The (t, p) reaction with the even isotopes of Sm

2.A.1

[ I

Nuclear Physics 86 (1966) 145--166; (~) North-Holland Publishing Co., Amsterdam N o t to be r e p r o d u c e d b y p h o t o p r i n t or microfilm without written permission f r o m the publisher

T H E (t, p) R E A C T I O N W I T H T H E E V E N I S O T O P E S

OF Sm

J. H. BJERREGAARD, OLE HANSEN and O. NATHAN The Niels Bohr Institute, University of Copenhagen, Denmark t and S. HINDS A WRE, Aldermaston, Berkshire, England Received 5 April 1966 Abstract: The (t, p) reactions on the even isotopes of Sm have been investigated at a bombarding energy of 12 MeV with the purpose of exploring the transition from spherical to deformed nuclei. The reaction protons were detected in the Aldermaston multi-angle spectrograph, the overall energy resolution being about 20 keV FWHM. Levels in 146,~°,15:,154,15sSm were established below 2-3 MeV excitation energy. A number of 0 + and 2÷ states were identified from the proton angular distribution data. The 0 + energies (4-10 keV) and maximum differential cross sections in mb/sr (4-25 ~'/o)were: 146Sm g.s. (0.29), 2.611 MeV (0.09); x~°Sm g.s. (0.57), 0.745 MeV (0.14); 15zSm g.s. (0.19), 0.685 MeV (0.14), 1.091 MeV (0.13); 154Sm g.s. (0.30), 1.117 MeV (0.03), 1.218 MeV (0.10); ~58Smg.s. (0.30), 1.068 MeV (0.02). E[

N U C L E A R REACTIONS ~4"'~4s' ~5°'152'~5"Sm(t' p)' E ~ 1 2 MeV; measured tr(Ep' O)' Q" I 14e,150,153,154,~aSm deduced levels, J, zt. Enriched targets.

I. Introduction T h e s a m a r i u m isotopes constitute an intensely studied region o f the p e r i o d i c table, the stable isotopes o f this e l e m e n t s p a n n i n g the range f r o m a single closed shell nucleus, p r e s u m a b l y with a spherical surface (144Sm, N = 82) to a s t r o n g l y d e f o r m e d nucleus (154Sm, N = 92). Extensive r a d i o a c t i v i t y a n d nuclear r e a c t i o n studies have clarified m a n y features o f the nuclear c o u p l i n g schemes n e a r the g r o u n d state o f these nuclei. T h e change in coupling scheme n e a r N = 88 is m o s t easily d e m o n s t r a t e d f r o m the spectra o f the even nuclei a n d the t w o - n e u t r o n transfer r e a c t i o n is therefore especially suited to study the phase t r a n s i t i o n in Sm. T h e present p a p e r describes a series o f a n g u l a r d i s t r i b u t i o n m e a s u r e m e n t s o f p r o t o n s f r o m (t, p ) r e a c t i o n s on even Sm nuclei at an incident b e a m energy o f 12 MeV. T h e evidence o n the (t, p) r e a c t i o n p o i n t s to a simple t w o - n u c l e o n s t r i p p i n g m e c h a n i s m as being responsible for the strongest t r a n s i t i o n s 1 - 3 ) . The r e a c t i o n is f o u n d to exhibit the following two characteristic features: (i) F o r even targets the a n g u l a r d i s t r i b u t i o n s are characteristic o f the o r b i t a l a n g u l a r m o m e n t u m c h a n g e L (which in such cases equals the final state spin Jf). O n l y n a t u r a l p a r i t y states are excited. t Work supported in part by Statens Almindelige Videnskabsfond in Denmark. 145

146

J . H . BJERREGAARD et aL

(ii) If more than one neutron configuration is important for a transition, the magnitude of the cross section depends on the relative phases as well as on the absolute values of the various components. The coherence of the (t, p) reaction can give important information on nuclear structure properties. The experimental techniques and the results are presented in sect. 2. The systematic features of the angular distributions are described in sect. 3. In sect. 4 the nuclear structure information implied by the data is discussed, the main emphasis being on the excited 0 + states. 2. Experimental Procedures and Results 2.1. P R O C E D U R E S

The targets ~vere made by vacuum evaporation of the metal onto thin (about 50 #g/cm 2) carbon films using the method described in ref. 4). The starting material was Sm 2 Oa enriched in the various Sm isotopes as indicated in table 1. The Sm 2 03 was placed in a tantalum crucible together with a sufficient amount of La metal. Upon heating to about 700 ° C the Sm20 3 is reduced to Sm, which subsequently evaporates. The evaporating Sm was either deposited directly on the carbon backings or it was collected on a piece of W metal in the form of a lump and subsequently evaporated from a crucible. The target thickness was measured by means of elastic scattering of deuterons at 6 MeV or of g-particles at 10 MeV. At these energies the elastic scattering obeys the Rutherford law. The scattering experiments were performed at the Copenhagen tandem, using surface barrier detectors in a well defined geometry. The results are given in table 1. These thicknesses are local, valid for the particular area irradiated in the scattering experiment. TABLE 1 Target c o m p o s i t i o n a n d thickness Target isotope

