of «l«o«t all tli« •••it'Hivva atMltti lt«r« •pins and...

¥li« gromitf •&* ( • «fi<l liw iirmt mmclUtA 9%A*»» of

«l«o«t a l l tli« •••it'Hivva atMltti lt«r« •pins and fioriUaa 0*"

aad 3^t rvtpaatiY^aljr* Vli« traaaiUon trom in* f i r s t

•xoi ied stata to tlio fround atata of tliaaa avan-avaa aualai«

lying iMitaaan tli« otoaad aitallaf ara often iiuoli fastar tban

that of aiagla partlola adall aoAal aatiaataa* tuiu t>atia»

viaur aad tHa oliaanradi larga a laetr io quailrupola aonaata

i n tha ration aaar A • a4» in tlia ragion of nautron d a f i -

oiant Ba and Ca iaotopaa* in tlia region froa A • ida to

A • i9g (tha rara aartha) and i n tha ragion of A :^ aj4 (tha

aetittidaa) iadiaata that thaaa aaalai ara <lafonM4* fha

gafomation af tha naalaaa aan aaoor dua to tha polar i i iag

aation of ona w «ara loaoalr haand nnalaoaa on tho ranaia-

ing aualaaa and thaaa laaaa naalaana nova in a olovly

ahangiag nan*tyhariaal potantial* fhia dafornation in tha

thaiia af tha naalana laada ta aallaotiva nodao of axai ta-

tioao* ftohr and Mattalaon^**^' introdnoad thia aallaotiira

•aiSal and oiiaaaaafollx gnva a good diaaription of nanr df

60

tli« properU«« 9t l«iw««ii«rir »iiot««r stAtts im tHa 4«fonM4

r«floii«

M«or«ii i i to tM« tto4l«tt tii« iia«l«u8 far «iF«}r froa

tiM «lOM(l t l M l l * lM«0«t« ll«»t«tlltt lUldMr in* iafllMIMdMl Of

deforalag for««t dm t» aMQr | i«rl iel«» outtida tti* oloMd

• I w l l and a t ta ia i aa aqull lbriua d«for«aUoa of ax ia l l r

ftymmtrie tbi^po* f or saeli auoloi tae oollaoUva aaiioa

Mparatas la ta roiat ioaalt yibraUoaal aad siaglo parUo l *

( In l i r ia t ia ) midaa. Tho roiat ioaal aoda of •xoltaUoa

oarraaponds to tao rotation of tlio aueloas ia ttpaoo alHiut

aa axis parpeadicutar to tiiair aala of ajrwMtry. fh9

rotattoaal opoetra mtny IMI « « 1 1 aadarotood ooatidoriag t)»at

tho ttolltativo rotat ioaal aetiaa af auoloi 1» a ia l lar to

tlio ratat&aa of a •jriMMtrio top a i ta taroa oaattaato of

aatioa !# Mf aad IC akara I i a tHa total. aa«aiar aoaaata«»

M ia tiM projaatiaa af X aa tba apaoa fixad axia £» aad iL

i a tiM aa^pMtaat af tfta total aafular aoaaatua alaag

ajnaaatrsr axia %** a ia tka aallaatiira rotatioaal aagalar

•oaaataa aad la parpaadiealar to tlia araaatrjr axia* fiia

aagalar •aaaatwa aaapliag aaliaiia for tHa daforaad aaalai

l a aiioaa i a f ig * i* I a avaa«avaa aaolai tHa groiiad atata

haa I • K • 0* flM ratat iaaal toaad atart iag froa taia grouad

atata daa to tlia aTMMtrj prapartiaa of avaa«avaa atraatura

l a l i a i t t a d to X « 0% i \ 4% d * * • • wiiioii l a i a good

N

1 C

•D V

E £-O

E u

CP

c "a 1 o (J

E 2 c u E o E

C

61

f l i i t m9r% 9t • • • r g / l«v«l« *r« knowi tm grûad s la t * r o t * *

lA Iht tluiory of ualf i«4 aodtl (eoll«etiv« aod*!)

