2 [ Nuclear Phystcs A100 (1967) 401--415, (~) North-HollandPubhshmg Co Amsterdam B 2 G I

N o t to be reproduced by p h o t o p r m t or microf i lm wLthout v, n t t e n permlss~on f r o m the p u b h s h e r

THE (3He, ~) REACTIONS ON EVEN TITANIUM ISOTOPES

J L'ECUYER and C St-PIERRE Physws Department, Umt erstte Laral, Qtwbec, Canada *

Received 9 May 1967

Abstract The angular distnbutmns of the alphas from the reactmns a6Yl(3He, ~)4~T1, 48Tff3He, aWTL and 5°Tl(6He, ~)49T1 have been measured at E3H~ -- 10 Me~¢ A number of In :- 3 transmons corresponding to the pick-up of neutrons from the lf~ shell, has been observed We have also found In ~ 0 and 2 transmons, indicating that the pick-up can also originate from the 2s~ and ld~ shell Finally s o m e In ~ 1 transltmns have been observed, indicating p-wave admixture lO_ the ground state of the e~en t~tamum isotopes SpectroscopLc factors have been deduced for the various transmons by means of a DWBA analys~s The experimental results have been compared with the theoretical pred~cUons of the shell model and of the rotatmnal model with Corlohs couphng

E NUCLEAR REACTIONS 46,~s,5°Tl(3He, ~), E ~ 10 MeV, measured ~(0) 4.,~-49T1 deduced levels, In, spectroscopic factors Enrtched targets

1. Introduction

Nuclet in the f : shell have recently been the object of considerable theoretical work

However, those nuclei are still far f rom being well known and experimental work ts

needed to test the different models which are presently proposed Accordingly we

decided to study the even t i tan ium isotopes using the (3He, ~) reaction The results

of this investigation were analysed using the D W B A Spectroscopic factors were then

obta ined and compared with the various theoretical predictions

Previous investigations of the t l t amum tsotopes revealed some rather puzzhng fea-

tures Since an (3He, ~) reaction amounts to the pick-up of a neut ron from the target

nucleus, one expects that the neutrons will come mainly from the f , shell which is m

the process of being filled I t should also be possible to observe neutrons from the

s-d shell which is the least bound closed shell One then expects to observe mainly

1 = 3, 2 and 0 angular m o m e n t u m transfer and possibly some rather weak l = l

tt a n s m o n coming from 2p admixture m the ground state of the even h t a m u m isotopes

This was observed prewously m the (p, d) work of Kashy and Conlon 1) and of Sherr

et a/ 2) and also m the (d, t) mveshgahon o f Y n t e m a 3) At the same time tt was found

that some of the hole states excited by the pick-up of a ne u t l on m the s-d shell were

also clearly seen m the (d, p) work of Rapapor t et al 4) This observation would then

indicate that the ground state of the even t l t amum isotopes Is more comphcated than

Research supported by the Atomic Energ~ Control Board of Canada

401

402 J L ECUYER A N D C ST-PIERRE

was first thought because in addition to having 2p admixture, one should also add terms coming from holes m the s-d shell

In the present lnvestlgaUon we took advantage of the high positive Q of those (JHe, ~) reacUon to look for as many levels as poss%le and we Uied to deduce the occupation number of the various sub-shells In addition m some cases we should then be able to compare our result with the pievmus (p, d) work Since spectroscopic lectors should be identical for (p, d) and (3He, ~) reactions, a comparison between otu result and the one of refs i, 2) prowdes a good test of the rellabflmty of the occupa-

tion number which we deduce

2. Experimental procedure

The experiment ~as done using the 3He ÷+ beam of the Laval 5 5 MV Van de Glaaff The energy was kept fixed at 10 MeV by an analysing magnet A quadrupole lens and a series of slits at the enU ance of the scattering chamber were used to focus and define the beam The beam was stopped in a Faraday cup and the current was continuously monitored Because of the large cross section for elastic scattering at 10 MeV it was necessary to limit the cmrent on the target to values which range from 5 to 500 nA as the angle is increased from 15 ~ to higher values

The alphas were observed with solid state detectors Most of the small angle meas- uIes x~ere carried out using two AE counters, one of 100/an and the other of 120 Itm

m a telescopm ai rangement The first detectm was used to stop the scattered 3He and the second was thick enough to stop all the alphas A fast coincidence module gave the signal required to analyse the pulses coming out of the detectors An antlplle-up-

T A B L E l

Isotopzc c o m p o s i t i o n o f the targets and (aHe, ~) Q-values

Targe t ;',, a'T1 "o arT1 o ° 48Tx ,,o 40Tl o~, o O T l Q ( M e \ ) (ref 5)