144Sm

144Sm 14sSm 15°Sm 152Sm 154Sm

94.5 0.4 0.1 0 0

Isotopic c o m p o s i t i o n (70) ~) 14~Sm l'SSm 148Sm 15oSm 15zSm 1.6 0.8 0.3 0.2 0.1

0.9 96.3 0.3 0.1 0.1

0.9 1.4 0.9 0.1 0.2

0.4 0.3 96.4 0.1 0.1

1.0 0.5 1.5 99.1 0.4

154Sm

Thickness (,ug/cm ~)

Conversion factor b)

0.7 0.3 0.5 0.5 99.2

205 ± 10 130± 7 207±10 110-4- 6 360-t-18

1.79 × 10 -4 2 . 4 0 × 10 -4 2.50× 10 -4 3.53 X 10 -4 0.86 × 10 .4

a) T h e target material was o b t a i n e d f r o m O a k Ridge N a t i o n a l L a b o r a t o r y , U S A . T h e percentages q u o t e d in the table are those given by the m a n u f a c t u r e r . b) T h e absolute differential cross sections in m b / s r are obtained as p r o d u c t s o f this factor a n d the differential cross sections expressed in the units o f figs. 2, 3, 5, 7, 9 a n d 11, respectively.

Using the known solid angle of the Aldermaston spectrograph, the value of the integrated beam charge and the measured target thickness, an absolute cross section scale was established for each (t, p) reaction, the estimated uncertainty being ___25 70.

Sin(t, p) REACTION

147

This estimate includes the effects of possible target inhomogeneities. The yield-tocross-section conversion factors are given in table 1. The (t, p) reaction experiment was performed at the Aldermaston tandem accelerator. The tritons were accelerated to energies of about 12 MeV and the reaction protons were detected in the multi-angle spectrograph of Middleton and Hinds 5) with an overall energy resolution of about 20 keV FWHM. The estimated uncertainty on the absolute Q-value determinations is _+25 keV, except for the case of 154Sm(t, p)~56Sm where the Q-value was determined to within _+30 keV. The excitation energies of the stronger groups have estimated uncertainties of 4-10 keV. Further details of the experimental procedures are described, e.g., in the work of Middleton and Pullen 1). E x IN MeV I

T

,

]

1

3

2

1

0

"'Sm (t,pf"Sm Et=1196 MeV

G_ ~_ U3

i

Lab angle : 27"5 B=11 509 kG 2500 FtC

3,2

~eO(0)

2[5

i

E E 15oF

c5 ~1 100

2~

23 24

30

~1

25

2927 28 •

10

12

"

21

18

S~Sm(0)

" LA

a8

4g

4

7

~9

50

51

- ~ 52

......

i

53

........

54

RADIUS OF CURVATURE IN cm

Fig. 1. Proton spectrum from the triton bombardment of :~Sm. The number of protons scanned across a 9 mm wide zone on the photographic emulsion is plotted against the distance along the plate. The calibration of the spectrograph furnishes the radius scale and the energy scale indicated at the bottom and top of the figure, respectively. Proton groups corresponding to levels in the final nucleus are numbered according to the table in the text (table 2). Hatched groups belong to target impurities. 2.2. RESULTS

The experimental results are presented in tables 2-6 and in figs. 1-11. Brief comments on the individual isotopes are given below. 2.2.1. The 144Sin(t, p)146Sm reaction. Altogether 28 states were identified. Angular distribution data were obtained up to the 2851 keV state; at higher excitation energies the background prevented the extraction of reliable yields. A proton spectrum at 0 = 27.5 ° is shown in fig. 1 and the angular distributions are given in figs. 2 and 3. Excitation energies and spin parity assignments are collected in table 2. Also given in table 2 are the levels suggested by Avotina et al. 6) who

148

BJERREGAARD e t al.

J.H.

1800

] 1800

GROUND STATE {, L= 0

16oo

1200

(0J

0.75 MeV L =2

600

i

t

~oo

/,,

600

4o0

~ iI

~.oo

[

~

~

i

1.66 MeV

i

~~oo

•

200

t

i

i

t

I

~ool

1o

i

'

0~__1

i

(4) 26°1

,

i

I

k

'1~~' t

0t

\

400

8oo ~.,, i

I

(2+3)

,~

L

JI /

800

1.39 MeV

T,,,

pt

ooo

300

8oo

200

,ooo

i

i

i

i

i

2.09 MeV

(7)

2.29 MeV

(10)

z6°r

/' 11

200

I ~' '

100

i

100

6o

~, 0 -- I

I

I

I

r

I~ I ~ ~~e -

2.16 MeV L =2

Izoo

OL~

(8)

2.23 MeV 300

1000 800

fl

2O0

°

200

o

(1)

' do

' l&'

(9) I

!

;~'I "

it i ~

"-.-*

•" ~, •

do

".

~6o' # , o ' 18o ~o ' 6b 1,5o ~ & ' l a O GeM. Fig. 2. Angular distributions from z44Sm(t, p). The proton yield is plotted versus reaction angle in the c.m. system. Absolute cross sections in mb/sr may be obtained from the arbitrary units (which represent the number of observed counts) by multiplying with the conversion factor of table 1 taken for the target mass. The curves have no theoretical significance. ~4o

lao

:~o

6o

p)

Sm(t,

REACTION

149

studied the decay 146Eu ~ t46Sm. Their scheme agrees fairly well with the more unambiguous level ordering derived from the present data. It is remarkable that several of the transitions to excited states and in particular to the 2 + states have maximum cross sections close to that of the ground state. In all of the other Sm nuclei the L = 2 transitions have smaller relative yields.