of Botir «a<l Mottol«oa*'« tbo auolout i s «oa«l<l«ro4 to too «

djraaaio i f i t o a vlitoii ooa porforn ofiall oooiliatlono alioat

fho doforaotf otmiio* Tlio auoloar otatos tliua foraod duo to

tboao eotloeUv* toi l lat iono aro doaoriliod as (tio vl l ira*

t ional apootra. Aooording (o tlia aaauaad aadaliy ajraaolrlo

•liapa of tlio aaotouf tiio vibratioaal asoitatioaa aro olaaoi-

f lod lata two typoo ' t oae i s gaaaa liaad aad tbo otaor i s

toota baad* th% oxoitod atatos goaoratad duo to a auoioar

surfaoo wavo arouad tbo aysnotr/ axis aro oallod 'gsoaa

•i l irationat baad** tboa tao auolous paasos iato « i oxoitod

statOf tbo sikiô of tlio auelotis otianôa oausiaii a ooatriftigai

strotohing duo to tho iaoroass of iioaoat of iaort ia* fao

osoll latioas oorrospoading to tao iaoreaso and doeroaao of

tho doforaatioa aaiatainiag axial syaaotry aro aalLod *lNita

vibrational baad*, Tbo gaaaa vitoratioaai baad baa & <• a aad

tbo bota vibratioaal band baa IC « 0*

0afrdoir aad oo<»«orkara ' bara eonsidarod tbo ooaao*

<|tiaaooa of rolaxing tbo roqairoasat of axiat ajraaatrjr i a avoa-

ovoa auoloi. fbojr bars oalouiatod tbo oaorgjr lavola aad tbo

trsasit ioa probabilitios oorraspoadiag to tbo rotatioa of tbo

62

iittol«ii« witliout may oiiaiig* of i«« i i t t«ni«i t tatc* M99r4img

%9 l l i ia ttoil«li tH* •qui l ibr iua mk9§9 of %h% auoloii* I s liico «

tr iwcial oll i faoltf and I s dstsraiasil ttjr ibs two {isruMslKirs

Qo '"'^ / • * ^ ' t t ^ 9 i * ^ « AsforMsUaa i^orsMStsr sAd y^ i s lAs

non-sxisliijr psrsmiisr whiob Is a Msasurs of dsvftstioa fro«

tits axial synmtiT* WIISKI thsrs is a dsviation froa tits axial

syoMistry i t lossrs oao of tbs priasipai aowMits of i a s r t i a

and inorsasss tbs oilisr. coassitusatlyt ^^ auelsiis rotatss

about tbs axis v i tb tbs largsst aossat of iasr t ia *

A) Oavydov and Hostovslqr ' bars trsatsd tbs itroblsa of

oollsoiivs sxoitatioas ttf takiag iato aooouat tbs i a t s r -

aotioa of rotations iritb bsta aad gaaaa vibrations* fbs

traasit ioa probabilit iss froa tbs various low lyiag Isvsls

of svsn«svsa aaolsi bavs also bssn sstiaatsd by tbsss worbev i-

Xtss fl^rstsaatios 0t &„ transition probabil i t iss for

2^ — ^ 0^ groaad stats traasitions in svsa«svsa aaolsi i a tbs

aass rsgioa 150 ^ A ^ 199 aad A :> 334 bavs also bssn studisd

br ssvsral aatbors * • froa tbs stadjr of tbsss systsaatiosf

attsapts bavs bssa aads to s]q»laia tbs largsr gMma rajr traa*

s i t ioa prsbabil it iss bstwssa tbs rotatioaal sasrgy Isvsl*

fbs sxpsriasatal a^ - - ^ 0^ trsasitioas ars sabaassd by fas tors

raagiat frba 90 to 300 as soaparsd to tbs siagls part iols

sstiaatsSf i a tbs abovs asatioasd aass rsgioa* i t i s also

kasstt^'*^^' tbat tbs traasit ioa prsbabil i t iss apprsasb tbs

63

11) tiM «lo««4 alivtl r«(ion, COICHM *' HM obMrv««i that tli«

•»liMio«Mat fMtor F (wHteli 1» tli« r*tlo of (ii« Mq^triaAaial

traacillOB prolMitoiUU«» to tbiil prodiotod by siaglo parUolo

o*ttn«t«) i t MpproxittAioljr oqual to fli^**^« vboro a i« «

eottttant wid g io tlio onorfjr of tlio transitioii in ilo/» flM

•tiidyr of tlio ofotoMitio iwbavioiir of E^ traaoltiono t»y IS)

Grodtins ' teM oHotMi ttiat tlio produot of oaliooooaoiit factor

r ttsd ttio onorgr ^ ( la MoV) of tbo tranoitiaa i s aoarly oqual

to if* ilowoirort la tor oiq[»«ria«ata ' tiavo provod taat at

least for aoao oaoei F jc £ io not a ooaotaat bot obaoi oo

eonaiderably* runic at al.^^^ hava pointod out tbat tbo

prodiaot of tHa raduoad traaaitioa probability B(IS! > aad tlui

oorraapondiag anarfy of tbo traaaitioa li. i s a oonotant for

Nd, Sa» Odi Of aad Hr auolai bavii% aa avarago valuo of ad»

aaaaatly* iti^pat aad Sobgat^^^ obtarvad tbat tbo valuo of

F daaraaooi t<^adttally vita tba iaeroaao ia tbo valuo of aon«»

axiality paraMotar y^* But «o far ao attoopt bao booa aado

to aoapara tbo axpariatatal traaoitioa probabilitioa froa tba

8^ grouad atata ratatioaal baad ( f irs t 3^ oxaitad stata) to

tba 0^ greuad otata vltb tHat of tba m (Davydov-Hostovsky)

fbo systaaatioo of tbo &^ trwisitioa probabilitis*

froa tbo 8^ atato of & « 3 vibratioaal baad to tbo 3^ and 0*

64

titmf off %h» gfvmA BlmUt rotAtloaal hmA HAV* b—a •tudi«d

•ad e0iip«r«4 ipttli I I M «irall«bl« •j(p«ria««i«l v«la«e fear

Qri tor la and Avoliaa* % D«aa«r at a l « ^ ' ann «iaao«aa aad

Stalaoa^^' far •^m* aaolai i a ttoa tfafforaod raftioa uaia« 0¥

(Dav]r<iav-#illyi»air) aatfal* may bava obaanrad^ ' tbat laara HrJL.

