:::u~t ';:i~~~:~h:::u;:~':~::~;i~~t~~::~i~~'r~'~~s: ev:f6~

....

Nali o nalLib r ary oi Ca nada

gi~a~~~a~~h:::;~~vision

'Olla wa, Can al;la K1AO N4

NOTIC E

'Bib lio tllequenalionaleduCanad a Oi rectiondLlcaialo·gage· Oivisiondes thesescanedrennes•

AVIS

Aep.~uclioninfOil-orin~~noflhi sfilmisgoverned bytheCan adianCopyriQht Acl ,R.S.C ,1970,c.c.30 Pleaseread.lhaauthorizalio~tormswhic haccompltfly

this 1Mesis.· . '

The qualityof1his microlicheis heavilydepende nl upon the qualityol lheoriginal 1hes is submilted formicrofilm- ing.E~eryet tentiesbeeo maceic ensurethehighest qu ality of,rep~oductjonpo.ssi,ble. .

I(pages a'emisslng,contaettbeliniversity wllich ,qrented tnedeqree,

: :

Laqualil~

de

cane micro lith ede,pend grafldemen\de la

:::u~t ';:i~~~:~h:::u;:~':~::~;i~~t~~::~i~~'r~'~~s: ev:f6~

ducl ian.

S'iL[l:Ianq uedes pages,veuillel'~Ommuniquef^avec runive<!ileqUI,~ ~6,!lere~~grade.,,' So~pages mayhavein d iSlinctprintespeciallyil L~qualited'i;"'pre ssi'on'ciecert~inesinigas1Hl~1 the.,ongmalpages were type dWllh'apoorlypewriler laiS.seradesire., surtoutsirespages origln alesont.'l~

ribbonor ifthe unive rsitysent us e poor pholocopy,• .dac t Ylographie,esaraidee.un.ub.al'UlsiJousil'u,niversitB

" ', -'. " '. " '(l:_

nousal llll parv enir~ nC ~ho\Ocopie demau...elsequ alilB

,Previouslycopyrighted materials (jour,nalarticles. Les doc\j rnenls quilOnJdej.1lI'objetd'undroild'au-

~'published",,!lIs,elc .)eren~~filmed . . leur(artidesdere~lle,exerrenspubllh.etc.jpeso ntpas m:crOlilrds, ' .- .

La

.eprOd~ction, m~~e

parti eile,de ce.microliirn

~~i. '

SDu rn iseareLoic,anadicnnesurIe droit,d'auleLlr,'SRC 1970, c.C-30: Veuillelprend.e.connalssancedes lor- mul.esd'aul0 risation'quiaccompagnenlceueeese..

THISDISSERTATION HASBEEN MICROFILMED

EXACTLY ASRECEIVED

/'lL-339131771

LATHESEA ETE MICROFILMEETELLEQUE

NOUSL'AVONS REYUE.

.'.;.

..

^,

{, " .

"

.:~\(l\i FRf(iu~~cy :~IPlOkAVE\P[CTRA OF14NII3

^AHnCllRBONYl SUl PHIllE

r/ ^#

.(

, b ,

:.:

. ,. .

^.

,. B~ksM~v~dyarand

^{Sinha.B:Sc.(Hons.}

^{i .}

^{M.Sc.(Patna}..}

~

.:

.. .

.t

,"

~par~ntcf.Phys

tcs.

·MelOrl ~rrl.v~rsfty

^or.Newfoundland

AU9u:st 1976. . ...

. Subllfttedinpartial.fulfil lalentof the,req~i ~~ntsfortile.de gree

o f

!-\aster:ofsctence'

·St.John's'

tJ .:

.~

^{. .. '}

." '.

'lel~foundl and

,.

',~'.

,"

;'W.1;~h' t~

,expre,ss mydeep"s ense0.(graU'tudeto my supervtser-,

'Pr01es!l'~r,P.D.P,~lthfor'hisgu'c1ancean helpdur i ngthecourseof'

w ot1.: ' ,, :

~ , ' , ', - - , ,," " : . "

. .1 UIindebt e dto Ih".R ,ti p p i naCo su&gestillathe,ideaofshift ing

.

· thf re(~'e~~1~~_ reson,-n c:s_~~,~ 1n

the

$Iuf~e . ·-

^{:,_.\ ;'}

'~

. I

a~kllOlll~d~~ th::~'~

^Of':the

comp~ ~ttO[1~l '~orlt done'~y

. D~.

'6:'Jleoers Ew-and""r .Paul'·

G111a~

ofK'tC t4predfctthe.14NH]

spect.rua.~

" .•' " . . 0\- \ '.

, ,,'~. ^' Th~ffpanC~Al,~upport:1~~a,fonns0r.-t~~MelOOr}al^University'.

0'( Newf oundlandG.raduate ,Fellowshi pand:te a chinaas 5i stantshipis•

'''''',l1y "'n."~d.ed, . ' :: ..'\ :,: . _ ,

\.

-·i' .'

"J".

~ .'.'

,'H i

:

-,!~.

:.

. ! ",

;:

v,

..

/ :.

".:'.

: ,

·r

" A B5T RM:T

. '. Fifteen.