40C

(11)

2.44 MeV

2.55 MeV

't

30¢

it

2CC

(12)

2.61 M e V

50

500

oo

400

5c

300

(13)

L=O

\

200

iP

10(] 100

¢n

t

2

i

i

i

i

_l

M V-

150

i

I

r

(1)

eo

t

i

i

2.74

i

i

t

J

i

0

(16)

MeV

I

i

i

701

1250F

60

200

i

i

i_

M;V

/

i

i

(19)

~"

100 50 :

50

0

'

'

'

'

1()0

'

140

18(:

O

~

100

140

180

0

t

20

I

f

60

f

~

100

I

140

I

180

Oct4. Fig.

3.

See

caption

of

fig.

2.

2.2.2. The 148Sm(t, p)lS°Sm reaction. The 148Sm target was rather thin (see table 1); consequently the spectrum (fig. 4) has less detail than e.g. that of Z46Sm. The ground state cross section is the largest observed among the Sm isotopes and all other groups have maximum cross sections at least three times lower than that of the ground state transition (fig. 5 and table 3).

150

J. H. BJERREGAARD et al. TABLE 2 144Sm(t, p)14eSm results, Qo = 6681-4z25 keV a) Ref. e) Level no.

Ex (keY)

Present work b) J~

0 1 2 3

0 747 1381 1382

0+ 2+ 34+

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1648 1811 2046

2+ (5, 6) 4, 5, 6

2157

(2 + )

2282 2440

(4 + ) 3, 4

2680

2829 2899 2904

(3168)

3-

3-

Ex (keY)

J~

0 749~:10

0+ 2+

0o.m. (deg)

(dtr/dco)c.m. (mb/sr) 0.29 0.28

27.8 5.1

~ 1387110

0.14

~35

1656110 1817!10 -2090:[:10 2163d:10 2231110 2288d:10 2442:t:10 2546~:10 2611:/:10 2653:[:10 2681d:15 2738:t:10 2786±15 2808:]:15 2851d:10

0.04 0.04

20.2 ~ 65

0.04 0.20 0.05 0.04 O.06 0.04 0.09 O.02

~

2+

(2 + ) 0+

3.5 5.1 5.1 '~42 42.9 5.1 27.8 5.1

0.01

0.03

2933:[:15 2979:[:15 2998~:15 3021:I:15 3056i15 3071d:15 3140~:15 3187::1:15 3240~15 3264~15

a) The incident b e a m energy was determined from the positions of the proton groups corresponding to the 160(t, p)IsO ground state transition (Q = 3706 keV) and to the xsC(t,p)14C ground state transition (Q = 4641 kcV). b) The m a x i m u m cross section and the angle at which it was observed are given in the last columns. If no cross section is stated, no yields could be extracted from the data. If no angle is quoted, the distribution was near isotropic,or in L = 2 cases the yield could not be measured at 5.Io. The ~ sign indicates a broad m a x i m u m .

Thus there is a definite change in the character of the proton spectrum as compared to 144Sm(t, p)l#6Sm. The absence of a proton group to the 0 + state at 1256 keV is remarkable. This state is strongly excited 7) in the reaction lS2Sm(p, t)~S°Sm. 2.2.3. The 1 s OSm(t, p)152Sm reaction. Most of the results from this reaction have been published previously a). To facilitate the discussion of sects. 3 and 4 the complete set of 15°Sm(t, p)lS2Sm data is given in fig. 6 (spectrum), fig. 7 (angular distribu-

Ex IN MeV

1~c(o)

IBO(O) Q. or

20C

E E

15¢

n" Ld Q_ (h

10C

< (") n" p-.

5C ~

1"Sin (t,p)lS°Sm Et = 11.95 MeV Lab. angle = 27.*5 B = 10.569 kG 2966 }1C

LO

25 o4-~32 31 ~ 30

..... ; 54

53

_

55

5'fi

57

RADIUS OF CURVATURE IN cm Fig. 4. Proton spectrum from the triton bombardment of 148Sm. See also caption of fig. 1. GROUND STATE 250C

(0)

1000

0.34. MeV

(1)

L-2

L-0 000

2OOC

600 15(X 400

100(

200

50(

8

~ 700

i

i

i i i i i i

0.75 MeLV=0

(2)

i

i

i

1.97 MeV

3ooi

i

J

i

i (25)

60(

50C

200[[

30C

20C

10C

0

2()

60

1OO

140

180

20

' 60

I 1~)O I 1,~ I

eC,M.

Fig. 5. Angular distributions from 14sSm(t, p). See also caption of fig. 2.

152

J. H.

BJERREGAARD

et

al.

