Energy levels of 38Ca from the reaction 40Ca(p,t)38Ca

Volume 23, number 8

P HY SI C S L E T T E R S

duced by this p r o c e d u r e we have p e r f o r m e d spin 1 c a l c u l a t i o n s (no s e a r c h : ) using the spin ½ b e s t fit p a r a m e t e r s . F o r a n g l e s l a r g e r than 60 ° we found s m a l l d i s c r e p a n c i e s ( l e s s than 20%). The spin 1 d i f f e r e n t i a l c r o s s s e c t i o n is usually s o m e what s m a l l e r . This m ig h t be c o m p e n s a t e d by using a v al u e of W, 5% s m a l l e r than stated. F u r t h e r m o r e the spin 1 an g u la r d i s t r i b u t i o n s show l e s s s t r u c t u r e at l a r g e a n g l e s c o m p a r e d with the spin ½ r e s u l t s , a f e a t u r e which is f a v o u r e d by e x periment. The v a l u e of r ' is s m a l l c o m p a r e d with the l o w e r e n e r g y r e s u l t s . This m a y indicate that absorptive processes, especially deuteron break-up, a r e taking p l a c e n e a r e r to the n u c l e a r s u r f a c e at h i g h e r energy. As to the value of V, the i n c r e a s e with i n c r e a s ing m a s s n u m b e r is roughly u n d e r s t o o d as a cons e q u e n c e of n u c l e a r and d e u t e r o n s i z e s , if one n u m e r i c a l l y c a l c u l a t e s [6]

Vd(rd) = (×d [Vn(rn) + Vp(rp) IXd), which means an averaging of the real parts of neutron plus proton optical potentials over the internal wave function Xd (Hulth~n function) of the deuteron.

ENERGY

LEVELS

OF

38Ca

FROM

21 November 1966

The g e o m e t r i c a l p a r a m e t e r s r ' , a and a' diff e r f r o m t h e i r m e a n v a l u e s a v e r a g e d o v e r all t a r g e t nuclei by l e s s than 12%. But they a r e much b e t t e r defined. In a s e a r c h with t h e s e p a r a m e t e r s fixed to the a v e r a g e v a l u e s one g e t s fits with a ×2 about t w i ce as l a r g e . As a r e s u l t we find that the optical model is well able to d e s c r i b e the e l a s t i c s c a t t e r i n g of 52 MeV d e u t e r o n s if one includes a s p i n - o r b i t t e r m . The a u t h o r s a r e indebted to Dr. E. H. A u e r b a c h f o r making a v a i l a b l e the ABACUS code. We app r e c i a t e many helpful d i s c u s s i o n s with P r o f . G. R a w i t s c h e r . We a l s o wish to acknowledge Dr. G. Schatz and the K a r l s r u h e c y c l o t r o n c r e w for t h e i r cooperation. 1. c.M. Perey and F.G. Perey, submitted to Phys. Rev. (1966) 2. L.C.Becker, J . C . H e i b e r t and E.Newman, Bull. Am. Phys. Soc. 11 (1966) 44. 3. B.Duelli, G. Mairle, U.Schmidt-Rohr, P.Turek and G. Wagner, Z. Naturforsch. 21a (1966) 969. 4. F.G. Perey, Intern. Conf. on Polarization phenomena, Karlsruhe (1965). 5. B. Duelli, F. Hinterberger, G. Mairle, U. SchmidtRohr, P. Turek and G. Wagner, Intern. Conf. on Nuclear Physics, Gatlinburg(1966). 6. G.R.Satchler, Nucl. Phys.85 (1966) 273.

THE

REACTION

40Ca(p,t)38Ca

J. C. HARDY*, D . J . SKYRME and I. S. TOWNER Nuclear Physics Laboratory, Oxford Received 24 October 1966

From the reaction 40Ca(p,t)38Ca, energy levels in 38Ca have been observed, and spins and parities assigned. The results are discussed with reference to configuration mixing in the 40Ca ground state and shell model calculations for 38Ca.

Two c o m p l e m e n t a r y s h e l l - m o d e l c a l c u l a t i o n s a r e c u r r e n t l y a v a i l a b l e f o r T = 1 l e v e l s in nuclei with A = 38. The c a l c u l a t i o n s by G l a u d e m a n s et al. [1] c o n s i d e r an i n e r t 288i c o r e with the additional nucleons in (2s½)m(ld~)10 - m c o n f i g u r a t i o n s , while those of E r n d [2] u t i l i z e a 32S c o r e , the additional nucleons being in the c o n f i g u r a t i o n (lf½)l(ld~) 5. E x p e r i m e n t a l l y , i n v e s t i g a t i o n of * National Research Council (Canada) Post Doctorate Overseas Fellow.