48T1 81 2 2 1 145 l 1 1 1 7387 4~T1 0 25 0 26 99 13 0 19 0 17 8 957 °°Tl 2 0 I 8 178 2 0 7 6 4 9 6 3 9

system associated with the first detector permitted us to reject pulses separated by more than 100 nsec and less than 3/lsec This system was found to be the most efficient way of rejecting the elastically scattered 3He which otherwise would have produced pile-up in the electromcs This arrangement allowed the observaUon of protons from 3 to 5 MeV, deuterons from 4 to 7 MeV and alphas from 12 to 20 MeV Clearly then the regton above 10 MeV, which is the region of interest here, contained only alphas At hlgher angles, where scattered 3He are less numerous, we used a single 300/~m detectors wath a pile-up lejecuon s~stem The resolution of the system varied between

TllaHe, ~) REACTIONS 403

75 to 100 keV dur ing the course of the exper iment , the resolut ion being slightly bet ter

with the second a r rangement

The targets were m the form of t i tanium oxide evapora ted onto a carbon backing

The backing thickness was 50 p m and the evapora ted layer thickness was abou t 75

~m Ov~lng to the high t empera tu re needed, we found it easier to float the ca rbon

only after the evapora t ion The compos i t ion of the isotopic mater ia l was as Indicated

in table 1

The 48T1 was present in all the da ta and since the 0 16 MeV state of 47T1 has a

relat ively large cross section it was identified and analysed in all the spectra This

analysis p roved to be very useful since all spectroscopic factors could then be nor-

mahzed to this unique case Also, the a lphas coming from this state were used to cah-

b ra te the energy of the system Other cahbra t lon points were provided by the reac- t ions 160(3He, ~)150 and 12C(3He, e ) l 1C

3. Experimental results

The ~ part ic le spectra taken at 45 ° are shown in fig I The peaks have been identi-

fied using the energy ca l ibra t ion points previously ment ioned In many cases the ex-

cited levels were observed by Kashy and Conlon 1) and we used their value of exci-

ta t ion energy since we did not have a bet ter resolut ion The energies of the other peaks

have been de te rmined f rom the present da ta and they are accurate to + 5 0 keV

Those energies co r respond to the 45TI 3 10, 4 79 and 5 78 MeV states, the 4VTl 3 45,

3 80 and 4 20 MeV states and the 49T1 4 20 MeV state The angular d is t r ibut ions cor-

responding to the var ious peaks are shown in figs 2, 3 and 4 The errors indica ted

are mainly of statist ical origin but in some cases ba c kg round subt rac t ion cont r ibutes

significantly to the lncer ta lnty and this has been Included in the error bars The ab-

solute cross sections were es t imated by compar i son with the elastic scat ter ing cross

section on 46T1 This p rocedure is not very accurate since at 45 °, the elastic cross sec-

t ion deviates f rom the Ruther fo rd fo rmula A t smaller angles however, it was not

poss ible to separate the peaks coming from con taminan ts in the target However , we

measured the cross section for elastic scat ter ing of 3He by 46T1 and our final accul acy

was + 2 5 %

A D W B A analysis was per formed using the Oak Ridge code T-Sal ly 6) In this

ca lcula t ion one uses a zero range app rox ima t ion and does not include spin-orbi t

coupl ing The opt ical potent ia l we used is of the fol lowing form

U(r) = - V(e~+ l ) - J - t W ( e x + 1 ) - 1 + Uc,

where

x = ( r - r o A + ) / a , ~c' = ( r - r o A ' ~ ) / a '

and U c is the C o u l o m b potent ia l due to a uniform sphere of radius roc A ~ Different

sets of optical model pa ramete r s were used for the calculat ion, but only two sets were

404 J L ' L C U Y E R A N D C ST-PIERRE

4 0 0 _

3 0 0

2 0 0

I 0 0

016 T j 4 6 ( H e 3 , ~ ) T 4 5

0 EHe 3 = I0 MeV ,1. : 4 5 o

elGb

5 78 0

• I l,,ttml*,~| ~,,-

¢

o - c o

g u~

g o

4ooJ 3 0 0 i

2 0 0 1

I O 0 1 . . . . . . .

.... ":.

4 8 3 47 Ti (He,o<)T i

ol 6 EHe3 = IOMeV

e la b : 4 5 ° 0 ,~ o

f 281 l! = t~ ~; 4 2 0 318 2aG 18T i~ ; I i38,o J i~3,~ '~55 ,'t

8 0 0

7 0 0

6 0 0

5 0 0

4 0 0

5 0 0

2 0 0

I OOq

16 0 0

;,

i

I I

50 ~, 149 TI (He~,oK) T E He 5 = 10 MeV

@ : 45 ° lob

47 47 0 , T' 2 6 2 T~ . II 4 203'8 2 4 5 455 0 I ~ I , I [2 23 I, 7, 6 I i '

i .

