of «l«o«t all tli« •••it'hivva atmltti lt«r« •pins and...
TRANSCRIPT
¥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
61
f l i i t m9r% 9t • • • r g / l«v«l« *r« knowi tm gr^uad 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 siki^o of tlio auelotis otian^oa 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 («^i 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 ajj^arivaatal 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 aa^ariaantal 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 eoai^iltfd 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 i^a
ralavant lofornatloaa to bo aaaul i» tba oatouiatiuaa*
Coluan 9 of tbe saao tabia givaa tba valaoo of traawiUua
probabllitios oaloulataa uniai a^uatiou \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
M O -^ 0 , ^ - j . * » ^ a
\J» tt
•<*^mm § -^ •*•« § fO c
4 <o
• - • K i n e. • c r « B 3 @ ae< a. « *n
^ • • H H-< M W fS? 9 ^ ^ 4-%C
e *% •-»
9 i ¥- «
. ^ M r o 5J «* J3
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Ui « < c> »i 0 J'^v
<?.-. ^ E "*• — ' M O %:
4 tJ »- 0 n »-' n
^ o* •
e c
0 r •«i »
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- . ** » <a i£» 0 g c
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s s •» r- © «-
• • => ? ^3 »
MO x 4
9
^J S g • • ** * o 9 e 4 < M r s ^
s s •1 * m •1 « •»: •
• ha c «• 0 M 4 > •
0 0 1 4 *K • Jkv,^ l -OB^ »C #*
f t * ^ s St
• 1 *1
b! CB • •J ^^ • mt f ft 8
IS3 IS? •* > %_r
1 S t r 1 S »« * • • i
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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*
^« l^onnto and nag«aanii» Hml, Phyn, 83 (1^66) 631.
*«Iuclear nata 'ihoats (>rattonal Aoadetsy of »oleace» "nqhtn^ton, f C, 196S).
U nacklin* 1. '^uarex. •>.'.IU :?cliult ariU ...NC. ^iiollnet f»by«». Rev. , 160 (t96T) 1011,
^. draft t sar , n .n , llai^emann, K* U llnsoamin aaii tU ^Itiek, •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. nai^eeiana, MuoU •liy'j. 97 (li^OT) 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 ^ivan in
ooluaasll aiMi ia «a<t iiia last oaluMa givat t&a aan^axiality
parwiatar y ^ takan froa t&a work of ^araliai 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 lar^aiy 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 ^avydoir-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* aoa^axiality 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 aia^iio
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» Z^is 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*
•n o JO
1/1 TJ
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Tli« cxiprttiiioii for tli« r«<lao«d E«| tr«ii«lilaa pro-
bAbitlUet fron th« 2^ •%«%• of X « a ntirftUtfuai Hand to
the a*** ana 0^ atata of tlia grouad atata rotationol band
daa to ttia D nodal^' ara
8 o 3 !l(E«i 2 a*)
5 a - Q, a aeA
Sia"(3 y^) •><•«••• ' ^ i i )
and
BCSg, 3*' ->• a*) mmMmmmmmmim
3a7\ 1 -
3-a si«*(3 y^)
yi>-s sitt*(3 y > ua;
vhlle tha oorraapoading aacpraasiona of ttiaaa tranaitloia
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,
O^Eg, 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 j^ivaa 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 ^Aottaiaea 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, ^ucl. 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, Ort^orlev 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^^opala 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 ro^uirod 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 oi^oriwintally. 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^.(^) *"^ (^i •
Tbio poeoliar bobavlour 1« not obaorvod in m^ aodol.
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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 ^idananalii 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, ^oi, 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 $»,
10* A,4* Oavydavi V.S, iiaatovalQr and A«A» Qtial>aa» ^tiol, Ptiya, 37 (1»«1) 134,
11» C.P. Calaaaa» ifiiol. P^a« 7 (ins?) 4Sd»
ia» r.K. ^efiavaa and f>.lt, Stalaoa^ pliya* Hav, 133 (l«41i 1374.
13. W,M« Curia» Naal, PHya* 33 U^4a> 974.
14* i i .S, Hi^pat aad M.U iaH lA t <f* Fi^a, ;ioo, Japan. 33 (1947) 017.
19. Urn Grodslnat Vlty: h%%U 3 ili>4a) dt$,
!«• 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 i^iiMlsbiitg
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, i^inklar, 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 •'•^« ^aoi^oa«^alit i . ^oLateiUna 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.