ne<~rou~~ '5t."t~'.i-n v~rSiO~) i,n~ o f

141fl3were

~~~~rnd '

^.

.If! _ at~O

^eo__

9.00C~ ac~u'ratelY ~aSU~d a~iJ .~5·s·~'~n:~~ 'th~

^.

..elec~ri~ di Po~e' l'lOme"~

^.:

cOll1lutedfrom

th e

Starkshiftsis 1.472i0.002

O~-whtdl

^{cot-resW!11withthe}

value\1.4 75't-0.006 0repot t: dre centl yby FUjlQ

'S~~~i%U.

^{Co' etion;weT e}

•applied.tol· 3lndK•§lines.,. . . -

' . ' . . . ' . L . V '~ ;

.Ntne0_ 1rotat ionaltransitio nSof Call1ony1'Sl.!lphide ,~ .

i~chrdlng

^oM,

Fe~ pai;-'a~ o~" trl~~it ~ue" ~ qU~ dNlOle 1n~rictior: o~3S

.

~uc1~~'. ~~.re.~~~rved; ' ~c~ur~~l.Y'·rrwi~Su·~,d.~~~ i1~s~gne~.Th~ .re\~u've·el~(:t~IC· ·

d1'pole

~n'~

^ofOCS

1n tll~ {lnOor~nd

⁽⁰²⁰⁰⁾

5tat~S

^{andthose of'18ots:·OlleS.;.}

.'..oc3

3s

arid

·oc~s·. ~n·~e. g~nd

^:stilte

'we~t c~'ted h·~ t:h'~ sta~ ~hi~

^.

.

'.~}~tl·~e e.;~ci:~~·c ·dl~le ~n't.;

^fP'f-

o13~ andot~~ .are resPl;~tivelY

t••0051'·',

. -

and 1.;0155.. :•. ' ,

.. ,

. c;

. (

.

38 IS

'1818

1\

20 21 22

?'

39 83

•• • •••••• 85

•••.•••• •:_.\81

••• •• • •" 88

s~:~~~1~~~c~~~~e.~h~f~Ul" .

^{',-';'" •.; •}

~

^{•••. •••".••'.. 22}

Identi fica t i on ofReflection Res onance-lines•• •". ;' •••. ?4'

i~~.f.~~~~et~~~R~s~n~,n~e;L~n~s .b: ;~Je~t~n~ . ~

^••:_

~ ~

^{' .}

'~ .

²⁴

2;2d VoltageCalibrati onofStarkCell.••~••• •••"," , 26

2;2e Analysls.of. thelines.'.''.' ••.•••.• • 26

2.2f ~aJ'lbrati.onof:~eFrequencyMe ter•~".•• 27

'R~SUnSANDDISCUSSIONS .:' ^<". 14 .

;:~, " ·x:~ndR~i:i~o~~~e;~:~~i~~~;: ~~

^{,NH3• ••• _.•••}

~.

Carbonyl Sulphide••• • ••• ••••••••••••• 3.3 Surrrnaryof Results••• •••••• '••••••• '."••

.

1-t. , EX;~ERmENTAr A~PA~Ti;s

ANDTECHNI QuE ," ,

'. i\:l:'Descl'i pUo naridnts cus et cnof Components-'.••'.",

t ~~ ~~~~:~eY 'f;ei~~~m;nt<';' : : ':,: , ::-: :' : ': ::-:

2.1c TheAbsqrp tfonCell.•',' ','':,•••~ . 2.1d VacuumSystem·,• • •'.; .•••'.'" • '.',' .'• 2.1e SignalHodulat;-orr.:".".

J.lt Detection"•••_.• ..2.1g·D~splay ;,0>.'.•••;

~sl:ract

'..••

~ . , , ~ > : ' . , ." .;' ;...' : .. '; ^{. '"~} . .

^·::H.

.Acknowledgement s. .. .~ .'..' •...•..; .. :•••'.'\~.•• •••ii'i. 'List'of ,Tabl es';'.' . ••• .• "','.,'" •• •" .'.;".

< .'. '

~

...., . .., " ,

~::t::F~9ures

.

~' . : " . '

.-,.'

: ,, ":':.4 ; " :.; : ~. '. ' .,' . ~ ~ '-( ':. :

I;INTRODUCTIOtI.':;'.:'. ; • • •••:.• ,. '..,'.••.'

~

;

" ~i~C~;~:r~I~,~R~ : .~ :: ~: ,:.:

^{:,-:-,:::'.':. : :.;::.:':. :.::. : ' :}

1.2 Some Pote nt ialFunct ions'of the Two' FQ1.d

Inver sion Bar.rier•.•.:.,: ••••.•• '••'•• ;'..','. .~

, ~}~;~~~o~fl~~.~~~~ ~~,~~~~:~ti~!1 .- >'-. ', ..'. ,~' . , ; ',. ..

,Illve n,f on Spectrumof·Ammo nf a•.';'.•• •••.'~.;•'. :,' "

1.5 Selecti on~ules :,,";'.•'•••:••••••".•••'.~.',', '• '1.6 Stark·.Effec t s• • ••,•.•--'•.• .•.• •••." •.•••'.' •.••; 7

i:~. ~~;~;~~~~~ . i~~;;~tt~n~·i~~;, ~~~~i~o~~~p~~~c~·~~~tu;

^:::':',;

'l~

1;'8 FermiResonance••';.•'.,.~,•••'.••.-.'~. .•• •• ••• 10

.42 .43

..: r-

44 3.1

Lo';"freqllenc'y,'i:h"O~d ~~ate ·lnversi·~.n Li;~~ '~f·. ~,4NH3 {S.~

^to1U:GHz)

S~ark

shiftseethe

(13. ,3lin·version '~in~;f ~~~3 .~.

J.3.,S'ta r k',

~hif.ts

^"of'the'

( 1~~,5)'~nvers~·~.n

^:

~in~',:

^of

,~.4.fflIJ

^.•.

" .-.', : ,, " ,. ' "" ,..' , . --. ', ii' ,

S-tark lIhi f t s ofthe0,..1Rotat ional-Li neof 0 CS'': . 3. 4,0:;','~.,·~ tat ion~I' T~II~sition5'of~.arbonYl'SUrphidc.... .,3•.

~,~t~~ ·,Sh~.ft ~·Of t~e. O.,+.~ flo~a~on~{ ~,!,nCOf

OCSjnth~.{OO O)Sta t e . Stirk'sh:i::ft, S

.(,f,,~lie, O;,~I '~O~llt~on~1 ii~e,

^'of"

~CS

^.'-"

··TABLE

in'

~h'~,

^{OOO)

'S~;te"

^.,',.,",

:>' . ' :"

3.9

s~~rk

^-

shj,ft'~'~f :,~~~,

^0...;1

Ro~aii~nal

^LineDf

'~33~

in th e(0 00)"State (Lo wercompooen t)

··3. JO

:!';ta~'k S~ifi:.~·~f the','O~ i Rotat1on~i i.i~e

^of

OCi3~

in. the,'(0 0 0)St:~ te}Middlec:omPonc":7},••

3~11'^{Starkshif ts of'the D +1Rota}tiol).al Line 0(,OC3.3S .in'the (0 0 0) State (Upperc:onfpooent ) .• ••'.. . .

' :3. 12'.~~ark '~hift5 ~f .

^{the 0"}

"' },:Rot_a~iona,l.

^{Line Qf oc34}

s

inth e(OOO)St a te ••

3.1.3 'St8~~

^shift's'

Q~' th~

^0...

l'Rotat~~~Bi Li~';'of :

^18ces

in the (OOO) Sta te'.;. . •••,. ••. .•• 3.14,Dip ol emoment s'oftJteIs ot opi c Specfc s oIC~~bonrl.

" Sulphid eindiffer~tYi b rat iona lState~.•

't. : .

4S

. .46

46

.46.

'•.47;

51 29

• ;••• • • •.•• ••.•.30., .,,-0

'LI ST OF FfGpRES

/. I.

i

Viewof

ihe'end~ of

the'septum-,•• va~uum.~ystem •••••~~'••..::~

,' " ' ,,; '

'.

Starkshiftsof,the 0'':;', 1r~tatiOllal^Hne'o f

013CSin,th"OOO)

state . '. " .". . . ':' .. '. . ~'

⁵³

5").; ,hift'. 'f '~'

^o-,

";'" '00'''''''

^of

oc3~s

1"-th,e,(000)s'ta te,(l,fMer'COlllPonentl'','.'...:,'.

~.

54 -Sta~.shifts.,ot:,the0...1r\ltati onal l ine.of

qc33\,n~. (O~) ""',;mddl' ,om

^P,' '''' ')•• •••••••••• c.o~letC'~~s.en'bl,yo.f^.-th~.X4.24C?,5t~1~d~tect~r._^{••• •'••;.. 31} (l:oCkdia9r~mofStar~modul a t i on mtcrwave

./~~ctro~e:r ~l

^....

'~ ':' : ~._~) '

^{'..: :.'•",', '"}

Complete1)1ockdiagramofthe Stark lIl~ dUl ated

.mf;crowav~spec'trcneter-et ecron te gear •~•-, ';.'

ca;l1bratfOncu·rve:f.or

th~' ~,st~i'n~s ,~aUge. " 4. ,.>

...:••••_, Ca,librationcur ve forthe St ar kfie l d '.'.'••• •'•• •• •'

t ..' . . . •

Ch!,rtshO\llUigtherotat1onalitine.serccture.' " " - o~,the inv~rs1onspecr um of ,ffil3• • •• • ',.•,'•• • • •'."

~l~art: stiOW1~9

^the,

d1st~fbut1.on of :,K-;I lfn~s .~f

^"

NH3,,•",""".,,~"-" •••• •• "":..~•','.~•'•• •• •

St~,rk ",Shifts ^of ~fie ~U.3J · inve~sion ^nee

^of14NH's'"

's ta rk

sh1f~~" o~

^the

(1.4.~) , i~version 'li~'e

of

14~1:s

^{•" ••}

~

^•

t • " . .,

Stark shiftsof the0-+1 i'otatforia-lline of

.0Ciinthe(000 )state."~:..,,',".•"': ','•~...~••

Stark shifts,

0t

~h e ,0-+1r,otati~al'lineof..

OC~In-the (10 0) state."," ••r,,•• • "•• .',' :~•

~2~r~ns~~:t10260)h;ta~,~~~a~i~n;~ .l~n~ ,~:~ ',' ..

s, ';," 52

No~al

^.mOdes..ofVibra.t ior;'of

F,e

^;1:4NH3

lIo1~ecule;

^{," ••}

~

^{,,,..) '. 15}

.Pot ent1!!1~u rvefor ~IH3" ,.... '" :"••~.-.'."• •• 16.

Ener-gy'leveldiagramfor,invers1on.:.SpJt tt1ngs of . 17,. d;'fferen't

1r.o'~es ~'6~ V1bra~10n ~f 14~1l3' "

^{••'...:':"}

~'

^{.• -.'. 17}

Ab~orpti oll Cel 1^,",',;•.~^{•••• •.-: ;••'••", '.'}..,.2~

..

^FIGURE

1.'1 1.2 1. 3

2.1 ).1~

2.2"

2.;3 2-.4

2.5

2",6 2:7 -2.8

2. '

3.1 3.2 3.]-

~3 ,\4

3.5

3.6

'3. 7

72 70 71 68"

ss ,:.'

3.29

'." '!"'" , ." , ,': " , ' ':

St ;;1;,'jS.hifts.of ee.c,-+~.rota,tional lin.~of ~' . ,DC Sn~he,~?~9)sta~e.(~PR,e.~ c~neri~) :^{.•;••" ':.:•} '$t;~k ~hf ftSof.t~;,8.~I!.rotati~alline.of" , "

DC.S,1n-t he(OOO) ;ta.,~f;'" • ~.:'•_••'_"••.••• • Stark',shifts

of

~he0...-1'l'ot at ion:l l ineof:

180CS"i'nthe(000)sta t e:,;~'^{...'• ••••-; •.:•• ••'}

~~i~h:~:r~~~\~~~:S~~fii~6 ;~~;~~, t~e~s~~7 . lin,~~',.~fl:~~f

Groiin'dstate

,,(l~ "2) i nv'e~~.o.n l1ne:'~f" 14NH;: ' ~ ..- :' .".",'.', ••

.Hain:,and

sta~ linc's~he 'gro"una'

sta te

Jl~ .~):inyersioll

^{li ne}

,Of.14NH3';••••,'..."

~

^{•••"•,.",' ','.'::'"•• • •', ,'}

Gr~u,nds'ta te'(15~,~)'inversi onlineOf"14NH3•.• •••~•• •• •

.Grolin d

st~.~ (15~5l 'i,nverS10n , l1~~ ^cif

^,14NH_3,^{.;.'•• '• •}

~, '< . ~ ', 6~

Gro~nd

^{s'te t e}

tt6.5l ,friv,ers1o~ ~ine'~f'

14mf3,• ••,.'.

v. • . . •

64

Grotin~

state:(16':,6)'

invers;'~n" li iie

^of

'14NH~

^{'•• ••}

~roun~

^{s-tete (16}

~

⁷⁾

·tnve~10n l ~

^{lie.of,14NK3• ".'':•••}

'~

^,',••

_Gr oundsta t~'^{(17.9)tnverstcnline,of}.~4NH3~ ~^';',

~round s~~te, (17. 10l f,nv'e~i ~n

^l,ine'of14

"~3, .: ~, ' :

^•'••

Ground

st~te

(17

.n i

tnvers tcn line

~f)4rlH3

•

GrO~nd .s~at~·(1B .}l)

^inVers.ion

l1 ne ofl~1I3 ~

· G.rO,u~d~tate ~,~lf:. 12)

tnverstonline0.(1:\113•

Groun,~ state(l~~13l i n~e~fon ,'line ~f14N1I3 ~

Ground'st~te {i.B~14J 1~verslon ~ine OfI4~~3

^{.::',','•••.}

~

^•••

Mafn·and St ark"11nesof'ithe0'+ 1-rota t-\onal tr,ansi ti onof~cs.i nthe ground.state.r :',.

3.28

" ~~:~s~~~0~t~7ogj,~~ s. t(l~B';;~!.~~~~'t:o~a~ . ;

FIGURE

..,

^-.

^{3 .'}

3.10

3.11

3,12

I

3.13 3.14

,3.15.

3'.16 ,3;17 '3.18 3.19 3.2.0 3.2 1

·3. 2.Z 3.23 3.24 3'.25 3. 26 3.27

.... .

f'..L-.

.j.

18

j ..

3.30 f.al n arid

S~ark 1fn~s--of \h e

^{o ..f.r.oudona!}

; ...

iransit!on~of 01.~S

ⁱⁿ

ti.; 9~ltf\d sta~ ~~ : "" .-.'~ ·i·.~_ ..': ,:,~ .

¹¹

3.3 1 M;a~n'.llndSu.rkliDoS.of th.e-0"'1ro uti.ona.t ... trl nsHtonof

cic

33S.~nth..9l"Ou~dstate.~;" ••"... . FIGURE

t...

. .

.

3~J2 MainandStar kHn~s'ofthe0"1rotation a l .

trln5ft1~-D" OCJJs · 1~·.~~~roun ~

^{.s.ta.te.•'.}

' .~

^:."::':-,'

~, . 3 .33 i;~~s~:~o~t:;k~~~;;~',:f z 90 :~t:~~tt~O~a.l ... ^~ ..;; ^{:., "}

"

" 3.34:::;~~~:~~~;·~\i:'f~t:: :';::~~~.:', .. .: ..

3:35'.I'Ialri'ands~i-~

'lines;-

ofth~

.

~"'1_rot~tl.on.'l

·tn'.'5~tton_9f:~Bocstn.the

ground,

state", ._ .

.81

82

i...·.·.·..\··..

':

..

~

\

., 0

~.

../ ...:'l

^c.

\

I

.J

-l·

I

If

o·

.,

^.

.

,' ..

",_ :

.1I~a~S~ ,.~f.

^{·t h.e}

1p.~e~!Ih~

^a,nd

~ichrie89

^o'f

,_~.~8 :ectrum . ·<ll=~n.1a

^,'"

hasp1ayed 8,ma j orrole1nthe develop,",n t;of'lIlic rQ\1lIve-s pect ro s c.opy., z e

h~ -P~~!·.i~a -l.~~e nUl:lb'~r Of,e~~U; D~8

^..

';~ble :i~~~s O~-,,~ith t9t~y

both.~xpe:illlen~a1':'techni'l~~~^{theory . ,_}

the .1.nvesUgationofrottit1onal·R..:U.a~:aridiat>pe~ti~of llIIlIlOn::l;':

.has'

s~~ ~~at'

^{'t h i s}

~o~e6u~e ha"PYJ:"am~da'l

^ed-uc-ture

~i~~'

^{th e}

1:ti.tr~qerf

^,a t o,"

/

. \

^.

.

^{. .' . . .}

· . ":1t~O~gh~~h^inVe,E'll10n~~;etrum^{·is,wel l}.r,Ud~eJo i~f.z:e,q~enc.il.es a~?ve,12~~z•.and,S~~il\lIea SUI~~n~8:eon~~u:.d~:to-72~~.~~,~.}'e~

thereremainhundred s-oflineabelow,the'la 8 ~fre quency,lind's o me abO'v'e

. . . . . '. ,

.

.re..which have:'~otbeen ()baerve4.mostprobab ly,bec.! " s e of theirlow

ab8~~Ptio~8'D Th~8'

's:L"tua t'i o n

;bec:..:m.e"~ ~pp:~r~n't

^'an:

ex:.,;.in~i FiS'.·;- .e ~ ...

wbi~h ,~ioi;.

^{'t hli}

~req~e~c.~~s p,f~~'ieted·b~ ·-8.Il"_~mPiric:al .~~l"lllUl_a·~fint

^.:

in.tr~d~e~d~~ c~ta'1n';

^,:md

'_8hOW~ : ^the. apP·rox:lmit~'-~f~;<iuenc.l~.~

^'ofa',c.

Q1\11t~~u~e"Df~:in.ll.&1wl:tl,,,,,e.ab8~:ipu~a- '8h_o~lddecrease'a~'t~ freqll~n~y deereai:e;,or

th~ im~"ubr ~o~en~ qu~~WIl. ' n~ber' ~

^'·incre a ses••' ,

. . ..,.{"h~b ,h~.,. ;r~ th~ri;:. ·.Hch ;';11>•• ~,iOO:d in:h1• .. .

.-

~h~p_~~r ;' eo~e~~~d '~i.t:h ~he ',~neYrll~1~

^,Of'

'~ht' '8llI1!l~i8 ;n'~l~~~i~."~

~ ~c:n~~al ·pot~nriall ba~rier~', ~:t'

^rioneot

- th~

^{. :}

aliff:i.den~l~, a'~~'\lrate: "

'.

'~ the:l.~', ~'r~dictlona .t~be r~a1~Y uBeftii '~ mierjw~~~ spe~~:rOBCOPy~ . ~h'"eU

^"

' ilea6Ur~erl~;' are";~adllY ~a4~

^{'t o}

ac~'~'ra~ies

^,ofi!.'

f~~ illind~ectths o~a .:

; "'.' ,'.' ,';,.-",: ,';': ', "". '-," ". : '. '-, i

~he.ories,are~nabl.e'to ind,icllte.t h e,qll8lltum .nUlllbe r s ofo~llervedl:111e~

ii~, 6im~le' eOlllpar is~ :of--'t~e ' ~b~e~ed ,'frequencie/!l'';''1th th~l~ ·~;~dlet~~~'.

'.- ',' - . - " . ,, : ., . , : . ' ' :- ' J.- : .'. '

·For~ple.^the,freque.iide·~p,r~dlcte~by"t h ethe.or y ofSpi~lto~_'St~e' a,n'd:Papousekforthe1:h if,S'

,w:Li:~' J ,";' .-7.·'di'ff~~ f~·OlII. t.he ~,~,serv~~

,fi: e quenci'e B

:,'-,'-'\.- '."'"

-:. " " " ,:

^" :,:-".

:. ...

^" ~

·by.amou nts r an g ing frOill51to10% of/theob8 erv~dfre'lllency, ..milespacing,

., "

-2 -

~:

.

'\

.;

^" .

not.use f;u la~_thMem1.ero~a.vefi:-equ.~:,c ies,be l ,:,'" 12. gH:;>;,bu t,later