Iqg 1 Energy spectra of tile alpbas f rom tile reactions ~6TI(~He, 2)15T1, 4STI(~He, :~)~TTI and S"Ti(~He, %)a'JT1 at a labora tory angle of 45 ° The energy of the incoming aHe ~vas 10 MeV

TJ(SHe, ~) REACTIONS 405

found to gwe satisfactory fits to the data They are hsted in table 2 The first set is nearly identical to the one used by Chne et al 7) for their analysis of the 4°Ca(3He, c 0 agca reaction at 10 MeV In the second set we took the entrance channel parameters from an analysis done by Yntema et al 8) of the 12 MeV 3He elasnc scattering on various T1 isotopes Various exit channel parameters, adapted from an analysis done

0

5 ~,,t~"~l 0 2

0 2 ~ ' 1 4 - f f t ~ E×: 0 OMen/ in = 3 OI

OI

0 0 5

0 0 2

001

OO5 \

I I I I

o,I- t, mb/~rO 05

0 0 2

001

-%

1 I 1 I

OI

0 0 I

O5 1

0 2 Ex=O 55MeV

In=2 OI

0 O 5

\\

0 I ' ',

005

0 0 2

0 0 I 0 o-

! l 20 ° 40 °

E x ; 3 I O M e V

' t t tit tt )i t

I A L ! I

t t f~ i t

i 1

Ex= 4 79MeV

E× ~ 5 78 MeV

0 2 [ ~ Lr 0

'\ 0 05 \ _

t i IO 8 0 l u ~ ° 60 °1 80 °1 IO0 ° 0 ° 2~0 ° 4 0 ~ ~ L ~ _ _ ~ -

Ocm ecm

Fig 2 Angular distributions o f the alphas from the reaction 46Tl('~He, a)45Tl The sohd curve represents the result o f a D W B A fit No such fit was attempted for the alphas leading to unresolved

levels at an excitation energy o f 3 10 and 4 79 MeV

by McFadden and Satchler 9) of scattering of 25 MeV alphas by various nuclei were reed The set hsted m table 2 is the only one to have gwen an acceptable fit It ~s interesting to note that tMs set has V, ~ V3H~+ 30 MeV which appears to confirm an observanon of Duhm et al lO) on 54Cr(3He, ~)53Cr We did not vary the exit channel V and I41 w~th the energy of the outgoing ~ since th~s does not affect slgmficantly the result (refs 11,12))

\ , \ \ \ Ex-O 16MeV OI

t [ In .5 0 \

\ ' k ' , 0 0 ~ 0 05

0 OI

\ , \

0005 / , , - d~ 0 005

m~ 0 0 5 l i d~.

<tin '% 0 0 2 X Ex=155MeV OI

0 0 1 ~ t ' t l , } \ 0 0 5

0 0 0 5 } {" ~ " \ 0 0 2

t

0 002 } 00~ /

f I ] I I L I

I O* ,30 ° 50 ° 7 0 ° 9 0 ° II0 ° 130 ° 150 ° ecm

OO5

0 0 2

O0

i'i 0 g

d.r',. 0 02

0 0 1

0 O 0 5

Ex=2 56MeV

tti 00, t 0 0 0 5

I I I I l

E×-2 81MeV In 1+3

i ' t

t - - 1 ,

l i I i i

°~I M OOb Ex-318Meg

I n - 5

0 0 2 1 * " t ,

0 0 0 5 t x

~ J , , O ° 20 ° 4 0 ° 60 ° 80 ° I00 ° 120 140 °

Gem

0 002

drtd~ 0 0 5 f m b,

/st 0 02

001

0 0 0 5 1

Ex=181MeV h ~ Z ' , ' / ~ ' ~ ' In- 2

\ ,

\

Ex :2 34MeV In-O

+/ "Si ' ' +', t { \'"

