Beta Spectral Shapes in the Decay of ¹⁷⁷Lu

In d ia n J . P h ya ,, 61A, 32U-3:^6 (1977)

K . V^ENKATA Ka mA ^ I A I I AND K . VeNKATA ReDDY

L a b o t'a io rif’^s (o r N u c lv a y Il(\sta rch . A i u i h r a Ih i iv e r s H y , W a l i a i r

( E e c e iv r d 20 J u l y J07<;. ir n iy c J IH S e p i v w h n ]O7(*0

Th(.‘- ])oiii s]KK:iraJ sluxj)(vs of tlu‘ 401 and *4S4 KdV brla Iraiisitious in llu' decay ol ^'^Ln liav(’i benii dcUa'muicd c ) i i p l o \ a n ijiicrm('cliala-imap,r beta ray ,sj)oclj‘(>jn(4('r and oiu' ionnd to be statistical Yithiii tlu> ex])cri- mejital niieertainties. TJie siia}M\s arc in sii])])or( of ^"-approximation and are lomitl to a^aia* vojy A^'(4J witli IIk' Nilsson model predictions Tfi(^ lai'ge differences l)i‘Uveen cx]u i inaad al ajid tJi(‘ojrt ical ¹<\^ j‘l values

may be explairnnl as due to t in* '’^"Lu nuckais almost at t1i(‘ limit of tlu;

(Ud()r 1 natioji reeimi.

Beta spectral shapes in the decay of '^‘Lu

1. iNTilOininTlON

decays U> v^jtli a hall’ lit<' ol (>.S days. Tlu^ negat ion dta-ay oi has boon si-udiecL by various invest.igatoi^. T\\r. ,s])in ot tlie ground state Avas nea.snred by Spec'k lV Jenkins (1050) to 1m‘ 7/2 whii'li is in a^n'mmmt A\itJi the st ron g coupling i^stiinale ot IVlottelson and Nilsson (1055). KotatioJiaJ Imads asso ­ ciated with this intrinsic (‘ontigui-afion haA''(‘ Ixmmi obs(‘rv(‘d at IIJJ keV (i r 0/2) and 250 k(^A^ ^{T — 11/2). An inst rinsic (‘xcitadion has iKam obs(M ^A (‘d at 221 ^{K v \}

m A77tff

Ifrom Formi-ivui 1C analysis Bashandy (10<>5) rc‘jM)i’ted lour bi la gronjis witli (md-point energi(‘s 40b.S 1 1.7, 2S5 j 2, 240 1 4 and 174 12 koV The end-jaunt- ot the beta grouj) going to the 221 keV kna^l is r(‘pf)rted by MaiinKa- and ]k)(4un (1055) t-o be 17b k(‘-V and tlxat of tln^ Ixda gronji It) llie lev^^l a^.1 112 keV to be 28J ked^ (log ft 7,7) 'Pho most intmise spcctmm haids to the ground stale with a. log tt viable b.S. Uk' iiilmisd ics a-nd caid-point enmgies of th(^ difreient beta groujis reported l\v dilfmimt authors ai'i^ giviai in the tabk^ I. Tlie 284 keV and 405 keV beta groups i\.n^ non-unique tirst-foi liiddun transitions. 14ie iK'ta-gamnui in the decay of has been m()asured by Klncsj- and Bashandy (¹⁰b²) as a function o f energy of the beta particles 44i(y Jbimd tlu^ anisotropy factor ^{W (0 )} proportional to p^jW aTid its Yalnc as d²⁽¹.48) ^ 1 0.057 1 0.00()8. Th(dr ana­

lysed data show th at the ^-approxiination for this transition repreaemts tlic I'csults of the 385 KeV 113 KeV ^y eascade in a v e iy satisfactory maiuicr.

No investigation on the shaj)es of the 7/2^ —> 7/2 " and 7/2+-> 9/2” beta transj- tions o f has been found in tlie litejatime aA^ailabk^ I f the ^'-ap|)roxiination holds for the ⁷/²' ⁹/²^ beta transition, tlic shape of the beta spectrum should bo statistical because the omugy independeuce ol‘ the beta-gamma angular corr(‘- lation parameter [p'^lW) has been observed and hence it is indcpendtuit of tht‘

individual m atrix elements. A unique determination of the latter is not possible 329

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Beta spectral shapes in the decay of^^'Lu

331

in this caso. As tho 384 K e V /? 113K eV y nascado has betMi showing approoiablo anisotropy, a determination of the shape uf this transition Avill test tlio validity or otliorwiso ol thf^ ^-approximation for this transition. I^lien* is hieh oi exact eyaluation o f eiid-point enei'gies of diftereiit. beta grou])s. Si) a systematic stiidf ol the beta spectrum o f is made using eoineidimee as W(⁴I as singles mode of operation o f the spectrometer.