TABLE 3 a4sSm(t, p)lS°Sm results, Q0 = 5 3 7 2 i 2 5 keV a) Refs. 7-10 Level no. 0 1 2 3 4 5 6 7 8 9 b) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Ex (keV) 0 334 741 774 1046 1072 1165 1170 1193 1256 1275 1279 1355 1369 1450 1504 1645 1682 1708 1760 1790 1809 1823 1848 1950 1972 2022 2120

Present work a) J=

E~ (keY)

J'~

(da/dg°)e.m. (mb/sr)

Oe.m. (deg)

0+ 2+ 0+ 4+ 2+ 32+ (1-) 2+ 0+ (6 +) 3+

0 337dz10 745110 780:k10 1050d:10 1070110

0+ 2+ 0+

0.57 0.17 0.14 0.01 0.05 0.05

27.8 5.1 27.8

(5 +) 4+ 2+ (4 +) (3-)

(4 +) (3-) (4 +) (4 +)

1649:k10 1689i10

0.02 0.03

18255:10

0.02

1974±10 2038±10 2120~:10 2166~10 2197±10 2444±10 2485±10 2576±10 2629±10 2660~10

0.07

~42

a) See footnotes of table 2. b) This 0 + state is probably identical to the 1.28 MeV (±0.05 MeV) 0 + state observed in the (13, t) experiment of ref. 7).

t i o n s ) a n d i n t a b l e 4. T h e e n e r g y r e s o l u t i o n o f t h i s e x p o s u r e w a s o n l y a b o u t 30 k e V FWHM because of the use of a more extended beam spot on the target. 2.2.4. The 1 5 2 S m ( t , p ) l S * S m reaction. T h e 152Sm t a r g e t w a s t h e t h i n n e s t o f t h o s e u s e d a n d s o m e w e a k t r a n s i t i o n s m a y h a v e e s c a p e d d e t e c t i o n f o r t h i s r e a s o n . O n l y five

TABLE 4 lbOSm(t, p)ls~Sm results, Qo = 53764-25 keV s) Refs. 8, x0-1~) Level no. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Ex (keV)

Present exp a)

J'~

0 122 366 685 710 810 939 964 988 1026 1041 1086

Ex (keV)

0+ 2+ 4+ 0+ (6 +) (2 +)

J=

(d~/d~o)e.m. (mb/sr)

0e.m. (deg)

0 123 ± 10 370i10 688±10

0+ 2+

0.19 0.04

27.8 5.1

0+

0.14

27.8

824 4-10

2+

0.05

5.1

10914-10

0+

0.13

27.8

14+ 32+

1132 1225 1235 1298 1385 1440 1511 1531 1583 1610 1684 1732 1757 1775 1905

(5-) 3+ 1293 4-10

0.05

17664-15

0.04

(4 +) 12(3-)

(5-) (3, -4 +)

35.3

a) See footnotes o f table 2.

Ex IN MeV

'S°Sm (t,p)~5'Sm 'ao(o)

~c(o)

E t - 12.02 MeV Lab. angle = 27*5 B = 10.569 kG 1845JAC

n 2oo E_ E E LO C5 cr JJ 13- loo 03 t.3 < cr

.o

H H

53

~

54

12

55

o

3

56

RADIUS OF CURVATURE IN cm Fig. 6. P r o t o n spectrum f r o m xs°Sm(t, p). See also caption o f fig. 1.

57

154

J.H. BJERREGAARDet

1000

0.12 MeV

al,

r

(1)

t 0.69 MeV

soo

L=2

800

'/

ff

(3)

L-O

i

I 400

L

300

t

600 _

~

4430

~

100

200

0 300

!

201

i

"F, L,

b

L=O 1

"

2

101

I

I

I

i

l

I

L

1,76 MeV

300

2~D

I

(25+26)

r 60 ~ 100

1~010 @cM.

Fig. 7. Angular distributions from 15°Sm(t,p)tSsSm. See also caption of fig. 2. 20(3

100

o

25

' ~

' 1~ eC.M.

1;o'

0

155

Sm(t, p) REACTION TABL~ 5

as~Sm(t, p)ls~Sm results, Qo = 53614-25 keV s) Refs. s, lo, 11, xg) Level no.

Ex (keV)

J"

0

0

0+

1

82

2+

2

266

4+

3

548

6+

4

919

(1-) (8 +)

5

927

6

1009

3-

7

1099

(0 +)

8

1120

9

1180

10 11

1209

12

1294

13

1343

14

1365

Present w o r k a) Ex (keV)

J"

(do'/dco)e.m. (mb/sr)

Oc.in.

(deg)

86~10

2+

0.30 0.14

27.8 5.1

1117+10

0+

0.03

27.8

1218:k10

0+

0.10

27.8

0

0+

1299-4-10

0.01

(4 + )

a) See f o o t n o t e s o f table 2.

E x IN MeV

180 (0) £L

E E E

~S:Sm (t.p)~S'Sm Et =12.01 MeV Lab. angle =35" B = 10.569 kO 2475 ~C

14C(0)

1°°t F

LO

rr LIJ

50

11

O3 ¢J

.< 7

12

.... 52

53

5/*

55

....A,,~ 56

.~

RADIUS OF CURVATURE IN cm Fig. 8. P r o t o n s p e c t r u m f r o m 15~Sm(t, p). See also caption o f fig. 1.

-A-_ 57

156

BJERREGAARD et al.