~~~ifi~at~o~a ~~'

^the,

proc~~"re

^•

.-su*:~s·

^{th at. by}

SChnabel' .!!. ~'

^{-' ar e}

.u-sefulfor 11.nl',l d entif teat i on in, th'1srang e. Ro_v er,withou t

, , " ;, , '

,'"

. .

lJIeasur ",lIIentssueh as t;.hese, thereis.no cr11:i qu eeither of' such the o rie s ,

or

~r'emplrical·a~~,:~;;'1in

^{..tiori.s.'r . :' ''' .}

"'On'e~undred!;;-;I~i"'eie';nfair ly','str'onginver8iori'li~es

of

) ~l 'i~ ~heg;oun~:j~~~~~'h~v~

^{'Le en'}

repJ~~ed ~ 'th~ NB~ .mon~~l"~Ph,

• " , ', . " ," ,I"

70 ,VolUlll.l'-I-V: Thea bl'ol,u t eint ens i t i e sof the se,linesare-10-'=- 'o r

·~r~a~e·r:" .:

^By

.r.Il1.';.1.n~;' t~

^..

temp~rs'tur~

of th'"

ga~ '

^the

highrot~t:i.onal

^<'

·- lev e1-...'ean bepop~lai:ed.^,i.nd~h":"rhe co";paratively..';;cakel"linescan

.

^{,' , .,'.}

" . ",

-,

..

^'.'

. .

al~obe observed. The obj ec t,Ofthe,pre.sen r1!Ork, b,"0·ob lle rVe,.8li ll1li;D.

. " , _, ,~:~~~~"~~::~:~:::. : :': ., ~::~~:::.~;~:::~E:~.:::::b~~:: '<."h~

~

- .

• _(mo r e Unea...ith'thepl'esentappsr; tus ,:-b:causein~t..lca ses the 1n1;errsi~ywa~,^{beloW' the.1imIt.of}2'~'10- em- 1• • •

.

^{" "}

A1'thoug h,theground's t a t '; .arrcngc st;'; o t a U oria l-

rc .... i>,

trand-

of.'diff~tent,iso t op 1<>,8P~~ie:s,^ofthem~iectlleⁱⁿd.iff~re(ll:' ~ibrat~o:'ai

... . , ( " " .', '. " e . , ' , '

•-"s t ate s bi:'i ng. de t e]:min ed.'~or'thisre a s on,whileusingth e (00 0) 0....1OCS lin e'fOr

~~11bratf:';n 'purpoB~s.

^{i t·ap.p ea r}e d "",,11toob s erve-;:OIJIe'ofrbe ,

'1::10;;.! in e

o.~,~Oc~ ,hSS~

^b;'e?

' u~ed'~D~~:~bie i:~~?~~ce' e~~,el'~en'~11 '~~tt~ii~

^{•../ •}

" ,CozII'iniand l'ola ce o an dpt:herst25) )',the re Is H,t t le'ref e r e n c e,inthe .'

~.~iit~·ratur~·~· theweak~r ·~ompo~ents' ·~~h~ .~l' iot,"~~~~J. t~ans~~i~s

^'i>

<;

'a.r.~s7<'gour.,.o fo;the5,.v.ibrat.iona~ 'state,scirot~~r.iso~?p.icspe~iea~f '\,~ ca i-bO.n?,!aulph:de-.Als o',,t~ere^isnO"n fer~~e.^to-th~ diPO-l~.m~mm.rll

, "

:-~:---~:-:~~:;':;~~~"e~ ' t~:~-~;:~;;;;~fm):-;:-(3~~, _~e~;;~~

du'ced,a tthe l~st'moinent,ilnd.aren.ol;1.nthe ,regu:L~rnume rica l,seq~enc:e.'.

.

^;

, ^{.. ' - , . - :.}

.'~.

