Spectroscopic study of 47,49,51V with the (3He, d) reaction at 10 MeV

~

Nuclear Physics A102 (1967) 433--442; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission f r o m the publisher

SPECTROSCOPIC WITH

THE

STUDY

O F 47,~9,51V

(~He, d) R E A C T I O N

A T 10 M e V

C L A U D E St-PIERRE, P. N. MAHESHWARI ~, D. D O U T R I A U X and L. L A M A R C H E

Departnwnt of Physics, Universitd Lacal, Qudbec, Canada tt Received 29 May 1967

Abstract: The (3He, d) reaction on 46,48,5°Ti was investigated with a 10 MeV beam of doubly-ionized 3He. The deuterons were analysed with a semiconductor E-~IE particle identification system. Levels of 4~,~9,5~V were observed up to excitation energies of 2.22, 4.22 and 4.25 MeV, respectively, with an energy resolution between 80 and 120 keV. The angular distributions were measured at lab angles between 15 ° and 120 ° and compared with the predictions of a DWBA calculation using the TSALLY code. The angular momentum transfer was identified as l -- 3 for 49,5tV ground states and 4rV 0.15 MeV state, and l = 1 for all the observed excited states of 49,51V and 47V ground, 2.08 and 2.22 MeV states. The 0.26 MeV 3+ hole state and 1.66 MeV ½+ hole state of 47V were also observed. Spin and parity could be assigned to most levels, and the corresponding spectroscopic factors were determined.

E

N U C L E A R REACTIONS 4~,48.5°Ti(aHe, d), E = 10 MeV, measured o'(Ecl , 0)47,40,~V deduced levels, lo, spectroscopic factors. Enriched targets.

]

[

1. Introduction T h e e n e r g y level s t r u c t u r e o f 4 7 ' 4 9 ' ~ V has b e e n o b s e r v e d by inelastic s c a t t e r i n g (p, n), (p, c0 a n d (p, y) r e a c t i o n s l - s ) . T h e r e a c t i o n (3He, d) has b e e n m u c h u s e d in r e c e n t y e a r s to p r o b e t h e s i n g l e - p a r t i c l e states o f the final n u c l e u s since this r e a c t i o n is k n o w n

to be a d i r e c t p r o c e s s w h i c h is e x p e c t e d to excite p r e f e r e n t i a l l y states

c o n s i s t i n g l a r g e l y o f a single p r o t o n (SP) c o u p l e d to t h e t a r g e t g r o u n d state. T h e p r e s e n t p a p e r r e p o r t s t h e ( 3 H e , d) r e a c t i o n o n 46'48'5°Ti to s t u d y t h e SP states o f 4"7,49, 5 1 V .

2. Experimental procedure T h e d o u b l y - i o n i z e d 3He b e a m f r o m t h e L a v a l U n i v e r s i t y V a n de G r a a f f was u s e d at 10 M e V w i t h a stability m e a s u r e d to be 3 keV. T h e b e a m was c o l l i m a t e d to a c i r c u l a r s p o t 0.24 c m d i a m . , a n d its i n t e n s i t y was b e t w e e n 1 a n d 200 n A o n the t a r g e t d e p e n d i n g o n t h e c o u n t i n g r a t e o f the e l a s t i c a l l y - s c a t t e r e d 3He particles in t h e d e t e c t o r . T h e d e u t e r o n s w e r e d e t e c t e d in a t e l e s c o p e c o u n t e r m a d e o f a 100 # m t h i c k A E s u r f a c e - b a r r i e r d e t e c t o r . T h e c o u n t e r w a s m o u n t e d o n a t u r n t a b l e , a n d t h e first d e t e c t o r h a d a n a r e a o f 25 m m 2 a n d was p l a c e d 10.2 c m f r o m t h e t a r g e t t h u s g i v i n g t On leave from Bhabba Atomic Research Center, Trombay, Bombay, India. tt Research supported by the Atomic Energy Control Board of Canada. 433