J.H.

groups were observed (fig. 8). The excitation energies are collected in table 5 and the angular distributions for four of the transitions are shown in fig. 9. looo~ GROUND STATE

,oo!

0.09 MeV

(o)

L-O

soo

(1) L=2

4O0 SO0

300

400 2O0

20O

I00

'

'

~

0

J

t

~120

(7)

1.12 MeV t00

1.22 MeV SO0

L-O

(11) L-O

4OO

.o It

30O

60

2O0

20,

{{{

lO0

140 F i g . 9.

18 D 2b eCM.

i

/

'

Angular distributions from lSzSm(t, p)z54Sm. See also caption of fig.

2.

The ground state transition dominates the spectrum, followed by the 0 + transition to a new level at 1218 keY. An upper limit for the cross section to undetected transitions below 1.3 MeV can be set at 5 % of the ground state yield whereas the limit of detection above 1.3 MeV is at 10% of the ground state yield. Thus, another major change in the character of the proton spectrum has occurred, as compared to the lighter Sm targets. 2.2.5. The t54Sm(t, p)X56Sm reaction. The 156Sm data are presented in figs. 10 and 11 and in table 6. The nucleus 156Sm is expected to be strongly deformed. Taking the state at 74 keV as the first member of the ground state rotational band, a moment of inertia slightly larger than that of lS*Sm is obtained. The levels at 250 keV and

157

Sm(t, p) REACTION

TABLE 6

154Sm(t, P) 15eSm, Qo = 45564-25 keV a) Present work a) Level no.

0 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Ex (keY)

J~

0 744-10 250-4-10 521±10 8104-20 8784-10 10684-10 11204-10 14414-10 1516±10 16119:10 17114-10 17404-20 17924-10 18514-10 1911±10 1970±20 2677~:10

0+ 2+

(dtr/dco)e.m" (mb/sr) 0.30 0.15 0.02 0.003 0.002 0.01 0.02 0.01 0.04 0.004 0.02

0÷ 2+

0e .m.

(deg) 27.8 5.1 12.7

27.8 5.1 ~42

0.02

42

a) See footnotes o f table 2.

Ex IN MeV

lS:Sm (t, p)'S6Sm E t = 12.03 MeV Lab.angle: 27.*5 n

EE E d rY Ld Q. Lf)

B = 10.569 kG %{ol 3150 jaC

200

~'C(O)

150

LO

1

17

2~ (J

&

6

18H

¢Y I--

0 51

52

i 53

i 54

"

] .... 55

RADIUS OF CURVATURE IN cm

Fig. 10. Proton spectrum from 154Sin(t, p). See also caption o f fig. 1.

%

158

J . H . BJERREGAARD e t al.

521 keV are probably the 4 + and 6 + rotational states, respectively, since their excitation energies are consistent with the I(I+ 1) prediction within experimental errors. The 0 + state at 1068 keV has a rather small cross section relative to that of the ground state. N o strong second 0 ÷ state appears in the (t, p) spectrum of 156Sm.

GROUND STATE (0)

!ooo! 0.07 MeV

(1)

L-2

3000

L=O

1500

0.25 MeV

30C

(2)

1 200

2000 I000I IOO

1000 500I q

i300

~

1.07 MeV

0/

I

l 1.44MeV

(6)

L=O

500

m) ]3oof

L-2

1.61 MeV

too

(10)

\ 200

200

\

300

100

'~~

I

eb

200

I

lbo

I

~0

I

18o

100

~

•

~

I

6o eC.M.

I

~o

I

18o

0

2o

6o

~oo

~4o

~o

Fig. 1 1. A n g u l a r distributions f r o m z54Sm(t, p)x~6Sm. See also caption o f fig, 2.

3. Discussion of the Angular Distribution Data 3.1. T H E L = 0 T R A N S I T I O N S

The angular distributions corresponding to transitions between states of spin and parity 0 + are shown to the left in fig. 12. These distributions all exhibit an oscillatory behaviour with relative maxima at 0 °, 28 °, 58 °, about 90 ° and (less pronounced) at about 135 ° and with a deep, sharp minimum at 44°; the second maximum is the

m Z

,ff tY I--

t~

"o

u

~g

60

90

120

150

180

u

3u

60

90

120

150

180

~CMDEGREES Fig. 12. Angular distributions from (t, p) reactions on Sm isotopes connecting states of J'~ = 0 + (left). To the right are s h o w n proposed L = 0 distributions. The number in parenthesis behind the chemical symbol refers to the level numbering of tables 2-6.

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BJERREGAARD et al.

highest and the third one is generally broader than the second. A similar oscillatory behaviour for 0 ÷ --, 0 ÷ (L = 0) transitions has been found in studies of (t, p) reactions in both light and heavy nuclei. The distributions in fig. 12 do not give evidence for systematic differences, relating to the nuclear structure situation. \

\

\ .,--,

Z :>tW i--

/

m

"10

\

\

/

0

30

eo

90

120

~50

~eo 8c~

0

30

eo

90

~20

150

leo

DEGREES

F i g . 13. Angular distributions from 0 + --+ 2 + transitions (left) and proposed L = 2 angular distributions (right). The ls~Sm(16) assignment is doubtful due to poor statistics. See also caption of fig. 12.

