYSICS
2 November 1984
LETTERS
By variation of the magnetic field. sin&z Zeeman components of the triplet arc brought into resonance with the corresponding sin&t state. At this field strength, the beat frequency reaches a minimum value O,in = 3us0/fi, as seen from cq. (2). Fig. 3 shows this behavior for the hf component with I= = 2. At 8 G, a minimum bear frequency of 12.8 MHz was measured, which corresponds to U&I = 6.4 MHz.Tbe situation is, howcvcr, complicated by the fact that, at this field strength, decoupling of the proton spin from molecular rotation bccomcs cvidcnt (onset of Paschen. -Back cffcct). In other words, we obscrvc also LAC between Zeeman components of different hf levels, as manifested in splittings and intensity variations of the Zeeman components (cf. fig. 3). Since under our conditions this
effect is still small, it was not taken into account. Using the values of us0 determined by LAC, the
Land6 factorgb-(f) of the BO triplet state was calculated according to tllc expression g,(r)
= I&$-W x
{I
- R#)l
so /Ilu(f? ’ I#}=.
-4[u
(7)
where minor contributions to the magnetic monmlt of the order of a nuclear magneton were nc&zctcd. The Land6 factorsgF and g, were then calculated for a symmetric top, with angular momentum h’cxcluding spins and separate couplings of the proton spins to I, by applying the well-known relations [8] gJ = [I .001/J@
I-is. 3. Magnetic licld dependcncc of the bwt frequencies of rhc I; = Z Zccman sublevels depicted in fig. 2. Lcvcl ant&row ing bctuccn diffcrcn( hf components is indicated by arrows. A correction for rhc earth magnetic rtcld has been included.
+ I)]
Y,.- =
k,:, /F(F + 1) 1
x [fqf-+ 1) t
F1(F,
+ 1) -I,&
+ l)].
(IO)
Based on the measured splitting of the Zeeman cornponcnts of the four hf levels, we obtained with cqs. (4), (7). (9) and (I 0) the gJ values given in table I.1711 standard
deviations
indicated
in the last column
rcflcc
in the dctcrrnination of the splittins an? of uSo. Within experimental error, the gJ values arc equal, thus justifying the proposed coupling scheme. The average cxpcrimcntal value of lg,l = 0.53 is close to a calculated value of lg,l = 0.5005 obtained forJ = 3 and N = 4. The discrepancy may be attributed to uncertninties
x [J(J+
gk-* = kJ/F, x 1F,(F,
1)+S(S+
w, +
I)-A’(fV+
I)].
(8)
+ 1 )I
I)+J(Jt
I)-‘*(1,
+ I)],
(9)
‘t-able I hlwsu:rd
beat frequencies ~(a$)
hf components
-p---
(in hllir).
F
w(a.l)/2n
7
23.3
-___-___-.-_
--___-
coupling strengths “~0 (in hlflz) and Lndd
shown in fig. ? ~_---__------------
fnctorsg
(cf. cqs. (7) and (8)) of the four
--.__-
YjoP -----___.
IRF(O) - g/m)
I
65(f) ----
0.776
058
-_
6.4
0.648
5.7
-_
Rfi
-.-
-
-
t 0.01
3
30.6
0.497
0.537
056
r 0.02
3
345
155
0.229
0522
0.54
z 0.05
30.6 _-__-_
14.9 -___
0.077
0.339
0.45 2 0.11 ----.---
4 _____
--_--
--
291
Volu~ne 1’11, number 3
CHEhliCAL PHYSICS LETTERS
a calibration error of the magnetic field, which was measured with a Gaussmeter with a quoted accuracy nf *3c70_ The influence of laser polarization on the beat amplitudes is described by eq. (5). In the case of R- and P-branch transitions, the components with lM1 = F are the most intense for perpendicular polarization, but are weak (p-branch) or absent (R-branch) for parallel polarization. In Q-branch transitions, the intensity variations are just reversed, the M = 0 component being absent in parallel polarization. The Fourier spectra in fig. 2 show the expected behavior of an Rbranch transition. The non-zero intensity observed for lines with 1Ml = F under parallel polarization is due to the earth magnetic field. The large intensity variations of these lines upon polarization changes enable their identification
Forschung is gratefully acknowledged. We thank Dr. U Briihlmann for the design of the Hehnholtz coil and fo: technical assistance.