434

c. St.-PIERREet al.

an aperture of 2.8 °. The A E counter was just thick enough to stop the elasticallyscattered 3He so that a coincidence between the A E and E detector could be used to gate the "elastic" pulses and prevent them from going to the rest of the circuitry. In order to reduce any loss of resolution at high counting rates, the A E counter was followed by an antipile-up circuit which gated pulse pairs separated by 0.1 to 2.0 psec. The A E and E pulses were electronically multiplied and a single-channel analyser selected the product pulse amplitude corresponding to deuterons to gate a 800channel analyser which recorded the ( E + A E ) pulses. The targets (about 75 pg/cm 2 thick) were obtained by vacuum evaporation of the enriched isotopes * of Ti in the form of TiO z on 40 pg/cm 2 carbon backings. The 48Ti isotope was enriched to 99.1 ~o, and the main contaminant in the isotopes 46Ti and 5°Ti was respectively 17.8 ~ and 14.5 ~o of 48Ti. For each isotope, angular distributions of the deuterons were measured between 15 ° and 120 °. The angular distributions for the elastic scattering of 3He from each isotope was measured every 5 ° between 40 ° and 100 ° using the A E counter. The reaction as well as elastic-scattering measurements were monitored with respect to a solid-state detector recording the elastic scattering from titanium at 90 °. The elastic angular distribution in the range 20 ° to 90 ° was also measured with a magnetic spectrograph using a position-sensitive solid state detector in the focal plane. These runs were also monitored with a counter at 90 ° recording the elastic scattering. The elastic angular distribution from Ti was compared with the Rutherford angular distribution obtained from tantalum which happened to be evaporated in a little amount with the titanium. 3. Data reduction

Typical deuteron energy spectra at 35 ° from 46'4s'5°Ti are shown in fig. 1. The spectra from 46Ti and 5°Ti contain peaks due to the 48Ti impurity in the targets. These peaks were subtracted in the analysis. A computer program was used to fit the peaks with the least-squares method. The peaks were assumed to have a Gaussian shape with an exponential tail to simulate the background. The absolute cross sections were determined by comparison with the elastic scattering measured with the same counter. The errors on the absolute cross section are estimated to be less than 20

%.

The excitation energies were determined within +_40 keV from the ground or first excited state. These energies agree with a measurement performed with the magnetic spectrograph using nuclear emulsion 6). The measured angular distributions have been compared with the predictions of a distorted-wave Born-approximation (DWBA) calculation using the TSALLY code 7). The optical-model potential used in the calculation had the form U = V c - [ V/(1 + e ~ ) ] - i [ W / ( 1 +e~')+4W'e~'/(1

+ea')2],

* Supplied by Oak Ridge Nat.;onal Laboratories, Isotopes Development Center.

435

TJ(SHe, d) REACTIONS

where

x = (r-rvA')/av,

x'=

( r - r w A )/aw.

The optical-model parameters are given in table 1. F o r SHe, the parameters were interpolated from values used in other (SHe, d) a n d (SHe, ~) reactions at similar I

500

I

Ti46(He 3 ,d)V 4z

OLAB= 5 5

2.08

40050O

I

0i5

200

x~

Ti48 (HeS,d)V 49 EHes=rO0 MeV

-,-

e,AB:ss o

o 400-

v49 .49 q 0 26~[ V

166

"~ 2.2 6--', -2.22

~'" •* ' ~

I

Ju3 600 z

soo-

[

l

o

~i

0

I

EHeS = I00 MeV

"~ "" " " ~ ' ' "

'

f";

"" " "

1.64 il

o

"

I 4 ,e 4

"I

S IF 9

I~

o_ 5001- ~464 r, / L ~ ~449 f)

~

.x2

ii ,r]

i!