The angular distributions shown to the right in fig. 12 all have the same general shape as the distributions of fig. 12, left. In some low-Q-value transitions a damping of the oscillation at large scatterir~g angles can be seen, but the relative maxima and the characteristic deep minimum are still situated at the same angles as observed for

Sin(t, p) REACTION

161

the well established 0 + ~ 0 + transitions. It is suggested that the distributions of fig. 12 (right) correspond to 0 ÷ -~ 0 + transitions. 3.2. T H E L = 2 T R A N S I T I O N S

The L = 2 angular distributions are shown in fig. 13 (left). These distributions exhibit more individuality than is the case for the L = 0 transitions, though the main trend is clear: relative maxima at 0 °, 43 °, about 75 °, and at about 112 ° with the 0 ° m a x i m u m as the highest. The height of the second m a x i m u m changes markedly from 146Sm to 156Sm. The L = 2 transitions are readily distinguished from the L = 0 transitions. The distributions in fig. 13 (right) have the same main characteristics as the L = 2 distributions, and it is suggested that the final states involved in these transitions have 2 ÷ character. 3.3. T R A N S I T I O N S W I T H L D I F F E R E N T F R O M 0 A N D 2

In one-nucleon transfer reactions, weak transitions often exhibit non-stripping angular distribution patterns and it is likely that similar effects occur in two-nucleon transfer processes. The m a x i m u m cross sections of the clearly distinguishable L = 0 groups discussed in subsect. 3.1 are all > 0.02 mb/sr and we shall tentatively use this limit as a dividing line. Transitions having m a x i m u m cross sections below about 0.02 mb/sr may be due to several interfering reaction mechanisms rather than to a two-neutron stripping process. States of 4 + character are known in 146Sm (state 3), in is°Sin (states 3 and 14), in 152Sm (states 2 and 9) and in ~54Sm (state 2). State 3 of ~46Sm is within 1 keV of a 3 - state, and thus the observed distribution is probably a mixture of L -- 3 and L = 4. In all the other cases the measured m a x i m u m cross section is of the order of 0.02 mb/sr or smaller. States o f 3 - character are known in 146Sm (states 2, 15 and 18), 15°Sm (state 5), in lS2Sm (state 10), in 154Sm (state 6). In 146, 15o, 152Sm the lowest 3 - state would probably not be resolved from neighbouring states in the present experiment. The 154Sm 3 - state is weak and this is also the case with the two higher-lying 3 - levels in 146Sm. Thus no clear evidence on the properties o f L = 3 or 4 distributions were obtained. Transitions with L = 1, L = 5 or L = 6 were not identified, neither were transitions violating the selection rule Arc = ( - 1 ) L.

4. Discussion of the Nuclear Structure Information

In this section, it is assumed explicitly that the reaction mechanism responsible for the observed (t, p) transitions is first-order, two-neutron stripping. 4.1. THE L = 0 TRANSITIONS The Sm(t, p) ground state Q-values are shown in fig. 14 plotted against the mass number of the final nucleus. The flatness of the curve around 152Sm has been noted

162

J . H . BJERREGAARD et al.

previously from analyses of mass data 13) and from an analysis of Sm(d, p) ground state Q-values 11). In a series of isotopes, where no change of nuclear coupling scheme occurs (e.g. the Sn isotopes), the two-neutron separation energies (or equivalently the (t, p) Q-values) decrease monotonically with increasing neutron excess. Therefore, the flatness of the Sm curve probably indicates that additional binding energy is gained around 152Sm by deforming the nuclear surface.

Qo(keV) 7000 \ \ 6000

\

\

\ \

5000

4000

= 1/,,6

i 148

I 150 FINAL

I 152

t 15/,.

I 156

HASS

Fig. 14. The Sin(t, p) Q-values p l o t t e d ag a i ns t the final nucleus mass,

The coupling scheme situation is reflected also in the magnitude of the ground state transition cross sections. Yoshida 14) has shown that with a pure pair-couplingscheme the differential cross section at the first maximum of zero- to zero-quasiparticle transitions is proportional to (A/G) z. Here, A is half the energy gap and G the strength of the pairing force. This rule was derived in the plane-wave Born approximation. For the present purpose the mass dependence of G may be neglected. In fig. 15 the magnitude of A2 as calculated from mass data 16) is indicated by open squares. In the same figure we also show the differential cross sections at the strong 28 ° maximum for the ground state transitions (open circles). The theoretical ground-state cross section increases from A = 144 to A = 150, where a maximum is reached. For the two lightest Sm nuclei the experimental trend agrees with the theoretical trend, but at A --- 150 the experimental cross section comes to a minimum rather than a maximum. This situation is not changed when all the L = 0 transition yields below 2 MeV of excitation are included in the experimental points. The decrease in total L = 0 cross section for 150Sm(t ' p) suggests that the 15OSm ground state and the 152Sm states excited with L = 0 have a "core overlap" less than unity, i.e. a change in the nuclear coupling scheme is indicated.

Sm(t, p) REACTION

163

We now consider in more detail the coupling scheme situation in the various Sm isotopes on the basis of the available data for the low-lying 0 + states. These states are

-

-

-

-

-

Theory

.....