t h e s e l e v e l s has been e n t i r e l y r e s t r i c t e d to r e a c tions leading to 3BAr (T z = +1) [3-7] and those p r o d u ci n g T = 1 l e v e l s in 38K (T z = 0) (e.g. ref. 8). The e x c i t a t i o n e n e r g i e s of t h o se l e v e l s whose spins and p a r i t i e s a r e known have b e e n c o m p a r e d with the c a l c u l a t i o n s , and quite adequate a g r e e m e n t was found [1, 2]. H o w e v e r , no e x p e r i m e n t a l i n v e s t i g a t i o n has p r o b e d the actual c o n f i g u r a t i o n of the l e v e l s involved, and a m o r e c o m p l e t e c o m p a r i s o n could not be made. This l e t t e r r e p o r t s an i n v e s t i g a t i o n of the r e 487

Volume 23, number 8

Ul I.-Z :3

PHYSICS

GROUND

STATE

LETTERS

E

2.0

21 November 1966

E

= 2.20 M e V L=2 (2d 2)

0J

: 3.72 MeV L: 3 (Id l f )

I I

c:l

1.0

0.1

"o

|

30

SO

;o

70

~m

;o

,o

- DEGREES

~Co (p.t)~Ca

.

.

.

= 4.36 L= 0 --.-- L : 0

o.~

Ep= 3 9 . 8

.

E

.

MeV ( l d z) ( l s 2)

MeV

elo b = 2 5 ° o

o

0

I--Z

u

u

p8

-*

I

E

tQ.

30

m

tn

.

o

N ,,4

•

..t ..t rg

~ ~

I

L

(L=2

0.4

0 U

I

I

= 4.84. MeV

?)

d

..°

20

I

10

0°1

1~.

" ~'-_,

CHANNEL NUMBER

,

,

i

T.

.i

Octn - DEGREES

Fig. 1. Angular distributions of t r i t o n groups from the reaction 40Ca(p,t)38Ca and a s p e c t r u m recorded at Olab= 250. The DWBA curves were computed using the following p a r a m e t e r s :

Tritons Protons

U

WV

(MeV)

(MeV)

(fro)

a

(fm)

~'o

129.2 50.0

53.2 12.0

0.64 0.65

1.40 1.25

The diagram shows it is quite possible that the angular distribution for the 4.36 MeV level contains a contribution f r o m the expected 5- level which would be unresolved.

action 40Ca(p, t)38Ca. In addition to the energies of levels in 38Ca (Tz = -I), a study of this reaction does provide information concerning their configurations, and comparison with shell-model calculations will reveal a number of discrepancies. The only previously published report involving 38Ca concerned the ~+ decay of its ground state and no mass was determined[9] . Natural calcium (97% 40Ca) targets were bombarded by 39.8 MeV protons from the Proton Linear Accelerator at the Rutherford Laboratory, and emitted particles were detected and identified by means of a semi-conductor counter telescope 488

whose dE and E pulses were fed separately into a m a s s a n a l y z e r [10]. T h e t o t a l - e n e r g y p u l s e s ( d E + E) c o r r e s p o n d i n g t o t r i t o n s w e r e t h e n r o u t e d i n t o o n e 5 1 2 - c h a n n e l g r o u p of a p u l s e - h e i g h t a n a l y z e r . S u c h a s p e c t r u m , r e c o r d e d a t 25 °, i s s h o w n i n fig. 1; t h e e n e r g y r e s o l u t i o n i s a b o u t 230 k e V . The reaction Q value was determined by measuring the energy difference between the 38Ca and 140 ground-state peaks under the following condit i o n s : 1) t a r g e t a n g l e 6 t = 0 °, c o u n t e r t e l e s c o p e a n g l e Oct = +25o; 2) e t = 180 o, 6ct = +25o; 3) Ot = 180 °, e c t = - 2 5 o. W i t h t h e s e t h r e e m e a s u r e m e n t s

Volume 23, number 8

PHYSICS L E T T E R S

21 November 1966

(% )±___ 5.6"i

Q°

I rnony levels

5.67

4.78

4.Q~

'~-

""-.4.12

4-

~.82 a.?4 2"

(s~/'(d~P--- 4,38

-~.62 3.,,

~

z"

(2°)

4.36

, o* 3~K+ p

3.72

~-

2.20

2"

o* - - -(fT/29(d%~ ~ _

2.54

2.17

4.84.

4,54

2"

T...>(fTn) (da~)'-....

r ....

3.38

2-

" ~ "- .~.. 1.96

. . . . . . .

2%."

2"

..--(d312 ~-.,- " I

" ~--.