2ooJ-!i t,,, 22 , s 7 s z Ii !lli[ fi-~ tli'

279

;~

,i! ;:

*

i

]]

31

f

0/ 500~-

Ti5O(Hea, d)V 51

MeV

E'~e3=!O0

I OLAB=3 5 ° 400-

52l

x~-

4 25

500-

241 1~',

I,

359

0.

I

II

t

200 -[

I00-00

I 5O

I00

i

! 1

" t / V49

I I

150 200 CHANNEL NUMBER

V4

250

!

500

Fig. 1. Typical deuteron energy spectra at 35° from 46,~8,S°Ti(SHe, d) 47,4°,alV at 10 MeV incident energy. The observed groups are identified by their excitation energy. The impurity groups are labelled by the final nucleus. The ordinate scale is slightly different for the three spectra and is adjusted for direct comparison in terms of absolute cross section for each isotope. energies. The set of parameters chosen gave a good fit to the elastic scattering from the three isotopes of titanium. Fig. 2 illustrates this statement for the case of 48Ti. The parameters for the exit channel were interpolated from the parameters used for n e i g h b o u r i n g nuclei.

436

c. St-PIERRE et al.

12~-

'A

' ---'

,

-r

,

j

Ti48(He3 He3 )Ti 48 j

,08~

ii

o4F

f

0.0 0

---4

_

_

_

20

i

: .....

40

60

~

80

_:..__~ I00 120

1 140

@C,rn.

Fig. 2. A n g u l a r distribution o f 10.0 M e V 3He elastically scattered f r o m 4STi plotted as the ratio to R u t h e r f o r d scattering. T h e solid line is the optical-model fit for the parameters given in table 1.

~=0

0

20

40

60

80

]00

120

140

~c.m. Fig. 3. Typical a n g u l a r distributions predicted by D W B A calculations T S A L L Y code for l ~ 0, 1 a n d 3 with radial cut-off at 4.11 fro. T h e p a r a m e t e r s used are given in table 1. TABLE 1 Optical-model p a r a m e t e r s used in D W B A analysis

incoming channel outgoing c h a n n e l

V

W

av

rv

(MeV)

(MeV)

(fm)

(fm)

(fm)

aw

(fm)

rw

(fro)

RC

(MeV)

W'

174 112

13.5

0,85 0,90

1.07 1.0

0.59 0.47

1.81 1.55

1.40 1.40

72

Ti(aHe, d) REACTIONS

437

Fig. 3 shows the angular distributions calculated for angular m o m e n t u m transfers 1 = 0, 1 and 3 for a radial cut-off of 4.11 fin. Curves calculated for a radial cut off at 6.23 fm or without a radial cut-off differ from these by less than 5 % at the first m a x i m u m and by less than 10 % at large angles. Transitions with different/-values are clearly distinguishable. Spectroscopic factors were obtained using the relationship between the measured and calculated cross section da - N 2 J r + 1 C2Sa(O)TSALLY, dQex p 2J i + 1 where Jf and Ji are the spins of the final and initial state, C the appropriate isospin Clebsch-Gordan coefficient, S the spectroscopic factor of the state in question and N a normalization factor which includes the overlap of the wave function of the proton with the internal wave function of the deuteron in the 3He nucleus. The value of N chosen as 3.1 falls within the limits of 3.7___0.6 used by Armstrong and Blair 9) in a survey of the (3He, d) reaction on targets with 28 neutrons, and within 10 % of the value used by Erskine et al. I o), and it is consistent with the value estimated by Bassel 8). It is expected that the cross section should depend on the value of I • s of the captured proton 9, ~0); to account for this effect in obtaining the experimental strengths, the calculated cross sections were multiplied by 1.22 for a ~ - state and by 1.10, and 0.90, for ~ - and ½- states, respectively. Although the shape of the angular distribution usually gives an unambiguous determination of the angular m o m e n t u m transfer l, there can still be two possible values for the spin of the final state. To choose the most probable value, one can be helped by the use of the sum rule derived by Macfarlane and French 11). The sum of the spectroscopic factors for the levels which are identified as fragments of a singleparticle level is equal to the spectroscopic factor associated with this single-particle level. In our case where the target nuclei were doubly even, and the excitation energies low enough to attain only levels of isospin T = To - ½ , the sum rule becomes