Experiment

1.0

2.0

3

/

\

,

\\ 3. ////'O'-

- - - -'O

l 0]

t 14.4

r 146

i 1~8

~ 150

0

I

152

154

T A R G E T MASS

Fig. 15. The g r o u n d state s u m rule 14). The open squares represent A~n, where d2n is half the energy gap derived as described in the text. The experimental g r o u n d state m a x i m u m cross sections are m a r k e d with open circles. The s u m o f the m a x i m u m cross sections for L = 0 transitions to states below the gap is marked by crosses. The curves are drawn t h r o u g h the points to emphasize the systematic trends, and they have no significance beyond that.

Ex(MeV)

I

O.lO

t 21-

0

0.10 0.1l,

0.02 0.03

0

144

0.29 1/.6

1L,8

0.14

0.1L

0.57 150

0.19 152

0.30 154

0.30 156

MASS NUMBER

Fig. 16. The 0 + states o f the even Sm nuclei. The n u m b e r attached to each state is the m a x i m u m cross section in mb/sr. The 144Sm 0 + states are taken from ref. 18).

schematically represented in fig. 16, the number attached to each level being the maximum cross section observed in the (t, p) reaction leading to the level in question.

164

J.H. BJERREGAARDet

al.

4.1.1. The nuclei 146Sm and 1565m. In the cases of 1465m and 1565m the nuclear coupling schemes are fairly well established as a spherical-pair coupling scheme and an aligned coupling scheme, respectively. The 146Sm state at 2.61 MeV occurs above the energy gap and therefore might be a two-quasi-particle 0 ÷ state. Such states presumably have been observed 17) in 11a Sn(t, p) 12oSn, but with low cross sections ( < 10 9/00of the ground state transition). The relatively large cross section for the 2.61 MeV level in 146Sm thus indicates that this level probably is not of a simple two-quasi-particle structure. In the aligned coupling scheme, the only 0 + state expected to occur below the energy gap is the fl-vibration 15). In a phenomenological description, a fl-vibration is a state with the same equilibrium deformation flo as the ground state, but exhibiting oscillations in fl around the equilibrium value. Thus the fl-vibrational state only spends a fraction of the time with a deformation equal to that of the ground state. In a (t, p) transition where the target has the same flo as the final nucleus ground state, one may thus expect the ground state to be more strongly excited than the fl-vibration. The observations for 156Sm are consistent with such a picture, if we tentatively interpret the 1.07 MeV state as a fl-vibration. 4.1.2. The nuclei 15°Sm, 152Sm, and lS4Sm. The application of the simple models in the transition region 15°Sm, l S2Sm and ~54Sm is a priori less justified than in the cases discussed above. However, it is of interest to investigate where the models fail. From fig. 16 it appears that the presence of three 0 ÷ states below 1.3 MeV of excitation, i.e. below the energy gap, is a common trend for these three nuclei. The low excitation energies of the excited 0 + states suggest that configurations similar to those of the ground states are involved. We first consider the 0.75 MeV 0 + state in ~S°Sm which is situated in the energy region where a two-phonon state is expected. Estimates using a pairing plus P2-force model and utilizing the quasi-boson approximation indicate a cross section for the 0 + two-phonon state of 10-2 to 10-3 times of that of the ground state. This estimate neglects the presence of four-quasi-particle configurations in the nuclear ground state. The observed cross section to the 0.75 MeV 0 + state is 25 % of the ground state cross section, so the simple model discussed above is not valid. If one maintains the twophonon description for the excited state one must accept a four-quasi-particle admixture in the ~4SSm ground state of a strength comparable to the zero quasi-particle part. This, however, is not compatible with the phonon model. Thus the magnitude o f the cross section to the 0.75 MeV state questions its two-phonon character. We next discuss the 0 + states of ~52Sm. Let us for a moment consider tS°Sm(0) to be spherical and 152Sm(0) to be deformed and let us disregard the zero-point vibrations. The large deformation deduced for 152Sm(0) from the observed value o f B(E2; 0 ~ 2) indicates that the "core state" 152Sm(0) minus two neutrons would be deformed too. Hence lS°Sm(0) and 152Sm(0) minus two neutrons would have vanishing overlap and practically all the cross section would go to a spherical 0 ÷ state. Experiment, however, shows that the ground state transition is slightly stronger