References
[ 1] S. Haroche, in: High resolution laser spectroscopy. [2]
even in congested regions.
5. Conclusions
We have shown that weak magnetic fields of a few gauss have a pronounced effect on the quantum beats of propynal. The beats permit one to investigate singlet-triplet interactions of single hypertine levels with natural linewidth resolution. At fields 5 3 G, the linear Zeeman splittings provide the Land6 factors of individual hyperfine components_ With fields >5 G, the nuclear spins become decoupled from molecular rotation and level shifts typical of level anti-crossing occur, which allows determination of coupling matrix elements.
r3 ]
[4] [5] [6] [7]
Acknowledgement Support rionnlfonds
of this work by the Schweizerischer zur Forderung der wissenschaftlichen
[8]
Na-
2 November 1984
[9]
ed. K. Shimoda (Springer, Berlin, 1976) pp_ 253-313. J. Chaiken,T. Benson. hl_ Curnick and J.D. McDonald, Chem. Phys. Letters 61 (1979) 195; J. Chaiken, hi. Gurnick and J-D. McDonald, J. Chem. Phj 74 (1981) 106,117; W.R. Lambert, PM_ FeIker and A.H. ZewaII. J. Chem. Phys. 75 (1981) 5958; A.H. ZewaiI, W.R. Lambert, P. FeIker, J. Perry and W. Warren, J. Phys. Chem. 86 (1982) 1184; BJ. van der &leer, H.T. Jonkman, G.hl. ter Horst and J. Kommandeur, J. Chem. Phys. 76 (1982) 2099; S. Okajima, H. Saigun and E.C. Lim, J. Chem. Phys. 76 (1982) 2096; Ii. Saigusa and EC. Lim, J. Chem. Phys. 78 (1983) 91; W. Sharfii, M. Ivanco and SC. Wallace, J. Chem. Phys. 76 (1982) 2095; 51. Ivanco. J. Hager, W. SharIin and S-C. WaIIace, J. Chen Phys. 78 (1983) 6531; P.M. Felker and A.H. Zewail, Chcm. Phys. Letters 102 (1983) 113. W. Henke, H.L. Selzle, T.R. Hays and E.W. SchIag, 2. Naturforsch. 35a (1980) 1271; W. Her&e, H-L. Selzle, T.R. Hays, SK Lin and E-W. SchIag, Chem. Phys. Letters 77 (1981) 448. P.hl. FeIker, W.R. Lambert and A.H. ZewaiI, Chem. Phy: Letters 89 (1982) 309. J. Chaiken and J.D. hlcDonald, J. Chem. Phys. 77 (1982: 669. Ii. Stafast. H.-Bitt0 and J.R. Huber, J. Chem. Phys. 79 (1983) 3660. 1-I. Bitto, H. Stafast, P. Russegger and J.R. Huber, Ciiem. Phys. 84 (1984) 249. C.H. Townes and A.L. Schawlow, Microwave spectrosco] (McGraw-Hi& New York, 1955). P.J. Brucat and R.N. Zare, J. Chem. Phys. 78 (1983) 1OC
CHEMICAL
3
2 Novcmbcr
PHYSICS LEl-l-ERS
HYPERFINE QUANTUM BEAT SPECTROSCOPY OF A POLYATOMIC IN A WEAK MAGNETIC FIELD WITH POLARIZED LIGHT J. MiiHLBACH,
M. DUBS, H. BITT0
Pll~si~aliscil-Cftentiscf~cs Received
Institur
1983
MOLECULE
and J. Robert HUBER
der Universitr?t Ziin~cit, Wintcrtlmrcrstrasse
190. CH-SO37 Zurich,
Switrerland
I6 July 1981
Resolved Zeemnn splirtings in molecular quantum beats arc used for the lirst time to ass@ hypertine components of n rriplet sublevel of a polyatomic molecule. I’rom linear Zeeman splittings and level anti-crossing, Land6 factors and spinorbit coupling clemcnts arc determined for propynal. Specitic Zeeman components are identified by changing the laser polarizalion.