arataaa dltarapaaaiaa bataaan tHa axparlaaafta aaa/aoa<»axiai

tliaory Itka larga iralna off Uia traasiUoii proaatilllty r a t i o ,

BCSgt a* ' — ^ a*>/ i («î a** —*• O^). tiara a** rapraaaala £ •»

vibrational baad aad a^ and o^ r%prmB»at X « o« ground atata

roiat ioaal t»aad, Upla fto«| Hfi aodal rat io off tita abova traa*

nit ion probabil it ias baa aot ba«n atudiad aad ooa|»arad witb

tba ajEp@ri«aatal rasulto* Also ao ootaporiooa bao baaa aado

batwaea tba ajjârivaatal tranal t i oa probabii i t iea ffroa tbo a^

atato off tba saaaa vibratioaal band to tba ground atata

rotational lavala and tbat off tba UH. aatiaato* bi tn tba

ineraaaad avai labi l i ty off roXavaat axparimiatal data ffor a

largo ataibar off avaa-avaa aaolai« i t i a iataraatiag to atud/

tba or aad m aadal traaait ioa probabil it ias and to aoapara

tbaa a i tb tba aiiparimintal valuta*

l a tba ffirat part off tba praaant iavaatigatioa U a

aaatiaa a) aa bava atodiad tba variat ion off tba rat io bataaan

tba aaâriaantal traaaitioa probabil i t iaa ffraai tba a^ ground

atata ratat laaal band (ffirat a^ axaitad atata) to tba si*

ground atata aad tba aaM traaait ioa probabili t iaa off m

65

••4«1 vitii til* ii»ii««xiftlitr prntmrnUr /^ or Uf tii«ory»

for til* A%t9ram^ •v«ii<-«v«ii aiioloi* tb* VAIIMI of y^ w*r«

t»lMB froa tiM work of VartiiAl wA DOM^ '• ri««« (3) aad

(4> allow tko vorioUoa ot tuo oooiro ftrooaiUon protoooilily

rolioo v im tiio Motttroa ntiaHor, M, oad proton niuilyort ii»

roopootivoly.

In tbo tooaod port Ua oootion 3>t tiio syotoaotio

Iboiioviour of tHo rodltiood tranoftioa prolioOiiity ratios,

BtCg, 3** - ^ a*)/i(Sj,» a^' ->- o*), of i** oaa mi Umory oan

tho oaao ratio elitaiaod froa ttio oxporiaoatai rosolto aa¥0

beea iavostigatod mm a ftmotion of ttio aoo<»a3iiality paraaotor

y^« For ooao niioloif i^ero tbo re«|Uiro<i oxporiaoatal iafor*

aatiotts aro avaHabtOt «o lianro alao otutiioa tHe variationa of

BCE , a** -^ a*)fi^y»Ua. a*' -^ a* v ^^ «<S» **' "^ ^^^.ap/ »(Ej, a** -^^*>oii • • • '««otio» of y^»

Ifeo a^^roaaioaa for tko f i rot aad aoooad a"** oxoitoa

loirola aro flvaa Iqr*'

»(t • y t • * ata* (f y^) e (a) . L - ( i )

^ a t t t

vli«r« T « i vfitb tli« alaua algft oorr«spoiids io tli« fir«t

3^ •xoii«a •iat« and ^ « a vltli tti« pla» slftii o»rr««poaa»

to tbtt Mooiid 2^ cxeiUd stat** In faotf for y^ « ^ nt

obtain tha anargjr lavala oorraapoaaing to axially ayinaatrio

ouolal of Bohr aad nottalaoa.

fbo W ffiodal alao pradieta ttia tranaition probabi-*

l l t l ea batwaea tba lov l f tng rotatioaal atataa« fba raduoad

alao trio quadriapola traaaition probability froa tba JTirat a***

atata aad to tba o*^ f round atata ia givaa Dgr 6)

* 32 A

3 « a ^iia'ia y^>

V W 4ai»( i y^) - • - u>

:aa.>^

and ft^ • i*3 X iO*^' A^^^ a« • - • - * • • - - • - . • - . • (4/

la axpraaaioa ( 3 ) i ^ ^ ia tba dafarnatioa paraaatar* fba

aqaitibritM dafarnatiaaa ^^ aaad ia tba aalaalatioaa a«ra

tiriMb froa tba iiarb of i^» and Sarnnnabi'^% oorraatad by

Marablab aad itaanttaaan^''. fba vaiuaa of y^ vara takan

fron tba r0t%r^mtt9 i9 aa aaatiaaad praviaoal/*

fba ganaral axpraaaioa d«ia ta nwrrdov and Koatovaiqr

for tba radaaad n^ tranaition prababilitr bataaaa tba

6'6

6 7

o a l U o t i . . . U f 1 and f i.«>

A__ X |<-f/a2mh>l 2-

wli«r« « | and aj. «r* ttio ia l t la l and tJLaal MiaiMira of

polfirlaiAUoa •tftt«t of tlio itaol«tis aad q,^ It Itia w **

oonpoii«iil of t6« etaotrlo qiiiidrupol« »o»0at« In porUouiar

tho roduoad is (ramlUon probability oorrespoadin^ to

•q«(3) l» givaa by*'