Sm(t, p) REACTION

165

than that exciting the 1.09 MeV 0 + state, which has been interpreted as being mainly spherical 3). A more consistent interpretation of the present data is obtained if one takes into account fairly strong zero-point shape oscillations; in 15°Sm(0) around /~o = 0 and in 152Sm(0) around a non-vanishing/~o. In such a picture, there is no longer a sharp distinction between/~-vibration and ground state, these states being strongly admixed; the 1.09 MeV state of 152Sm might still have a very small equilibrium deformation. A similar picture follows for 15°Sm, with the vanishing equilibrium deformation in the ground state, and the finite deformation presumably in the 1.256 MeV state. The recent data 7) on the reaction lS2Sm(p, t)lS°Sm show that all three 0 + states are excited with approximately equal cross section in this reaction, suggesting an interesting analogy between the 0 + states of 15OSm and 152Sm" The two lowest 0 + states in ~54Sm are excited with intensities that are consistent with the assumption of a deformed ground state and a corresponding/~-vibration, cf. the case of 156Sm. From the above picture of 152Sm(0), however, one would expect that only part of the L = 0 cross section is available for these two states. The data, indeed, show the existence of a new 0 + state at 1.218 MeV which has an appreciable cross section. The nature of this state cannot be ascertained, though one might speculate that it originates from the 154Sm ground state configuration but has a Po different from that of the ground state. The closeness in energy of the second and third 0 + states in 154Sm raises the question of mixing between these two states; thus, it is questionable whether the 0 + state at 1.117 MeV can be considered as a pure/~-vibration. In summary it appears that neither of the two extreme models that apply for 146Sm (spherical, pair coupling scheme) and lS6Sm (spheroidal, aligned coupling scheme) can be used to explain the properties of the 0 + states of '5°'152'XS4Sm.

4.2. THE L = 2 TRANSITIONS

For a pure two-quasi-particle state, one expects 14) the cross section to be proportional to Uj1 Uj2 and the cross section should therefore decrease as the shell is filled. The decrease for the first 2 + state in the first half of the shell, however, may be partly compensated by the phonon amplitude of this state, because the phonon matrix clement 14) contains a factor (%1 Vj2 -q- Vj.1 Uj2 ) which is largest in the middle of the shell. In the deformed region the available L = 2 cross section is spread over several states (2 + rotational states, ~-vibrational states and intrinsic excitations); however, a considerable enhancement may be found for the first 2 + rotational level, since this state is built on the pairing-favoured ground state. One might therefore expect the (t, p) cross sections to the first 2 + states in the even Sm isotopes to decrease with increasing neutron number, until the rotational enhancement changes the trend. The maximum cross section for the first 2 ÷ state in 146Sm is 0.28 mb/sr, the largest found for any 2 + state in the Sm nuclei. In 15°Sm the maximum cross section for

166

J.H. BJERREGAARDet al.

the 2 + state decreases to 0.17 m b / s r a n d in lS2Sm it reaches its lowest value, 0.04 mb/sr. I n 154Sm a n d lS6Sm, the 2 + cross sections are close to that o f 15°Sm (0.14 a n d 0.15 mb/sr, respectively). T h u s the observed t r e n d is consistent with the expected trend, a l t h o u g h the m i n i m u m i n 152Sm p r o b a b l y also is connected with the change of e q u i l i b r i u m d e f o r m a t i o n between 15°Sm a n d ~S2Sm. It is a pleasure to t h a n k Professors A. Bohr a n d B. M o t t e l s o n for m a n y illuminating discussions a n d for their s t i m u l a t i n g interest in this work. We are indebted to Dr. S. B j o r n h o l m a n d to Mrs. C o n n i e Olsen for help in p r e p a r i n g the targets. The nuclear track plates were meticulously scanned by Miss N o r m a H y n n e , Miss Sara L i n d s t r 6 m , Miss Mette Nevald, Mrs. K i r s t e n Skau, Mrs. Sus V i l m a n a n d Miss Vibeke Osterberg.

References 1) R. Middleton and D. J. Pullen, Nuclear Physics 51 (1964) 50, 63, 77; S. Hinds and. R. Middleton, Proc. Paris Conf., Vol. II; (1964) p. 463 Nuclear Physics 67 (1965) 257 2) J. Rook and D. Mitra, Nuclear Physics 51 (1964) 96 3) S. Hinds, J. H. Bjerregaard, O. Hansen and O. Nathan, Phys. Lett. 14 (1965) 48 4) L. Westgaard and S. Bjornholm, Nucl. Instr. 42 (1966) 77 5) R. Middleton and S. Hinds, Nuclear Physics 34 (1962) 404 6) M. P. Avotina et al., Phys. Lett. 19 (1965) 310 7) J. R. Maxwell, G. M. Reynolds and N. H. Hintz, Phys. Rev., to be published 8) Nuclear Data Sheets, issued by Nuclear Data Group, National Research Council, USA 9) M. Guttman, E. G. Funk and V. J. W. Mihelich, Nuclear Physics 64 (1965) 401 10) B. Elbek and E. Veje, private communication (1965) 11) R. A. Kenefick and R. K. Sheline, Phys. Rev. 135 (1964) B939, 133 (1964) B25, 139 (1965) B1479; M. N. Vergnes and R. K. Sheline, ibid. 132 (1963) 1736 12) J. S. Greenberg et al., Phys. Rev. Lett. 11 (1963) 211 13) R. C. Barber et al., Phys. Rev. Lett. 12 (1964) 597 14) S. Yoshida, Nuclear Physics 33 (1962) 685 15) A. Bohr and B. R. Mottelson, Nuclear structure and energy spectra, to be published 16) J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nuclear Physics 67 (1965) 1 17) S. Hinds, J. H. Bjerregaard, O. Hansen and O. Nathan, to be published 18) P. R. Christensen and F. Yang, Nuclear Physics 72 (1965) 65 19) Y. Yoshizawa, B. Elbek, B. Herskind and M. C. Olesen, Nuclear Physics 73 (1965) 273