.

re

the

pot'~U~l~nera.Y^-isplotted.~'^{• •}func.~ion^ofthed~tllnc:e^. ofthe 1I":.tOllo

fn.

tb.Il..-plane ~^aCU",,, or't'IIt'f ;no sh e n.18Ff.8:.1.2i.

:.

~bt~~ed. ~e~. ·is ~~~ le1"

^of

h~ight ~1

bet"';'eo.t.hee....

f~_f,P~u"L~1l8:: '

.".-fu

nlt.t.os:e n

at~ ca~. tunnel thJ;~~h.,.the pot~t1a~.bu~.~;r .~d.

Bojlrlvert.

th emole<::ul. r"pyra mid . The-effect i vemagnitude0[,thepoten tialbarrterto

In.!'HJ leach:"lb~anQllalleV1e:

(v+ )andC(v-). Th..epU tt.in g of b

~t!,r .he.igh~ V I' bee~~a ~ero

'UI'theharrieT becc.eai.D.f1al~e. ^{Bee.uu ,tb..l-.11at .1b ratl Dl1.allewel'1.}

oal....;. -.,..etdc.

tha _~ower'~-i.er of ue~ ,.·tt ·o t 5U!>-le~ela u" ~~etrlc:

^.

..

an~

^theuPPel:fa

.nt.l-.;-e-t.rl~

^{to,1nvenl _ • .;...}

~raAa1t.i~ b:~_

'r "'"- ...b-leve1~of'th.•,'~.,lbra Uon.ust a r t.'iacalled.tnve....t.on. The invers i on• fre qUenc y

~D

^be.tu;r:har

"el<p1liu'~ bY~C~~1d.~~t1_

^o!the

pr~·peJ;

^poteatW

. " ",

. .

' ".- ; ' ...

. Va ri ou spoten·tilllfunct1.ousfo r'th.l11trog en.atOlllas.t.tCoes

•through th e

·~l.n~

^of

t~. h~1?"ogen atO!ll~ h~.,e beett~

su'u uted bydlff',.rent authoTs,wi th'anss.\ll1Iptionth at the inver.iotiDOU""isaSl!lo<:. iil t e dwi t h.toll.,

"'v"2

. :bim~ ing'~od~

^of

, . "'''''i~

.^andthat"

th~. invenion':'~~b;·",;,"'~an

^befOr1ll.ulat...

~

in teI1JlS of.a8ine1epar tic l e . "",v inaul1deJ;th. lllfluenc",of.twofol d

. " . .

potentia.!. but nstr-in ",dtoastng l e·co.:.ordinat",:

".

. . . .

.-

Nu_ rous·the o r et icalpa"peu ded tna:wit h1Dv a nloaspUt t ing dlr f col

-, :'

1D:bo~1i"

^the

fo~

^{of th.}.pot eD.U al

~~ctiOlls

^{us ed:}

~lld

^{..op prox f.ni mUI_d...}

wt:'1 :::

. ' . .

-.-- - --

. j .

- --

so'lvfng'theS"hr5d1nger'seqUat i on: Thus, DennisonBndUh lenbeck(2) treated tbe

dou~le JDinilllu~

po t e n t ia l prob:elll

throUgh ·~.K. B

.. _apPt'O:dmati;'ns

~or. the

ground aswel1-as~exci tedv:1bratio;'"lstat,,: Theagree mept"f or't he.

". . ,. '

, ",

groun ds~a-tewasYel'}'-g~odandit-"'as to~thin20%for fhefirstexClt"d

.

"

a n dND3''''ith t he'pot""tialf"nction

.

.-, .

wea:.e K.aandbareconotantii'~,.:andy.isproportional,to x;:The\I.K.II ••

. , "

.

^{" _}.

.1IU'!thod..~used fo~the solutionof'~ SChr&li,;gez::' sequa t i on..Thisgive~

res~t8 ~ic:Jl

^{. ,}

compa~lIbl,~'

ⁱⁱⁱ

acc-"~a~\ith ' t~os~

" "

M:i~ni~g'

^s'

pot';ntt~l'.

Butthe~a1tlescalcu lated for,t he firste~ i te ~.,~ ta te ' arenotsatisfactory.

• CostailJ- andSuth e rlan d (5),h a ve~~eda potentialfun c ti on..hichill

. .

. ..'..

- ^\

^{. '}

. ^-

moreobviously and-d i r e c tly ;relatedto the UlOleo:;ularIlOtionina B1mple"'ay·.

V(x)..-C'..e"lI z.("*)+1)f;ech4{~j

..

~e~ ~' ~IJ' ~d p·'~re :,,_on;;'tants. Th~

^variablex

isth~,

^{di stance.of}

~~"

i ~~atOm

^{frOlllthe.'plane}

~ftheH-ai:o='; n.i

energy lev:l

differen~ell

obtaiile1,: by hlmaTf'ingo"d agreement Wl!hexperiment~llYobseTV~d^yaluesfo;"tIH3~ ~'

ApprO':d~te barrl~r height~ ';~r 'Nil3

^{an d,ND3}

obtaine~ t~reby

';"r",

2~;~ ·;~~l

and2~6B'c ",-1respe c t ively, ~

Nt'Yt on and.Thomas:(4.'chos e a differentpo~.entia.lf~n.~t'ion

V-tkr'Hly)2_+t'k~

(A,n

^2•

-.where Ara~d_Mareo:;ha nges in theb.;Ii.d length~nd'bOnda'ng b respe~tively;

'and krand.k'~:ar..th eco r r e.spondin gfo r c e

~"

.

S..al~nBnd.Ibern.( 6) uSeda pote nUa lofthefoh

whe r ea,b, c-a " d,~^a'rethe'potential"coMtanu'andq isth enor=l

::' ,

. '

' . . "

-.~OOrditl,?-'teofmoti o n. Th~agreell"ntbei:we~60the caicul tl t ed'.s ndobserVed v..lu~~·for^the,en".rgyle ve lsof IDt3 an d ND3isfarb,ettlfi,'thanpr e vi ously

.. -

.Ds.:tbu rgandPr~pin^.{"7l.usedtheone ':"di lllens io nalpotettiial

, v(:x)....':'(R2_11:2) 2 /8&2;

· -. ' .:

..~wh er e2Ris'th~distancebetwe~nthe~lIliniJl\a-of the

tw

poten tia lwella,

Vi bratio n - I nve r aion Interaction

All t.he.

th,;oretl~~ pa~ers

.;Liste'd"above'

~ave

^aimedat'p r e d'i c t l n g

. ' . . '. .. ,

. ) . -

.. ..

·th~-dependen~,:,o f the1?-ve rsion:spl i ttirigon-theqUant ulIInumb~r02asso ciate dwith·

. -~", . .

the"'2U1Q.de'lnwhiehth epyrami d,height changealIlOstdrast"iFslly. 'The rela t ive

-auece~a

^ofthe

on~i:me~'ional trl!latment" c~mf!fl from ~h~

^{fa ct}

'rha t~:a

•

v2.~ormai

_.^mode',:lS,

~runarll~

_:,'

invol~ed i~

_-.

·inVeTll~on.

^Butother'

l'lo1:m.J~d~~

ofv1bratioli.. als oaffE' et.t~einvers i onconsiderably . Thiswaa{intre a.118ed byWee ks'!.!

!l',

(9,) .•

Th'ey

_us~d"po t entia l~~ergy'o;:onsisUng^ofa~^double

mnill-lJIll

po t';nU al

:l~"o~vi~~ the · 1n"~~Blon-c()Ord~n~·te.

^{plu s}

the

p':'ten Ualo f asys te m'o f

f~ve' ~~O~l~d ~~~JJ.lators

represen ting-

~he

re lllainl ng'Uve

.

. .

v1hrati~ar,^{de gree s'offre edom.}

I

L

The. aU!Ill:\a t'ion ;ls ' c;iver-theremai n i n g five'vib;r aUonal .wdes andqi;l~,th~­

'apprllpr~~te v~brational , co\~dinate.

^The'form

o~ 'the -p'oten'~~al ~~~

^by

~~e~\s

" , - .'.. -- , ' . ' \

V~^(Toy:.-2F.(."O~^(r)+2Gcos (-~) Jot-

v.(x)..2 (1!

+

G)

1rt.<

\xl

<OC

ft.

" F~ ^{';nd. .}

^{LUO' OO.{Lhn,}

^nn'

^Lh;

^{two min'''':} n:nu~ ~\;U: (~) .- ^{fe.F au'.G}

are assllJDed to

.

bemi l d'f unc ti on!} oithe. ::re mai n;ln gvib:ra~ionalcoo rdina tes, and can be'exp J:esae d in aTa ylo r,se r ie sfo'-r'~m:allV1.bnlti on al amp·1!tude.

The

C~irent av~llable'

^{data'on't he}

inv~'~sio~::"s~~itt1n8"i~

Illml 3·( 10 ) ar e

sunnaris~din

^{Tabl ei;l.'}

~

^..

~~e~~< le~~~' ~i'at,:a~'f~'~

^\ov'"l Yi n g.v i.b ; a u onil

•'is8ho~1~Fig',.10 3 . "'._~.

"

""

.

'V.spirkQ.!:!& (11)have also'developedanef f e ctive.inversion. rotat'ion

Handlt~ni~~'

^{to des cribe the}

cent.:r1~u~~~·cj::i.·~~"oJ:t.i:0i1

^{an d'Coriolis}

; . . - . , .

int~ractlonsⁱⁿth~,gro~nd a~d^excited,v1~r~tiOn-inV~:r6iOna't ates of'aIDIll\>nia. but tha t_doe s not wor kwe l l inthe Ililc row ayeregion.,

1.4 EffectsofRotationon theIn ve rs ion Spectt'UmofAmmonia.

. . " Q

.

..'

The fac tth at· themolecu l eia rotating causesth~'pur e inversion"'!