2. Theory
l_ Introduction Quantum
is a powerful tool to the highest spectral resolution [l]. Combined with molecular beam techniques, it allows detailed investigation of the perturbation among single rovibronic levels in poiyatomic molecules (2-71. The present discussion is restricted to quantum beats in molecules due to spin-orbit coupling. Previous quantum beat experiments on molecules by applying a magnetic field were mainly performed to prove the spin-orbit nature of the coupling [3]. A more detailed magnetic study on pyrazine [4] showed line broadenings and shifts of the beat frequencies in the Fourier spectrum at low fields. These effects were attributed to first- and second-order Zeeman interacstudy
tions.
beat spectroscopy
atoms
For
the triplet
and niolecules
at
nwthylglyoxal
[S],
llypertine
levels was resolved,
(hf)
the Zeenlan
splitting
of
but no as-
signnwits
of the levels were given. In the present communication, we report the magnetic field dependence of quantum beats in the fluorescence decay of a single rovibronic level of propynal (HCXCtIO) [7]. The Zeeman-split hf components were clearly resolved and assigned to the four hf components
of the triplet
sublevel
involved.
Level anti-
crossing was observed, which provides direct information on the coupling strength of the interacting levels. Furthermore, within the Zceman multiplets, specific components were identified by changing the laser polarization.
In describing quantum beats in molecules like propynal, we consider molecular eigenstates obtained from zeroth-order Born-Oppenheimer (BO) states by diagonalizing the molecular Hamiltonian which includes spin-orbit coupling us0 _If the coupling is restricted to two zeroth-order BO states, separated in energy by u, the eigenstates are of the form
la)=als)-Pit),
Ib)=/3ls)+cXlt)
(1)
with a spacing k&,6)
= [(A$
+ 4L&]?
(2)
c? and f12 give the singlet and triplet character of the eigenstates, respectively [S] . The laser pulse produces coherences in the excited state when two or more states such as la> and lb) are connected to a common ground state lg) by allowed transitions that fall within the coherent laser bandwidth. These coherences are related to the off-diagonal matrix elements of the excited-state density matrix, which is expressed in the basis of molecular eigenstates. Within the spectral resolution provided by the present experiment, the hyperfine structure of the levels becomes important. For a qualitative discussion, attention is now focused on a single hf component_ It is characterized by the total angular momentum F (including nuclear spin) and its projection ill onto the di-
0 009-26 14/S4/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B-V.
Volume
I1 1. number
rcction of the generate states the discussion rwtic sublcvcls
CIII:LlICAI.
3
PHYSICS
magnetic field B. The field splits the dcIi) (i =o.b; for simplifying the notation, is limited to two levels) into 2E‘+ I magwith a Zceman energy
AEz = gF(i)p,$lM
= fioL(i)r2f.