/ "\ ~u' } \ \

I o ° 5 0 ° 5 0 ° 7 0 ° 9 0 ° I i 0 ° 150 ° I

8 c m

t

002 I Tii'tt!i

I J i

I I I I ,

Ex-3 45MeV In-5

{ I " f *

I

I i , r

l ' , 't ,

Ex:38C MeV It=3

i

0 0 5

~ 4 2 , % ~e~ ~

t ' 0 O 2

001

0 005 } 1

0 ° 20 ° ~0 ~ 610 ° 80 ° ro0 ° L )~ ~v~m

Ffg 3 Angular distributions o f the alphas from the reacnon 48TI(3He,~)47TI The sohd cur~e represents the results o f a D W B A fit N o such fit ~s shown for the alphas leading to levels at an exct-

tatlon energy o f 2 56 and 4 20 MeV

Tl(3He, ~) REACTIONS 407

O2

OI i

0 0 5

0 0 2

0 0 1

d__~ d.~-

mb 0 0 2 7~r

001

0005

0 0 0 2

>X~',

-u_ L

Ex=O OMeV i n = 5

\ ---~

t ] " ~ f

I 1 t

tt t

I t t I

0 021, Ex= 155MeV |

t t+ o o, I~, t t t ooo5) [I 1

. I I i ! 0 o 2 0 ° 4 0 ° 6 0 ° 8 0 ° ICO o 120 °

@cm

Fi g 4

0 05~ ' ' ~ -

| --h

[ i I I i t

I 19,< ' I ~. Into

oo2J~ / ~) d~ I I I I I mb/s ~

O 0 5 F ~ t ~H,~ , Ex=2 62MeV

0 o 2 { \ \ ) t t

"~J . . °°iL" I I t

0 0 5 - - ~ - 54 I E x = 4 2 0 M e V j t ~4 , i n : 3

0 0 2 i Q ~

0 0 l

1 L I ! I 0 ° 2 0 ° 40 ° 60 ° 8 0 ° 100 °

6 c m

A n g u l a r dmtnbut lons o f the a lphas f rom the react ion 5°Tl(aHe, :z)49T1 The sol,d curve represents the result of a D W B A fit

TABLE 2

Ophca l model parameters used m D W B A ca lcu la t ions

V W ro a r" o a" roe (MeV) (MeV) (F) (F) (F) (F) (F)

3He l 175 15 1 07 0 854 1 81 0 592 1 4 c~ I 40 10 1 75 0 520 1 75 0 520 1 4 3He II 97 10 1 07 0 754 1 81 0 592 1 4

II 130 24 1 47 0 51 1 47 0 5l 1 4

Both sets o f parameters predicted similar angular distributions but their magnitude was found to differ uniformly by about 20 ~o It was finally found that set I, with a radial cut-off at 4 5 fro, was slightly better The presence of a cut-off did not change qualitatively the angular distribution but could alter its magnitude by as much as

408 J L'ECUYER AND C ST-PIERRE

20 ~/o This devia t ion is again systematic and depends only on the value of the cut-off

r adms To obta in the fo im factor , the code calculates the wave functmn for the t rans-

ferred neut ron in a Saxon well o f r adms 1 2 A ~ fm and diffuseness 0 65 fm The dep th

o f the po ten tml was adjus ted so as to r eproduce the b inding energy o f the transfe~ red

neutron

In terms o f the previous calculat ions, the exper imenta l cross section can be writ ten

m the fol lowing way

( ~ ) e x p = NSO'DWBA(O)"

where S is the spect roscopic fac tor for the level under s tudy and 0"DWBA(0) the cal-

cula ted cross section, N is a n o r m a h z m g factor which depends on the pa r t i cu la r type

o f reac t ion which is employed F o r the (3He, ~) react ion, N has been found to be o f

the o rder o f 30 but large var ia t ions have been not iced 7 , ~ ) In our case, we used

sum rules on the spect roscopic factors and compar i son with spect roscopic factors

ext rac ted f rom (p, d) exper iments to set the value o f N equal to 20

3 1 T H E R E A C T I O N 46TI(3He, :~)4~Tl

The spect rum of this react ion conta ins only six peaks The first three peaks cor-

r espond to L = 3, 2 and 1 neut ron t ransfer The peak at 3 1 MeV is weakly excited

and appears to be compos i te Its angular d is t r ibut ion seems to be fitted by an l = 3

t ransfer but this might be for tu i tous The peak at 4 79 MeV has been shown 13) to be

made up o f two states at 4 73 and 4 79 MeV showing I = 3 and 2 angular m o m e n t u m

transfer These states as well as the l = 0 state at 5 78 MeV are the analogues o f the 45Sc

low-lying states at 0, 0 013 and 0 94 MeV The shell model predicts that 46T1 has fore

neut rons in the lfff shell Accord ing ly the 1 = 3 t rans i t ion should co r respond to a

state having J~ = 5 - Higher subshells should be admixed an the g round state wave

funct ion due to pa i r ing cor re la t ion and accordingly the state ob ta ined via the l = 1

t lansltxon should co r re spond to the 2p~ subshell and have 3 - as J~ One does not

