- Email: [email protected]
Microwave spectroscopy of supersonic molecular beams: Single- and double-resonance experiments with OCS and HCCCN
.-
-.
By applying the principles of microwave Stark _modulated spectroscopy to continuous_supersonic. beams a new tt&hn&e for -high-r&olutio_n rotational spectroscopy has been developed. The capabilities pf the new technique have been- demonstrated through inv&tigat&~oi the spin-rotation s&it&&s in O’?CS and HCCCN. S’rmu+neously the method allowed a diagnostic of supersonic molecular beams. Relative beam intensities. supersonic flow velocities and translational temReratures’of pure and seeded beams were determined from ;pc&ros&pic ineasurements of signal -intensities. Doppler--shifis and line- Gdths. respectively_ Microwave-microwave double-resonance experiments established deviatiohs from-the Roltxmann populations of rbtationgl energy levels in supersonic~molecular beams.
..
-For high dilution the flow field is mainly -de1. Introduction termined by the carrier gas which is cooled -. more extensively during the expansion than -the pure The merits of supersonic free expansion of gases molecular beam. This- means that ‘those molecular for spectroscopic applications have. been demondegrees of freedom which equilibrate quickly with strated many times. The techniques reported so far the thermal bath provided by the carrier gas,.i.e. include laser-induced. fluorescence [l], moleculartranslational and rotational, are more strongly beam electric resonance [2], beam: maser. spectroscooled in a seeded beam. copy [3] and many.others [4-71. .Traditionally, rotational transitions of moleA. supersonic- jet is formed when a gas- in a cules or molecular complexes in supersonic beams reservoir at thermal equilibrium is expanded have been -observed with the electric resonance through a nozzle into vacuum_ Thereby:thermal method or tith beam maser spectroscopy. Reenergy of the static gas is converted to- energy cently, Flygare and co-workers have developed a associated with the-directed mass 1flow in the exnew method to measure rotational trtinsitions in a panding. jet. In- order to produce -a continuous pulsed jet [S]. They combined the .principles~of molecular -beam a skimmer must. be used in a pulsed Fourier- transform microti;2ve-sp.ectroscopy differentially pumped system. Significant cooling, of translational and rotain a- Fabry-Perot .cgvity with a synchronously tional degrees of $e_edom o4Girs~during the-superpulsed supersonic jet- directed transversally to the sonic exp_sion:--~lbrational ..degrees _-of-:_freedbm microwave field. They obtained .a substz&d_re; are much less cooled. As a -consequence of the duction of the Doppler linewidth ~$&~li limits thetranslational cooling and decreasing particle denresolution in ‘static micro&&e spectroscopy. Hotiever,- they -obServed:a- complicated-line shapesa&sity the mole&les -do not experience_c_ollisions for incriasmg; _&s_tancesIf- they .travel‘in- a;_system‘*th ing from the braid solid angle of:tie jet traversing~ a-!+ &@ba&&&nd p&sue; -:.I .-_: _. the cavity. After-reporting our- first-rest&s with-$ In many tipphcations the molecules. fo be. in-different-‘experimental technique 1[9]the. rep.ort of an experiment ‘somewhat similar- to ours- came to _vestigated are.se$e_din;a sm&concentration into our -ztttenti& -l%rrir&et~ al.: [lO]_ measured the a- m,onatomic carrier gas, ustGlly helium or argon. -. 10301~0104/~4/$03~do .Q -Elsevier-Science Publishers B;\i. _ __ -_:. ; (l%rth~Holland PhysiCS Publishing Division) 1 ~. ,_ 1 .: .:
z
H.S.
Ziui et al. /
Microwaw
spectroscopy of supersonic molecular berets
microwave absorption of CsCl in a supersonic beam with the help of a small cylindrical cavity. The work reported here combines the principles of microwave Stark spectroscopy with the generation of continuous supersonic beams. A preliminary account of the method has been given recently [9]. Lately Campbell et al. [ll] added a Stark field to the Fabry-Perot spectrometer of the Flygare type in order to measure dipole moments. In our experiments the supersonic beam axis is collinear to the propagation of the microwave radiation. In addition to yielding highly resclved rotational spectra like in beam maser spectrometers such an arrangement opens the possibility for simultaneous diagnostics of supersonic molecular beams. From spectroscopic measurements the translational temperature, the supersonic flow velocity as well as the relative beam intensity could be inferred in relation to the beam source parameter settings_ Furthermore double-resonance experiments on two successive rotational transitions gave information on the relative populations of the corresponding levels in supersonic molecular beams.
_
1.
beam was passed through a -specially designed groove guide cell collinear to the microwave radiation but in opposite: direction. The microwave absorption which was modulated by the Stark effect was detected with a microwave superhete:odyne- receiver system. The specticnieter was controlled by a small computer PDP-8/I which was used for data collection and analysis_ 2. I. Su,versonic molecular beam source The supc;sonic beam source was of the differentially pumped variety. The beam was generated by expanding the gas through a converging nozzle with 50 to 200 pm diameter into the source chamber. Stagnation pressures ranged from 0.2 to 2 atm. The central part of the expanding jet was separated with a skimmer of 0.7 mm diameter and passed the buffer chamber where it was collimated finally with an iris. The skimmer was made from stainless steel by electro-erosion. Details of the supersonic beam source have been described previously [4]. A schematic view is given in fig. 1. _7.2_ Microwave groove guide Stark cell
2. Experimental
arrangement
A continuous supersonic beam was generated in the molecular beam source_ The well collimated
BUFFER CHAMBER
Investigations of rotational spectra of collisionless molecules in a supersonic beam with a waveguide spectrometer demand a waveguide structure which is open along the whole length in order to
SOURCE CHAMBER
NOZZLE I f
EDWARDS DIFFSTAK 16Of 700 M
t Fig. 1. Supersonic beam source.
GAS INLET BALZERS DIF 320
. .
..-
~.
..-
.-.
:__:
allow efficient 1pumping to siiffic~entlji~lo&_ pies’_ sures: This. .requirement could be, fulfi%d :-with -a groove guide [12] which’consists of ‘two: i’ m long parallel. aluminum plates. A rectangular~grcovd was milled lengthwise in the center.int_o both-plates. The cr&s &&ion bf our groove’guide is: sh_n.in fig. 2. Transverse electric (TE) and transverses magnetic (TM) modes are transmitted~along t,he.groove guide. The. dominant. modes.,TE,, a& TM,; are the only low-loss modes possible [12]. All other modes radiate out through the opening between the two plates. The microwave electric field of the TE,, mode is concentrated in the groove region and decays exponentially with increasing distance from the grooves in the opening between the plates. Thus the microwave electric field overlapped optimally the supersonic beam which was sent down through the center of the groove guide._.The separation between the plates and the dimensions of the groove were chosen such that the. cutoff frequency of the TE,, mode lies at.4.4 GHz. The groove guide could accommodate a molecular beam up to 30 mm diameter. The TE,, mode of a standard X-band rectangular waveguide could be transformed into the TE,, groove guide mode or vice versa without exciting radiating modes [12]. The groove guide is mounted in a vacuum jacket which is evacuated with the help -of three evenly distributed diffusion pumps with pumping speed of 280 L’s_‘_ The vacuum jacket-is connected via a short piece of flexible tubing to the supersonic molecular beam source. It is mounted on two x-y precision setting tables from a lathe which allow alignment of the groove guide cell to the molecular beam axis.
_ iL-,
2a
._ -
_--. :-
.__. .. -’
Fig. 2. Cross section of the- groove guide, u = 10 m& b = 40 mm,c=22mmandd~120n&n.
_--. _:.,-:.-The dired~ooii:of.pi-b;~~gatidn of- the molecular _I beam was -c;?llinear to that of the rnicr&wavc radi.‘--ation but in opposite. direction.-- in- order _to &lo&. ..,-for -efficient .pu-mpihg of the molecules’ emerging ‘: -from the: end-‘& ‘the @c&e guide the microWave .-- ~---- -’ radiation was. not fed .throu&‘a titisition scction~ f to the groove guide as at the other&d. Instead the microwave radiation was split symmetrically &th ‘- a dual-directional coupler and transmitted through two.waveguid& into the vacuum jacket. Two-small
horns illuminated’s larger horn at the end of the groove guide which excited the TE,, mode as shown. in fig. 3. At the other end a transition section [12] converted the radiation to the X-band waveguide. The molecular beam entered the groove guide assembly through a 6 mm hole drilled into a 90°- bend (cf, fig. 4) The complete assembly is shown schematically in fig. 5. _ For Stark modulation the two halves of the groove’ guide were electrically isolated from the rest of the assembly. One of the plates was driven by a zero-biased square-wave voltage while the other plate was grounded. The electric field lines of the Stark field and the electric component.of the microwave field are perpendicular to one another_ The selection rule AM = + 1 applies- for the quantum number of the projection of the angular momentum. 2.3. Microwave superheterodytte receiver system The microwave emitter-receiver system was modified from an earlier version of a superheterodyne detector [13]. The master oscillator (Varian X-13 klystron) was phase-locked to the harmonics of a 100 MHz quartz oscillator-multiplier chain. The difference frequency -between klystron and harmonic was mixed subsequently with the signal of a frequency synthesizer- (Programmed Test Sources, model PTS-160) to a constant interme&at& fiequ&y of the synchronizer (HewlettPackard,-model-8709A). The synthesizer frequency was- controlled by the small computer in steps as small as -100 Hz. The frequency of .ihe master oscillator could thus be swept in discrete steps of the same’size.
The microwave output of the groove gu&spectrometer. was -first -fed to a low-noise m&Wave
4
H-S. Zivi er al. / Microwave speczrascopy of supersonic moledar
beams
a
XklAND WAWEGUIDE.
I
I
-WAVE
X-BAND
W.WE GUIOE
GUIDE’
ELECTRICAL MSULAWJN
Fig_ 3. Excitation of the dominant mode of the grcove guide: (a) side view; (b) top view.
I
TRANSITION
GROhE/X-BAND
GUIDE
b
WAVE GUIDE BEND WITH HOLE
GROOVE
GUIDE
ELECTRICAL’NWLATKW
TRANSlTlON
GROOVE/X-BAND
X-BAND
GUIDE
WAVE GUIDE
--
l I Fig. 4. Transition from the groove guide to the standard rectangular waveguide; (a) top view; (b) side view.
280
280. I/s
I/s
280
I/s
7001/s
Fig. 5. Overallview of the spectrometer assembly. . amplifier (Watkins-J&n&n, &d&l 5310-432). Its output. was mixed in a balanced r&e:--preamplifier combination (RI%G, model DMl-18/16 j with the local o@l+orsignal. The local oscillator klystron was phase+cked to a frequency -exactly 30 MHz apart frog the master oscillator. ‘The 30 MHz signal ca&er &as elimidated by a first phase-sensitive detector. Demodulation of the 1 kHz stark modultition sidebands was accomplished in a second phase-sensitive detector. Its outp_ut could be presented on a recorder or sent to the small computer for signal enhancement by summation of several spectral recordings.
3. Theoretical description of the experiment In order to estimate the -sen.:itivity of our spectrometer. a simple model was introduced for the calculation -of the absorbed microwave radiation by the supersonic beam as a function of Al+ input power. Here we summarize the -theoretical -work, a full account, of which will. be published separately [14]. I 3.1. Model assumptions
-
It is well established that molecules in. super-sonic:beams move. independen!ly from-each qther if the- beam is observed sufficiently f&-away from the nozzle. Under these conditions the: xnoieculeS -do _not Suffer any &l&ions during the time scale
.-
__
1
52100 I/s
of the experimer& The ~sem_iclas:;icaltime-deperident hamiltonian k(t) for a single. collisionless molecule in the beam interacting with the micro-wave radiation-field &d the St&k field is ‘given by H(t)
= T,,,;+
j_l-‘J/2
-ET-‘D”‘(
a, p, y
-EsT-W+Y,
)zi!& cos( Of -
p, y)7Mrs(r)
kz)
+Hhfs_ (3-I)
The first term represents the- translational energy, the second term the rotational enesgy, the third and fourth terms the interaction with the micr& wave radiation and the Stark field, respectively, and .the last term accounts for possible Qperfine interactions. J denotes the angular momenturn and I the moments of ,inertia-tensor. The electric-field E cos(or Y kz) of the microwave radiation with frequency w and propagation coiistruu\-t k along-the z axis and the Stark field &s(t) interact with the permanent- electric ~&Polk moment Mr in the molecule-fixed system. s( t).specifies ~he~switching fbiction of. t& Stark field. The three-dimens&& representation D(‘)(&; /3, y) of ~-the rotation- group d+(3) ~expressed i& &l+ui angles. LY, p and y relates. the -mol&ule-fixed ~system to the laboratoy-fixed. -system. II(‘) in. its standard complex form- must be transformed with f to Cartesian co&di&af&1~ _ Follow&$ pi&tice for the d&r&ion ‘SE..ihe dynamics- of spectroscopic transitions the
co&&-
6
H.S_ Ziui et al. / Microwave spectroscropy of supersonic nroleculai beams
multi-level molecular system will be replaced by a two-level quantum system [15]. The Stark interaction in the hamiltonian (3.1) can be omitted for the calculation of the absorbed microwave power if the switching frequency is small enough for modulation broadening to be unimportant. The translational motion will be described classically_ This is justified to very good approximation in the present example since the velocity of the molecule only determines the residence time of the molecule in the microwave radiation field. A finite duration of the interaction induces the time-of-flight broadening. Thus the following much simplified hamiltonian approximates the complete hamiltonian (3-l)
h ( f ) = Ao,.s3 + Ahs, cos( at - kz).