2. A^pPAUATCS ANTD K^xPEKIMKJ^TAL PROCEDl'RK

The Sieg])ahn-Slatis beta-i'av' spe(‘t roniett'j- \n ith plastic M'ell-tyj>e detector used in the investigation is deserib(‘rl bv Nagarajan vt aJ (lObt), 11)70). The modi- licatiou for beta gamma coinc'idmKu^ studies is dt^scribcd by Ra.viudramith ^{vf a l} (1073). The deloctor (‘ffieieii(‘y is unitrV down t(» 50 keA'^ and t he baek-scatteriug (dTcct is 0.2% at St) kcA^. TIk^ ai rangcmient o f baffles for dist(Ttionl(\ss opcnut ion, the lidelity o f tli(‘ spectral distrafnit ion and the cojtccI. moth^ o1‘ analysis Avere dis­

cussed by Nagarajan c( a l(1000, 1070). Th(^ ga-mma tilianmd consists of a JSal(Tl) mount.ed on an RCA 0810A ])hotomult ipliei with a n^sohition of 0% at an ciuu’gy of ⁰⁰¹ K(^V.

Th(^ source is supplied by Bhabha Atomii? Resear(‘h (y(mtre, Bomlmy as iut.eciiini oxide in 1101 solution in threci consignments. The source's arc pro- dueod by the ueutron irradialioii of oni’iehoiP'^'djU in Bond)ay. 3’be sourcre is (examined for any possible traec^s of impurit ies l)y n'cordiug the Ge(Li) s])ectruin and no impurities are found. Thin sources of diameter 2 mm and thichness 180 /////(in- a-rc^ prepared on aluniinised m ylar foils of thickness J 8 0 //rz/eur. The energy n^solntion o f tlu^ gamuui eliauiud is 8% for tihe Otil keV y la’ansition in The gamma-diseriminator is sot. to acc(^pt the full energy ])tuik of iuteroi?t.

The beta spectrum is an nod collecting tlu' coiiKjidein;<^ counts at inteiwals o f roughly 12 keA^ down from low turorgy to 3D0 keA^. Both the detection elTieicmcy of the beta didector and ft— y eoincichmcc officioncy (\f the eoineidenoo circuit are maintaiiUMl const n ut throughout tlui experimental region. The coincidence (jount rate is corrected for the b(da-gamma. angular (correlation due to R(^ddy (1975). The energy region between ISO IceV and 390 keV is subjected to shape analysis. As usual the program BETAS HAP determined t.he exact cnd-j)oint energy to be 391 keV. The ('xporimeutal x>fhjits are fitted into a sha[)c o f the form C ( W ) — k ( l - ] - a W ) . The Icast-scpiare fit Amine lor a is ‘a* ~ 0.007

This shoAVs that the shape o f the 7/2 9/2~ beta transition in ^’ ’Lu is statistical within the experimental iincorl-aintir^s. Tliree such runs are analysed and the results are given in table ².

2.2. A n a h j s i f i o f o u te r (7 /2 '—>7/2“ ) beta t r a n s i t i o n : There is a legion of onl}^ 100 keV for the analysis of the 7/2^ -> 7 /2 ' outer beta transition in ^’ ’ Lu ill the singles beta s]iectrum. In order to get a A v id e energy range for the shape analysis o f the outer-most beta transition, the inner beta with an intensity of 7,%

332 K. Venkata Ramaniah and K. Venkata Reddy

I iibltt 2 bbapo tii'itor data for tlie ^ 0/2~ bota transition of

Rim Nil Ko(KoV) Sliapo factor

cootTiciout a 4-0.0 0 7 ^ ^ 0 .0 0 6

: m ± 2 -^o.oo:i no.ooti

:{!)] 12 4 O.OOG^k0.00(1

I li(^ .sluij)t‘ ^iMctor for' (jiioof llu' rmi.s is shown in li^nic! 2 .