~C2SII(p) 2J+ 1

s

1 (n)jl, N-Z+ 1

where J is the spin of the final state, N and Z the number of neutrons and protons, respectively, in the target nucleus and (n)s and ( p ) j are the average number of neutron and proton holes, respectively, in the J single-particle state in the target nucleus.

4. Results 4.1. T H E 51V S P E C T R U M

Transitions were observed to the ground state, to the previously known 4,5) 2.41, 3.21 and 3.59 MeV states and to a state at 4.25 MeV excitation energy. The angular distribution corresponding to the observed levels are shown in fig. 4, where the solid curves are those from the DWBA calculations. The extracted values of the

c . St.-PIERRE et al.

438

spectroscopic factors C2S a r e given in table 2 with the SP total strengths as expected from the sum rule reported in sect. 3. The spin and parity o f S~V ground state is well k n o w n to be 77. The agreement between the observed angular distribution and the calculated curve for l = 3 is excellent. Since no other l -- 3 transition is observed, it was assumed that the ground state contains all o f the f~ SP strength. The normalization factor N was adjusted to match the expected value of the spectroscopic factor for this state. 30 20

I.O 05

~

.

.

Ex:O0

I0

MeV

*

0.1

05

olb

0

05~I

I

I _~

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I

O4

I

.~,

Ex=5 59 MeV

~,ef

Ol 5 O,

:

00[

0.02I I

i I0

I

O, I - -

0

I

I

I

20

40

60

I00

EX=425

MeV

IIL

~ _ _ _ J _ _ _ i _ .

80

N

120

140

0

20

40

60

80

I00

120

140

Fig. 4. Angular distributions of states observed in 5°Ti (3He, d) 5xV at 10 MeV incident energy. The errors in the absolute values of the cross sections are less than 20 ~. The solid lines are the DWBA predictions. All the observed excited states have angular distributions corresponding to l = l transitions. The large transition strength to the states at 2.41 and 3.21 MeV excitation strongly indicates a ~ - assignment since they exhaust most of the p~ SP strength. The uncertainty of the spectroscopic factor for the 3.59 MeV state is somewhat larger than for the other states. The corresponding deuteron group is very close in energy to the group from the 2.22 M e V doublet produced because of the 48Ti content of the target. The intensity of the impurity group was determined by comparison

Ti(3He, d) REACTIONS

439

with the amplitude of the group arising from 49V ground state. It is not possible to decide between a 3 - and 1 - assignment for the 3.59 MeV level. The 4.25 MeV state is most probably a fragment of the SP p~ state since the energy difference between the p} and p , subshells is about 2 MeV. Another evidence is that most of the p} SP strength is used within the experimental uncertainty, if the 3.59 MeV level is assumed to be ½-. A 3.07 MeV state was also observed, but the deuteron group was not resolved well enough at forward angles to permit a sure determination of the/-value. TABLE 2 Results for 46, 48,~OTi (3He ' d) reactions Nucleus

'~V

49 V

Excitation energy (MeV)

Iv

J~

C2S

~C2Sexpeeted

SPstate

0.15 0 2.08 2.22 0.26 1.66

3 1 1 1 2 0

7a,~ ~ a+ =1,+

0.49 0.03 0.26 0.14

0.58 0.66

f~p-~.