(3.2)
st and ss are dimensionless spin-l/2 matrices, 0,. is the rotational transition frequency of a molecule moving with velocity v and X denotes EMf/t2. The dynamics generated by the hamiltonian (3.2) is completely characterized if the two-level matrices si, i= 1, 2. 3 or, equivalently, their expectation values ej are known as functions of time c. The equations of motions of the 5(r) are given by do,(r)/dr
= -c+u,(t).
U(r)
= U(t)(o(O)),
U(0) = 1.
(3 -3)
From the solutions of eq. (3.3) the power absorbed by a single molecule can be calculated. The result for a single molecule has then to be averaged over the molecular velocity distribution in the beam. 3.1. Solution of the equations of motion The system of eq. (3.3) matrix notation as
can
be expressed
= L(t)(&)).
in
(3-4)
where (U(I)) is a column vector with components o$r),i = 1. 2, 3. The coefficient matrix 0
- UL.
--h cos( wt - kz)
0 -kz)
0 (3.5)
(3-6)
satisfies the equation
dU(t)/dt=L(r)U(t).
(3-7)
Eq. (3.4) is a system of linear differential equations with periodic coefficients. According to the general theory of such systems [16] U(t) can be written in the form U(t)
= Y(r)
exp(rK),
(3.8)
where Y(t) and K are square matrices of the same dimension as L(t) and U(t)_ Y(t) is periodic with the same periodicity as L(t). The matrix K is constant. A detailed mathematical analysis of the structure of the solutions of eq. (3.4) -will be given in ref. [14]. Here instead of an exact solution eq. (3.4) is solved in the rotating-wave approximation (RWA) [17]. An analytical solution can be obtained for the RWA. The solution for a two-level system initially at the ground state is expressed as
- (h/N)sin
d~,(t)/dt=Acos(wt-kz)uz(r).
h cos(wt
(c(t))
u, = -[x(LV-~L.)/N’](I
-
du,(r)/dr=w,,u,(r)-Xcos(wr--~)q(r).
d(c(r))/dr
is periodic and skew hermitean. The solution of eq. (3.4) will be expressed by its mattizant U(r),
uZ= [X(w-w,.)/N’](I
- (X/N)sin a, = -1
+(X/N)‘(l
-cosNf)coskz (3.9a)
Nt sin kz, -cos Nf cos kz, - cos Nr),
Nt) sin kz (3.9b) (3.9c)
where N denotes [(w - o,)’ + A’]“‘. In order to judge the quality of the RWA the solution in eq. (3-g) must be compared with the exact solution of eq. (3.4). A general-comparison under what conditions the RWA solution is sufficiently accurate will be presented in ref. j14]. It could be shown for the case at hand that the two solutions agree well if the incident microwave radiation does not exceed several mW and if the frequency of the incident microwave radiation does not deviate more than about half an order of magnitude from the transition frequency considered. The solution in eq. (3.9) will therefore be used to estimate the microwave power absorbed by the molecular beam.
3.3.. Estimation $ the-absor&d
:-
hi&ow&e
&diatidn
absorbed-by. a singlk.molecule interacting for a-time B.-with the radiation fikld is calculated from-eq. (3.9j to be -__ .- ~. .- : -T&
poti&
P( oj-
. _.;-_,
-+j,
(n&&j$iIi_-zve.
.- .. -_
-:
+,g
-The: e&z&ion i& & (3.10) has -to be averaged ovkr the’ velocit;y distribution bi the inoltiuies- in the-su$ersonic-beam.‘The mean-velocity ZJ*d two different t&mptiratures-T,, and T, ch&cteiize -the velocity distributions of the translational degrees of freedom-parallel and perpendiculai to the betirii, respectively: These tem&atuies are defined operationally tis estiliatioh parameters foi the width of the density functions associated w&the molecular velocity distributions in the two directions. The perpendicular motion of the molecules can be neglected for our strongly collimated beam with a divergence
of = 0.7O in the microwave
interaction
region. The divergence was estimated from the geometry of the nozzle, skimmer and collimator. The molecular velocity distributionf( u,,)du,, parallel to the beam axis f( u,,)du,, a (M/2=R7.,,)1’2 xexp[ -M(vii
-u)‘/2RT,,]du,,
(3.11)
f( o)dw a (4 In 2/.rrllwZ,)“* In 2(w - w0)2/Ao&]do,
s 3.581
x
..
-:.-.
.:-_.
_-
-..
.(&i>: q+)&j&
-
:
_.
r;;;
. .
:.._.:_’ :;
: &,c__‘ :.
,-
Y._‘:. .-‘:__,.
._-_.
~. ,-,.\:-...:._-;_ ---. : T_:-
-I -._.
;_.+;+ .I..
_._
-_
.,
-for iii argqGs&&d 0-Q d&m with zir;zixing rat& df:OC: : &i-A-J -:-20. -~&~&Hi f&d’& t&.&p&-_ ing gas is alriiost e&ti~&lj~det&ni~ed by the-&rier gas :&t-this ‘dilution.--T~ansl~~o~al: temperattire-- T,, and stip&d& fl6w --velocity u were estimated a+$ding.to- &e’&dde&freez& model [18] (cf. see-_ tibn 4.3). T,, i’7.5 -K. atid u f 544 m ’ s-’ were obtained fdr a stagnation pres&e of 500 _Toti leading to a mean transit time of the ~mole&les through’ the grooG+ guide of -1.8 ms: The transit time gives rise to a-&&,tif-flight broadening of less th&n 300 Hi. The &nsl&ional temperature of 7.5 K in turn results & a Doppler bioadening of 1.5 kHz. Since. Doppler .broadening- is dominant the density function f(o) can -be tak&n ti an. almost constant factor in front of the integral in eq. (3.14) (P(o))
=/(w)lP(w)dw.
(3.15)
Inserting eq. (3.10) and (3.12) one obtains = 2;‘/*
xexp[ -4 where
In 2( nXw/Ao,,)
In ~(w-~~)~/A&,]J,,(XB),
n denotes
the number
of -molecules
(3.16) in the
groove
guide-~ Eq. (3.16) must be maximized -with
respect
to E in X = M,E/h
for- w = oO. The-opti-
~mum value of E is. found from the equation
(3.12)
where w,, is the resonance frequency of a molecule travelling with a speed equal to u. The half width (hwhm) boo introduced in eq. (3.12) is given by Aa, = 2w(2RT,,
_.-.
.L.‘:, -.I.. .
b&$
thg
Y _._L_,_
(P(w)>
leads to the di&ribution_.f(f(wjdwof the resonance frequencies [ 171
xexp[ -4
&&~+jn z,__i
-7 _
In ~/Mc’)‘/~-
10-7w(T,,~M)1’2,_- (3-13) . . where M denotes the -molar mass of the molecule tinder- investig+on;_R- tFe.gas cons& and c the ve&city oflfhe .+&wave radiation for the domitiant mbde m the: &o&e &de._ We now c&&t& the .average absorb& @w&r (P(W)) from‘- the micio&ave radiatidn for-. all .-
2./&M)--hB1,(M)=O.
(3.17)
Jo tid J1 represent Bessel functions of order zero and one; respectively_ For reasons to be discusseg below the physictiy‘relcvant solutiori of eq. (3.17) is the one.with the smallest numerical value.-From tables in ref. [19ja value of -A0 = l.iS was found. For -a representative cake using the dipole ‘moment Mr = 0.71521.- D -of ~.OCS.[20]. and B =.-1 ms the optimum value of- the electric field ainplitude.tias estimated tq be E-G 2 x 10S6 V which-corresponds to an-input mi&waire power of - 1 nW. Furthermoie wedn‘eed.a_ estimate of: the numbei 6f tiol& cules under study in -.th; beam. Using formGlas Given in ref. [18]‘we calculated a total- xiuml+r __of
-.
__
10” particles in the groove guide for : a$d&e diameter of 100 pm, a stagnation pressure-of 590 Torr and a temperature of 25OC_ If we further assume that the population of the rotational states follows a Boltzmann distribution with a characteristic rotational temperature of similar magnitude as the translational temperature we obtain a number of 107 OCS molecules in a 5% mixture with argon available for the.7 = 0 - 1 transition. Under these conditions 2: 10e5 nW will be absorbed from the incident microwave power of 1 nW according to eq. (3.16). The approximation invoked in eq. (3.15) becomes inappropriate for large input powers. This fact requires the solution of eq. (3.17) to be the numerically smallest solution which could be confirmed by a numerical evaluation of eq. (3.14). It can be visualized by the following arguments: Under the influence of the radiation field the molecules execute the Rabi oscillations [15] representing a sequence of absorptions and emissions between the levels involved in the transition_ The larger the input power, the faster is this oscillation. For a given input power the amplitude and the frequency of the Rabi oscillations depend on the detuning of the frequency of the incident radiation from the frequency of the transition involved_ The larger the detuning, the smaller is the amplitude and the higher the frequency of the oscillation. Due to the finite width of the molecular velocity distribution only a fraction of the molecules is exactly on resonance with the microwave radiation. For each group of molecules within a definitive velocity interval there is a different sequence of absorption and emission. The different sequences partly cancel each other for the mean interaction time resulting in a net decrease in absorbed or emitted power. The higher the power of the driving field, i.e. the higher the various Rabi frequencies, the more effective this cancellation will be. A comparison of experimental and theoretical values of absorbed microwave -power is given in section 4.1.
OCS -in order to test- t-h@_thcoretic$l Rredictions discussed in section 3. Both’ pitre.~aml‘Ar~ a& He-seeded beams were studied. Ouly the J.~.(l$l rotational transition fell into ‘the f&uenc$ range accessible with our instrument. .The seeded beams with a mixing ratio of 1: 20 between QCS and-the noble gas produced stronger signals -and smaller linewidths than the pure.beam as shown in figs. 6 and 7. The nozzle-to-skimmer distance z, was varied until an optimum in the signal intensity was
ocs J:l--0 p0:400Torr d,:lOOpm 2,:14mm P,,:lnW
v
-
I
12162959.3
KHz
--
..
Fig. 6. Rotational transition J = 12 0 of OCS-in a-pure b&m: pO: stagnation pressure; d,,: nozzle diameter: I,: nozzle-tc+ skimmer distance: Pm,: input microwa% power; number of sweeps: 30; time constant: 0.5 s.
~._ function ofthk
12162958.2
V
KHz
1oKHz F’ig. 7. Rotational
transition J_= 1 + 0 of OCS in an argonoteded beam; number of sweeps: 1: time constant: 0.5 s.
found at z, = 14 mm for a nozzle~diameter of 100 .pm. The rotational transition J = 0 --, 1 in pure as to an
experiment tiith a static gas instead-of a-molecular be&. This finding could only be interpreted as an induced.emission signal for the-supersonic beam. If an inversion of the populations of-the ;r = q-and J:=-1 levelsoccurred~d+ng the early-stag-es of the expansion rthe -spectroscopic. experiment onthe molecular be% would show ti stimulated emission signal ins&d,- of:the -exp&ed-.abso&tion s~giml. Later it: wa$ :fdU_nd. that an absorption signal -was obt&re&for -the J 10 -i 1 transition of- cyanb: .&etglene (HCCCN) -m a helium-seeded-beam. .‘-. --1 . ^_
-as
-HoA
-eqQ
3(1=J)‘+3(I*J)/2-12*J’ ,2I(?I_- 1) J(iJ - 1) ‘I ._
H,, = c(Fd);-
,- (4.1)
‘.