Imp;. I. Sffmniu <M\orgios and inlrmsitii'S and Id|j FI. valnns urn iiK'niporatoil IVoin tho ]TinKf'n1. wrirk.

/ ?0 300

391 nev

-too 4 SO iOCJ Ennigy m koV

Fig. f. F. K aiialyHiH oC thn muglos Imia spontiiiin on subtract ion tlu^ four difilornnl.

grt^ups rnsullod with oiid point enorgios as shown lu ttio tigiire.

Beta spectral shaj)es in the decay o f

333

and with tho H^portcd sliapt^ is roiislructod jiccoi’djiig io tlu' tdnunlji : A\i{p)(ip =~

Kp fC {W )(W ^^- W )H p wluTo l\w, iutoiisily laotor K J is [W aroii of the a: gross speotruiij and .^'is ilio area vviUi K - 1 in tli(^ aciua- tiou. This oonstruciod spnct-riuu is sulitrai'tod all<(M' iioriiuilisatioii ii'oin

IpIlo gloss H])Ootruiii. Tlie rosultiiig ^{s j k u' Iv i u i i} is ^{i t r} sliapc' analysis fi'ojii ISOlvoV to 500 KoV, thus n'lncwiiig th(‘ iu11uour(i of Uu‘ i j l i u m hoi a group, liy duturmining tJic oxacl und-point (Mungy from t h r graplis u\ llir iilCrASIlAP pio- gram, the experiuuuita] poiuls are iitt(‘d into a ska] factor of (he I'onu (¹-- uTf), A least-square fitting resulted in, a -0 .01 7 I O.OI Coi'an emkpoinl t uerg^v ol d03d::2 KoV. Tliis sliows ilu'almost allowed mdiirc* ol ihi^' Ixda liansilion The josalts for three nun are given in table 3 TUv shape iador ]ilol loi' ojie ol llu‘

runs is shown in figure 1.

J?,im No.

the 7/2' ■“> 7/2“ l)eta transition

K (KoV) Slxqni factor

cootlTi<‘ioii( (/

--0.017J 0.01

— ⁰ oooj ⁰ ni

2 0 OJO ! O.nj

3. VALIUrTY OK f-ArPROXlMATlOJ^

The sha])es of the tAAa> Ixdia transitions aai‘ jilmosl sl.atisdeal Idu'si^ are shown in (iguies 3 and t I'dirtlKM', flu* c*orrelation coidTlici(>n,(s and the r(xliie(’d correlation eoLdheieuts for th(‘ 3Sr> K eV i l³K eV h(d,a-ganiinai eas<‘ade im^ fairly iudepeiuhmt o f beta (nu.:g\ within Ui<‘ <“\j>enu)(ai.lal eji-oi'S as ii^porO'd by Ihxldy (1075) The log ft valui^ is only 7.1! for 30J KeV^ bida liansilion A*! th(‘S(^ hiets are in acuau-danee wuh thc^ reipnieinonts lor the validity ol ^-approxiinatioji 'Thus it m ay becionduded that the 391 KeA' Ixda transit ion in is ol uon-iuii(]iie hrst-forbidden nature and fits int(» f-aj)])]‘oximation. Similarly the 403 Ke\

beta transition with its log ft value oJ O.S and statistical shajX' is also in accor­

dance with the f-approximati(»n.

4. Febmt-Kfeio Ai^a l y s is

The total beta spectrum is used lor the estimation of inleiisitic^s and log ff values of different beta grouxx^ ^{T\u^} ouiej- beta group witli an eiid-ix»int cmergy 493 KoV is subtracted Avitb its nearly statistical shape iioin Ihe gross spectrum.

This subtracLion ivsiilted in the 1st, inner beta groiq) v\ilb end-]xiint eiimgy of 391 KeV as shown in Figure 4. This is exactly same as that obtainerl tinough. the coincidence mciasureuienl. A further subtraction of the 391 K('v liela with its statistical shape resulted iu another lieta group with ^■-=- 250 1 4 KeV. The

and log ft values for diffeveiiT. beta groups are given in table 1 along with th(» previously n^ported results.