expect to observe the effect o f 2p~ and l f_: subshells since they he at a much h~gher

energy The 1 = 2 and 1 = 0 angular d is t r ibut ions should cor respond to the p~ck-up

o f a l d~ and 2s~ neut ron and consequent ly lead to z a + and ½ + state Those assumpt ions

fo lm the basis for the p lesen t spin ass ignments

Table 3 gives the spectroscopic factors for the var ious levels of 45T1, as well as their

spin, pa l l t y and lsospln The spect roscopic factors ob ta ined m other exper iments are

also shown for compar i son The 1 = 1 level at 1 58 MeV exci tat ion energy was not

c leal ly seen by K a s h y and Conlon J) but it s tands out vely well hele and its angular

d i s t r ibu t ion is unambiguous and shows an l = 1 pa t te rn A notab le po in t here is the

absence of any l = 0, T< level co r respond ing to a hole m the 2s, subshell Cor-

i e s p o n d m g states were seen m 47T1 and ¢9T1 but we were unsuccessful m our effort

to locate it In 45T1, unless it is pal t o f the compos l t e 3 1 MeV peak

TJ(aHe, ~) REACTIONS

TABLE 3

Summary of the data deduced from the present experiment

409

E . (MeV)

I n Jn S(aHe, 7) S(p, d) (ref 1))

33 58 10 79 ~)

78

016 1 55 181 2 34 2 56 2 8 l

318 3 45 3 80 4 20

46Tl(aHe, ~)4~Tt

3 ~- 27 25 2 ]~ 1 5 07 1 I - 0 52

3 2,- 2 ? 0 }~ 0 82

4STl(aHe, ~)47T1

3 -;- 35 38 l }- 033 11 2 ~+ 16 07 o ½- ] o

(0, 1) (~+, 3-) 0 26-0 43 1 ~- 017 05 3 ~- 020 0 4 3 j - 075

(3) (7~-) 0 23 (3) (-,_) 0 40

~OTl(aHe, ~)49T1

0 3 ~- 4 0 4 4 1 36 1 ~- 048 0 4 1 55 2 23 3 {- 0 62 0 6 245 0 ½~ 1 5 2 62 2 ~+ 0 98 0 7 4 20 3 (~-) 0 51

S(p, d) (ref ~))

25

~ 0 14

39

0 26

a) Results from ref la)

3 2 THE R E A C T I O N 4STI(aHe, g)l:Tl

Several levels were seen m this reacnon Owing to the condmons of the experiment it was not possible to observe levels of exmtatxon energy higher than 5 MeV and thus we did not see the analogue of "7Sc States corresponding to the transfer of an l = 3 neutron can be seen at excltahon energ,es of 0 16, 2 81, 3 18, 3 45, 3 80 and possibly 4 20 MeV The first level at 0 16 MeV takes the major part of the I f : strength It should be noted here that the 47T1 ground state has spin 5 and negative parity and consequent- ly should not be reached via the pick up of an f~ neutron f rom 48T1 This is confil reed by the experiment At 45 ° for example, the ratxo of the cross section of the ground state to the 0 16 MeV state is of the order of 1 This observation was also made m other experiments 1,4)

410 J L 'ECUYER AND C ST-PIFRRE

The state at 2 81 MeV is an I = 1 and l = 3 double t This has a h e a d y been observed

by R a p a p o r t et al 4) and indeed in our work the angular d i s t r ibu t ion of the a lphas

leading to this state could no t be fitted unless we assume such a mixture The spec-

t roscopic factors tha t we deduce are app rox ima te ly equal for bo th members of the

double t in accord with the results of Kashy and Conlon 1) I t was suggested tha t the

1 = 3 m e m b e r of this double t co r responds to a 25- level 14) This ass ignment arises

f rom J dependence in (d, p) measurements However , we find it ha rd to reconcile a

5 - ass ignment with the present observa t ion since the lf~-lf~ spht t lng should be

a r o u n d 5 MeV (refs 4, ~s)) Accord ing ly the admix tu re o f lf~ in the g round state o f

48T1 should be very low leading to a very small spect roscopic fac tor for a t rans i t ion

to a state be longing to this subshell In our case we obsetve S = 0 2 co r respond ing

to an a m p h t u d e for the lf.~ admixed wave which is s imilar to the 2p} a m p h t u d e