0 0.15 1.64 2.22 2.26 3.89 3.89 4.22 4.49 4.64

3 1 1 1

7a:~-~-

0.58 0.05 0.19 0.47

0.70 0.80

r~

1 1 1 1 1

(2-) (½-) ½½½-

0.07 0.19 0.13

0.80

P~,

0 2.41 3.21 3.59 3.59 4.25

3 1 1 1 1 l

7 22(a) (½-) ½-

0.75 0.57 0.18 0.035 0.08 0.25

0.75 0.86

f~ p~-

0.86

p½

0.04

Pk

4.2. T H E 49V S P E C T R U M

Fig. 5 shows the angular distributions obtained for the lower observed excited states, namely, ground state, previously known 1,2,5) 0.15, 1.64, 2.22, and 2.26 MeV states and also to 3.89, 4.22, 4.49, and 4.64 MeV states. The curves are D W B A predictions. The angular distribution corresponding to the ground state is characteristic of an 1 = 3 transition in agreement with the known assignment of ~. Within the experimental error, this state exhaust the full f: SP strength.

440

c . St.-PIERRE et al.

The weak transition to the 0.15 MeV state is l = 1 in support of the { - assignment obtained in/%decay work s) on 59Cr. Malik and Scholtz t2) obtain a good agreement with the observed lower level scheme by describing these states in terms of the Nilsson model with Coriolis coupling using a deformation parameter/7 = - 0 . 3 9 . N o calculation of the expected spectroscopic factor for these levels has been performed with this model.

L° F

~ ,

/

OSF

E,=o o M~',,

./

01 t

"t,+

°

I

I

I

I 0!

-p ~_J

"

- x

04 //~\.

-\

f

E x =0 15 MeV

/

/

0 2 L-

±

1

~ - ....... 1

.

k

~

___

I

_J

15

001 50~

L

I

_ [

~_._~

.~__

k

J O, I .

,i

20

.

.

.

.

.... ~__

~

__~

Ex :4 22

,",4eV

10[ 0 5 -

I0

~ ,

0.5

o OI

0 0 5 . - - 1

20

40

60

80

I00

I;~0

i40

20

....

J _ _

40

_

~

60

[

80

--~

t

tO0

.

[

120

_

]

i40

ecru

ecru

F i g . 5. Angular distributions of states observed in 4STi ( 3 H e , d ) 49V at 10 MeV incident energy. The errors in the absolute values of the cross sections are less than 2 0 % . The solid lines are the D W B A

predictions.

The transition leading to all other excited states are assigned l = 1. Most of the p~ SP strength is exhausted by the 1.64 MeV state and the 2.22-2.26 MeV doublet. As for 51V, we expect the states with excitation energy above 4 MeV to belong to the p~ SP state. The 4.22 MeV state would thus be assigned ½-. The angular distributions corresponding to the 4.49 and 4.64 MeV states were not well fitted with the predictions of the D W B A calculation for an l = 1 transition. However, the general shape would favour an l -- 1 assignment. The cross sections for these two groups is equal within

441

Ti(3ge, d) REACTIONS

10 ~ , and for angles larger than 35 °, it equals that o f the 4.22 M e V group. Finally, another group was observed at an excitation energy o f 4.84 MeV, but its angular distribution is not clear enough to permit a n y / - a s s i g n m e n t 4.3. THE 4rV SPECTRUM In fig. 6 are shown the angular distributions corresponding to the ground state,

,o\

04F / ~

Ex:O

0

E× : 166 M e V

MeV

o,!/ 005

[

÷

Oi

i

k

003

•

r

,i

1

r 00!

i

. .j

±

I Oi

j,$~,,.

,

:

E x :0 [ 5

÷/ --.<

o.s!

,

\ x

~

~

:

-

:

50,

McV

2 ~k

"-h.

'

q b~

,

E× : 2 . 0 8 M e V

\ "-t..
©5

">.>~

OI

oosi

,

#

,

,

E x =O 2 6

MeV

_~___•

O4

~

• 20, E×:2

÷"".