2 Nuvcmbcr
1.EI-TERS
EII
e
1984
r1e
(3)
This expression is valid at low magnetic fields when the spins arc not decoupled from the molecular rotation and the Zecman splitting is small compared to the scparation &,b) given in eq. (2). wL(i) denotes the Armor frequency of state Ii>. The Land6 factorsgEas well as the transition probabilities arc calculated by firstardcr perturbation theory from the corresponding values of the zcroth-order BO sta~cs and the mixing cocfficicnts of the wavcfunctions (set below). For laser polarization parallel to B. only transitions with Mf = 0 arc allow4 and consequently only beats between Icvels with AM = 0 arc observed. No beats will be defected when only state la) is present. The beats bctwecn states 10) and lb), obeying the selection rule M = 0, will split into 2/= + 1 components (2F - I for I*‘+ F - 1 laser transitions) with a splitting given by
-lq,Fq =l>
-_ lq&=l>
Fig. 1. Schematic level di3pam for quantum beats in 3 magnctic field. 13~1 csciration from 3 sin_elcgxound-srarc Zccmar component to two hf ciecnstatcs is shown (-). together with the rcsultin~ fluorcsccncc (- -). The left side rcfcrs to pi~~allcl rhc right side to pcrpendicuhr hccr cscitition. Quantum bat! arc produced by cohcrcnces between lcvcls with cqu4 AI mlucs (...).a~ WA CISby Zcernan cohcrenccs with ltiY I = 3 ( ‘- -).
A4 = Is,.&) -+@)MBB/fi.
(1)
On the other hand, with the laser polarized pcrpcndicular to B, transitions with 4M = +1 arc allowed to both states lo) and 16) (cf. fig. 1). Under these conditions, three different types of cohercncc arc possible among sublevels of excited states: (i) Cohcrences between levels Ia) and lb) with &If = 0. These occur at the same frequencies as with parallel polarization but show diffcrcnt relative intensities among the magnetic sublevc)s. The intensities arc given by the Hijnl-London factors, or may be cxprcsscd by the 3j-symbol I Al 0:
1.;
f’
1
-H-q
Iv
q
(
2
).
(5)
r/ = 0 for parallel and y = f 1 for pcrpcndicular polarizition. f:K denotes the total angular momentum of the ground state. (A small influcnu? of detector gcomctry and polarization has been r~glcctcd in this quiditativc trcatmcnt.) (ii) Zeeman beats 191 within state Ii) obeying IAMI -5 7. Thcsc beats arc observed at twice the Armor frcquency wL(i). With the weak field employed here. these beats arc not prominent for the following reawhere
sons. If the coupling is weak between sindct and triple states, either the intensity or the beat frequency is low With stronger coupling or at a hi&er field, the level spacing no longer remains constant and the Zeeman beats are split into 2F - 1 lines which are all located a the low-frequency side of the spectrum. Properly iden. tified, these beats permit direct determination of the land6 factors of the eigenstatcs Ii). (iii) Eecman beats between states 10) and lb) with l&VI = 2 at frequencies
(6) =
lw(u.b)+
[wL(u)-uL(b)]nl+[oL(u)toL(t,)]I.
Analogous to the ordinary Zeeman beats, these oscilla. tions are observed only when neither the laser cxcitation nor the detection have cylindrical symmetry with icspcct to the field. Ntliough the transition moments of thcsc beats arc similar in magnitude to those with AM = 0, the beat amplitudes have different signs for tmnsitions F + F and F + F + 1 in emission. ‘Ihcrcfore, they partially cancel each other due to the fact that we detect the total fluorescence to all final levels. 289
\'dulllr
3
I ll.llunlbcr
CllEhtlCAL PIIYSICS LISTTERS
‘flw dcwctcd amplitude is expected IO be reduced by roughly a11 order of magnitude. depending on the transitim cscitcd.
.-.--_ 2 Novcmbcr 1984
f.3
K'.l
3. Expcrimrntnl
I %-oi propyml
sccdcd
in I bar of xenon
was ex-
tmdcd through a putscd nozzle in a supersonic frecjet apprrrtitus dcscribcd previously 16.71. The only addltion 10 Illis :Ipprcr;llus was 3 Iiclrnll0ltZ Coil (5 Cm X 5 CIII Jiamcrcr) riiounrctl in ltic vacuuni chamber with IIIC rictd direction parattct to the jet propagation. The csci[alion. mgncric field and dcicclion axes were ~uu~ually pcrpcndicular. No compensation was made for the horizonttit co~llpo~lcnt of the earth magnetic licld. A pair of prisms was used to rolalc the laser potarim;ltion. TIE temporal laser pulse width of 5 ns providcd 3 col~crc~l~ bandwidrll of ==ZOOMHz. Ttic fluorcsccncc decays wcrc f’ouricr rransfomcd according IO WIIIIIIOII
proccdurcs
including
a phase-shift
correction.