S o tJ

8(Eat 0* - ^ 3*) • — 1 - . (1 - - | - ) ( i - - % - ) * - • • ( « )

iriiara

S , • J l aad q « - i i f i - - • • - . - • - « • ( t )

Kara C^g i* * * aaargy of IIM 3'*' at«ta af/groiwd at«ta

rotational baadf £<|g io tha aaargy of 3* atata of tba

gawi* vibrational baad and o ia tha anarty of u^ atata of

tba bata vibratioaal baad, Uaia ^ tba ralatioa (6) tba

traaaition probabilitiaa bava baaa oaloulatad for 35 oaaaa,

fba aiagta partiala radaoad traaaitioa probabilitiaa,

BCEJ, 0* *^ a**") ^ Imvb baaa aaloalatad uaiag tba ralatioa

8{E«, 0* -*• 8*) • a. l iA*/^ a* x iO*^* o»* a» id)

Th« •xp»riatat«l traatiUoa probatolliU** tony*

b««ii eoaiîltfd from Iftieltar !>«*« f«bl««^% la •»•• o««*»|

%%% traasitioa probebilitidii ti«r« lM«a oaloulaud irom

hair-llf* a*a«ar«Mat« «li«r« ti^ (Ur«ei a««siar4iM«»f» «r«

ttot possible*

(b) insults and a i a o t f ioa

Coluaas 3 to ii and i3 of tbo iabia 1 giva iâ

ralavant lofornatloaa to bo aaaul i» tba oatouiatiuaa*

Coluan 9 of tbe saao tabia givaa tba valaoo of traawiUua

probabllitios oaloulataa uniai aûatiou \Q), Uara wa

dafioo two f00tora f^^ and r ^ aa followa

p , J .f fftt ^»i M 9(EJ)B,1

and

r . t . . f» i • - - - • • • • - . • - (la) SP 8(83)5,

Ihara ^(E^) i t tba aaparlMtatal raduoad i£» traaaitioa

prababllitri <>( 82)011 ia tlM ratftioad &^ traasltioa proba

bil i ty oalatilatad froa tlM Oavytfov-Hostovaiqr aoaal and

BCE^)^, i t tba tiagla partiola raduoad 4 ^ tranoitioa

6\S

•w •« C3 « »l as H* t» o o ST »- »: a: K m m , -r a ?> CT • - u y a

o o o p o o o o o o o o o o o o o o o o o o o o o 0 0 0 0 0 « f c v i « V i » - * - * - * - » - * 0 0 O 0 Q Q - * v j » Q " ^ u « - *

o - * - * o o - * o o o o o - » o - » o o o o - * o o - * - * - * o O Q 0 f t ' * * O < H - « * V P * 7 « v £ . N 3 C C - * * £ - 4 C 0 0 3 - * v 0 - ~ J - * O O i 3

o o o o o - » » o - • v l * - * ^ ^ - * o - * - * - * - * - * - • o o - • o ^ o

a » V j l w o O v l « ® - J ' - J O * V S ' V J » S c » M D C % - * 0 - 3 o O O » O v > l O O

o o p o o o o c o o o o p o p p p o p o o p p p p

to fo to -* -* - * « » — » - » - * .»

-» O O * » V » I V D ® 0 C * > f 0 0 > K J O 9 V M 0 » O O a > v J » O w l 0 »

o o o o o o c c c c o c o c c o o o o o o o o o o

O O I O W M O O O O O O C O O — - * - » - » 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o - k O s j i o o o o 0 0 r 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 f 0 0 0 < * > 0 f O \ j i v 7 * C K O ^ C C \ j i U t v n v 7 > U t a i U l V J « - « h O « | i O - * ^ o ^ 0 ^ O * o « ^ * ^ 3 C ^ 3 o e — 0 0 0 0 0 0 0 — 0 .oroa%

• < 4 \ j i M O - ^ 0 0 ^ 0 . v > v j . C t v i i ! V j » v j < e ^ « ^ 4 t > f O V J t - « h - « 0 O O - ^ N * * O l O - » k V « r - » a o s - 4 v c a > - * \ > f O - ^ - < t w P - 3 - J O - * O W I S J

I * » • 1+ • * l-f ! • 14 I * I * !•«• 1+ 14 I * 1+ 1+ 14 14 I * 14 14 14 | 4 14 14- I *

O O O O C O O — C O C C O C O O O C O O ^ O O O - *

K tC re 9C -* - * ^ _ » - . - . j V 3 - * « » « » ^ ^ . k ^

I * 14 14 14 14 14 14 14 I * 14 l 4 14 | 4 | 4 14 l 4 14 | 4 | 4 14 14 | 4 14- | 4

\f\ \f -^ ^ 4k

CCf» c : ( £ 0 4 k C . C v ^ c v ^ ^ ; < . v > . v « l . - * 4 ^ < « » • < > c ^ ^ ; ^ > o ^ l v ' « • | u ft

- 1 SS ',« -3

1 • • ar • •

• ss 9 c • 0 * i

ftj l-» S | • e «<

m

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4 <o

• - • K i n e. • c r « B 3 @ ae< a. « *n

^ • • H H-< M W fS? 9 ^ ^ 4-%C

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. ^ M r o 5J «* J3

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Ui « < c> »i 0 J'^v

<?.-. ^ E "*• — ' M O %:

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s s •» r- © «-

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9

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s s •1 * m •1 « •»: •

• ha c «• 0 M 4 > •

0 0 1 4 *K • Jkv,^ l -OB^ »C #*

f t * ^ s St

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IS3 IS? •* > %_r

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70

Hefercnoft for th« Tat»l« I

Y. Yonhlfitivat B, nitbelr, ii» Uertlclad and M.C« Oiasen, Mwol, Phy^. tn (196T) 3T3,

fj.HT, nronliev^ .i«4« Cetnidovi V.A, tvanovt '/.N. Uutsonlco anU \ M . P«l®lthov, ^ttcl, Phys, 43 (li»63) 609*

^« lônnto and nag«aanii» Hml, Phyn, 83 (1^66) 631.

*«Iuclear nata 'ihoats (>rattonal Aoadetsy of »oleace» "nqhtn^ton, f C, 196S).

U nacklin* 1. 'ûarex. •>.'.IU :?cliult ariU ...NC. îiollnet f»by«». Rev. , 160 (t96T) 1011,

^. draft t sar , n .n , llaiêmann, K* U llnsoamin aaii tU Îtiek, •luol. !»hys,, T6 <1996) 1.

n.fl, Burson, P#I-*, % Houdsmlt and J, aon l jn , Pliys, Uev, 15<? ( t9«7) 1161.

K, K9mp and fJ.fl. naiêeiana, MuoU •liy'j. 97 (liÔT) 672.

n,h, Vla lsan, IC. Itslcy and I . viylloz, Muol. Fhys. 93 (196T) 394.

K. Korknan and \ . Saoklln, Vuol. t'liys. 62 (1^166) 561 .

t . >C«ssthalyl» f. OoaH»t«r» I . t>e»9l and L, I'oea, MttCl, Phys. 91 (1967) 692.

A.«?. navydov, V.«?, noatovaky, ?[ucl. Phys. 80 (1964) 529.

h» PCasxthalylt I* Darkas, I . UasAil and L. Poos, Huet. Phys. 71 (1965) 662.

A.ff. apstra, »rucl. Ptiys. 97 (1967) 641.

n .» . todraav, Bul l . Aead. So l . ii^m 24 (1960) 1466.

n. <=:ibak, M.C. Olenen and »). Sklltoreldt Muol. Pbys. 19 ( i960) 523.

71

<l) f>.n« iit«l9on and t* Qrtnininn, ^uctoar imta A 1%I63> 21*

r) n, araeUer, and E.M, Ifernatelfi, l»tiy«. »er. 129 (1)163) 177<{,

a) U nansQii «t al«, Muol, Physi. 33 ( l a s i ) 6;I4.

n ) P.H. Fonaan, Phy«. tiiittarft 3 (l;}d2) 153,

ti) Vnolear Data Hhaeta (National 4oadei^ of ^iolonoot i^'ashlnftion, DC. 1965 )•

v) F.tC. Moaowan and 9,\1, -jtalnon, Phy», Uev, 122 itmi) 12T4,

«) f>.n« n«st«r» M. 4. loorot l" . * Durdaa and C, u lilaaa^ JIUOI. ^hy«j, 22 <l'J01) 104.

*m) ^ ^ l e t l at a t . , •Cgl. Daatke \^ld«iiskat}, fielskab, iat. fvyii. Madd. 33, 1o,12 (IMO).

* Calealatad fron batf U f a .

72

prob«toiliU«0 from ttm tirmt %* « t a U io tli« u'*' (rofui4

• t « t « . Tli««» values f^ anA F ^ hava baaa îvan in

ooluaasll aiMi ia «a<t iiia last oaluMa givat t&a aanâxiality

parwiatar y ^ takan froa t&a work of âraliai aaa ttoaa^^^*

Aldar at a l * ^ ' aludiad tha ajrataaaUosof t ^ traaait lon

probatoilltlaa aad polataa out that tba iataraotiona of tHa

rotational aa<3 irltoratloaal baaAa ara raaponsibla for ttia

aahaaeaaant of tlia i ^ traaaition proliabll ittoa, MatHaa and

Mitaott^' furtiiar aapltaalaad tha oeourraaoa of oollaetiva

vibratloas and thair ralat ioa with atiail atruotura. flio

rat io 0(^j|)^xD^^^^3)jB balng olwaya groatar tliaa ona ooa-

f l raa tha faet tbat tba f l r a t 2^ atataa ara larâiy oolioo* la) tftva* Hajput MBit Salmal ' founa ttiat ttio aakaaoaaant tmt^t