.(4.2)
..
where LeqQ -is the quadrupole coupling constant and ~c the’spin-rotation coupling constant. In the case. of cyanoacetylene -the hamiltonians must- be_. kxpre$sed- first ma- basis F1 by.‘coupling the angtilar. momentum-Jwith’thespin II: of the nitrogen. nucle&. -The f&&basis:P is the : k&t -.-of- the. coupling of.Ft with the spin &of t+proton.--To. fist order ~the hyperfme- energy is. gii+rby ._ :-_=I-_._-
.-.
dcS_
b&m generated~’ under-. optimal conditions. :-The: experimental~valu~ are _.comp&& with theoretical curves &&ui&d fi0.m eq& ($14) +id.(5_lSj_ :1,-i_:: Line+ths bettieen-2 and 10. kHz~(fw&n) @err’ obtained depending on the conditions during the supersonic expansion: The- lineshape &s well &i proximated_ by .a. gaussian lineshape in all G&S. The variation .of -the.linewidth with the supersonic beam- parameters will be further explored in. se& tion 4.3. The smallest linewidths obtained allowed the observation of spin-rotation splittings. -??he measurement of this splitting for the J = 0 -i 1 -transition of O”Cs in natural abundance has been reported pieviously [9]. The ! H spin,rotation splitting of the J = 0 + 1 transition of cyanoacetylene_could be observed in a helium-seeded_ beam.. (fig. .9). -Due- to- the quadrupole moment of the -nitrogen- nucleus -.this transition is splitinto a triplet. The central line of the triplet showed a further splitting a result of the spin-rotation ‘interaction with the hydrogen nucleus. Cyanoacetylene tlms exhibits a hybrid coupling case with -strong quadrupole coupling and -much tieaker spin-rotation coupling of a different nucleus 1211. The quadrupole and the spin-rotation hamiltonian for a linear molecule are given, respectively;. by
well’as in seeded OCS beams was observed with a shift of MO0 of-the signal phase as compared
;nput pow~i_f~r-~-l;iL~~~~d~~
_- -.
C&8--
0.6--
.
:.
I
0 .
:
.
0.4--
: .
o :
0
. .
0.2--
0 --
. l
E
.
0
l
.
c).2--
-0.4--
I
c
I
I
t
I
I
Cl6
0.4
0.2
I
*
0.8
*
1
*
1
20
:
’ I
' 40
-l+-H-LP 100 60 80
[nw] '"
Kg. 8.Signal power ;IS a function of input nicrowclve power: q : experimental values: a: theoretical k~es :hrorerical values according to eq. (3.15).
E,,
=
4.2. 1Microlttave-n1:cro~~:ave double-resonance esperinlen ts
~Q+~sRt’“w+Gt(‘w
= -eqPY(J,
I,,
+c(*'N)[F,(F, -J(I+
F,) +
l)--,(I,
+ 1)
I)] +C(‘H)[F(F+l)
--I*V,+Q--,(F,+1)],
according to eq_ (3.14); 0:
(4.3)
tvhere Y(J. I,, F,) represents the Casimir function 1211. The selection rules for hyperfine components i~f rotational transitions of linear molecules AJ = +l, AF=O. fl, AI,=O, AI,=0 ZIi, .AF,=O, lead to a spin-rotation splitting of 3c(‘H)/2 for the central hyperfine component of the quadrupoie triplet. From the measured splitting of 4.2(2) k J-lz the spin-rotation constant c(‘H) = 2.8(2) kHz \~as obtained. A list of all measured transition frequencies obtained with equal conditions during the generation of supersonic molecular beams is .st~~wn in tabie 1.
The observation of an emission signal for OCS prompted us to gain further information on the relative popularions of rotational levels of molecules in supersonic beams. For this purpose the experimental arrangement was modified to allow microwave-microwave (MW-MW) double-resonance experiments on three successive rotational levels. An oversized waveguide with a cross section of 100 mm by 10 mm was inserted into the beam path in the buffer chamber_-Two-small holes in the narrow walls of the guide let the be&n travel perpendicularly to the_wavefront in‘ the guide--The end of the waveguide was terminated in reffectionIess absorbers. The over&e waveguide was excited through a transition section- from’the appropriate standardwaveguide. -. -.: .For both OCS and ~c$~~GacetyIene the -rota-
I
: 0
-v 9098301.1
-Transition
-J; F,. F-, f, -~l,-,~-40,-_.-
ocs
0’3cs
l+k& __ ..
F,:F
- .- ..0;1;3/2~_r1.2,3/2 :.-
:-- ..- :0,1,3/2 <_1,2,>j/2
n) &I &sitio~ns’me&&d
and HCCCN
Intensity c)
; --: 60
70
1
80
:
90
.
_P[nW]
loo
-+‘O- transition of
-
._
‘-- -. 9098299.7 -. --- -ii_. -. 90983039 . -. ~.
in molecular beams a) Spin-rotation
(ftihm)’
i2123791.7 -‘._
: 1 ‘: .12123796.5 ._- .-
coupling constant
2.8
1.00
2.6 2_?
0.04 088
3.2
0.47 --. 0.81
2.8
3.0. 3.0
. -:
be&s Gith ‘seeding ratio of 1: 20. sta-gnation pressure of l@JO Toir,~n&fe diameter of 1 14’r&. A-i:/=-.: _, : ,_ _ ,_..--. ___~_. _.
b):Frok fit-.+&& @+.&&~fin~hape.:-. .::-- _-:~.:. I-:: -.:.___.-!’
_.
._’
;_. ..-.
I __ . .
-_ .-
: 50
levels J = 1 and J = 2 could be drawn from‘ the change in’ signal intensity of.the transition J = 0 + 1 aS a function of the pump power. The power for observing the signal was held constant-at 1 nW.
Linewidth b,
,-
__12162932.1.
‘in kelium-s&d&i --I !O@$-h; and no&e-t&~er~dist&edf
__ .-
: 40
signal power of the J=l
coupling constants (in kHz) of,OCS
Frequency
-
1,-J/2 -, o.-;1/2 _:l,-,3/2 ~.. _-: 4 d;- ,1/2
.-
30
-_
frequencies, linewidths and spin-rotation
Molecule
; -; 20
OCS -in an argon-seeded beam. as a function of the pumping power of the J = 14 2 transition.
-_ _-. tional transition Y-= 0 --, 1 was keaslired as-pr&iously while the transition J = 1 d-2. was pumped. Qualitative conclusions tin- the,popuIationsmof the
Transition
: 10
Fig. 10. Relative
KHz
Fig. 9. Rotational transition J = 0 4 1 of HCCCN in a hehumseeded beam; ~number of sweeps: 3: time constant: 0.5 s. ‘.
TabIe’l
; 1
-_.
-
_._
.-;..__ -_._. . .-. 1 : ,._. _. _--~- -.:_-_ *._ .-
.-
H.S.
12
Zivi et al. /
Micronace
specrrascopj
The results of these experiments are given in graphical form in figs. 10 and 11. Increasing pump power decreased the emission signal intensity in the experiments with OCS in helium- and argonseeded beams. This observation is consistent with a population transfer by the pumping from the J = 1 level to the J = 2 level. A decrease of the population of the J = 1 level will reduce the population inversion to the J= 0 level and thus decrease the emission signal for the corresponding transition_ The populationsp( J) of the three lowest rotational levels of OCS in the supersonic beam exhibit the order p(O) p(2). Fig. 12 represents the results of similar experiments on cyanoacetylene in helium-seeded beams. The intensity of the absorption signal of the J = 0 - 1 transition grew with increasing pump power. Analogous arguments yield the order of the populations as p(O) > p(1) > p(2). In view of the simi-
OCS/He
HC,N/He
beams :
1:20 ..
_
.’
z.y 14mm
d,,: 1OOpm
po: 1000 Tow
-_
l/lo
A 120 -l.lO-D
-
10
20
.
-
30
40
.
a
a
50
60
70
D
0
0
90
100
S LOO--
s
0
1
80
: - plnwl
Fig. 12. Relative signal power of. the J =I -+ 0 transition of HCCCN in a helium-seeded beam as a function of the pumping power of the J = 1 + 2 transition.
1:20
do: 100 pm
ofmp~ers&icmoieculti
L.y 14 mm apO:1250 Torr
.p,:lOOO Torr
larity of the
two molecules studied the emission for OCS was surprising. The only apparent difference between the two molecules lies in the magnitude of the permanent electric dipole moment which amounts to 0.71521 D for OCS [20] and 3.6(2) D for cyanoacetylene [22]. Above a certain pump power the signal intensities of the J = 0 + 1 transition do not longer change as can be seen from figs. 10-12. This must be attributed to a cancellation of the absorption-emission cycles of molecules in different velocity intervals as discussed in section 3. This fact also prevents a more quantitative analysis of the existing double-resonance data.
.p,: 1500 Torr
l/l,
0.6
4.3. Diagtzostics of super.soCc molecular beams
0.4 t
I : : ; : ; : : : : ; : : 0
1
10
20
30
40
50
60
70
80
90
-_P[flW]
100
Fig. 11. Relative signal power of the J =.l + 0 transition of OCS in a helium-seeded beam as a function of the pumping power of the J = 1+ 2 transition.
The spectroscopic measurements of molecules in the supersonic beam easiIy provided additional data which characterize the beam further. The parallel interaction between molecular: beam and microwave radiation was essential for’t_his application. Macroscopic flow.velocity, translational tern-. perature and apparent signal intensity could be
fti~~~idn;-bf(&~
@&&.&&)f-
:~~-e&&.
&&i_
a- *e&&e
;_~-
‘-
:,.
j&.._&.-&&&ed
_
g_-~;_.
as
&i-‘the :&liik m!aistatic
Ao =Lw,ri/c;
(4.4)
where o, is the resonance frequency of a particular transition under static conditions_ The second measurement in the_static gas needed to determine the Doppler shift could be perfcrmed with the same equipment alth&gh yith !ess accuracy due to the much larger‘ linewidth in thlr,static gas._The supersonic. flow velocity could then be calculated from eq. (4.4). The translational temperature Ii*,, could be obtained from the width of the Do]:pler-broadened resonance lines. Solving eq. (3.13) for T,, .we obtain T,, = 7.798 x 1012M( Ao,/w)~_
OCS/He
1:20 2,:14mm
d,,: 100 pm
(4.5)
In our experiment two effects might contribute to the line-broadening. Besides the Di~pler broadening the time-of-flight broadening I:‘+ust be considered. The finite interaction time of the molecules with the radiation field increase.;. the hnewidth further. This effect could safely be-neglected in our arrangement_ The interaction time in the 1 m long groove-guide is never less than 0.9 ms even for the fastest helium-seeded beams with molecular velocities up to 1.1 km s-l_ _A gaussiari lineshape is expected for the Doppler -broadening according to eq. .(3.X) which could be justified experimentally within the measuring accuracy. The current density I of the ;su,.ersonic beam measures the flow of beam partl‘?zs. The intensity of ;a rotational transition- is proportional to the current density I of the particular- molecule_ The intensity .is further dependent ‘on the .-$opulation difference between the- two rotational- states .connetted by the transition. ‘Both current .densities and- population. differences’vary: as. a_._function-of-. the cor$tions during the generation of the&per_-, .- I-._ -1 . soriic beam. -.
ated-at=ambient tcmper&urc of -22 &24C. m--‘. 1. --k lsimble $hencmenological description of Ithe sup.ersonic exp_ansion by the sudden-freeze. model will -be- employed _in-order to interpret the .experir mental results.~.T~s model [18j ~assumes that-the transition. from hydrodynamic to free molecular flow occurs instantaneously on a half sphere-with radius fi from the center of the nozzle. Within the half sphere the expansion is described by the equations for isentropic hydrodynamic flow. At the surface of the-half sphere, temperature T,, particle
16--
16-0 14--
12 --
lo---
a--
0
D D 0
6 --
4--
0
0
0
:
14
it al. ,I Microwaw- specrroScopy $super~onic mqledar. beams
H.S. OCSA-fe
-m
‘. :_-.
_. -. :
_ .;: _-:_..
1:20
do: 100 prn~
Zs: i4 mm
[m/s]
”
+ 1200 --
1180 --
1160 --
1140 --
0
1120-0 I
I
200
-
400
600
800
Fig. 14. Mean flow velocity as a function of stagnation
1000
l)[Ma(r,)]‘/2}-‘.
+(y-
pr = pO( 1 f (y - 1)[Ma(r,)]2/‘2) ES/He do: 100pm
(4.6) -‘/lr-“,
(4.7)
P,, [Torrl
1400
pressure of OCS in a helium-seeded
density pr and flow velocity uLIare given by [18] T,= T,{!