•spect:ru...to be'

i1pli~ i'~to

-a ,large .nUIIll:!erofli nes ;_.each

li~~ cor~esp~:i.ng .

"Withagiv~ll'J.Ksta t e ofa s)'DIlllet i ictop.llIOl e.; U1e.•,Jisth~'q~antumml~be'~

symmetryaxiS. . .

~~ro t.~t1onalst i u ct u:re wasf11"st r,e solvedby~leanyand

t.>:.~~::~~_2~:::_~~_~~:~:~~~::_~~::~:~~_~: '

^Sheng

^ss,

^{& (13.>.. They}

~'"l't'essed

.In thepaper.byWeek s.!.t~....was qiven..a~

I

~:a.~p[int~

.:theobs.eiVedfrequencies in.t h..e,fo:r:m

, ' :

.

.:rhb fits'th~^{low,Jaod K'}'::~iueg'~'etter^{tha n thehigh.}

(.1+1) K2.+eK'++~••

/

-,~,\,

'. - ' ,

.

v..v~ell:p [AJ(J+'i)

4:

B \1;2 + CJ2.(J + l)2+D,J(J+l)i',+EK4 ] This:f.o:mul~·i!llWll,YS9i:e'" v'po s1t1ve-,con tr~yto,Shen9 '" f.o>:mU la.

t1l1,BHts ,:,-l i:li~e's'ⁱⁿ't~e^{ground.state,:w1t h},J,~16t.o ~ith~~.1.3"M!b:exe e p,t· ' .for thelineswi.'tli__K' '':-"3n. whe r e'n-.1.2..3;.'~••

Scnnabel!.i .& (15) ex tende d Cost.a in's,fo~~auptohigherpo;..e"a

si: ~:':: :::u:::~;:;,:::'o:::'~: ::: _::,:':;:: ::::::v::::"iml ~::-

cJ ;be 'an;oma~~ us

de;;iation s'ofl\"3lines

· frO~,,:the

^..

ab6,~e, f~muiae ,

l

^{'-'ha veb,' on ••}

pi",.,'

^{byN"':onandtenrueon}(l~)0'<h"~•• , ,of'P,~""ing.'

.L. \

{"f.l~ l

...-

3le v e ls'byaVibra.~o?-r~ta.tioni~te~ac tion .. The yde rive.da

1

^{'0';'' ''}

^{'0< '"} do"bl.~

^{SP,',itting,Of,1,<,1..}

3.1~W~1 ,

^{••• :','' ' '.}

, ...~ Av..(_l )J nJ(J + 1).(J( J :1).-2},[~(J+1)-

61-

. ", "

\onere.a :wa sca lle da'rotatiori';'vibra.t1on'con"tan t, butit:15:re.a.llyafunction

·)of.1(.1H ): ' \. . ., ' .

Sel~c tion'Rules.

~en.~n ele1~ri~^fieldh,app~ied·,to^{a'polargas,i,t.}in~t~~aet~vi~h '.th a elec tt:'ic dipo le,caus inga apUttit\gofth erot a tio nal energ yl"e18.~

.'

e

tlJ"O +'- -

.

-

^{, ' .}

.

'Thellele et i onrules'forpure-invers i on.tra~ullit1ons"ina.a ~t~ie top1D01eculeere

" ' ". .- , + .'The .,fe'e t rie',dipol eIlIOmen t,can_be.re'present~d,byavecto~~

~ose^magnitude,isme~sured^byth~di~tdbutlon^of'chargeinth''-,inole~le iihd the

distance"be'~~en th~ c~~tre~ <Of~h.e

^{chB3ges'.,I.e •}

:H(1 ) . ,.t . E

nie

'firs~ ordet'pe;tutbll.~iOn 'e~·~l:"gie~" aJ:e,obtaiJl~d

^from,an

~~rsge"~f

^the

pertu~~st'i~'n

^{te rm"H(l)}

, -'iri

the:'Hamiltontau""'

"'.

int er act ion-energy 11'1 exp r<ls s ed11.&

, : , > . (. , .. )

'\:Y. .

^{I "}

whi chrCJ!ul tsin"th ..s:,l'"l a r a n cl!

.~f

finestnu;:tureof

t~~~"-

rotationallevel speCtrum. 'Ibisiskno..nasS.t ar k ..ffeet.,_:

. . t , ["", ' ,' . " ~ : r.

"Ih~~'~

^"1is

~t.~~ eha~ge

on th"e.it,h

)l-~;~icl'e ~d-ti, ',~-S

^{-t he}

~ctbr 'dista~cl!'" ~.;

^,-

theithpa.rticle fromt'h~^originofacoo~inate,_lIy.tel\fiXed-inth~.^{mo,leele. ·'} nie's"uuinaU op.,is"a ve ;-

all t~e

^nuclei'

~'nd the ele~tr?nB ' in

^the

ii.:.~~~";le'.:

-,"

, . ,' ,,' 1j , : " .-'':

If-thestllr kef{~ct perturbatio~lsconsiderably'''"'',:l~eT:t~an,th e. ',_

~_., .~.

^{Lev e L., . .• •}; ._ _ • • ••_ • •

j -

^{be - • •}

~.~- .

the-St al:k spl itt i ngs . The pel:tutbaUonte rtii

trC.

¹\ s theinteraction ener gy", _

iIe:tw~en ~he"~1~ctr1~ ~ie.ld t a~~ ~he lD;)lecU.l'~rdi~b~

^{...'.lD;)Clen t}

t.

.ovel-"the"unperturbed s tute.)Le.;"

" '"

Thetrsnil i d o ns iilVolvinginveJ's19J.lobey thes ele cU.l:lnrule

A.J..0, ..lI.K-.0, .lI.M_

o,

r::"i0'

.

^{'.' .. ;}

"'h~re .~ is the .qu}!b~u;"

^{nUl:lbel:,per}t fli.nin g

't~

^the

p~jection

^of.3inth e E~diTectlon^{-. The}St.al:k,ef~e'ct'~f^{th e}in v er s i ondou bii ngot'am1llOnill.

repr e,s ent Pasp e cial eue e inthesenseth attho!dipole-.noment'of'~~n1..a'

is

.onl~ ~'seIll17erm:"neo.t'~

.b e c a.us e'

,o~

th e

.1n~r~l~~ .sPl1;t~~g:· H~nc~.

i.t d6es

no t·show' th efirs t'oroer ,S t arkeff~ct'. The second o;de r Stark shift

o f

&llmlOtiia

· is

g1v!"it.

b y

'(I n. '-'; 'A~'-0.50 65u2E2

Vq

whe re"'. l s·; nMHz,\I

i~ D!lb;e ~n'1t~;' ~nd ~

^,in

~o1ts

^perClll.

llec~use

^theE2.

" .:. ....,. '. ".'... ..

' . . '." .

contributions:to ener gyaredege ner a tei.n±E. only.1+ 17"esolv&.b l e Stark 1ine:"-re s ul t,. 'Al l I e veis

for

^}I.01,0aredoubly_ciegenera~e^{in .iM•.The ..'.}

'l1l,ee;:c-p l:eaaion~o~^theStark'shif~^{for o-r}rota.tiO?al·tra~i~i';'ns ofOCS ls ,g :lve n'b y'{27)

. Av:':.'0.1351·Il'-f?

ve

:Fo r

t.hh .

transi t i on ther eison lyone.Stark'c ompone n t .whose

~ntegr~ted

.<~t.ensitYr

^{equal sthat}

oLt~e ~r=.l.li~e~

^Thisis

,~~ advlI.~.ta.ge

ⁱⁿ

't~~

^{. .}

, lIl~asuremel1tfof'the'di p oleandqUadrup ole tll:0mentsoftb eca:r:bonylsU1!hlde molecule.

,

.

^{. '}

fu,tatibnalSp e ctT8of.Line ar'p~lyatOl'l\io^{MOle ='ies}

"Hi.le~~~e8 w1.th

^..

pe.r~~n~t ei~'~'t,r1/d1Po le, ~ents' ~ive 7o~atlonai

spe ctra,IlJId'fot,the se th e sel e 'et l a n.ru l eis4.1" i.1.'

- 10 -

~

^{. .. .}

BVI'the'effe'ctiv~'r o t a tiona l. par;ametel:for thevib r,!-t;i o n a l stat'f!v,,is

.

.

giv enby

BV=Be":

.~~i(Vi+ 'f)

",whereBe1s_the rotationalCO<lsta n tCor equilibr i.u.aconficurllcion. The"

. I . " ,. ." .

l':Il)Wllat l o n extends over all-vibr at ions...ith- thedegene rateonesin c l ud ed

~ " " . .

:,on l Y~rice:.,Vi.b } h,"~::,ratiOn~lq~n t~nUIllber a~d,dil~:pt;~'."'.d~gr~e

0:,degeneracy.-fo~thei IiiOdro fvib r a tion. For,alIon.,~egenQrat9L-.ode

\..

In apolyaro;'lemolecule'

~t'

^IDayhappenth at two vibrational

~ . ' . .

.d~".,i~'~~ a .',dOUbl Y

""?"?"

modedi:~_ .2' .e~c . 'D~isr_he,-c-entr-!~

(\lgal,?i~tor:t~on"cons t~~t for^theVibrati"nal,~tatl!.V. 0.1isa small

const~nr

^{wh t e,li..}

~asur~s ~~e

^{correctioniIi B}

^fo.f

^{tha t·rood'e.}

" .".

'l\

1.8 Fen:>l R';'sonano:'.e·

.

levelsbelongingto'different'v~brati~ns(or combinationsof vibrat10'u.') may have nearly the's~m~, e~ergy.that is, may'beaCd<l~ntlY'.d.e8enerat~.

(I' Th~pe:rturbationfunci::1c,ln

.w

ishereeS$~nti.allygi;"enby the:anhaim.onic eereeinthepot,:".nti al ,",ner~••whi l e.1/1~an dIjIID_a;etheeu r c'appro~i-

~ , .-'.