f^ of tha Eji traaaltloaa f)^nva^ to \i^ atata daoraaaaa

graittally with tlia laaraaaa in ttia valaa of j»on«»ailality

par«Mtar y^ of âvydoir-Filippoif tkaory*

BxpariMMtal trwiait ion probabil it iaa ara tabalatad

in aoiaaa 10 af tabia U <So«parlaoa of tHata axparliMintal

Yaliiaa v l tb tlM tbaorati««l valuaa aaioulatad u»ing i a

ttaaory aad/ai«tt* part lala valuaa akowa tbat UH aatinataa

ara aloaar to tHa axpariaantaS Talnaa tbaa tba a la l ia

part la la aatlnataa. Tbia IndlaaUa tba otiparloritjr of m

nodal ovar tlia alngla part lala nodal for tba dafornad avaa-

avaa aualai*

73

ih« factors Fj^ Md F ^ ars plotud •itttnot tit* aoii-«xl«tity 141

p«r«Mt«r y of 0f ttioorjr. A« roportoH oarlior ' tlio

factor F^. door«a*«a gradttallx witb laoraaoing vaitio of

aoa-ftxlality paroMtor* But in tbo |iro«eat oaao wo liavo

oboorvod tbot tbo factor f ^ iaoroaooo olowLy witit tho

iooroao* ia ttio value of tb* aoaâxiality paraaotor, fno

variatlans of ¥^^ aad F ^ vitti noa-axiallty paraaotor y^

aro stiown in f i t . (2)* Fraa tiio finora I t la oloar tiiat

tbo IM oatitMttoa arc bettor opproxitiatioitK tban tbo aiaîio

partlolo eatlttatos for tbo dafomadi auoloi, fbo diaaftroo-

«eat in tbo two valitioa of oabaaoa«M»nt faotor F ^ and t>'

arc qttito largo for aaall valtioa of y ^ and dooroaaoo far

bifbor valaoo of y^« Tbo two faotora follow an ontiroljr

difforont trend* fbo variation of tbo faotor r ^ witb

neutron nvmber i« ebown in fig« Oaj* In fig* i3b) tbo

variation of F ^ witb proton nuab«r» Zîs givea« i t can

be seen froa tbeae figurea tbat tbe faotor V^^ laoreaaea

aa tbe aagio anaber ie approaobed and again deoreaeea aa

we go awoif froa tbe aagio aiubor*

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bAbitlUet fron th« 2^ •%«%• of X « a ntirftUtfuai Hand to

the a*** ana 0^ atata of tlia grouad atata rotationol band

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protiabilitiaa due to OH »odal ' ara

»(tg» a** - ^ 0*) »6 A

Ci ••s l - M i - - ^ ) * - * U3^ aa 4^*

and

75

^^ • g\ 'V

B(B^, a*' - ^ 0*) • 2«- - 1 . ( i« 3 | - ) ( i - - S i ) * • • « ( u i

Hliart Q y a t • «ad q> «r« all j^y«ii in o^** dt 4 aad ?•

Uving ih« Taltits ot y^ 4at*r«iiMi4 ^roa tUt r«Uo^^^

K(4} • Bj^(4^}/K|(d^) fUKi tU« •xp«rl.»«nt«l irala«« of • fia4

49 tti« ^2 tiraaviUon proiiat»tltUa« i>«y« tfa ealoulatad

from mq»» ( t i l to ( U ) ana tiioir raiioa, B{&^^ 2* *-^ 3^)/

B(E„» a '*- «>'*')» itava Hoaii diofairMiaod. tbo ot^uilioriiui

doforgwUoa para«at«r ( ^ to iakaa fraa tti« «ortc of naranialc

and ilasnuaaan % flM oxpariaoatal r«<tao«<S li^ traasltioa

probaHilltias tiava iMioa oo«|ill«<l froa too roooot roforoaooa

and tliolr ratios liavo boon oaioulatad. ftio anlianooiMnt

factors for tlaa traasitioo froa tho a* stats of & « a vibra

tional t>aa<l to tbs 3^ a»A O stats of ttis groima stats

rotational band ars also oalouiatsd. ws dsfins tbsss factors

as

'»Ri • . t T ^ ^'*^

« ( E , , 3* - ^ 3*)jj^

» ( e j» 3* ' - ^ 8*>^^

76

r i a * l t f tti« ra t io of iii« triuisiUoa {^roHaHilili**

9(&2» ^ *~^ ^ '«^DR ^ ^ ''^^^ eal«iii«t«d to «osipiir« XOm

•xporiMtttftI iralttoa with tlia tboory*

l a tablo a eoltwa^ 3 aa<l 4 gtvo tii« r«l«iraat data

to oftloulat* tho tlioorotloal tri iasltion probability ra t ion,

OÊg, 3** -»• a*)/tt(tij» a** -•• a*> ituo to w** aatl w» ttodtia*

Coluwa 9 of tht Sana tabla givaa tbo axiyariaaatai traaait ioa

probability rat ioa, Tbe tbaoratioat ratioa ilCfc; * a^ «^ %*U

B(E-t 3* -*• 0**) of Davydov-Tilippov aaUDavyaov-Hoatovaliy

aodala bava baoa jîvaa in ooiuMis^ aad 7« tbe last ooiaaa

givaa tht ratioa of tba radaoad traaait ioa probabiiit iaa

Z"B(8a, a*' -*• a^VaCv a** -*• '^'^hm^/C^^H^ ^*' -*" ^^f

KEj. a** -^ ^*)Jm •

Fig* (4) abowa tba babavioor of tba axperiaaatal

ratioa B(BJJ, a** - » a * ) / i ( « j j , a** - ^ a*) agaiaat tba aoa-

ax la l i ty paraaatar y^* f i < , (9) i a tba plat of tba aiMia

ratioa ealoulatad froa tba Davydov-JPilippov and Darydov-

ttaatovaiy BMMIala vtraua y^* tlia oorraapoadiag rat io as) aeeordiat to aobr aad Âottaiaea i a i,43*^ aad ia aboaa i a

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i?ef0reno«(>i for tho Table It

ft) Y» Yo«liiK«wa« a. aieb«ic» n. ileralclna and 4,C, oleaen, ûcl. Phys. T3 (1965) 3T3.