1200
beam.
~~r=n,Ma(r,)(l+(y-1)[Ma(r,)]‘./2)-i’~. (4.8) The subscript 0 refers to the reservoir, y denotes the ratio c,/c, of the moIar heat capacities, Ma(r)
1: 20 Ls-‘ 14 mm
v’nlax
c 1.0 -0.8-0.6 -0.4 --
Fig. 15. Apparent
0 0
intensity as a function of stagnation
pressure of OCS in a helium-seeded
beak.
-._
200 Fig:l6.
400
-,600-‘~
*.-
-loo6
12ow
I
Translaticinal temperature as a function of stagnation pressure of ?cS
the Mach number as. a function of the distance from the nozzle and g the velocity ..of sound: Outside the half sphere. the pqrtkles rngvk on straight trajectories_ It is only outside the half sphere where for Sgebmetrical reasoxis an anise tropy:of the tr&latiotial t&per&e develops. If -. Oe/Ar cl,: 100pm
1:20
. z.g 14 mm
.
- Po D-4
I
1400
in an -argon-seeded beam, .-
the condition (u,,) x- (uI ) is fulfilled then one obtains at distances I-> r, from the -nozzle the relations T,,(b) = r,, k&-J
=
qtrflrj*,
(1-9)
(4.1oj .-
HS.
16
OCS/At
Zivi et al. /
spectroscopy of supersonic mofecdar&e&k
Microwave
1120
dor100~
zg: 14mm
0
0.6 --
0 0
0
Fig. 18. Apparent
irsten.sity as a function of stagnation
pressure of OCS in an argon-seeded
f-44 = Pf(‘f/‘Y~
(4.11)
u(r)
(4.12)
=
Uf.
the mofar heat capacities entering eqs. (4.6)-(4-S) is estimated according to
1) -I- X,Yc/hc
From eq. (4.9) it is seen that the experimentally determined temperature T,, approximates the thermodynamic temperature r,. The utility of the sudden-freeze model lies in the fact that good empirical approximations are known for Ma( rrj and p(r). Ma(r,) is related to the Knudsen number Kn, in the reservoir [23]:
y = XSYSAYS -
Ma( rr ) = 1.2 f&t;‘“.
a0 = (yRTojM)“2,
(4.13j
The Knudsen number is given’at 25°C by ISno
= 318/p,J,
(Torr umj
(4.14a)
= 188/podo (Torr pm)
(4.14b)
for helium and by Kn,(Ar)
for argon, p(r) is empirically well established by 1241: p(r) = 0.157 po( do/r)‘.
(4.15)
In seeded beams there is a large excess of carrier gas. For seeded beams Kn, is approximated by the value of the carrier gas alone. The ratio y of
beam.
-
1)
s,/(Ys-lj+xJ(Yc-l)-’
(4.16)
where x, and X, are the mole fractions, ys and y, the corresponding ratios of seed ;uld carrier, respectively. The velocity of sound u. is calculated simply by (4.17)
with y from eq. (4.16) and M =xsMs + xcMc, where MS and MC are the molar masses of the seed and the carrier, respectively_ For gas mixtures with a ratio of 1: 20 between OCS and noble gas the following values are used: y = 1.65 and a0 = 775.4 m s-’ or a, = 315.8 m s-l for helium or argon, respectiveIy, at 25OC. Table 2 shows a comparison of the measured values of the translational iemperature T,, and the supersonic flow velocity u with the v&es calculated according to the suddenfreeze model. Within a series of measureme& the stagnation pressure pa was varied at ti fixed nozzle diameter do and nozzle-to-skimmer’distdnce z,. The sudden-freeze model assumes idea&gas be-
-.
i. _-_ _; i -.,_ ‘.- c.. H;S_r ziut _ii $;
.I
L i
_; -_
.
L
,,.
-.
-_.
:
.-_ ;;_-”
Obsetvxi-and
-_I$
-.
l_:_--c:.’ ,‘._;,’ ..?__ .
caIct&tt~~~+t
‘.
.-__
;-
..-.
:
_-:‘.___--_,;‘Y
velocity (in-‘m 8:.%) a& __-_ .._ .
f.&lleI
~200 300 4aO500 600 700 800.
. -.
-:-.
“::.-_-.;:
. 1112
-. 1146 -: ..
‘/
1140 11.52 1162
: 1155’
1000 ?I00 1200 1300 1400
-1181 1186 1192 1197 1204
1500
1211
1172
1166 1171 1174 1177
.’
~14.7 11.7 :.~ ’ 9.5 -8.0 6.7 6.1 5.8 -5.4 5.1 5.0 4.9 4.9 4.9
a) Nozzle &meter of 100 pm. nozzle-to-skimmer b, Estimated uncertainty of 7 m s-‘. ‘) Estimated
uncertainty
.;
i6.3
-- 19.6
:
:
__--
531‘
_--537
8.0 7.0 6.2 5.6 5.1 4.7 4.3 4.0
’
3.8 3.6 3.4
.L
_‘..
:
._._.
-:
.:.
r
._-;
‘_-‘;-f,,‘__
T : 1T :._.-
l?j.
‘._
-_ -_, -
_,
-.
--
CdC.
-.I.
.-:_
544::‘
6.0. .’ -_ 5.2 ..,
--:
4.2
4.2 4.3
5.5 ‘4.7
-548 549 549.
‘4.4
4.3
549. 545 -544.
549 549. 549
~
4.0 ,3.9’ 4.0
_ .-_
15.1 ..1x1 -’ . -6.9 -7.5 _ : 6.5
548 548.
temperature
_,. .-:
:-
538
545. 546. 547
~.__-
.,
544 545 548. 549 549’ 550. 552 552
distance of 14 mm and reservoir
.:5.0 5.4 5.7
_-_
5.7 6.1
-j_7
I :_
-.
-4.0 -3.8 3.5 -3.3 3.1
of 25°C.
of _I K.
haviour. Large deviations between observed and. calculated values in table;2 must be attributed td non-ideal effects during the expansion, such as cluster formation and _viscous_flow in the nozzle_ The latter -results in the formation of, boundary layers decreasing the effective nozzle diameter. This affects mainly the translational temperature and- the intensity of the beam. Table _2 shows for helium-seeded beams that ideal-conditions prev&f for stagnation pressures up to 1000 Torr. Argonseeded. beams. behave by far less- ideally than helium-seeded beams. This- fact can be inferred from ‘the differences of the real gas corrections of helium and argon.. It is -also well_ known that a plethora of multimers his formed.during exptision of argon-seeded beams at higher stagnation pressures.-T&decrease of the su&rsdr& fldw velocity above’ 1200 Torr. has to be: attributed _to the apparent 1 ‘deqgqe -of : t@i. noz%& diameter, ‘which dominates the increase in pressure. This behaviour leads to al lo.wer- Mach ~nt_rmberaccording to es, (4.i3).and (4.14b) _and in turn to a decreased flow velocity from e$ (48). ’ -. -- _-I
.:. .:._:-
~.... -53j.: ~. 1 _ 542
11.9 9.6
i
,_:.
.-_-‘.. . -_ ..
obs_ bl_--~.-
1160. 1163 -1165 1166 1168 ‘1169 1169 1170 1171 1171 1172
900
_=
.;.: Y:<.~,~‘:;?+ ._: :‘.-I_::- ._I-._f_ ,._.I i-r: ~ .- :, ._;_‘*r’,_: :_.,;I tr&Sl&otkl t~tnpe&@ (i&, K) Of -0.e in .su@x@nic he f! .;_ ;_._‘i-_ .;-_, ; QCS:kr=_!:20_ T -._~.-‘.__,.~:~ 1 ;‘-: -T-II ._ ‘:
5:-<_-_ ;_..‘ .
-1 _
_=:.._
--~:=I__ ‘.
-f tkf:
~~$&&ir’&&~,:f:.‘_~.
._ _..
TabI&-
~~&&&>y +&&&&
i&&@_+
..~
_
5. Conclusions
We have demonstrated the feasibility of bbservirig absorption or emission of microwave power by rotational transitions of molecules‘in a supersonic beam. We-.havey used a broadband groove guide spectrometer with Stark modulation in the 8 to 12 GHz range. The microwave radiation interacts collinearly with the molecular beam. The inethod allows for exceptionally h&h resolution of .rotationd spectra due to the narrow- velocity distribution of the molecules in the supersonic beam. Dipole moments may be determined from the Stark splittings though with. reduced resolution imposed. by the mhomogeneity _of the electric-field jn the groove guide: The only disadvantage :at present appears to bc the very limited sensitiv$y. The_l&h resohrtion must be bought at the expense .-. of-.thc-sensitivity.. -Simultr&eously the method h& also -&$ided accurate and convenient diagnostics ~of-supersonicmo1ecufa.r beams. In- the c:onventionaf perper@+ lar ju&n~ement of- microwave. radiation- and .
_.
.:
H.S. Ziai el al. / Microwave specmxc~py of supersonic moiedar
18
molecular beam such diagnostics with considerable effort.
are possible only
Acknowledgexnent Financial support by the Schweizerische Nationalfonds (project no. 2.219-0.79, 2.612-0.80 and 2.079-0.81) and by the authorities of the Swiss Federal Institute of Technology is gratefully acknowledged_ Furthermore we wish to thank 1Mr. M. Andrist for his expertise in setting-up the microwave superheterodyne detection system and Mr. W. Groth for the construction of the groove guide spectrometer in the workshop. We are grateful to Dr. P. Felder and Mr. 0. Diener for the construction of the supersonic molecular beam source. Messrs. G. Grassi. M. Oldani and M. Rodler helped us with the synthesis of cyanoacetylene.
References [l]
[1] [3] [4] [S] [6]
D.H. Levy. L. Wharton and R.E. Smalley. in: Chemical and biochemical applications of lasers. Vo!. 2, ed. C.B. Moore (Academic Press. New York. 1977). T.R. Dyke. G.R. Tomasevich and W. Klempcrer, J. Chem. Phys. 57 (1972) 2277. S.G. Kukolich. DE Ontes and J.H.S. Wang_ J. Chem. Phys. 61 (1974) 4686. P. Felder and Hs.H. Gtinthard. Chem. Phys. 71 (1982) 9. P. Huber-Walchli and J-W. Nibler, J. Chem. Phys. 76 (1982) 273. D. Bassi. A. Boschrtti. S. Marchetti, G. Scolcs and M. Zen. J. Chem. Phys. 74 (1981) 2221.
beams
..
[7] S. Yamazuki,.M Taki and Y_~Fujitani, J. Chem..PhyS. 74 (1981) 4476. (81 TJ. Balle, E.J. Campbell, M-R. Keenan and W.H. Flygafe, J. Chem. Phys. 72 (!980) 992: E.J. Campbell. L.W. Buxton, T.J. Balfe. M.R. Keen&r and W.H. Rygare, J. Chem. Phys. 74 (1981) 829. [9] H.S. Xvi, A_ Eauder and Hs.H. Gtinthard. Chem. Phys. Letters 83 (1981) 469. [lo] H. Witek, T. Tiining and J. Hoeft, in: Rarefied gas dynamics. Voi. 11 (1978) p. 1053. [ll] E.J. Campbell, W.G. Read and J.A. Shea, Chem Phys. Letters 94 (1983) 69; E.J. Campbell and S.G. Kukolich. Chem. Phys. 76 (1983) 225. [12] T. Nakahara and N. Karat&i. J. Inst. EL Corn. Japan 47 (1964) 43. [13] F. Schoch, L. Prost and Hs.H. Gtinthard. J. Phys. ES (1975) 563. [14] H.S. Zivi. A. Bauder and Hs.H. Gtinthard. to be published. [151-L. AlIen and J.H. Eberly. Optical resonance and two-level atoms (Wiley. New York, 1975). WI V.A. Yakubovich and V.M. Starshinskii. Linear differential equations with Periodic coefficients and their applications (Nauka, Moscow. 1972). 1171 A. Yariv. Quantum electronics (Wiley, New York. 1975). [ISI J.B. Anderson, in: Gasdynamics. Vol. 4. Molecular beams an< low density gas dynamics, ed. P.P. Wegener (Dekker. New York. 1970). u91 M. Abramowitz and J. Stegun. Handbook of mathematical functions (Dover. New York. 1970). WI J.S. Muenter. J. Chem. Phys. 48 (1968) 4544. WI C.H. Townes and A.L. Schawlow. Microwave spectroscopy (McGraw-Hill. New York, 1955). [22] A.A. Westrnberg and E-B. Wilson. J. Am. Chem. Sot. 72 (1950) 199. P31 M.A. Flucndy and K.P. Law!ey. Chemical applications of molecular beam scattering (Chapman and Hall, London. 1973).