.

m<t:tioneigenfunetio~~.of the._twovi b ra tio n allevelsthat pcrturb ....

s,ch

·'(2)

"

I' . .

\ -u- . ' . f

SinceV1. tot allylIJm1etr c;VidvilllI-zeroWlle&s.0aDd~o

. ' \ . • 11 i

au oftbe~_spec-i.e . ~l .e.•of tll eSA~lI; -t.ry'!;type).

,tI~

tJ:le

relionanc e~.^{fair ly}~oaei~:-:-KAl t wt eofthe~h:U·t.·

·cao =beob't:alnecl.c~r41n8^{to tbe}f1rst-ord~rpert~rb.t.1oqtheory"fro,.

. ' \

. .

) t.hesecular deterad_nt • • .. . .

\ ' / E : ' ." V,. . ., '.:

• \ W

n i ~~,E""0."

• I. . . . . ' . .

where.,Enand,,~:1.are.the:,;,nperturbed_{en~r~VIl .}

The~~eparatlo;".^of·:the·_pert.urb~~^{levels 1.a},g1~e~^,by

\ -.Ai".. ~ ·~.4t~D~n2H\ ! ^{. .}

w here

1!5

~"E: ^-\E£'b th.·~~~r~t:io~ .~etve~"' , ~e ~~rtul:~ed i~~;_.

· .: .. '"Hos tlo f.

th~ pd~~

^{ot OCS'}tevetswhtch

~rtrub each oth~~ ~~

·

t~o~e ~~t.b qua~,t.-~'n~ete .(v~.~/LIJ·~~)' ';'~ ~l:~·.v:~"!" lr.~. ·~~) : -

'SuCha.~rof bvell:'willbed~s~I\.~ ~ecrby BUbacri p t.~and.1.

respectively_

•an d(0,2° , 0).

"', '.- . . .

TheHut.~lrrif Per~rb:tD&:.l~l~.:tD·OCSare (l.00.0)

(4)

whereW12 h.tt,eiD~era~t1oDenusyan 4k·u •coostant~oragiven'· ."..

mol ee ule. Thepertur be d wavefunc:U=. a ra.lx~reof the~per­

etur b e d wave func:t l on san elare81ve4~:.,

· ' ·0 .'0 . ; "' 0

'h-.~1-~1jI2 'h..b"'l +ah.

whe re· [[62

;

z !j!J2!'2i

t u)",i

~1 62 + '~ ~ur211

,.

(5)

.... _ ----_.-

:~

. ... .

-.1..-

~,1 2-

(7) (6) b..

~[fl'l~'

⁺

i.r~1'21,21~ ^-,,6)

^,l:i

. ' 2[112

'+

^41!J12f2

]1i .

Th'eactu~l^Bvaiue~"ofthe in.teract.,i"-g·l.:.ve15·1lJ:'~^givenby

'ar e'sh own t.oAc~-.

. ... .

.

""

Uripe":i:u,~b~d

^{'vnue:of'02 is}

~O~~d

^{frora'th e}

~.e~a\-~tion

betw cent.he:

ro'tation~l

^{'i ev'el8of}

8tat~s

^{·(OOO) and}

(OJ.~',

^O).Thefl:'eq ue n c y

" ".' '0 " " ,'" " '.. "', ':- ' ,, '... ,'. ,

shift of the~(020)levelduetoFermiresc aaacemaybeobtained,froJ\l

. ,: . ' ,

'. " ,

the

kaci~

^{value of}02", '.

P'~

un.pertu:be'd valueofellJDaybe d.eterldned

~lnc~the fr e quen c y change of the'(lOo)state'VlllSr.·be equal'andopp~s1.r.e .

tc:'~that ~f ' (02·~O) . .~e~ frOll1e~u8"tlon ~!l at,a~d b(~~n. ^., ~lc~a~ed

~ndWitobtaineduS'1~ge'iilat.~on(~)•.

1.9

Quai'lrupol~~terattion'b'Y

^a

" ~:L~g1e

^Coupling

'Nucieu~

.'u

.e , ~yst~'

captai ns a'

~u~diuPol~';cle

^..s.'

.:~~,:",~lnterac'~1'~D cif

th~~qUadriipole,7iththe'n~er~al ~ectrona,~UPI~,tOg~~';t~~,~;^the~UCle~r

~spin

1. rd

^ther?ta~io~al an~u1Br~ment~'!'j'to.f~~^ar~;ultant

F.

'wheret.hequantumnumberFtakesoneottheva l ues

F -:r+'l~: , ":'J+ J. :_·~~ ^{'. ••} lJ~';' I! ~ ~

Fr01ll quantummechanica~cons i d er a t i o ns, thefirst--orderquadn>po~e

, ./

-13-

. . . - .

8?d Y(J.-I',F)a~ib.e~9~erfunct ion..

~4,C( C+1).-,I(1+l) ..J(J+l).

Y(J.

?

^{F) ....?(2J-l )(tJ+3)1.'21-'1)}

. , '

SJ,6orp~1onspe.:.tra.ar e

lU"+1, IJF,"0,, 11. AI- O.

~e -Totati~al'~~rc~uC~Cics'~ertu~~ed by :qU~d.ruP;;l~· ~~upi1ng:~re_ 81ve~

by

.' ',v. . .

vo;-~ (~qQ)

^{-(Y( J +l,','l ,}"!."' ) -Y(J:,

I;~, F)J Wher~

^-\1₀^'is

th~ ~npe'rturbed rot,itio~a1

^.fz-equency,

~~d

^'PI

co~r~3~ndS

.eo.

the

low~'r'6 tat~re la t 1?e~the rotat1onai l~vel:w1thout hyperl'~e ^{i '}

!.

,/

J,llvel

vi' vi V3.9. ~ V.,..9.lt Boo:'

- ^Bn+

0

o'

^,~'? -0.005054

O'

^{O' 35.81 -(I.1S17}

,: 0°

^"0° 284.56 ,'-0.5 35

0

J o'

O' 512.,02 -0 . 3041

'

·0 "

^{0',' "-:'0.35 '-0.0036}

0:

"0 r ,.~ -+<1.048

6 " "0 '0°'

~

^{0.99 :.:.0.012}

0

z

^-'0°

,

, 0 :4 3

:-'1

·

~

.: ..

^-.'.

:'1(;-

EXPERIMENTAL APPARA'l1lSAND TECHNIQUE

2.1,tlescri~tionand Discussion ofComponents

Aa1cr~wavlispect rc ee ter ees~nt1ally con5i~tsof ) l) II ...om:~of^..', 1llO~~chromad.cradfadonwithproperfreq'u~nCy-rang".(2)~fteq,;ency...o·nitor.·

.-; " ~

'"

,.- :

:- "

(3)an absorption cell,eo n ta ialn g the gasunder 1nve.stigat1on. (4) a

" :,' -".

';detecto r ','-and (5)a de n c'e for _spectral presentation . In this sectiona brief~escr1llt~onof these componenu wi l lbe&iwm~,

2.-1a Sources

The microwave,t"ad!at i on sourcesemployed herevere twoWa t ki n ll-

.'.Joh n s o,n,Ba c kwar d-llaveOScihators.· ""'d<;"lY.1'2020-2 an d Y.1 2019-1.

~ti.q_~~e x

and,.1 band s're sp ective ly.The .1,b andha~frequen cy,'r"n~e:f:.ro;',~~Q'-

to

e.c~~''' ;;d.

the-x,bandr'from.

S.O

to'1?-. 4,cne;'

Th~

^{powe'r'outp;t}

f~m

-t he s e o9d i la t o r s

is

50 to lOOJ:lW.These

.

!;l.W. O^"sc illatorswere',wunted^, in tb!!Hewlett-P,ack.ard^. S",~~pOsct1l~tO:^••eaet esse A.-Tbefre~ueocy~veep^WaSe~~tro.l1~dby.,:

varyi:ag the electrodevolt~~ - <lf_.the B.W.O._. tub!!by

.

mean$ of' a50K~ teri.',t ...rnpotent~omete'r,~onner.~~d·t~.^ther;~f,t.of,a^4',to'24~~ts^D._C.,~t~'r.

It waSpos sibleto obtain

a

widevariety'ofsl ow sweeprat~';_bY,v a T?"lll g the

~~ivi:,~.~~lt;'~e.

^of

th~

^motor

o~ .

by adj;"';tiDg

~f

^{-e.the-swe ep}

OS~ll~~t~f~~

2.1b FreguencyMeasuremen~

...-.- ' . .

.Aportionof_t h e microwave po.wer~u.~put',rromt.he'~.W',Osc1llator15 coup1ed_'outto the frequeI\cy",~as,ur~~gden"e,by_.1--0So~

a

10 <l:b-direct:ional~up1~r

.

.

The frequency'

is

measured on a Hewlett-Packard'El e c t ro n i c"Counter~H:.Idel52~S

t .,

-1 9,..

I

_~ equ ipp ed with'tl,";' 11C~lett-rtlcka ~d!r~qllcn~y 'con~e;i:.cr.(3to12.~.~.GiI7:)"

Mndel 525 5A;

'011. ," v::,::::,:::::::,':o:": : :::::':: :::::":::7':t50"'i'~

.a.ae TheAbao r p t i on Cells

The,ab's o r pt i o nc~li swer e m",.,d c~f ten~footpi('c" ,. ofS.~band.' w<'\v,,&uideofinte.r!ordir.llinH~o ns2.840".x1. 3 40",'wit k ,,'ce nt r al'fla t ' pl ot"

. . ' "

^. ""

•.