1}) U,h» f?lendlng9r, f. :. rriUiiMon and J.U. aaniltoat l hya« '?«v. 179 (IMJ) 1314,

o) h, Vamoll, l.ri. llaiailton and li.L* ti9bin<?on, lUi B. Uov. C g d a n ) 1365,

d) n.P, Ortôrlev and l.P, ivoUna, NJUOI, Phys. IJ (19001 ^m,

0) r.K, loGowrmi and l»,ll, Htel<«on, S»liy*?, Kev. 123 (li*Gl) 12T4,

t) n«P. Canton, 1.4. Craenberg, ]i,f!. Ha, »•'»• iSurglnyan end i m . .Jromley, vbyn, Uov, 13T (is*69) 1532.

g) n» nubol* •• t* i atiiaenn and :,:i, .lipajeiraklf Ptiy». tiav. G^(lOtl) t30,

h) Y»A, n i l s , ^ttoloor lo ta ^beeta, n^(iaTO) a43»

1) f.'I, PalmRf .?•*•• "oo(^ and P, Vonu^ôpala Uao, £>bys. liav. OgCt'JTO) 1135.

80

ftf«(8). fro« tiMM tlgw i t i» oliviout that in* on

••U««tot fiv* iMtttr f i t to %h9 •xp«riMAt«l v«lu«s M

eo«pur«tf to ttto W ootlaiitoo «ii<t tho valao 1,43 of Aolur

tm4 Mottolooa* Hit agrooMittt of %k9 oxporiaoatal v«laoo

with im •otisfttoo It qui to good In «l«oot «l l tbo nuolol

in tho tfoforatd rogion (for viiioH tlio roûirod data co e.

«Ar«il«l>lo) ojceopt in plfttiniw aooloi as i« ovidoat fro»

fig,(6>. Aitnougii, tbo ratio uu^^ a** -»• a^j/Uifcijf a*-*» D*> of DH aodol doos quailtativoly raprodaoo t&o laoroaoing

trond of tbo oxporiaoatalljr oboorvod valitoo vitli atoaie

voigtit in platiniia auoljl in a twttsr way as ooi ;>arod to

W aodolff tlM foraor dooa not indioato tbo abrupt Ifl treaoo

in tbo ratloo wltb tbo atoiiio woigbt of tbo platiaua nuolol

a« round oiôriwintally. Ibo abrti^t ebaagoo la platiauA

nuolol Moy bt duo to tbo ouddon doeroaoo of doforiiatlon ao

wo novo bojrond y^ • 98 wboro tbo nuolol aro oonoldorod to

bo pooudoopborioal*

jmotbor Intorooting foaturo i t tbat for tbo nuolol

wltb aotttron nuabor tfO altbougb «o obtain an agrooaont of tbo

Oft ootiaatoo wltb tbo oaporlaoiitat valuoof tbo ratio of tbo

abovo traatltloa probabllltioa for tbooo nuolol lioo bolow

tbo goaoral trond of tbo eurvo ao oboon In f lg^.(^) *"^ (î •

Tbio poeoliar bobavlour 1« not obaorvod in m^ aodol.

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82

H«f«r«iiott« for t\A9 Tabls III

a> Y, Yosihisttwa, tt. Dlobek, H. Uerskind and ;i .a. ulesea, Vucl, Pbya, T3 ( l»W) 2T3.

b) Ti. Varaoll, r,:t, tfatslltoti nnri luU, uobliiBon, tMnyM, d&v, Cjj(lOTt) 1385,

o) ^.IC, 'IcOnwim and P. I. Jtolsoa, Phys, llov, 132 (IslQl) 13T4.

d) n,r, Ca«ten, J,". Graenbarg, -t.-i. ^lo, t».A, iiurglnyon and ' ' , 1 . nromley, 9hyn. r«v. 19T (1803) 1533,

^

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Probakljr t M okc«rr«« alMorMa totliaviiiiur i a in* ra t io of

l a <laa la tlia a r l U o a l aautrott aiwiMir i»a iraf* at and 3T>.

Ia taUla 3 tba axparlaaatai valufla of au^v '^** '^ ^*i

and a( f i , , a* ' - ^ 0*) ara glvaa i a ooluaiise aad T. Collars «t

and 9 giva tHa aaaa raduead traaai l ioa probabil iUaa oalaa-

latad utins ^Q** it$) aad (14) of f>M aodal aad t&a last iao

eolaaaa gtva thalr rat ioa a(iSj, a** - ^ 2**')4gjjp/tti*'a»a*' -*• a*)^^^

and B(gj , a** - ^ ^*^sxp/*^S» *** " ^ * * * W '•»P««*A^»Ay • '

thasa nuolai for vliiob Mta raiavant inforMiliona ara arail-*

ablo to oaloulata ttiata ratios*

In f ig* (T) tlM ratioa ^^^^j. aad F^^^ ara plottad

against tha aoa«>axiality para«etar y^* fli« iaoraaaa of

ttiata raiiiot with y ^ l a not aa olaar as that of tna ratioa

of E^ transition probabilit ias frotn ttw 3**" ground stats

rotational band to ttia 0^ ground atata as oosorrsd in f ig . (a^.