[241 J.B. Anderson
and 3.B. Fenn. Phys. Fluids 8 (1964) 780.
-.
By applying the principles of microwave Stark _modulated spectroscopy to continuous_supersonic. beams a new tt&hn&e for -high-r&olutio_n rotational spectroscopy has been developed. The capabilities pf the new technique have been- demonstrated through inv&tigat&~oi the spin-rotation s&it&&s in O’?CS and HCCCN. S’rmu+neously the method allowed a diagnostic of supersonic molecular beams. Relative beam intensities. supersonic flow velocities and translational temReratures’of pure and seeded beams were determined from ;pc&ros&pic ineasurements of signal -intensities. Doppler--shifis and line- Gdths. respectively_ Microwave-microwave double-resonance experiments established deviatiohs from-the Roltxmann populations of rbtationgl energy levels in supersonic~molecular beams.
..
-For high dilution the flow field is mainly -de1. Introduction termined by the carrier gas which is cooled -. more extensively during the expansion than -the pure The merits of supersonic free expansion of gases molecular beam. This- means that ‘those molecular for spectroscopic applications have. been demondegrees of freedom which equilibrate quickly with strated many times. The techniques reported so far the thermal bath provided by the carrier gas,.i.e. include laser-induced. fluorescence [l], moleculartranslational and rotational, are more strongly beam electric resonance [2], beam: maser. spectroscooled in a seeded beam. copy [3] and many.others [4-71. .Traditionally, rotational transitions of moleA. supersonic- jet is formed when a gas- in a cules or molecular complexes in supersonic beams reservoir at thermal equilibrium is expanded have been -observed with the electric resonance through a nozzle into vacuum_ Thereby:thermal method or tith beam maser spectroscopy. Reenergy of the static gas is converted to- energy cently, Flygare and co-workers have developed a associated with the-directed mass 1flow in the exnew method to measure rotational trtinsitions in a panding. jet. In- order to produce -a continuous pulsed jet [S]. They combined the .principles~of molecular -beam a skimmer must. be used in a pulsed Fourier- transform microti;2ve-sp.ectroscopy differentially pumped system. Significant cooling, of translational and rotain a- Fabry-Perot .cgvity with a synchronously tional degrees of $e_edom o4Girs~during the-superpulsed supersonic jet- directed transversally to the sonic exp_sion:--~lbrational ..degrees _-of-:_freedbm microwave field. They obtained .a substz&d_re; are much less cooled. As a -consequence of the duction of the Doppler linewidth ~$&~li limits thetranslational cooling and decreasing particle denresolution in ‘static micro&&e spectroscopy. Hotiever,- they -obServed:a- complicated-line shapesa&sity the mole&les -do not experience_c_ollisions for incriasmg; _&s_tancesIf- they .travel‘in- a;_system‘*th ing from the braid solid angle of:tie jet traversing~ a-!+ &@ba&&&nd p&sue; -:.I .-_: _. the cavity. After-reporting our- first-rest&s with-$ In many tipphcations the molecules. fo be. in-different-‘experimental technique 1[9]the. rep.ort of an experiment ‘somewhat similar- to ours- came to _vestigated are.se$e_din;a sm&concentration into our -ztttenti& -l%rrir&et~ al.: [lO]_ measured the a- m,onatomic carrier gas, ustGlly helium or argon. -. 10301~0104/~4/$03~do .Q -Elsevier-Science Publishers B;\i. _ __ -_:. ; (l%rth~Holland PhysiCS Publishing Division) 1 ~. ,_ 1 .: .:
z
H.S.
Ziui et al. /
Microwaw
spectroscopy of supersonic molecular berets
microwave absorption of CsCl in a supersonic beam with the help of a small cylindrical cavity. The work reported here combines the principles of microwave Stark spectroscopy with the generation of continuous supersonic beams. A preliminary account of the method has been given recently [9]. Lately Campbell et al. [ll] added a Stark field to the Fabry-Perot spectrometer of the Flygare type in order to measure dipole moments. In our experiments the supersonic beam axis is collinear to the propagation of the microwave radiation. In addition to yielding highly resclved rotational spectra like in beam maser spectrometers such an arrangement opens the possibility for simultaneous diagnostics of supersonic molecular beams. From spectroscopic measurements the translational temperature, the supersonic flow velocity as well as the relative beam intensity could be inferred in relation to the beam source parameter settings_ Furthermore double-resonance experiments on two successive rotational transitions gave information on the relative populations of the corresponding levels in supersonic molecular beams.
_
1.
beam was passed through a -specially designed groove guide cell collinear to the microwave radiation but in opposite: direction. The microwave absorption which was modulated by the Stark effect was detected with a microwave superhete:odyne- receiver system. The specticnieter was controlled by a small computer PDP-8/I which was used for data collection and analysis_ 2. I. Su,versonic molecular beam source The supc;sonic beam source was of the differentially pumped variety. The beam was generated by expanding the gas through a converging nozzle with 50 to 200 pm diameter into the source chamber. Stagnation pressures ranged from 0.2 to 2 atm. The central part of the expanding jet was separated with a skimmer of 0.7 mm diameter and passed the buffer chamber where it was collimated finally with an iris. The skimmer was made from stainless steel by electro-erosion. Details of the supersonic beam source have been described previously [4]. A schematic view is given in fig. 1. _7.2_ Microwave groove guide Stark cell
2. Experimental
arrangement
A continuous supersonic beam was generated in the molecular beam source_ The well collimated
BUFFER CHAMBER
Investigations of rotational spectra of collisionless molecules in a supersonic beam with a waveguide spectrometer demand a waveguide structure which is open along the whole length in order to
SOURCE CHAMBER
NOZZLE I f
EDWARDS DIFFSTAK 16Of 700 M
t Fig. 1. Supersonic beam source.
GAS INLET BALZERS DIF 320
. .
..-
~.
..-
.-.
:__:
allow efficient 1pumping to siiffic~entlji~lo&_ pies’_ sures: This. .requirement could be, fulfi%d :-with -a groove guide [12] which’consists of ‘two: i’ m long parallel. aluminum plates. A rectangular~grcovd was milled lengthwise in the center.int_o both-plates. The cr&s &&ion bf our groove’guide is: sh_n.in fig. 2. Transverse electric (TE) and transverses magnetic (TM) modes are transmitted~along t,he.groove guide. The. dominant. modes.,TE,, a& TM,; are the only low-loss modes possible [12]. All other modes radiate out through the opening between the two plates. The microwave electric field of the TE,, mode is concentrated in the groove region and decays exponentially with increasing distance from the grooves in the opening between the plates. Thus the microwave electric field overlapped optimally the supersonic beam which was sent down through the center of the groove guide._.The separation between the plates and the dimensions of the groove were chosen such that the. cutoff frequency of the TE,, mode lies at.4.4 GHz. The groove guide could accommodate a molecular beam up to 30 mm diameter. The TE,, mode of a standard X-band rectangular waveguide could be transformed into the TE,, groove guide mode or vice versa without exciting radiating modes [12]. The groove guide is mounted in a vacuum jacket which is evacuated with the help -of three evenly distributed diffusion pumps with pumping speed of 280 L’s_‘_ The vacuum jacket-is connected via a short piece of flexible tubing to the supersonic molecular beam source. It is mounted on two x-y precision setting tables from a lathe which allow alignment of the groove guide cell to the molecular beam axis.
_ iL-,
2a
._ -
_--. :-
.__. .. -’
Fig. 2. Cross section of the- groove guide, u = 10 m& b = 40 mm,c=22mmandd~120n&n.
_--. _:.,-:.-The dired~ooii:of.pi-b;~~gatidn of- the molecular _I beam was -c;?llinear to that of the rnicr&wavc radi.‘--ation but in opposite. direction.-- in- order _to &lo&. ..,-for -efficient .pu-mpihg of the molecules’ emerging ‘: -from the: end-‘& ‘the @c&e guide the microWave .-- ~---- -’ radiation was. not fed .throu&‘a titisition scction~ f to the groove guide as at the other&d. Instead the microwave radiation was split symmetrically &th ‘- a dual-directional coupler and transmitted through two.waveguid& into the vacuum jacket. Two-small
horns illuminated’s larger horn at the end of the groove guide which excited the TE,, mode as shown. in fig. 3. At the other end a transition section [12] converted the radiation to the X-band waveguide. The molecular beam entered the groove guide assembly through a 6 mm hole drilled into a 90°- bend (cf, fig. 4) The complete assembly is shown schematically in fig. 5. _ For Stark modulation the two halves of the groove’ guide were electrically isolated from the rest of the assembly. One of the plates was driven by a zero-biased square-wave voltage while the other plate was grounded. The electric field lines of the Stark field and the electric component.of the microwave field are perpendicular to one another_ The selection rule AM = + 1 applies- for the quantum number of the projection of the angular momentum. 2.3. Microwave superheterodytte receiver system The microwave emitter-receiver system was modified from an earlier version of a superheterodyne detector [13]. The master oscillator (Varian X-13 klystron) was phase-locked to the harmonics of a 100 MHz quartz oscillator-multiplier chain. The difference frequency -between klystron and harmonic was mixed subsequently with the signal of a frequency synthesizer- (Programmed Test Sources, model PTS-160) to a constant interme&at& fiequ&y of the synchronizer (HewlettPackard,-model-8709A). The synthesizer frequency was- controlled by the small computer in steps as small as -100 Hz. The frequency of .ihe master oscillator could thus be swept in discrete steps of the same’size.
The microwave output of the groove gu&spectrometer. was -first -fed to a low-noise m&Wave
4
H-S. Zivi er al. / Microwave speczrascopy of supersonic moledar
beams
a
XklAND WAWEGUIDE.
I
I
-WAVE
X-BAND
W.WE GUIOE
GUIDE’
ELECTRICAL MSULAWJN
Fig_ 3. Excitation of the dominant mode of the grcove guide: (a) side view; (b) top view.
I
TRANSITION
GROhE/X-BAND
GUIDE
b
WAVE GUIDE BEND WITH HOLE
GROOVE
GUIDE
ELECTRICAL’NWLATKW
TRANSlTlON
GROOVE/X-BAND
X-BAND
GUIDE
WAVE GUIDE
--
l I Fig. 4. Transition from the groove guide to the standard rectangular waveguide; (a) top view; (b) side view.
280
280. I/s
I/s
280
I/s
7001/s
Fig. 5. Overallview of the spectrometer assembly. . amplifier (Watkins-J&n&n, &d&l 5310-432). Its output. was mixed in a balanced r&e:--preamplifier combination (RI%G, model DMl-18/16 j with the local o@l+orsignal. The local oscillator klystron was phase+cked to a frequency -exactly 30 MHz apart frog the master oscillator. ‘The 30 MHz signal ca&er &as elimidated by a first phase-sensitive detector. Demodulation of the 1 kHz stark modultition sidebands was accomplished in a second phase-sensitive detector. Its outp_ut could be presented on a recorder or sent to the small computer for signal enhancement by summation of several spectral recordings.
3. Theoretical description of the experiment In order to estimate the -sen.:itivity of our spectrometer. a simple model was introduced for the calculation -of the absorbed microwave radiation by the supersonic beam as a function of Al+ input power. Here we summarize the -theoretical -work, a full account, of which will. be published separately [14]. I 3.1. Model assumptions
-
It is well established that molecules in. super-sonic:beams move. independen!ly from-each qther if the- beam is observed sufficiently f&-away from the nozzle. Under these conditions the: xnoieculeS -do _not Suffer any &l&ions during the time scale
.-
__
1
52100 I/s
of the experimer& The ~sem_iclas:;icaltime-deperident hamiltonian k(t) for a single. collisionless molecule in the beam interacting with the micro-wave radiation-field &d the St&k field is ‘given by H(t)
= T,,,;+
j_l-‘J/2
-ET-‘D”‘(
a, p, y
-EsT-W+Y,
)zi!& cos( Of -
p, y)7Mrs(r)
kz)
+Hhfs_ (3-I)
The first term represents the- translational energy, the second term the rotational enesgy, the third and fourth terms the interaction with the micr& wave radiation and the Stark field, respectively, and .the last term accounts for possible Qperfine interactions. J denotes the angular momenturn and I the moments of ,inertia-tensor. The electric-field E cos(or Y kz) of the microwave radiation with frequency w and propagation coiistruu\-t k along-the z axis and the Stark field &s(t) interact with the permanent- electric ~&Polk moment Mr in the molecule-fixed system. s( t).specifies ~he~switching fbiction of. t& Stark field. The three-dimens&& representation D(‘)(&; /3, y) of ~-the rotation- group d+(3) ~expressed i& &l+ui angles. LY, p and y relates. the -mol&ule-fixed ~system to the laboratoy-fixed. -system. II(‘) in. its standard complex form- must be transformed with f to Cartesian co&di&af&1~ _ Follow&$ pi&tice for the d&r&ion ‘SE..ihe dynamics- of spectroscopic transitions the
co&&-
6
H.S_ Ziui et al. / Microwave spectroscropy of supersonic nroleculai beams
multi-level molecular system will be replaced by a two-level quantum system [15]. The Stark interaction in the hamiltonian (3.1) can be omitted for the calculation of the absorbed microwave power if the switching frequency is small enough for modulation broadening to be unimportant. The translational motion will be described classically_ This is justified to very good approximation in the present example since the velocity of the molecule only determines the residence time of the molecule in the microwave radiation field. A finite duration of the interaction induces the time-of-flight broadening. Thus the following much simplified hamiltonian approximates the complete hamiltonian (3-l)
h ( f ) = Ao,.s3 + Ahs, cos( at - kz).