334 K. Venkata Bamaniah and K. Venkata Beddy

0. Dis(n:ssiC)N

S h a p e s o f the 7/2 > 9/2" ^{a n d} 7/2 * -> 7/2' beta ir a t w iiio v

The j(l(^a oi' using NjIssoji jiuxhd to iuterprcl tlie Ixda decay of stems fj*nm the fuel tlia-t trlui lev(d strut,turn ol ^’ n i f lias been exjilained on this basis.

b\)P strongly (hdbrmod odd-A uucl(‘i tii(^ energy levels have been successfully (hiscribixl as singles [lartich^ states in an axially s^nmietric potential \^^itl) rotational stales basiid on (heni. A study ol the Ud-a ()(u;ay ot i"'^Lu huids itst^lflo test, tin- pretlicitions of Nilsson niodtd neai thc! limits of the region vvhcic strong coupling theory is known to ¹h^ ajiplicable

Tb(suei,i(ra.! (expressions ioi* both udativistic and nou-relativistic matrix (dfumaits for bnt.ai tradisitions of arbit-rmy forliiddenm'ss using Nilsson model wave fuiKdions bav(» bixm dtnndopcd by Bogdan and ^fomig ^{et a l} (lObll) for one ant) two parti(“l(^ (oniigurat-ions in a defonneti ptheutial. with ¹⁰b neutrons and a shell model orbit.al (2f 7/2)“ ft i* the last ntnitron can he assigned from Nilsson diagram t he Nilsson st.aU' 7/2(514). The 72nd proton td‘ ^”’Hf is in a ( \ h 11 /2)“ stale cbarac¹(a'iz(Ml by tin; Nilsson lev(d 7/2(404). Using tJn^ 7/2(514) and 7/2(404) Nilsson orbit.als for the initial nmitron and final jiroton and taking into account,

S ™ ⁰.²H a common valuta lor tlu^ defo matiou t.aramc.ttT Bcrlbitu' and Lipnik (l9(iS) gav(‘ tlu‘ init.ial and iiiial wa vtdimctions as

- - 0.219 I 4 1‘{ 1 1 0.975 | 4 4 4 - :::

\'i2 -o .2 5 :f 155:f + |-o.2o() 15:i;i ^ - 0.9451554 - :

The m atiix elenuuit, ratios for llui two beta transitions aic obtained as :

T r a n s it i o n M a t r i x (dem ent ratioff

7/2 ' 7/2 ^{xjz ---} 0.5f)lS; ^{n jz} - --0.2 994 and

wir: - - 0 .0 0 5 6 1 8 7/2+ 9/2 ~ xjz - 0.546:1 and n i z - ^-0.2912 whore in tlie notation o f K otani (1958)

X ^ cv i y ; n = ^ O A i \ a x r \ CO ^ C A j a , y and ;r — (7-d J B i j

The p vraimders a:, a, y, etc are t be ratios of tlu^ various matrix elements to a standard m atrix elemiuits, so th at | ^{7j'^} | can bo taken as a common facttir in the trausitii m ])robabi ¹ it^{y .}

The tluxM’otical shapti factors arc' calculated for both tlie 7/2+—> 7/2^ and 7/2‘ —> 9/2" beta transitions o f employing the Nilsson model m atrix element

Beta spectral shapes in the decay

3:J5

parameters and using Simms (1905) expressions. The theoretical predictions are compared with tht^ ex]M3rinieutal simper fact'ors with proper normalisations.

These are shown in figures It and 4 for lh(‘. tw(> transitions Tlie experinuaital

2 . 2 CCUI)2.I5

2.«

»,H APE F A C T O R o r 7 /? BETA T R A N & J T IO N O F ’ ^ L u

I

1<3. in Kov

F ig , 3. ►Shano facto r plot of iho >-11/2“ ija iin itio ii in IohhI square littcej w ith C((o - ^1(1 Pr/(ct) w ith a - 0.0073 [ (laslwal line is tho NilNSou luodnl roduHiem.

!?b

iro 165 CCui)

tJ^hopc of //!><?■ //i h'f/n h-O/lK^'On ii/ ,

Fig. 4. vShap) fiic.tor plot of tho 7/2'-►7/2“ ilrM-nsiMon m nflcr fiuhtnudio?i of tho 1!H k('v hota group Solid Inm : J^nast-sqimro fit witli V{cj - /l| J - (0.017-j O.oOO rn] dnshi d hno

is the Nil'^son modr-1 ro d u clio n .

shape raetors as can he s(,( n from I h(‘- fignnts, are in aci'.oi’danci^ wi1 li tlu‘ pedietioiis of Nilsson scheme. Tlu^ same mati ix cl('inents parameters for- tlie 7/2 ’ -->9/2'' beta tiansiiion also prodiei the enorgjr iiuhqaouhoice ol the heta-oaninm eoj-re- lation, thus fully sup])ortiug tli(5 Adiclity of ^-appjoximatioji.