22

MeV

'°i t

0 ~/

Ol

l

00~

t0

•

40

_ i

eo

eo Ocm

E~o

~2o

I~o

01[

• 2o

......... t 4o co 80 (9c m

r

r{~O

~2@

,4a

Fig. 6. Angular distributions of states observed in 4°Ti (3He, d) 47V at 10 MeV incident energy. The errors in the absolute values of the cross sections are less than 20 )~. The solid lines are the DWBA predictions. 0.15, 0.26, 1.66, 2.08 and 2.22 MeV states. These states have been previously observed in S°Cr (p, ~) [ref. 2)], 46Ti (p, 7) [ref. 3)] and 47Ti (p, n) [ref. 1)] reaction studies, but no spin-parity assignments were made. These states were also observed in a spectrographic work by Rosner and Pullen 13) with the (3He, d) reaction at 16.5 MeV. The very strong l = 3 transition to the 0.15 M e V state suggests a -}- assignment. The ground state is weakly excited but the angular m o m e n t u m transfer is definitely

442

c. St.-PIERREet al.

l = 1. This a s s i g n m e n t agrees with the results of Rosner e t al. a n d rules out the earlier ~-- assignment for the g r o u n d state. The measured value of l o g f t = 4.9 in 47V (fl+) 47Ti decay 3) is consistent only with J~ = ~ - . This spin value is also in agreement with a d e t e r m i n a t i o n by the atomic b e a m magnetic resonance method 14). Two, positive-parity states were observed in this isotope. They are the 0.26 MeV state o b t a i n e d with a weak l = 2 t r a n s i t i o n a n d thus identified as a a ÷ hole state a n d 1+ the l = 0, 1.66 MeV state identified as a z hole state. M o s t of the SP p~ strength was o b t a i n e d in the l = 1 t r a n s i t i o n to the 2.08 a n d 2.22 MeV states. The spectroscopic factors extracted in this work are consistently 25 % below the values of Rosner 1a).

5. Conclusion The states observed in 47'49'51V were all by the transfer of a l = 1 or 3 p r o t o n except for the s~_ a n d d~ hole states in 47V. N o theoretical calculation of the spectroscopic factors expected for these states is available for c o m p a r i s o n with the values extracted in this work. The g r o u n d state of 47V was assigned ~ - in agreement with Rosner, who performed the same reaction at a higher incident energy, a n d with Redi e t al. who used the atomic beam, magnetic-resonance method.

The authors are indebted to Dr. B. R o s n e r for c o m m u n i c a t i n g his results prior to publication. T h a n k s are also due to Dr. B. Cujec for supplying the results of her spectrographic work o n the same reactions. The authors acknowledge the c o o p e r a t i o n of the V a n de Graaff group w i t h o u t w h o m this work w o u l d n o t have been possible.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

G. J. McCallum, A. T. G. Ferguson and G. S, Mani, Nuclear Physics 17 (1960) 116 G. Brown, A. MacGregor and R. Middleton, Nuclear Physics 77 (1966) 385 H. Albinsson and J. Dubois, Phys. Lett. 15 (1965) 260 H. O. Funsten, N. R. Robserson and E. Rost, Phys. Rev. 134 (1963) BlI7 K. Way et al., Nuclear Data Sheets (National Academy of Sciences - National Research Council, Washington, D.C.) B. Cujec, private communication R. H. Bassel, R. M. Drisko and G. R. Satchler, ORNL-3420 (1962) unpublished report R. H. Bassel, Phys. Rev. 149 (1966) 791 D. D. Armstrong and A. G. Blair, Phys. Rev. 140 (1965) B1226 J. R. Erskine, A. Marinov and J. P. Schiffer, Phys. Rev. 142 (1966) 633 J. B. French and M. H. Macfarlane, Nuclear Physics 26 (1961) 168 F. B. Malik and W. Scholz, Phys. Rev. 150 (1966) 919 B. Rosner and D. J. Pullen, Bull. Am. Phys. Soc. 11 (1966) 840 and private communication O. Redi and M. A. Graber, Bull. Am. Phys. Soc. 12 (1967) 474