(3.2)
st and ss are dimensionless spin-l/2 matrices, 0,. is the rotational transition frequency of a molecule moving with velocity v and X denotes EMf/t2. The dynamics generated by the hamiltonian (3.2) is completely characterized if the two-level matrices si, i= 1, 2. 3 or, equivalently, their expectation values ej are known as functions of time c. The equations of motions of the 5(r) are given by do,(r)/dr
= -c+u,(t).
U(r)
= U(t)(o(O)),
U(0) = 1.
(3 -3)
From the solutions of eq. (3.3) the power absorbed by a single molecule can be calculated. The result for a single molecule has then to be averaged over the molecular velocity distribution in the beam. 3.1. Solution of the equations of motion The system of eq. (3.3) matrix notation as
can
be expressed
= L(t)(&)).
in
(3-4)
where (U(I)) is a column vector with components o$r),i = 1. 2, 3. The coefficient matrix 0
- UL.
--h cos( wt - kz)
0 -kz)
0 (3.5)
(3-6)
satisfies the equation
dU(t)/dt=L(r)U(t).
(3-7)
Eq. (3.4) is a system of linear differential equations with periodic coefficients. According to the general theory of such systems [16] U(t) can be written in the form U(t)
= Y(r)
exp(rK),
(3.8)
where Y(t) and K are square matrices of the same dimension as L(t) and U(t)_ Y(t) is periodic with the same periodicity as L(t). The matrix K is constant. A detailed mathematical analysis of the structure of the solutions of eq. (3.4) -will be given in ref. [14]. Here instead of an exact solution eq. (3.4) is solved in the rotating-wave approximation (RWA) [17]. An analytical solution can be obtained for the RWA. The solution for a two-level system initially at the ground state is expressed as
- (h/N)sin
d~,(t)/dt=Acos(wt-kz)uz(r).
h cos(wt
(c(t))
u, = -[x(LV-~L.)/N’](I
-
du,(r)/dr=w,,u,(r)-Xcos(wr--~)q(r).
d(c(r))/dr
is periodic and skew hermitean. The solution of eq. (3.4) will be expressed by its mattizant U(r),
uZ= [X(w-w,.)/N’](I
- (X/N)sin a, = -1
+(X/N)‘(l
-cosNf)coskz (3.9a)
Nt sin kz, -cos Nf cos kz, - cos Nr),
Nt) sin kz (3.9b) (3.9c)
where N denotes [(w - o,)’ + A’]“‘. In order to judge the quality of the RWA the solution in eq. (3-g) must be compared with the exact solution of eq. (3.4). A general-comparison under what conditions the RWA solution is sufficiently accurate will be presented in ref. j14]. It could be shown for the case at hand that the two solutions agree well if the incident microwave radiation does not exceed several mW and if the frequency of the incident microwave radiation does not deviate more than about half an order of magnitude from the transition frequency considered. The solution in eq. (3.9) will therefore be used to estimate the microwave power absorbed by the molecular beam.
3.3.. Estimation $ the-absor&d
:-
hi&ow&e
&diatidn
absorbed-by. a singlk.molecule interacting for a-time B.-with the radiation fikld is calculated from-eq. (3.9j to be -__ .- ~. .- : -T&
poti&
P( oj-
. _.;-_,
-+j,
(n&&j$iIi_-zve.
.- .. -_
-:
+,g
-The: e&z&ion i& & (3.10) has -to be averaged ovkr the’ velocit;y distribution bi the inoltiuies- in the-su$ersonic-beam.‘The mean-velocity ZJ*d two different t&mptiratures-T,, and T, ch&cteiize -the velocity distributions of the translational degrees of freedom-parallel and perpendiculai to the betirii, respectively: These tem&atuies are defined operationally tis estiliatioh parameters foi the width of the density functions associated w&the molecular velocity distributions in the two directions. The perpendicular motion of the molecules can be neglected for our strongly collimated beam with a divergence
of = 0.7O in the microwave
interaction
region. The divergence was estimated from the geometry of the nozzle, skimmer and collimator. The molecular velocity distributionf( u,,)du,, parallel to the beam axis f( u,,)du,, a (M/2=R7.,,)1’2 xexp[ -M(vii
-u)‘/2RT,,]du,,
(3.11)
f( o)dw a (4 In 2/.rrllwZ,)“* In 2(w - w0)2/Ao&]do,
s 3.581
x
..
-:.-.
.:-_.
_-
-..
.(&i>: q+)&j&
-
:
_.
r;;;
. .
:.._.:_’ :;
: &,c__‘ :.
,-
Y._‘:. .-‘:__,.
._-_.
~. ,-,.\:-...:._-;_ ---. : T_:-
-I -._.
;_.+;+ .I..
_._
-_
.,
-for iii argqGs&&d 0-Q d&m with zir;zixing rat& df:OC: : &i-A-J -:-20. -~&~&Hi f&d’& t&.&p&-_ ing gas is alriiost e&ti~&lj~det&ni~ed by the-&rier gas :&t-this ‘dilution.--T~ansl~~o~al: temperattire-- T,, and stip&d& fl6w --velocity u were estimated a+$ding.to- &e’&dde&freez& model [18] (cf. see-_ tibn 4.3). T,, i’7.5 -K. atid u f 544 m ’ s-’ were obtained fdr a stagnation pres&e of 500 _Toti leading to a mean transit time of the ~mole&les through’ the grooG+ guide of -1.8 ms: The transit time gives rise to a-&&,tif-flight broadening of less th&n 300 Hi. The &nsl&ional temperature of 7.5 K in turn results & a Doppler bioadening of 1.5 kHz. Since. Doppler .broadening- is dominant the density function f(o) can -be tak&n ti an. almost constant factor in front of the integral in eq. (3.14) (P(o))
=/(w)lP(w)dw.
(3.15)
Inserting eq. (3.10) and (3.12) one obtains = 2;‘/*
xexp[ -4 where
In 2( nXw/Ao,,)
In ~(w-~~)~/A&,]J,,(XB),
n denotes
the number
of -molecules
(3.16) in the
groove
guide-~ Eq. (3.16) must be maximized -with
respect
to E in X = M,E/h
for- w = oO. The-opti-
~mum value of E is. found from the equation
(3.12)
where w,, is the resonance frequency of a molecule travelling with a speed equal to u. The half width (hwhm) boo introduced in eq. (3.12) is given by Aa, = 2w(2RT,,
_.-.
.L.‘:, -.I.. .
b&$
thg
Y _._L_,_
(P(w)>
leads to the di&ribution_.f(f(wjdwof the resonance frequencies [ 171
xexp[ -4
&&~+jn z,__i
-7 _
In ~/Mc’)‘/~-
10-7w(T,,~M)1’2,_- (3-13) . . where M denotes the -molar mass of the molecule tinder- investig+on;_R- tFe.gas cons& and c the ve&city oflfhe .+&wave radiation for the domitiant mbde m the: &o&e &de._ We now c&&t& the .average absorb& @w&r (P(W)) from‘- the micio&ave radiatidn for-. all .-
2./&M)--hB1,(M)=O.
(3.17)
Jo tid J1 represent Bessel functions of order zero and one; respectively_ For reasons to be discusseg below the physictiy‘relcvant solutiori of eq. (3.17) is the one.with the smallest numerical value.-From tables in ref. [19ja value of -A0 = l.iS was found. For -a representative cake using the dipole ‘moment Mr = 0.71521.- D -of ~.OCS.[20]. and B =.-1 ms the optimum value of- the electric field ainplitude.tias estimated tq be E-G 2 x 10S6 V which-corresponds to an-input mi&waire power of - 1 nW. Furthermoie wedn‘eed.a_ estimate of: the numbei 6f tiol& cules under study in -.th; beam. Using formGlas Given in ref. [18]‘we calculated a total- xiuml+r __of
-.
__
10” particles in the groove guide for : a$d&e diameter of 100 pm, a stagnation pressure-of 590 Torr and a temperature of 25OC_ If we further assume that the population of the rotational states follows a Boltzmann distribution with a characteristic rotational temperature of similar magnitude as the translational temperature we obtain a number of 107 OCS molecules in a 5% mixture with argon available for the.7 = 0 - 1 transition. Under these conditions 2: 10e5 nW will be absorbed from the incident microwave power of 1 nW according to eq. (3.16). The approximation invoked in eq. (3.15) becomes inappropriate for large input powers. This fact requires the solution of eq. (3.17) to be the numerically smallest solution which could be confirmed by a numerical evaluation of eq. (3.14). It can be visualized by the following arguments: Under the influence of the radiation field the molecules execute the Rabi oscillations [15] representing a sequence of absorptions and emissions between the levels involved in the transition_ The larger the input power, the faster is this oscillation. For a given input power the amplitude and the frequency of the Rabi oscillations depend on the detuning of the frequency of the incident radiation from the frequency of the transition involved_ The larger the detuning, the smaller is the amplitude and the higher the frequency of the oscillation. Due to the finite width of the molecular velocity distribution only a fraction of the molecules is exactly on resonance with the microwave radiation. For each group of molecules within a definitive velocity interval there is a different sequence of absorption and emission. The different sequences partly cancel each other for the mean interaction time resulting in a net decrease in absorbed or emitted power. The higher the power of the driving field, i.e. the higher the various Rabi frequencies, the more effective this cancellation will be. A comparison of experimental and theoretical values of absorbed microwave -power is given in section 4.1.
OCS -in order to test- t-h@_thcoretic$l Rredictions discussed in section 3. Both’ pitre.~aml‘Ar~ a& He-seeded beams were studied. Ouly the J.~.(l$l rotational transition fell into ‘the f&uenc$ range accessible with our instrument. .The seeded beams with a mixing ratio of 1: 20 between QCS and-the noble gas produced stronger signals -and smaller linewidths than the pure.beam as shown in figs. 6 and 7. The nozzle-to-skimmer distance z, was varied until an optimum in the signal intensity was
ocs J:l--0 p0:400Torr d,:lOOpm 2,:14mm P,,:lnW
v
-
I
12162959.3
KHz
--
..
Fig. 6. Rotational transition J = 12 0 of OCS-in a-pure b&m: pO: stagnation pressure; d,,: nozzle diameter: I,: nozzle-tc+ skimmer distance: Pm,: input microwa% power; number of sweeps: 30; time constant: 0.5 s.
~._ function ofthk
12162958.2
V
KHz
1oKHz F’ig. 7. Rotational
transition J_= 1 + 0 of OCS in an argonoteded beam; number of sweeps: 1: time constant: 0.5 s.
found at z, = 14 mm for a nozzle~diameter of 100 .pm. The rotational transition J = 0 --, 1 in pure as to an
experiment tiith a static gas instead-of a-molecular be&. This finding could only be interpreted as an induced.emission signal for the-supersonic beam. If an inversion of the populations of-the ;r = q-and J:=-1 levelsoccurred~d+ng the early-stag-es of the expansion rthe -spectroscopic. experiment onthe molecular be% would show ti stimulated emission signal ins&d,- of:the -exp&ed-.abso&tion s~giml. Later it: wa$ :fdU_nd. that an absorption signal -was obt&re&for -the J 10 -i 1 transition of- cyanb: .&etglene (HCCCN) -m a helium-seeded-beam. .‘-. --1 . ^_
-as
-HoA
-eqQ
3(1=J)‘+3(I*J)/2-12*J’ ,2I(?I_- 1) J(iJ - 1) ‘I ._
H,, = c(Fd);-
,- (4.1)
‘.