4. Results 3nd discu.ssion Fig. 2 stiows tlie I-ouricr transforiu of the tluoresccncc drc:~y of propynal in a magnetic field, obtained for excitation of ItlcJ’,K’= 3,l ..-J”,K” = 2.0 rotational transition of’ the GA (St + SO) band (for spccrral details. cf. rcf’. [Cl). It is important 10 IIOW that a si/r_& rotational transition is cxcitcd. which is coupled IO 3 nearby triplet rovibrational slate of appropriate synuuctry md angular IW~ICII~~III. The two proton nuctcm spirls 1, and J? ',I propyml give rise IO a ~t~tilling into four III COII~~~IWIIIS with I*’ = J + I, f 12 :’ 1 _ .3.3,4 for the rransition under study. The largest ~cmlribution 10 tl~c splitting is due to rhc inkractions of /, rrntl fz wiIh ltic clcciroii spin S. We assume Ilund's
rouplirlg
c3sc bp 181.
A wcdc magnetic ficld splils cacti hf conlponent into ZJ.‘+ I ZCCIIUII conlponcn[s. As depicted in fig. 2, al a fictd of I (_i Iwo hf bca1 signals arc co~nplc~cty resolved illro 5 3110 7 tints. corresponding to I:= :! and 3, rcspcclively. Two 3ddilioilat componcnis with simltcr splittings ccnlerctl al %:30 MHz arc resolved at higher iictds iuro 7 and 9 lines. in perfcc( agreement with J = .i. t’ur~hcr cvidcnm rhat the observed beats belong IO
Fig. 2. I:ouricr-lransformcd fluorcsccncc decay of propyml withour applied magnetic ficld (lop), with hscr polarization parallel IO n rnapnctic field of 1 G (center) and with larcr poIsri;r;rtion pcrpcndicubr IO the ticId (bottom). ‘1%~splitting in the top 1:ouricr spectrum is rauscd by rhc uncompcnwtcd cmh magnetic field.
I~IC four hf components of one triplet sublcvcl is provided by the mcasurcd L.andC factors. The observed splittings in the magnetic field arc dcpcndent on the singlet .triplct state mixing. TIlc coupling strength us0 which is needed to calculate the nixing coefficients was determined from lcvcl anti-crossing (LAC).
CtiF.hllCAL
Volume II I, number 3
PHYSICS
2 November 1984
LETTERS
By variation of the magnetic field. sin&z Zeeman components of the triplet arc brought into resonance with the corresponding sin&t state. At this field strength, the beat frequency reaches a minimum value O,in = 3us0/fi, as seen from cq. (2). Fig. 3 shows this behavior for the hf component with I= = 2. At 8 G, a minimum bear frequency of 12.8 MHz was measured, which corresponds to U&I = 6.4 MHz.Tbe situation is, howcvcr, complicated by the fact that, at this field strength, decoupling of the proton spin from molecular rotation bccomcs cvidcnt (onset of Paschen. -Back cffcct). In other words, we obscrvc also LAC between Zeeman components of different hf levels, as manifested in splittings and intensity variations of the Zeeman components (cf. fig. 3). Since under our conditions this
effect is still small, it was not taken into account. Using the values of us0 determined by LAC, the
Land6 factorgb-(f) of the BO triplet state was calculated according to tllc expression g,(r)
= I&$-W x
{I
- R#)l
so /Ilu(f? ’ I#}=.