O"

__{ds/2)----

38

38

,,Ar2o EXPERIMENT

ERN#

GLAUDEMANS ET AL

2oC o,s TH'S EXPERIMENT

Fig. 2. T = 1 levels forA = 38: 1) experimental results for 38Ar [3-7]; 2) calculations by Erne [2] and Glaudemans et al. [1], including predominant configurations; 3) levels in 38Ca determined from the present results. it was p o s s i b l e to take account of the unequal oxidation of the s u r f a c e s of the t a r g e t , and of any slight deviation of the b e a m f r o m a c e n t r a l p o s i tion. Energy c a l i b r a t i o n was obtained f r o m the 160(p, t)140 and 12C(p, t)10C r e a c t i o n s . The value obtained for the 40Ca(p, t)38Ca Q value is -20.459 + 0.025 MeV, all c a l c u l a t i o n s being made using the 1964 M a s s Table [11]. The c o r r e s p o n d i n g 38Ca m a s s excess and the energy of the four obs e r v e d excited s t a t e s a r e shown in table 1. A n g u l a r d i s t r i b u t i o n s of the t r i t o n groups a r e also contained in fig. 1. The c u r v e s shown in the figure were computed u s i n g a p r o g r a m coded by Yates and b a s e d upon the z e r o - r a n g e DWBA theory f o r m u l a t e d by Rook and M i t r a [12]. S i m i l a r c a l c u l a t i o n s for 40Ca(t, p)42Ca have b e e n shown [13] to account v e r y s u c c e s s f u l l y for the o b s e r v e d a n g u l a r d i s t r i b u t i o n s using p a r a m e t e r s d e t e r m i n e d f r o m the e l a s t i c s c a t t e r i n g of 12 MeV t r i tons on 40Ca [14]. These s a m e p a r a m e t e r s were used in the computations for fig. 1. Although the

Table 1 Observed states from 40Ca(p, t)38Ca. Ex(38Ca) (MeV)

Mass excess of 38Ca (keV)

0 2.20±0.03 3.72 4-0.03 4.364- 0.04 4.84 4-0.04

-22 0504- 25

L

Jff

0 2 3 0 (2)

0+ 2+ 30+ (24-)

emitted t r i t o n s in the p r e s e n t e x p e r i m e n t a r e somewhat m o r e energetic (14-19 MeV), no other p a r a m e t e r s a r e available, and a r b i t r a r y v a r i a tion of these p a r a m e t e r s , though p o s s i b l y i m proving the fits, can hardly i n c r e a s e t h e i r c r e d i bility. It may be noted, however, that a r e d u c tion in Wv to about 35 MeV c o n s i d e r a b l y i n c r e a s e s the detailed a g r e e m e n t . The L values giving b e s t fit to the data a r e shown in the figure and again in table 1. 489

Volume 23, n u m b e r 8

PHYSICS

LETTERS

1) t h e a n a l o g u e s of t h e l e v e l s a t 3.38 M e V (0 +) a n d 3.94 M e V (2 +) i n 3BAr w e r e not o b s e r v e d ( m a x i m u m c r o s s s e c t i o n s < 0.08); 2) t h e 3 - l e v e l a t 3.72 M e V w a s p r o d u c e d w i t h c o n s i d e r a b l y g r e a t e r s t r e n g t h t h a n t h e DWBA calculations predict; 3) a l e v e l w a s o b s e r v e d a t 4.84 M e V i n 3 8 C a , w i t h a t e n t a t i v e a s s i g n m e n t of 2 +. Result 2 is interesting in that it is not possible to construct shell-model admixtures for the g r o u n d s t a t e of 4 0 C a , w h i c h c o u l d e x p l a i n t h i s e n h a n c e m e n t in t h e s t r e n g t h of t h e 3 - l e v e l , w i t h out p r e d i c t i n g at t h e s a m e t i m e a s i m i l a r e n h a n c e m e n t of t h e 0 + l e v e l c a l c u l a t e d to b e a t 3.6 MeV. T h u s , t h e n o n - a p p e a r a n c e of a 0 + l e v e l at 3.4 MeV (result i) must be taken a s an indication of significant deviations from the assumed simple shell-model configurations for 38Ca. Similarly, an assignment of 2+ to the 4.84 MeV level would show the existence of t h r e e 2+ levels below 5 MeV, a situation also at v a r i a n c e with the calculations.

Table 2 Comparison of predicted and observed maximum St c r o s s sections. Predicted

Observed

Relative c r o s s s e c States in 38Ca tions assuming for " ~o+(40Ca g.s.)* JY, Configuration 13=0 ~=~t or=-0

Maxim u m ~ $ j~r cross section

0+ (d~)-2

1.95:~ 1.95~ 1.95~

1.95

0+

2+ (d~)-2

2.3

0.5

0

0.6

2+

3-

(f~)l(d3)-3

0

0.1

0.3

0.4

3-

0+ (f~)2(d~)-4

0

0.2

0.7 0.2

0+

0+

1.4

0.3

0

10.5

2.3

0

0.3

(2 +)

(s½) -2

2+ (s~)-l(d2~)-1

* See text for definition of symbols. Normalized. $$ F o r L = 0, the c r o s s section at the "second m a x i mum" is given.