The log ft A^alnns ]nedieted by Nilsson model for tJio 7/2^--> 9/2"^ and 7/2"'—>

7/2" bed.a transitions in are 6.!1 and 5.8 lesjieetively while the experiirumtal values are 7.8 and 6.8 respectively. Thus theie is a (ionsideiable disparity botwoon tho ft values for i/he two beta; transitiiuts and the theoretical Nilsson model estimates.

6. Conclusion

From the present results, the fii'st conclusion is that in the case of ^’ ’ Lu, thi^

Nilsson model yielded matrix elements predicting almost statistical shapes for both tho transitioits and also energy indejiondont beta-gamma correlation for tlu^

391 keV l.ransition Avhioh is in support of f-approximation. This conclusion is

336 K. Venkata Ramaniah and K. Venkata Reddy

also by reJativoly Ioav log ft valiitjs, the almoet zero anisotropy for the bf'ta transition as well as the almost allowed beta spectrum sliapo. The Ifiigo diiferejxcio betwe('n the JMiLssoii model ft values and the experi- menbd It values lor "'^’^Lu nucleus juay be* p artly due to tlx fact th at this nucleus is ab)xost at the linxit of tfxe dofovmatiojx region. In this region, the deformation is (ih.nxgiug lap id ly IVf>m nu(*Jous to uiudeus and it is difficull to assign to the delormatiori the sxuue values tis loj- the nearx^st ixuolei. AJs(> a very sigixilicant iniprovemeixt x>f tU(i ft values iu agreejiiexit with (experiment can be expected ii' one perloi’uis tiu' ealeuhition of it v^aliK^s taking into xx;ceonnt also the eorrec- l.ion m atrix elmiumts ocuairing IVoin the (inite luiclem* sizt^ tdTocts. Such an im- provnnnent h a s hexai (i«miojxstrate(l by Jiogdaji el a l (1070) hi tlie (sase of

Refekiiincjes

Kaslmiuly K., MiJitsu M. (>.. Stiyod ^{K L.} Htiicl JC L, Assiiu M. 19Hfj. Z . Phys.

186, JOS.

Oorl.hor <r. lV. L im ik P . 1068. Nuc l . P h y s , 78, 448 (loyU au D., Oarjiui N. & P u ia FJ,. J970. /I. P n y s . 24*0, Bogdan D. IDOtk N.tcl. P h y s . 48,

DoLigliiM F). rt. (045. P h y s . JU u. 75, l{Mj8.

l^Uriosr iVI. fS. Fta'-iliaudj’' E. 1902. Z, P h y s . 167, 1(F().

Fvotaui '1\ & Floss JF. I05S, P r o g . Thtoi' P h y s . ( K y o t o ) 20, (il.'k M annioi F^. F.^oc‘lim K. 1955. P h y s . P e v 97, 108,

Mottolson B. K. tV', Nilsson S. (1. 1959. MaL P y s . Skr. Piet. Sds K 1, No. 8.

N agam jan T. UavincFraimtli M. X, V onnkata x^oddy K. J909. NueJ. h i s t . Mot h. , 67, 77.

Naga7“ja n T. I'ljiv in d ran alli M. V<Mika-la Rrckh- Fv. 1970. Ahir.1. l u s t . MHh. 80, 217.

IkivinU raim th M Flan C. .N. Kaoo B. M. (V. Vonkatn Jio d d y F\ J971. N^cl. I*hys. d*

Sol ii l Stair. }*/iifs. (In d ia) 158.

liodd.l FI. V. 1975. P h D T h e s i s , Andhra. ( h i i v e r s i t y S im m s V. C. I9ri5. P h y s Pi v. 138, B784.

Spoc'k 1). -11. .lo n k in s A. 1955. P/iys. Itrv. 101, 1811.

Tnim g N. D. cV. Dulonny 11. I9(i7. P h y . J l e v . 159, 862, Wioldiiig Till his. ITnivorsiyl, of' Stnckhnlrn 1956.