In eoaolosion i t maa Oa aaid tiiat tiia mi aodal tt&ioli

takas into ssoouat tbs oollsetivs asoitation of a l l typaa

iA ttoa oalottlatioas of transition prooali i l i t ias i s in battsr

agraaaaat witti tlia axpariasatal valiias oirar a aida raaga of

naolai in daforwad ragioa tliaa tlia i# aodal aad vilirational

aodal of solir aad Mattalaon. Taa axoaptioaa ara paaado*

aphariaal platiaita aoalai alMaa typical toahairiour haa bsaa

poiatsd out W aaay aarliara *^

84

U A* Sobr and a,tt« i4ot%«l»oa« % l , Daiiftk* n4*aalittli

a« ! •«• iiottaltoii ana 3«i>. Nllsaaa, i£|il. Ummlm îdananalii HmU »>•• ifcrlftar i (lilSJ^ 3,

3. fC, Aldart A, uoliry f« liuliisy a. ^ l U i a o n and A.uialkort ilev, alad» flisra.t 38 (t^Si) 433*

4. 0« Matiiaa aad j«»&, Mllaaoa« Aiptiii*» !)•««•», aod aaaoa-Hay Spaoiroaoopy (itartli iiollaad Publiatiiikft Uo«t ilaatardas (1945) p* 4ai .

!S. J*i). Hagarat Aaii« iiav« Haol, ôi, 15 Uil49) a4l*

Q» A*i»« Oairydav and 6«F. ri i lppov, ."luol* li>iiya, S U ^ l) 083*

7. A^s, Davydov and ^.S. tiaatovaky* Nuol. i^bya, la ili/3>^>

5. A.S* Pavydav aad V«ii« HoatavaKy* Miaot« l liyat 6a U^64) 939*

»• A,S, Davydav aad A,A. CHaban, ifuol, Pliys* ao (li»6d> 4 $»,

10* A,4* Oavydavi V.S, iiaatovalQr and A«A» Qtial>aa» ^tiol, Ptiya, 37 (1»«1) 134,

11» C.P. Calaaaa» ifiiol. Pâ« 7 (ins?) 4Sd»

ia» r.K. êfiavaa and f>.lt, Stalaoa^ pliya* Hav, 133 (l«41i 1374.

13. W,M« Curia» Naal, PHya* 33 U^4a> 974.

14* i i .S, Hi^pat aad M.U iaH lA t <f* Fiâ, ;ioo, Japan. 33 (1947) 017.

19. Urn Grodslnat Vlty: h%%U 3 ili>4a) dt$,

!«• A, iSohwartioiilld, Myra. Man 141 il^dd) 1314*

85

IT. »• eoldii«l>«r atttf A.«. Sunymr^ Atpli*-, a««ii*, and 0«Mi»» diir S|»««tro»oopy (Wortli HollAiid iîiMlsbiitg

141 (!»«•) UOO.

19. ir.F* Vartlml luid li« tloie* ifuol. Ftiy*, A144 (li»7tl) MS.

20. E.F. arig<»rl«v ABd ikt.l>. AvoUna, Naol. Ptny. i» (itfdO) 24a.

3 i . <l. d« uo»r. a. Goldrla^ and il, iînklar, f*ii|c«. Hair. 134B (1964) 1032.

32. O.i , Baa aod 2 . Syaaaaidi Hml^ Ftiya. 2$» (is»61) 42.

23. ^.H. Marabalak and J.O. Haaauaa«a» i<u6l. Fiiya. 43 (1^63) 471.

24. F.ii. i lalaon and U, arodsla«» i«raolaar i'ata ia&loa Al (1^83) !•

35. Q. Alaga* iK. Adiar, A* Dolir and n. Mottaiaont Jiat. Fr«» Madd. l>aa. Vld. ilalali* an (1)155i i«fo. k».

29. H.C, Bart»ar« H.c;. iiuokvortii, i i .a. Moi f •'•^« âoiôa«âlit i . ôLateiUna and f. i aa ttoontm/san, Piura. uav. i<at(. 12 (li»d4i 997.

27. U. [Paulin^y f»)iya. iiav. U t t . 19 (19«9) ftci.

28. £• KuMur and M. Baraiisar» iluoi. Fliya. Alio U90i*i 529.

29* ii.A.J. liarlaeotUf O.ii. Qoldiialiar and iiraia iiiueK« my a. Hair. 179 (1999) 1S04.

30* «.K. Shallaa. Ilttot* fFliya.91 (1992) 339.

31. H. Ikagwalt K. Suglyaaa, f. YaKasakl and M. 4alcal« Maal. rnya. 41 (1993) 130.

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