W e a r e g r a t e f u l to M r . M. J. L. Y a t e s f o r t h e u s e of h i s c o m p u t e r p r o g r a m , a n d to M r . P. F. B a m p t o n a n d H. M a r c h a n t f o r t h e i r h e l p i n p r o cessing the computations. We also thank Dr. F. C. E r n 6 f o r c o m m u n i c a t i n g h i s r e s u l t s p r i o r to p u b l i c a t i o n , a n d D r . A. D. W. J o n e s f o r s e v e r a l helpful discussions.

Fig. 2 shows the energy level diagram for 3 8 C a a s d e t e r m i n e d f r o m t h i s e x p e r i m e n t and, f o r c o m p a r i s o n , t h e l e v e l s o b s e r v e d in 3 8 A t . Also included are the levels calculated in refs. 1 a n d 2, w i t h t h e i r p r e d o m i n a n t c o n f i g u r a t i o n s . If t h e g r o u n d s t a t e of 4 0 C a w e r e , i n f a c t , c o m p l e t e ly d e s c r i b e d by a c l o s e d (s, d) s h e l l , t h e n only those natural-parity hole states that appear in t h e c a l c u l a t i o n s of G l a u d e m a n s s h o u l d b e p r o d u c e d b y (p, t) p i c k - u p . T h e r e l a t i v e l y s t r o n g p r o d u c t i o n of t h e 3 - s t a t e , t h e n , m a y b e t a k e n a s c o n f i r m a t i o n of s i g n i f i c a n t a d m i x t u r e s in t h e 4 0 C a ground state, a fact already noted by several a u t h o r s (e.g. r e f . 15). It i s i n s t r u c t i v e to c a l c u l a t e t h e e x p e c t e d r e l a tive cross sections assuming simplest configurat i o n s f o r s t a t e s in 3 8 C a , w h i l e t a k i n g f o r t h e g r o u n d s t a t e of 4 0 C a :

References 1. P . W . M . Glaudemans, G. Wiechers and P . J . B r u s saard, Nuel. Phys. 56 (1964) 529 and 548. 2. F . C . E r n d , Nucl. Phys. 84 (1966) 91. 3. P . M . E n d t and C . V a n d e r Leun, Nucl. P h y s . 3 4 (1962) I. 4. I.J.Taylor, Nuel. Phys.41 (1963) 227. 5. W.R. Phillips, Nucl. Phys. 60 (1964) 544. 6. R.G.Allas et al., Nucl. Phys.61 (1965) 289. 7. F.C.Ernd, W. Veltman and J.Wintermans, to be published in Nucl. Phys. 8. J.J$/necke, Nucl. Phys. 48 (1963) 129. 9. J.E.Cline and P.R.Chagnon, Phys.Rev. 108 (1957) 1495. 10. P. S. Fisher and D. K. Scott, PLA Progress Report 1964, Rutherford L a b o r a t o r y Report (NIRL/R/81) p. 90, and to be published. 11. J. H. E. Mattauch, W. Thiele and A. K. Wapstra, Nucl. Phys. 67 (1965) 1. 12. J . R . R o o k and D. Mitra, Nucl. Phys. 51 (1964) 96. 13. R. N. Glover and A. D. W. Jones, Nucl. Phys. 81 (1966) 277. 14. R. N. Glover and A. D.W. Jones, Nucl. Phys. 81 (1966) 268. 15. R. Bock, H.H. Duhm and R. Stock, Phys. L e t t e r s 18 (1965) 61.

~o + (40Ca g.s.) = ~@ ( c l o s e d s h e l l ) + / 3 ~ ( f ~ d ~ 2 ) v + . . . T h e r e s u l t s a r e s h o w n in t a b l e 2 f o r t h r e e c h o i c e s of or,/3. It s h o u l d b e e m p h a s i z e d t h a t t h e s e m a y only b e u s e d a s a r o u g h g u i d e : t h e r e l a t i v e c r o s s s e c t i o n s a r e q u i t e s e n s i t i v e t o t h e c h o i c e of p a r a m e t e r s a n d a r e c e r t a i n l y not r e l i a b l e t o b e t t e r t h a n a f a c t o r of 2. T h e b e s t o v e r a l l a g r e e m e n t i s o b t a i n e d w h e n ot ~ /3, a r e s u l t q u a l i t a t i v e l y s i m i l a r to t h a t of r e f . 15. T h e m o s t s i g n i f i c a n t f e a t u r e s of t h i s e x p e r i ment are that: *

490

21 November 1966

*

$

*

*