.(4.2)
..
where LeqQ -is the quadrupole coupling constant and ~c the’spin-rotation coupling constant. In the case. of cyanoacetylene -the hamiltonians must- be_. kxpre$sed- first ma- basis F1 by.‘coupling the angtilar. momentum-Jwith’thespin II: of the nitrogen. nucle&. -The f&&basis:P is the : k&t -.-of- the. coupling of.Ft with the spin &of t+proton.--To. fist order ~the hyperfme- energy is. gii+rby ._ :-_=I-_._-
.-.
dcS_
b&m generated~’ under-. optimal conditions. :-The: experimental~valu~ are _.comp&& with theoretical curves &&ui&d fi0.m eq& ($14) +id.(5_lSj_ :1,-i_:: Line+ths bettieen-2 and 10. kHz~(fw&n) @err’ obtained depending on the conditions during the supersonic expansion: The- lineshape &s well &i proximated_ by .a. gaussian lineshape in all G&S. The variation .of -the.linewidth with the supersonic beam- parameters will be further explored in. se& tion 4.3. The smallest linewidths obtained allowed the observation of spin-rotation splittings. -??he measurement of this splitting for the J = 0 -i 1 -transition of O”Cs in natural abundance has been reported pieviously [9]. The ! H spin,rotation splitting of the J = 0 + 1 transition of cyanoacetylene_could be observed in a helium-seeded_ beam.. (fig. .9). -Due- to- the quadrupole moment of the -nitrogen- nucleus -.this transition is splitinto a triplet. The central line of the triplet showed a further splitting a result of the spin-rotation ‘interaction with the hydrogen nucleus. Cyanoacetylene tlms exhibits a hybrid coupling case with -strong quadrupole coupling and -much tieaker spin-rotation coupling of a different nucleus 1211. The quadrupole and the spin-rotation hamiltonian for a linear molecule are given, respectively;. by
well’as in seeded OCS beams was observed with a shift of MO0 of-the signal phase as compared
;nput pow~i_f~r-~-l;iL~~~~d~~
_- -.
C&8--
0.6--
.
:.
I
0 .
:
.
0.4--
: .
o :
0
. .
0.2--
0 --
. l
E
.
0
l
.
c).2--
-0.4--
I
c
I
I
t
I
I
Cl6
0.4
0.2
I
*
0.8
*
1
*
1
20
:
’ I
' 40
-l+-H-LP 100 60 80
[nw] '"
Kg. 8.Signal power ;IS a function of input nicrowclve power: q : experimental values: a: theoretical k~es :hrorerical values according to eq. (3.15).
E,,
=
4.2. 1Microlttave-n1:cro~~:ave double-resonance esperinlen ts
~Q+~sRt’“w+Gt(‘w
= -eqPY(J,
I,,
+c(*'N)[F,(F, -J(I+
F,) +
l)--,(I,
+ 1)
I)] +C(‘H)[F(F+l)
--I*V,+Q--,(F,+1)],
according to eq_ (3.14); 0:
(4.3)
tvhere Y(J. I,, F,) represents the Casimir function 1211. The selection rules for hyperfine components i~f rotational transitions of linear molecules AJ = +l, AF=O. fl, AI,=O, AI,=0 ZIi, .AF,=O, lead to a spin-rotation splitting of 3c(‘H)/2 for the central hyperfine component of the quadrupoie triplet. From the measured splitting of 4.2(2) k J-lz the spin-rotation constant c(‘H) = 2.8(2) kHz \~as obtained. A list of all measured transition frequencies obtained with equal conditions during the generation of supersonic molecular beams is .st~~wn in tabie 1.
The observation of an emission signal for OCS prompted us to gain further information on the relative popularions of rotational levels of molecules in supersonic beams. For this purpose the experimental arrangement was modified to allow microwave-microwave (MW-MW) double-resonance experiments on three successive rotational levels. An oversized waveguide with a cross section of 100 mm by 10 mm was inserted into the beam path in the buffer chamber_-Two-small holes in the narrow walls of the guide let the be&n travel perpendicularly to the_wavefront in‘ the guide--The end of the waveguide was terminated in reffectionIess absorbers. The over&e waveguide was excited through a transition section- from’the appropriate standardwaveguide. -. -.: .For both OCS and ~c$~~GacetyIene the -rota-
I
: 0
-v 9098301.1
-Transition
-J; F,. F-, f, -~l,-,~-40,-_.-
ocs
0’3cs
l+k& __ ..
F,:F
- .- ..0;1;3/2~_r1.2,3/2 :.-
:-- ..- :0,1,3/2 <_1,2,>j/2
n) &I &sitio~ns’me&&d
and HCCCN
Intensity c)
; --: 60
70
1
80
:
90
.
_P[nW]
loo
-+‘O- transition of
-
._
‘-- -. 9098299.7 -. --- -ii_. -. 90983039 . -. ~.
in molecular beams a) Spin-rotation
(ftihm)’
i2123791.7 -‘._
: 1 ‘: .12123796.5 ._- .-
coupling constant
2.8
1.00
2.6 2_?
0.04 088
3.2
0.47 --. 0.81
2.8
3.0. 3.0
. -:
be&s Gith ‘seeding ratio of 1: 20. sta-gnation pressure of l@JO Toir,~n&fe diameter of 1 14’r&. A-i:/=-.: _, : ,_ _ ,_..--. ___~_. _.
b):Frok fit-.+&& @+.&&~fin~hape.:-. .::-- _-:~.:. I-:: -.:.___.-!’
_.
._’
;_. ..-.
I __ . .
-_ .-
: 50
levels J = 1 and J = 2 could be drawn from‘ the change in’ signal intensity of.the transition J = 0 + 1 aS a function of the pump power. The power for observing the signal was held constant-at 1 nW.
Linewidth b,
,-
__12162932.1.
‘in kelium-s&d&i --I !O@$-h; and no&e-t&~er~dist&edf
__ .-
: 40
signal power of the J=l
coupling constants (in kHz) of,OCS
Frequency
-
1,-J/2 -, o.-;1/2 _:l,-,3/2 ~.. _-: 4 d;- ,1/2
.-
30
-_
frequencies, linewidths and spin-rotation
Molecule
; -; 20
OCS -in an argon-seeded beam. as a function of the pumping power of the J = 14 2 transition.
-_ _-. tional transition Y-= 0 --, 1 was keaslired as-pr&iously while the transition J = 1 d-2. was pumped. Qualitative conclusions tin- the,popuIationsmof the
Transition
: 10
Fig. 10. Relative
KHz
Fig. 9. Rotational transition J = 0 4 1 of HCCCN in a hehumseeded beam; ~number of sweeps: 3: time constant: 0.5 s. ‘.
TabIe’l
; 1
-_.
-
_._
.-;..__ -_._. . .-. 1 : ,._. _. _--~- -.:_-_ *._ .-
.-
H.S.
12
Zivi et al. /
Micronace
specrrascopj
The results of these experiments are given in graphical form in figs. 10 and 11. Increasing pump power decreased the emission signal intensity in the experiments with OCS in helium- and argonseeded beams. This observation is consistent with a population transfer by the pumping from the J = 1 level to the J = 2 level. A decrease of the population of the J = 1 level will reduce the population inversion to the J= 0 level and thus decrease the emission signal for the corresponding transition_ The populationsp( J) of the three lowest rotational levels of OCS in the supersonic beam exhibit the order p(O)
OCS/He
HC,N/He
beams :
1:20 ..
_
.’
z.y 14mm
d,,: 1OOpm
po: 1000 Tow
-_
l/lo
A 120 -l.lO-D
-
10
20
.
-
30
40
.
a
a
50
60
70
D
0
0
90
100
S LOO--
s
0
1
80
: - plnwl
Fig. 12. Relative signal power of. the J =I -+ 0 transition of HCCCN in a helium-seeded beam as a function of the pumping power of the J = 1 + 2 transition.
1:20
do: 100 pm
ofmp~ers&icmoieculti
L.y 14 mm apO:1250 Torr
.p,:lOOO Torr
larity of the
two molecules studied the emission for OCS was surprising. The only apparent difference between the two molecules lies in the magnitude of the permanent electric dipole moment which amounts to 0.71521 D for OCS [20] and 3.6(2) D for cyanoacetylene [22]. Above a certain pump power the signal intensities of the J = 0 + 1 transition do not longer change as can be seen from figs. 10-12. This must be attributed to a cancellation of the absorption-emission cycles of molecules in different velocity intervals as discussed in section 3. This fact also prevents a more quantitative analysis of the existing double-resonance data.
.p,: 1500 Torr
l/l,
0.6
4.3. Diagtzostics of super.soCc molecular beams
0.4 t
I : : ; : ; : : : : ; : : 0
1
10
20
30
40
50
60
70
80
90
-_P[flW]
100
Fig. 11. Relative signal power of the J =.l + 0 transition of OCS in a helium-seeded beam as a function of the pumping power of the J = 1+ 2 transition.
The spectroscopic measurements of molecules in the supersonic beam easiIy provided additional data which characterize the beam further. The parallel interaction between molecular: beam and microwave radiation was essential for’t_his application. Macroscopic flow.velocity, translational tern-. perature and apparent signal intensity could be
fti~~~idn;-bf(&~
@&&.&&)f-
:~~-e&&.
&&i_
a- *e&&e
;_~-
‘-
:,.
j&.._&.-&&&ed
_
g_-~;_.
as
&i-‘the :&liik m!aistatic
Ao =Lw,ri/c;
(4.4)
where o, is the resonance frequency of a particular transition under static conditions_ The second measurement in the_static gas needed to determine the Doppler shift could be perfcrmed with the same equipment alth&gh yith !ess accuracy due to the much larger‘ linewidth in thlr,static gas._The supersonic. flow velocity could then be calculated from eq. (4.4). The translational temperature Ii*,, could be obtained from the width of the Do]:pler-broadened resonance lines. Solving eq. (3.13) for T,, .we obtain T,, = 7.798 x 1012M( Ao,/w)~_
OCS/He
1:20 2,:14mm
d,,: 100 pm
(4.5)
In our experiment two effects might contribute to the line-broadening. Besides the Di~pler broadening the time-of-flight broadening I:‘+ust be considered. The finite interaction time of the molecules with the radiation field increase.;. the hnewidth further. This effect could safely be-neglected in our arrangement_ The interaction time in the 1 m long groove-guide is never less than 0.9 ms even for the fastest helium-seeded beams with molecular velocities up to 1.1 km s-l_ _A gaussiari lineshape is expected for the Doppler -broadening according to eq. .(3.X) which could be justified experimentally within the measuring accuracy. The current density I of the ;su,.ersonic beam measures the flow of beam partl‘?zs. The intensity of ;a rotational transition- is proportional to the current density I of the particular- molecule_ The intensity .is further dependent ‘on the .-$opulation difference between the- two rotational- states .connetted by the transition. ‘Both current .densities and- population. differences’vary: as. a_._function-of-. the cor$tions during the generation of the&per_-, .- I-._ -1 . soriic beam. -.
ated-at=ambient tcmper&urc of -22 &24C. m--‘. 1. --k lsimble $hencmenological description of Ithe sup.ersonic exp_ansion by the sudden-freeze. model will -be- employed _in-order to interpret the .experir mental results.~.T~s model [18j ~assumes that-the transition. from hydrodynamic to free molecular flow occurs instantaneously on a half sphere-with radius fi from the center of the nozzle. Within the half sphere the expansion is described by the equations for isentropic hydrodynamic flow. At the surface of the-half sphere, temperature T,, particle
16--
16-0 14--
12 --
lo---
a--
0
D D 0
6 --
4--
0
0
0
:
14
it al. ,I Microwaw- specrroScopy $super~onic mqledar. beams
H.S. OCSA-fe
-m
‘. :_-.
_. -. :
_ .;: _-:_..
1:20
do: 100 prn~
Zs: i4 mm
[m/s]
”
+ 1200 --
1180 --
1160 --
1140 --
0
1120-0 I
I
200
-
400
600
800
Fig. 14. Mean flow velocity as a function of stagnation
1000
l)[Ma(r,)]‘/2}-‘.
+(y-
pr = pO( 1 f (y - 1)[Ma(r,)]2/‘2) ES/He do: 100pm
(4.6) -‘/lr-“,
(4.7)
P,, [Torrl
1400
pressure of OCS in a helium-seeded
density pr and flow velocity uLIare given by [18] T,= T,{!
1200
beam.