F u l t h e r m o r e the cross sect ion for p icking up a neu t ron f rom the f ; shell is p r o p o m o n a l

to the neu t ron occupancy number in this shell On the o ther side the cross sect ion

for cap tur ing a neu t ron in the same shell depends on its number o f vacancies If U)

is the emptiness and V~, the occupancy o f the shell

a (d , p) oc U2 = K ( J ) o'(3He, ~) V 2

This number K should then depend mainly 16) on J, and K(~) should be at least an

o rde r of magni tude larger than K(~) If we use the (d, p) result of R a p a p o r t et al 4)

we find that for the 0 16 MeV level K = 1 5 and for the 2 8l , K = 4 5 This difference

is too small Accord ing ly we favour the ~ - over the ~ - ass ignment

A number of o ther l = 3 t rans i t ions were observed at 3 18, 3 45, 3 80 MeV The

first one was previously observed by Sherr et al 2), but the spect roscopic fac tor that

they r epor t is much lower than the one we deduce The other two states are weakly

excited The state at 4 2 MeV is compos i t e Its angular d is t r ibut ion is typical of an

l = 3 t rans i t ion Sherr et al 2) have repor ted unresolved mul t ip le peaks at 3 84 and

4 30 MeV They p r o b a b l y co r re spond to the peaks we observe at 3 80 and 4 20 MeV

Aga in with this Isotope, we observe the p ick-up of p : neutrons These co r re spond

to states at 1 55 and 2 8l MeV, which would then be assigned spin and par i ty of 3 -

Reasons ana logous to the ones previously given would make it highly improba b l e to

observe any ½- levels

In add i t ion to the previous states, we also observe states cor respond ing to the re- 3 + and mova l o f ldk and 2sf neut rons Such states would have spins and parInes of

½+ respectively They are observed at l 81 and 2 34 MeV, respectively The 1 81 state

was p iev lous ly fitted by a mixture o f / = l and 2 t ransi t ions x) or 1 and 3 t ransi t ions 4)

In our case the angu la r d is t r ibut ion has an unambiguous l = 2 shape This is not sui-

pr is ing because the (3He, ~) reac t ion favours higher angular m o m e n t u m transfer and

consequent ly l = 2 over l = 1 angular d i s t r ibu t ion In other words, our da ta shows

very clearly the presence o f an l = 2 angular m o m e n t u m transfer leading to a ~ ~

state Howevel , this state would most p r o b a b l y obscure any weak l = 1 t i ans i t ion of

ql(3Ht, ~] REACTIONS 41 l

the sort r epor ted by K a s h y and Conlon l) at this energy Surpr is ingly bo th I = 0 and

! = 2 states were observed by R a p a p o r t et al 4) in their (d, p) exper iment s tar t ing f rom 4ST1

Final ly there remains one state at 2 56 MeV The shape of its angular d is t r ibut ion

was a ht t le bit d~fferent f rom any of the other shapes so tha t an unambiguous l assign-

ment was difficult However , we could determine tha t it is main ly of an I = 0 or 1

charac te r R a p a p o r t et a! 4) in their (d, p) work observed two levels at 2 543 and

2 575 MeV cor responding to an l = 1 and l = 0 t ransi t ion W e could have observed

either or bo th levels Consequent ly we gave a spectroscopic factor co r respond ing to

each case These should then be considered as higher limits since most p robab ly the

peak is an unresolved double t

3 3 THE REACTION 5°Tl(ZHe, ~)49T1

The spect rum of this reac t ion is much simpler than m the previous case Peaks cor-

r e spond ing to the pick up of an f~ neut ron are seen at 0 and 2 23 MeV exci ta t ion

energy They were also observed by Sherr et al 2) and by Kashy and Conlon 1) A no the r

l = 3 peak can be seen at 4 20 MeV However in this case as well as for o ther states

having an exci ta t ion energy of more than 3 5 MeV, we do not believe tha t any definite

spin ass ignment should be made Those states are indeed ra ther weakly excited and

at this exci ta t ion energy they could easily indicate an fl- admix ture m the wave func-

t ion Indeed Cohen et al 15) have observed many l = 3 states between 4 and 5 M e V

(at 4 24, 4 38 and 4 52 MeV) m their (d, p) exper iment on na tura l t i t an ium and one or

more of these states could be identified with the peak which we observe However ,

the deduced spectroscopic factor is again ra ther high for an f~ t rans i t ion A n l = 1

t rans i t ion can be seen at 1 36 MeV It was previously seen in the (d, p) work of

Rle t jens et al 17) States having l = 0 and 2 were observed at 2 45 and 2 62 MeV