, '

s1xequid is t "n tpill ar sof ins"l"ting matc J"t. 3l . Con n e ,c'tionte. th eStark

" ', ' ...; .

electrodeis eade by a

, "

brassrodthro u gh

..

ah ermetic seal^' " in the,. side _ai loI

.

l th",ccll;wll1c hrc rm na t l?si~'ascr~wth r e a de d int o'th.e.pl at" ; '.ByJmunting

cut-off.~_r~q,:,endls^for'the dOllllnantTE~o,~~de^for,~he's;J,".and'xband wa ve gu i d e s are 2.078,GHo:;4.'.301GHz,a n d 6.S'!!,"-GIl',~e9pect1vely.o.

. ! .

It1s COllU:lon practic,eto useoversizedguide.such as S'b and

, , ' ,

gu~de.for the.. ain ab\,orpt i on ce l ltoav o i dsaJ~ ra~1rigthe",ole.culea

w~~h

^excessivers diation,'{al,Soto avoid,

exces~i:'le

^,guide

losse~

^.;the

.ea s e where,t h efi:~que~ciesexceed20 gH,Z). qu,O~ing'fr01llWal t e r Gordy.

"Sincethere":~e^no~ouple.r".T-section s,'slots.etc.'in theab s or pt i on

ce~l

^{..i t}

~s

possibl";'

t~use ove,~sized g~id~ with~ut ~~C1.ting

un ...te d

. "

^{-~ .}

.

^{' . ,, . '}

mode s. •'••••• •Here !'otDukewe have us e d S-:bandguide'(3"x11.:1" )ve r ll;

effectively for absorption'cellsin'the region: from 3 to

5

mm wave':'lerigth•

• ••••••Inother're ion sovers izedcellsarc,de s i r ab l eto avoidsaturating t.he mol eculeR:.. Uh ra, at:1on.'~(29)

guide swithhorns,'or tap e red sec eIens ofguide,and th:1s'hn sbeenthe

.' ", ",

~rai:ticein micro ...ave spectroscopyformany years: In th e'case ment:1oned by \.IalteJ::Sordy the ratio ofthe~-band";i~th^tothat~f^th;.a.easmID ban dgui d e wouldhave be"n2.'S4"/o.ll"",'25.8.WU,,'inthislabora'tory

t~e;~t'iO ,-1a.on~y 2'.S~">O. 90~ ~

^{3:i 6.}

ye~.Gor~y !It~t~d:that

^{the;'had '..}

~o .

morethnn'theus ual't r oubl e.with ref lect ions",

The~ic.ro..ave,po~rp~ssea:a8showninFig. ,2:S.t hrOUGh a directional'coupler.a variable atten us tor••series 'ofta p"r e d lIIst,chlllg, wavel\U:~de^{sectiona,'and,}then.int~^{the'absorption}'ceU:.-' whi chh'oidsa1nIl~1l­

sa~pleofth~gas. Theat t cnu~t.or "c,antro,l,the amount-of.lDic or wa v e,power allowed to pa....t.h r ough the absorptioncell.'an dalso at tenuatE! theun'fante~

.

~reflected ~:ves gener'~t'~d

chieflys'tthe endsof

t~e'

'S tar kelect r o de'

8n~ ~t

,t he w:indo"'!I.Thedir ect ional coupler placeddirect ~y,af terth e source does

.

- ' ."

~otpr ovi d eany appreciableattenuation betwe en sourceandde t e ctor.,but

, . '. .

..

p:ovldes,1%oofthe,lIlkrowave.'poWer.ee thefre'luenc~;"eter'forfr"qu~ne.y~ea~u:";'ent.

7' . -,."...

1

I

.;20 •-

', .,

'.

,,,,., .

Tb~u1b _re.ure~t1 y ~onoe~ tedto I~lc:>.I"'"17It~'byan ,:",t1e t

throughthei~broa d11d_fl!,IbOU~·.";"~.thirdalong thei rl~&th."tbeva cuUlll

.y.t~,

(Fig. 2,.2)

~Onsisted .

of';'

~u.ber ~f &t"p-e:OCIt~:

and.::01d't rl Ps G.'

- ^.

_{-21- •}

Shoal~lodu1ation

. .

^.

' . . ' " , .. . 'I

,I fan electric.fi" l disIIppl,i e dtoepolar,;I\Ol "cu le its absorption fr eq uen ci e s are shifted.be,causeofth e StarkeU"c!=. I f.atsoee:instantthe B.W. 08ci11a'tol:;frequency'co~ncideswiththat of ani:tbsorpt ionline.andII .pe riodi c

e~c,;'t~iC

^'fi'Cldis

ap~l.;ed.

^{'th e n'the re w11,1'beea}

c:orresPo~diltg

^{t-,i.:J q}

vadation inth e powerdetected bythecryst a l ,.si nceth~.Star... co mponents ofthc ' lin e are sh iftednlaUve tothe ,source.freque ncy,',n..e,swi t ch in g c n n bedoneelectronically'IIi:radiofre q'ue n cy.andthe' re su lti ngIIOdulationof .

the·..J:ci:owav c"

po;"er abso~hed

^b;thegas

~a~ th~~

^be

'de;cct~d

^bJ:'a

radi~;

~ec~~y"<tu~ed^{to th,;,}modu1a ting frcqu..ncy , Thi si~^the'pri.n~,ip~e^of;the

~tarkI:IOdu latio nspectromet er'in t roduced by,Hughes.and Wi1l ialllS(18).

i~

^{adii tion}

~'o' 1ncreasing sensiti~ity

^by

a.vOid~ng

aov frequency.

-2';' -

2.1 f ~

," ~e'o ,:,tp u t from'th e ab.8orp tion ce'11"':Os detecte d'byH~,,!lc tt-Pack~td Cryst41Detec tori Mod-"1

X 42 4

or'J42II,~ (ne~...tive'bl"sed).,. Theout pu tofthe Cryst,al'det".,c to rwas'f~d.into.apreampl ifier. , a~dthentoarecei~er-t~ed . tolOOKIlO:(both"

IIl!ln~factu~ed ~

,'

Ind~strial

ColllponEmt $. ' .

Incorpo~ated) .

The'cryst al- its e lfcon~iB tsofa

smaIl'

^pieceof,~se;":i.conducto~

lIIate r~al~i'"con tactwith a·fine',t. unqsten"'hisker:~

Sucha syste mbeha ves.8Sa rect i fier'fo rcur r ent.at ercreee vefreq uen ci e s.

. ,"

. ' .

ThecrYat~l",:i~.~unted^'ona holder wh o s eoutet~ng,iBⁱⁿ.'cont~c t^{withth e} waveguidewal1s.'Th.einnerco~lluctor.towhich,the tungst e n "h isker is .

cio~rieete:d. lea~s , ~cross

^th'ewaveguide :.an.d';0ac ts

~8

^{'t he}.a.:. tenna

c~ ,

col lectin gmicrow averad ia tion ;

a~d the

^{rec t ified'}

o~tput

^{signalpaeeea'to the}

" , . ..

, '.

cosJ<ial'll-.N.C .'-connectOl: . 'l:'heasse1llp~Yof~beX4 24Acrys t aldete ct ori8 showninFig~2,.3.

F'ar.the'display

'~f

t.he, ou t p utsi q rialfr01llthe 100 KJlz'recei ve reit.her

a_lIewiett-J'aCk~rd

^7035A

: X -Y

recorderOr.a110 0B·strip

c;ha"C'~ ~-"';';rd'erw~~

^{use d.'}

E'o r !:he.pr e lim1nar y,s e " r ch'of'th e a!:lSQrptioil'l1n es the'x-yreco r d e r ~

"nd .~or

^the

· fi~~l analY~'is· Ofgth~ ,

^lin:'stJ:1e

. ,jtrip:"~art

r<.K:Or der·was uead, The'

.ro~PM' ^" "'k « " ' ';'

of"0,' o<Ow...

'POCt<"~'Ph

^'"

'h~,~ i, Fi,.i ,,: . ~

Exp e rime n ta lTechnique

Searchof Line s

. , . .

Theabfi'orpt lim ceil

an~

^the

'glassW3re ~re ~~llY,

^{evacu at ed'.to}

a'

pressureof0.002 tor r."In fa c t"t J:le

'p~~ng

out·ope ra t'ton.,;:as

c~nti~~'d " io~

- 23-

by,i n tenn it t e nt 'h eat' iugof telie g"ide

lob

'ensur e t'tia t'

the

ab~or·~t:i.on

^{'cel l'a Dd the}

, re~t

^ofehe vacuoe syste41wereeo";-"lete l y

·

f~ee fr~ "ny

trae",'of abs o rbedgas es'."Fu'r t h",r.,

'th'~

abso r ption

·cel1'wa s'

flushe~'

s" ve r al'

~imes ~'ith ·~'9.99%· 1~NH~ gnS

^sup p lied byMa'thes on

- , " '•• ' '.';" " '.,f'

?fcanadaLtd.,by lettingin'the,gas,t h r o.ughtheinlet.:~aehflush wa.sf~l1~wedby:~v~c.u.atl..ono~,^tl:e•.vacuu~^system. 'nli~,p:o~ss^was,~~ated

;sElve ral

t , '"

^{to,ens ur~th~tve r y}l\tt.~"

.in'th'.,abs orpti onC:e~~^{:;andel1"91 8sS},w".r.es•.

•'<. •Finally, a freshsampl e of

.c:>: .

·ammoniagas,~roD1the~o t t1ewa sintrodu ced1.nrotli'e..bsor ptioncell until,the,pre~SU,J;elJ'oseup tO,ltor r. Then,ebeexceee-or\t~e g~,Swas remove d'froQ thecel. ).bypWllp 1.ilg'i t out,andeooU,n g,in thetrap untilthepressurew;;'n i downto the'o p t m_ .l ev el .'i.e... to 0.01torr:

Usingthe fo=ulagivenbySc1mabel~ ~",(l5)" ., an emp iri c al sp ec t l1Jlll

wa~ gm;;~r~ted'.:· ·~h~.- l~tens·ltJ.?S

^of

th~sel.ineoi.

a't"lOOOC..fere also calculated.'Af te r'ra1.a i.tg'the

't_peratur~

^{of'"thE!" .}

'gu i deto'

ab~u~ 900~,

"s earcli

f~r

tho,se Jin e s"

"'hose" ,t~~i-er:i~l-inte~lt~"S '

;. w~r~'

^{of the.orderof}

²

^{xiO.,.'JClII-l.}wa s IIl6.deon a

~~ow-6w~e~

^cha.rt

recorder.