~~r=n,Ma(r,)(l+(y-1)[Ma(r,)]‘./2)-i’~. (4.8) The subscript 0 refers to the reservoir, y denotes the ratio c,/c, of the moIar heat capacities, Ma(r)
1: 20 Ls-‘ 14 mm
v’nlax
c 1.0 -0.8-0.6 -0.4 --
Fig. 15. Apparent
0 0
intensity as a function of stagnation
pressure of OCS in a helium-seeded
beak.
-._
200 Fig:l6.
400
-,600-‘~
*.-
-loo6
12ow
I
Translaticinal temperature as a function of stagnation pressure of ?cS
the Mach number as. a function of the distance from the nozzle and g the velocity ..of sound: Outside the half sphere. the pqrtkles rngvk on straight trajectories_ It is only outside the half sphere where for Sgebmetrical reasoxis an anise tropy:of the tr&latiotial t&per&e develops. If -. Oe/Ar cl,: 100pm
1:20
. z.g 14 mm
.
- Po D-4
I
1400
in an -argon-seeded beam, .-
the condition (u,,) x- (uI ) is fulfilled then one obtains at distances I-> r, from the -nozzle the relations T,,(b) = r,, k&-J
=
qtrflrj*,
(1-9)
(4.1oj .-
HS.
16
OCS/At
Zivi et al. /
spectroscopy of supersonic mofecdar&e&k
Microwave
1120
dor100~
zg: 14mm
0
0.6 --
0 0
0
Fig. 18. Apparent
irsten.sity as a function of stagnation
pressure of OCS in an argon-seeded
f-44 = Pf(‘f/‘Y~
(4.11)
u(r)
(4.12)
=
Uf.
the mofar heat capacities entering eqs. (4.6)-(4-S) is estimated according to
1) -I- X,Yc/hc
From eq. (4.9) it is seen that the experimentally determined temperature T,, approximates the thermodynamic temperature r,. The utility of the sudden-freeze model lies in the fact that good empirical approximations are known for Ma( rrj and p(r). Ma(r,) is related to the Knudsen number Kn, in the reservoir [23]:
y = XSYSAYS -
Ma( rr ) = 1.2 f&t;‘“.
a0 = (yRTojM)“2,
(4.13j
The Knudsen number is given’at 25°C by ISno
= 318/p,J,
(Torr umj
(4.14a)
= 188/podo (Torr pm)
(4.14b)
for helium and by Kn,(Ar)
for argon, p(r) is empirically well established by 1241: p(r) = 0.157 po( do/r)‘.
(4.15)
In seeded beams there is a large excess of carrier gas. For seeded beams Kn, is approximated by the value of the carrier gas alone. The ratio y of
beam.
-
1)
s,/(Ys-lj+xJ(Yc-l)-’
(4.16)
where x, and X, are the mole fractions, ys and y, the corresponding ratios of seed ;uld carrier, respectively. The velocity of sound u. is calculated simply by (4.17)
with y from eq. (4.16) and M =xsMs + xcMc, where MS and MC are the molar masses of the seed and the carrier, respectively_ For gas mixtures with a ratio of 1: 20 between OCS and noble gas the following values are used: y = 1.65 and a0 = 775.4 m s-’ or a, = 315.8 m s-l for helium or argon, respectiveIy, at 25OC. Table 2 shows a comparison of the measured values of the translational iemperature T,, and the supersonic flow velocity u with the v&es calculated according to the suddenfreeze model. Within a series of measureme& the stagnation pressure pa was varied at ti fixed nozzle diameter do and nozzle-to-skimmer’distdnce z,. The sudden-freeze model assumes idea&gas be-
-.
i. _-_ _; i -.,_ ‘.- c.. H;S_r ziut _ii $;
.I
L i
_; -_
.
L
,,.
-.
-_.
:
.-_ ;;_-”
Obsetvxi-and
-_I$
-.
l_:_--c:.’ ,‘._;,’ ..?__ .
caIct&tt~~~+t
‘.
.-__
;-
..-.
:
_-:‘.___--_,;‘Y
velocity (in-‘m 8:.%) a& __-_ .._ .
f.&lleI
~200 300 4aO500 600 700 800.
. -.
-:-.
“::.-_-.;:
. 1112
-. 1146 -: ..
‘/
1140 11.52 1162
: 1155’
1000 ?I00 1200 1300 1400
-1181 1186 1192 1197 1204
1500
1211
1172
1166 1171 1174 1177
.’
~14.7 11.7 :.~ ’ 9.5 -8.0 6.7 6.1 5.8 -5.4 5.1 5.0 4.9 4.9 4.9
a) Nozzle &meter of 100 pm. nozzle-to-skimmer b, Estimated uncertainty of 7 m s-‘. ‘) Estimated
uncertainty
.;
i6.3
-- 19.6
:
:
__--
531‘
_--537
8.0 7.0 6.2 5.6 5.1 4.7 4.3 4.0
’
3.8 3.6 3.4
.L
_‘..
:
._._.
-:
.:.
r
._-;
‘_-‘;-f,,‘__
T : 1T :._.-
l?j.
‘._
-_ -_, -
_,
-.
--
CdC.
-.I.
.-:_
544::‘
6.0. .’ -_ 5.2 ..,
--:
4.2
4.2 4.3
5.5 ‘4.7
-548 549 549.
‘4.4
4.3
549. 545 -544.
549 549. 549
~
4.0 ,3.9’ 4.0
_ .-_
15.1 ..1x1 -’ . -6.9 -7.5 _ : 6.5
548 548.
temperature
_,. .-:
:-
538
545. 546. 547
~.__-
.,
544 545 548. 549 549’ 550. 552 552
distance of 14 mm and reservoir
.:5.0 5.4 5.7
_-_
5.7 6.1
-j_7
I :_
-.
-4.0 -3.8 3.5 -3.3 3.1
of 25°C.
of _I K.
haviour. Large deviations between observed and. calculated values in table;2 must be attributed td non-ideal effects during the expansion, such as cluster formation and _viscous_flow in the nozzle_ The latter -results in the formation of, boundary layers decreasing the effective nozzle diameter. This affects mainly the translational temperature and- the intensity of the beam. Table _2 shows for helium-seeded beams that ideal-conditions prev&f for stagnation pressures up to 1000 Torr. Argonseeded. beams. behave by far less- ideally than helium-seeded beams. This- fact can be inferred from ‘the differences of the real gas corrections of helium and argon.. It is -also well_ known that a plethora of multimers his formed.during exptision of argon-seeded beams at higher stagnation pressures.-T&decrease of the su&rsdr& fldw velocity above’ 1200 Torr. has to be: attributed _to the apparent 1 ‘deqgqe -of : t@i. noz%& diameter, ‘which dominates the increase in pressure. This behaviour leads to al lo.wer- Mach ~nt_rmberaccording to es, (4.i3).and (4.14b) _and in turn to a decreased flow velocity from e$ (48). ’ -. -- _-I
.:. .:._:-
~.... -53j.: ~. 1 _ 542
11.9 9.6
i
,_:.
.-_-‘.. . -_ ..
obs_ bl_--~.-
1160. 1163 -1165 1166 1168 ‘1169 1169 1170 1171 1171 1172
900
_=
.;.: Y:<.~,~‘:;?+ ._: :‘.-I_::- ._I-._f_ ,._.I i-r: ~ .- :, ._;_‘*r’,_: :_.,;I tr&Sl&otkl t~tnpe&@ (i&, K) Of -0.e in .su@x@nic he f! .;_ ;_._‘i-_ .;-_, ; QCS:kr=_!:20_ T -._~.-‘.__,.~:~ 1 ;‘-: -T-II ._ ‘:
5:-<_-_ ;_..‘ .
-1 _
_=:.._
--~:=I__ ‘.
-f tkf:
~~$&&ir’&&~,:f:.‘_~.
._ _..
TabI&-
~~&&&>y +&&&&
i&&@_+
..~
_
5. Conclusions
We have demonstrated the feasibility of bbservirig absorption or emission of microwave power by rotational transitions of molecules‘in a supersonic beam. We-.havey used a broadband groove guide spectrometer with Stark modulation in the 8 to 12 GHz range. The microwave radiation interacts collinearly with the molecular beam. The inethod allows for exceptionally h&h resolution of .rotationd spectra due to the narrow- velocity distribution of the molecules in the supersonic beam. Dipole moments may be determined from the Stark splittings though with. reduced resolution imposed. by the mhomogeneity _of the electric-field jn the groove guide: The only disadvantage :at present appears to bc the very limited sensitiv$y. The_l&h resohrtion must be bought at the expense .-. of-.thc-sensitivity.. -Simultr&eously the method h& also -&$ided accurate and convenient diagnostics ~of-supersonicmo1ecufa.r beams. In- the c:onventionaf perper@+ lar ju&n~ement of- microwave. radiation- and .
_.
.:
H.S. Ziai el al. / Microwave specmxc~py of supersonic moiedar
18
molecular beam such diagnostics with considerable effort.
are possible only
Acknowledgexnent Financial support by the Schweizerische Nationalfonds (project no. 2.219-0.79, 2.612-0.80 and 2.079-0.81) and by the authorities of the Swiss Federal Institute of Technology is gratefully acknowledged_ Furthermore we wish to thank 1Mr. M. Andrist for his expertise in setting-up the microwave superheterodyne detection system and Mr. W. Groth for the construction of the groove guide spectrometer in the workshop. We are grateful to Dr. P. Felder and Mr. 0. Diener for the construction of the supersonic molecular beam source. Messrs. G. Grassi. M. Oldani and M. Rodler helped us with the synthesis of cyanoacetylene.
References [l]
[1] [3] [4] [S] [6]
D.H. Levy. L. Wharton and R.E. Smalley. in: Chemical and biochemical applications of lasers. Vo!. 2, ed. C.B. Moore (Academic Press. New York. 1977). T.R. Dyke. G.R. Tomasevich and W. Klempcrer, J. Chem. Phys. 57 (1972) 2277. S.G. Kukolich. DE Ontes and J.H.S. Wang_ J. Chem. Phys. 61 (1974) 4686. P. Felder and Hs.H. Gtinthard. Chem. Phys. 71 (1982) 9. P. Huber-Walchli and J-W. Nibler, J. Chem. Phys. 76 (1982) 273. D. Bassi. A. Boschrtti. S. Marchetti, G. Scolcs and M. Zen. J. Chem. Phys. 74 (1981) 2221.
beams
..
[7] S. Yamazuki,.M Taki and Y_~Fujitani, J. Chem..PhyS. 74 (1981) 4476. (81 TJ. Balle, E.J. Campbell, M-R. Keenan and W.H. Flygafe, J. Chem. Phys. 72 (!980) 992: E.J. Campbell. L.W. Buxton, T.J. Balfe. M.R. Keen&r and W.H. Rygare, J. Chem. Phys. 74 (1981) 829. [9] H.S. Xvi, A_ Eauder and Hs.H. Gtinthard. Chem. Phys. Letters 83 (1981) 469. [lo] H. Witek, T. Tiining and J. Hoeft, in: Rarefied gas dynamics. Voi. 11 (1978) p. 1053. [ll] E.J. Campbell, W.G. Read and J.A. Shea, Chem Phys. Letters 94 (1983) 69; E.J. Campbell and S.G. Kukolich. Chem. Phys. 76 (1983) 225. [12] T. Nakahara and N. Karat&i. J. Inst. EL Corn. Japan 47 (1964) 43. [13] F. Schoch, L. Prost and Hs.H. Gtinthard. J. Phys. ES (1975) 563. [14] H.S. Zivi. A. Bauder and Hs.H. Gtinthard. to be published. [151-L. AlIen and J.H. Eberly. Optical resonance and two-level atoms (Wiley. New York, 1975). WI V.A. Yakubovich and V.M. Starshinskii. Linear differential equations with Periodic coefficients and their applications (Nauka, Moscow. 1972). 1171 A. Yariv. Quantum electronics (Wiley, New York. 1975). [ISI J.B. Anderson, in: Gasdynamics. Vol. 4. Molecular beams an< low density gas dynamics, ed. P.P. Wegener (Dekker. New York. 1970). u91 M. Abramowitz and J. Stegun. Handbook of mathematical functions (Dover. New York. 1970). WI J.S. Muenter. J. Chem. Phys. 48 (1968) 4544. WI C.H. Townes and A.L. Schawlow. Microwave spectroscopy (McGraw-Hill. New York, 1955). [22] A.A. Westrnberg and E-B. Wilson. J. Am. Chem. Sot. 72 (1950) 199. P31 M.A. Flucndy and K.P. Law!ey. Chemical applications of molecular beam scattering (Chapman and Hall, London. 1973).
[241 J.B. Anderson
and 3.B. Fenn. Phys. Fluids 8 (1964) 780.