These observat ions confi rm the ones made in the (p, d) work 1) and con t rad ic t

the ass ignment o f Y n t e m a 3) in h,s (d, t) exper iment F ina l ly we canno t make an3'

ass ignment to the weakly excited 1 55 MeV level This state was repor ted by Sherr et al 2) with an uncer ta in l = 1 ass ignment where as Booth et al i s ) In a resonance

fluorescence measurement indicate ~ - as the p robab le spin value Since we do excite

this level one would be t empted to exclude the [ - ass ignment for it would p robab ly

indicate a ra ther complex structure for this state On the other hand second order

processes of the type leading to the observat ion of the 47T1 -~- ground state could

very well explain the present s i tuat ion

4. Discussion

41 SUM RULES

If we sum the spectroscopic factors of all the levels belonging to the same subshell ,

then, according to M a c F a r l a n e and French 19), we measure the occupa t ion of this

412 J L ECUYER AND C ST-PIE[IRE

shell in the target nucleus Indeed one can show that

S , ( J ) = Ns, 1

where N s as the number of neut rons in the J shell However, m most cases we do not

observe all the states belonging to the same shell since we do not include the analogue

states For tuna te ly the cont r ibut ion of those analogue states can be estimated theo-

retically and the sum rules can be deduced over T< states According to Faench and

MacFar l ane 2o), these are

Z S,(J , T>) = ( 2 T + I ) - ' P j 1

S,(J , T<) = N j - ( 2 T + I ) - ' P j , t

where T is the asospm of the target nucleus and Pj IS the number of protons m the J

shell We can make a first order correction to the previous sum rule by assuming the

following values for P j P .+ = 2, P_/+ = 4, P~- = 2 and P~- = 0 We can then de-

duce the value of ~ , S , ( J , T<) an the various cases and compare it to the shell-model

predacnon This as done in table 4

TABLE 4

The value of the sum rule ZS,(J, T<) for the tltanmm isotopes

Nucleus v - 2 - ~ ~ exp theor exp theor exp theor exp theor

46T1 2 7 3 3 0 52 0 1 5 2 7 0 1 3 4ST1 5 1 5 6 0 50 0 1 6 3 2 1 0 1 6

° °T l 5 1 7 7 0 4 8 0 0 9 8 3 4 1 5 1 7

Some general features of the t i t an ium ISOtopes can be seen immediately in this table

The most interesting is the large admixture of the 2p~_ subshell It appears to be uni-

formly present and looks insensitive to neu t ron n u m b e r A second point related to the

first, IS the smaller than predicted value of summed f~ spectroscopic factors Thas is

related to the first observat ion since one expects that the sum ovel f~_ and p~ spectlo-

scoplc factors will be equal to the numbe i of neutrons outside the 4°Ca core

Indeed this number is equal to 4 and 6 as expected for 46T1 and 48T1 However, in

5°T1 it appears that we have not observed some 27- levels since the f? strength looks

abnormal ly low The d . strength is also weaker than expected and we do not th ink

that all the ~ + levels have been identified The smmtlon m the ~ + subshell could be

considered satlsfacto~y if it were not for the complete absence of any 21 + level in 4('TI

The number of particles m a definite shell should be compared to the numbet of

holes an this shell The number of vacancies in a shell can be deduced from a (d, p)

experiment The results of Rapapor t et al 4) on 46TI indicate a hole number of 6 in

j~

z2.

/2

I

M S

d ~

7/2- __5/2- .

3/2- "I

2- I 5/?- I

MS

d ~

L_~_- 7/2

_ ~ 5 z 2

_ _ i L L

[ z z L

MS

Ex d "rr In S Ex S

I , 1 I i _,.5_Z LtZ2T_ 0 f f "

479 312" 21 I

I J ~ ° I

LSB 3/2 I

LCL Z L ~ 3_ . . . . . . .

0'~2~3 0 12 34 E X P E R M B Z

45Ti

Ex d rr In S S

~ 2 ___ I ?/2 2,, ~ I tE i'/2~. .3 ~ P

12.81 712 .~ i * 31 14

2x3~l I/2" ~ [ o

x.55_ ~z2_ I[ . . . . . . . ~ ) ~

I

6 i ~ 3 4 6 q ~ 3 E X P E R MBZ

47 T

Ex j r r In S Ex S

IN_20 7/2- 2,1- I

IZZ* -- ..2_.5~ ~ 7/ZL 3 L_ - - - -

7, 2 - 5 1 . - - L

(~ [ 23~4 0 1 2 3 4 5 6 7 E X P E R MBZ 4 9

T I

Fig 5 Energy level d iagrams showing l values, spins, p a r m e s and spec t roscopic factors for the var ious levels observed in thB exper imen t The predict ions of McCullen, Ba3 m a n and Zamlck 2t) (MBZ) for the }- levels are s h o w n on the r ight The predict ions o f Mahk and Scholz 2_,) are on the left