Th~ ,telllPe~at~rl! '~;"~d no~'

^be

u~se~ furth"r,~s

^thesea ls io the absorp~iond",1.1sta r te' dle ak 1.n9 at hi gher tcmpcr;;, tur:e s..

, ,

_.24~·

i:21>

'I <h ,n t :l.r"iea t i o n'

< i

ReflectionRes ona nce- Line s

'I~ iden't~fY_

^the

reso~a~ce-li,;es-~~'th1n"

^{thesUi. d'..;;}th e abllorp -. ' tion ce.n.washi<ftilY .evacuated with'inte~itt...nthe at i ng ,80,<1.8

to

leave .litt le

' ~r~e';'- Of

^{'I "NH]'}

~al!l

^{'i nthe}

~ae,,~';' 6YSi:~. n:" outPllt:~~ltllgli:

,. . '-": . ' ," , ' . ,' ," '

ofthe-cr yst alwss.d,feectl)' fed to theX-Yr~"'td er.IlDdagainasweep

was'taken

at

thestep sof 100 MIIzfot the,f requ<me y range4.0to'12: 4

G!j..%. asdonepr ev io usly with thega~in'the,c.e lla.-Many!~~nl'.9.ti!,3ppeac,ed

w1.th ;d~inl$hed ht_~n91;Y, · 'Th~~e

^{we re ,}

I'O~

^S,lblYr·f,e

,r,,~~~ance 1~e.9

withinthe gu:1.de. As3.lurt her,check. on the nature ofthe originat.

~h~8e

^l1nea,.the

~pec~~nt ~a8'repeated

^after

ra:l.81ngth~ yt"p~rature

^'.

of't heg~ideby'.sODto.f!'ODC. ,Thes'e lincs appearedaiai n, but wer e ,"disPlaCed

~~

-the IDwerf.requency"liideby·...n

_a"';~~t. wh~Ch

^{depende don :....}

'the,thenaa~expaaetcnof t,heguid e. As expla;inedbe lo w,thi sf~eql'ency;';'.

shifLduetotemper atur e- VlIrlationl11 the: characteristicasso ch t e d' ,'With the

r~sonance 11~';-~

^{onl y._·':1n.'th iS,}

~'nn~r~ :

^{th e.}

~es,~na~~""liries)~_.'

..lt J.l;nth~gui dewer,:,'u~igUoufl1yldentlf.tedaod_el:lJdna ted fro mthe .lis t~or.f ur t he rin~e8t.1&a.tion.

2.2cShif~i!ll!.the Re90nanceUtl<!SbyH~St1~g'th~Guide_

one.of,themOB~ser10-'"pr o bl e.osinlIlic~ave specttnscopyi~th a t

,

ofdist:lngu1sh1.~~abso rp t io n dueto th e~t:rialunde r ",tudy!r01lltheunwaii~ed r'e sonance s setu~witw.n^thewsv~gui4e'~Y8tem^.itself."'Sl',ch's tllUding ";sves

ad~e. f~~IIl·~e·fleetio.nS

^bee-en

~i1ght':dis~nt.u'uit'14:

ⁱⁿ

the ~sveiui~e

_2~._

l'<>-i:t kul"Tl Y at

tl", ~oUPl~ne .

^{.j o.int s.'windo ws, .et c,_ Tlws<:}'resonancesoverlap

;andobs c u r etl,' 1! Sta rl<1.1.0 1'$

as

",J,J.

'ho ,o,on.:::k:::o:",:h:o:;·:~:;::::d.:: ::~l::d:'iP:s.:;:;d ^Of, ~vio,

'«,,,noy,

to

'iVOO:: li ' '<~ ,

where.v..;vclo c ity o f'.theJd.CrOl'll,e sinthe.gI11dQ~ ~~

'·<i. ""' ,,n, i~te~er.

~..:l c n g t h oft'hecabs o rpt.Io

Hh e n the.

~s~iption

^{ee 1 1is.}

h=t~d

^its,length1nc re'as c's ttl

\ .

^{' ,}

. .. L^t,'' ' '

Le I

+

een,

l!.T"":inerc...eein crnpp--ra ture,

of~ resi:allt!lecb" tu r J:neofthe Sta r k.lfne~caus<!d hy.these'

-:

:inthe'd e S i pl"o fthe',S.t.a r k m>dulation

; ,

' .

cell,,t he distancebetwe e, l.'-thesap Ill..and.th eW3US of,t he guidemay not re...,:inUnchang<!dthroughoutit sle n gt h ,cauging'a vat"btion :intheelect r i c

" ""'d'" ;h,""""q"" "'"'';i.'''."" ''' ,.,."i~

. '

^{', <h,} ko,",.d"

".,' ,f"

the, Held strength. ~Th~'a"cj~l:~'valu~of th"f'~,e1d~Yhe,~btilined'b)' .calibratio n~:i,th.isub~tanc.·e,whos e dipolc. .~nt:'i~,lr.no,ro acc"~:'telY .^'For

v"lt:(\'E~·.cal:ibrat:ion^ofthe.guide'i1e~e ,^carbonoXY$~lph:i<1e^{(160'I}C 32 5 )"as}

~ :::~'::f:~:b::Z,;' . ::,:h: . :7:::::::i:::::': ';,Z, ;:: :: :::':::::d

fOtd~ffcre;;t>"Ql ~agesaridIi;"clcc"td~'f.ic li:l;'s tIl:llg t l,·(voits/ ~~)^,;,a&

_,-,_~~~'!~!L~rOl\l' ~f~~'"

^{, " ' ..}

,

r. ~ ~ ~~1

, " ' ,

, , '-",,---

Av~S ta'ikshiftintm"andu~-().714 9D.

vOlt..etc~ r~ading

^{V'an dthe}

e11!~tr'iCf~'i<l~'stre~&~~ E~ ,~i/l ";asd"';'~' fO~~both

. " " " ,' : " ,

""" ,

^.

th';guid es. n,ecal:ib ration-curves1"~e rep~duce,~ln.F:i g : 2;7:

the

r"so1U~ion' o~

^Starklines,

the b"-~put-'freque~cY-Vildati~

^was

i(jnt:rol~'~d :~y,

a'50 k,:olilll

~en~tu:rn ~o'tC'.ntio~ter, ':~~owi;;" ~tiven

^bY"O'

'4 ~ 24

VOltS.,'D.c ." mo-tor

v~

^a

wO~.,te.a~ ..

^Ily

~ee~in g

^,

t~e,'·dt:i..vi~~.~l~agC'., at?(1.

volto

"2~d .

^mal.ntai"ill!:·, Af,at'~oo ~1; .'n~8\;eCp~ate,0£·0.1eec.z 101Hz:permi n ut eW~9 obtain~d.

crysta lcurrent,whichIss190'a measureof,th ss1g1l41strength,vee

'k~Pt ~t

¹²⁰

~a··. ·

^{Thebandwidt h}

~f,

the 100 Kl12:

reCei~er

^{1188'selectedto}

.',". 'The ,display

.

,of,the output

.

signal.fron.,the

100

KHz· re,c e!ve r,)-lasmade onthell t rip chart

re~order ; ,

^the'paper spe e d bemg'

'i" " .

lIlaint~lnedat 0.2in ch per mi n u t e. Thev£,ltage'Scaleu~al1ychosen ,was 250mV.f ull scal edef lection•

.2.2f Cali.b rat i onof the'F reque ncy- Me ter

U~~ng t~,,~r~~dstate()+lrotatlolla1tranSi.t~nalheq}L~nc:y ofOCS

,,~,~,",t~~~!i~~uencY

^'sta nda r d.'t he::lIP

fr(!,quencY-IlI~ter

^{.sa s}

, c,ai~br~t~d:

·Th(-~verilg~·'reault.^{of,th e}'96 samp'leawas,12162 . 970Mitz~ ^!h.etheoreti<;=al

~ . " ~~l'~e

18'12162.984MIll':whi chla:cal culated

u~ing Co~t~inIB val~e

^of'

36488;8128MHz for theJ •2+3 linesof'oes and the Laildho1t-Borna te1n

' "

, -

, '

.

v~iue fo~'

^{D of 1,.3i'x'10 -3}

~z.

^{::Thewetgh;ed}

averag~'f~~ ~he r8t~o, O;~8 th';'or~~ical' f~~quenc)'and t~~ obaervcd

frequency:ls

1..00000ll, Th~

·corre ctiontotheObae~e;d'frequeilci~8^1s+0,014MHl':~,^{which is}less thslI th e r.II',B.

err6~

^{'of:to.02 isMHz.}

Hcn~

^{in'the'p re aen:t'work no}'cor r e c tio ns

. "', ,' : . ' .-

.

~~re,^{applie d,tothe}~requeuCy-:lliete~readi~gs.' X,~^{willbeno.ted'th at}on~y ooestandardfrequencyi s lIet!ded,beca";sethi s !ssufficiollt·to calibrat~'

·the

~~stalintJ:af"~equenCY-lI\8tar,

'1tIofrequene:Y:eearota~~ona;l'~~:e -~s_given.,by,the'formula,''.

v·=2 B (J+l l~4 D{J+ll, ,'

- . .

,." " ,

Whe r,e'Jisth6.:-otationalqU,anturlnumberof the lowerstate . Cbviously ,.' f';lrthe0_1 tran"'ition •