-4[u
(7)
where minor contributions to the magnetic monmlt of the order of a nuclear magneton were nc&zctcd. The Land6 factorsgF and g, were then calculated for a symmetric top, with angular momentum h’cxcluding spins and separate couplings of the proton spins to I, by applying the well-known relations [8] gJ = [I .001/J@
I-is. 3. Magnetic licld dependcncc of the bwt frequencies of rhc I; = Z Zccman sublevels depicted in fig. 2. Lcvcl ant&row ing bctuccn diffcrcn( hf components is indicated by arrows. A correction for rhc earth magnetic rtcld has been included.
+ I)]
Y,.- =
k,:, /F(F + 1) 1
x [fqf-+ 1) t
F1(F,
+ 1) -I,&
+ l)].
(IO)
Based on the measured splitting of the Zeeman cornponcnts of the four hf levels, we obtained with cqs. (4), (7). (9) and (I 0) the gJ values given in table I.1711 standard
deviations
indicated
in the last column
rcflcc
in the dctcrrnination of the splittins an? of uSo. Within experimental error, the gJ values arc equal, thus justifying the proposed coupling scheme. The average cxpcrimcntal value of lg,l = 0.53 is close to a calculated value of lg,l = 0.5005 obtained forJ = 3 and N = 4. The discrepancy may be attributed to uncertninties
x [J(J+
gk-* = kJ/F, x 1F,(F,
1)+S(S+
w, +
I)-A’(fV+
I)].
(8)
+ 1 )I
I)+J(Jt
I)-‘*(1,
+ I)],
(9)
‘t-able I hlwsu:rd
beat frequencies ~(a$)
hf components
-p---
(in hllir).
F
w(a.l)/2n
7
23.3
-___-___-.-_
--___-
coupling strengths “~0 (in hlflz) and Lndd
shown in fig. ? ~_---__------------
fnctorsg
(cf. cqs. (7) and (8)) of the four
--.__-
YjoP -----___.
IRF(O) - g/m)
I
65(f) ----
0.776
058
-_
6.4
0.648
5.7
-_
Rfi
-.-
-
-
t 0.01
3
30.6
0.497
0.537
056
r 0.02
3
345
155
0.229
0522
0.54
z 0.05
30.6 _-__-_
14.9 -___
0.077
0.339
0.45 2 0.11 ----.---
4 _____
--_--
--
291
Volu~ne 1’11, number 3
CHEhliCAL PHYSICS LETTERS
a calibration error of the magnetic field, which was measured with a Gaussmeter with a quoted accuracy nf *3c70_ The influence of laser polarization on the beat amplitudes is described by eq. (5). In the case of R- and P-branch transitions, the components with lM1 = F are the most intense for perpendicular polarization, but are weak (p-branch) or absent (R-branch) for parallel polarization. In Q-branch transitions, the intensity variations are just reversed, the M = 0 component being absent in parallel polarization. The Fourier spectra in fig. 2 show the expected behavior of an Rbranch transition. The non-zero intensity observed for lines with 1Ml = F under parallel polarization is due to the earth magnetic field. The large intensity variations of these lines upon polarization changes enable their identification
Forschung is gratefully acknowledged. We thank Dr. U Briihlmann for the design of the Hehnholtz coil and fo: technical assistance.
References
[ 1] S. Haroche, in: High resolution laser spectroscopy. [2]
even in congested regions.
5. Conclusions
We have shown that weak magnetic fields of a few gauss have a pronounced effect on the quantum beats of propynal. The beats permit one to investigate singlet-triplet interactions of single hypertine levels with natural linewidth resolution. At fields 5 3 G, the linear Zeeman splittings provide the Land6 factors of individual hyperfine components_ With fields >5 G, the nuclear spins become decoupled from molecular rotation and level shifts typical of level anti-crossing occur, which allows determination of coupling matrix elements.
r3 ]
[4] [5] [6] [7]
Acknowledgement Support rionnlfonds
of this work by the Schweizerischer zur Forderung der wissenschaftlichen
[8]
Na-
2 November 1984
[9]
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