414 J L ' E ( U Y E R AND C ST-PIERRE

the f l shell A l though a htt le too strong, this number can be considered an accord with

our da ta at least to the extent that at enhances the holes to part icles rat io The same

au thors also repor t the exci ta t ion of l = 2 and ! = 0 states at 1 81, 2 34 and 2 56 MeV

m 47T1 Consequent ly it appears that the 46T1 gl ound state is more comphca t ed than

it was thought since, in a d d m o n to the 2p~, admix tu re of 2s~ and ld~ holes are p iesent

Similar results were not repor ted fol the other isotopes

4 2 EXCITATION ENERGY

The systematxcs of the level energy ale quite clear in the present expe i iment Mos t

of the l = 1 strength is c a m e d by one level 1 5 MeV above the ground state Only in

the case of 4VTi as th~s I = I s trength splat Similar ly the I = 0 strength 1s found mainly

m one level a round 2 4 MeV Again an 47T1 this s t rength m~ght be shared between

levels at 2 34 and 2 56 MeV The l = 2 t r ansmon is somewhat pecuhar , because it

looks insensmve to the neut ron number and its separa t ion energy ~s always approx i -

mate ly equal to 13 5 MeV A s |mflar behav lour of l = 2 and l = 0 t ransi t ions can

also be found in the states ob ta ined by removing a p ro ton f rom the same isotopes

4 3 REMARKS

One would hke to make a deta i led compar i son between the expe~lmental da t a and

theoret ical ca lcula tmns Such ca lcu lanons ~ere done by McCul len et al 21) for the

states having (f;)" conf iguranons Accord ing ly they can be c o m p a r e d with the l = 3

t rans i t ions only A list of their p re&ct lons for the energy levels and spect roscopic

factors can be found in ref 2) The predic ted values of the exci ta t ion energy and

spect roscopic factors of the var ious t r ansmons are general ly in fair agreement with

exper iment (fig 5) One should note in p a m c u l a r that there exists a good cor respond-

ence o f pred ic ted to observed levels i f t ransi t ions to which we assign an uncer ta in l = 3

are assumed to lead to ~ - levels We would then have found the first three p re&cted levels i n 45Ta, the first six an 47]'1 and the first three in 4°T1 The spect roscopic factors

a ie general ly in fair agreement except for the more highly excited states where they

ai e expel amentally less rel iable

A n o t h e r a p p r o a c h towards the exp lana t ion of the odd p a n t y levels of the t l t anmm

isotopes was taken by M a h k and Scholz 22) They s tar t f rom the exper imenta l fact

tha t T~ ~sotopes are deformed and try to explain the level scheme m terms of the

ro ta t iona l model of Bohr and Mot te l son They find tha t a large CorIohs coupl ing

te rm cons iderab ly mixes bands differing by A K = __+ 1 This mixing would explain

the fact tha t ro ta t iona l bands are not Immedia te ly appa ren t m those nuclei Their

p red lc tmns can be found in fig 5 In o rder to make deta i led compar i son , one needs,

apa r t f rom the excatauon energy, the p led lc ted spect roscopic factor o f the levels

Since these spect roscopic factors are not avai lable we cannot make further comments on this model

In order to give a l ea sonab le exp lana t ion of the excited states of the var ious t i ta-

mum isotopes, it is cer tain that ~t will be necessary to consider more than only the

TILSHe, 0t) REACTIONS 415

f~ shel l I n p a r t i c u l a r , t h e in f luence o f c o n f i g u r a t i o n s h a v i n g pa r t i c l e s in t he 2p~ a n d

ho l e s in t he l d~ a n d 2s~ subshe l l s s h o u l d be e x p l o r e d O n l y t h e n will i t be p o s s i b l e

to m a k e b e t t e r c o m p a r i s o n b e t w e e n m o d e l s a n d e x p e r i m e n t s

References

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(Umted States Atomic Energv Commission, Washington, 1960) 6) R H Bassel, R M Dnsko and G R Satchler, ORNL Report No 3240 (1962) 7) D Chne, W Parker Alford and L M Blau, Nuclear Physics 73 (1965) 33 8) J L Yntema, B Zeldman and R H Bassel, Phys Lett 11 (1964)302 9) L McFadden and G R Satchler, Nuclear Physics 84 (1966) 177

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J D Fox and D Robson (Acad Press, New York, 1966) p 605 14) J L A l t y , L L Green, G D Jones and J F Sharpey-Schafer, Phys Lett 13 (1964)55 15) B L Cohen, R H F u l m e r a n d A L McCarthy, Phys Rev 126(1962) 698 16) B L Cohen, Nuclear Spin-Panty Assignments ed by N B Gore and R L Robinson (Acad

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