IL NUOVO CIMENTO VOL. 40 A, 1~. 3 1 Agosto 1977

Study of Some ~60 States at High Excitation Energy (*).

A. 0UNSOLO, A. l~OTI, G. PAPPALARDO and G. RACTTI

Is t i tu to Naz ionale di F i s i ca .Nucleate - Sezione di Catania Centro S ic i l iano di F i s i ca lVucleare e di S tru t tura della Mater ia - Catania (**) Is t i tu to di F i s i ca dell' Universit& - Corso I ta l ia , 57, Catania, I ta l ia

1~. SAUI~IEI~ and E. :F. DA SILVEIRA (***)

D~partment de Phys ique Nucl~aire - C E N Saclay, B . P . 2 91190, Gi]-sur-Yvette , France

(ricevuto il 14 Matzo 1977)

Summary. - - The particle-particle angular-correlation method is applied to the reaction 12C(6Li, d)leO-->or Deuterons were detected at O 1 = 0% Spin and parity of some highly excited 160 states are deduced. Analysis of the correlation patterns indicates that a direct transfer is a dominant mechanism. The angular correlation corresponding to the leO21.s-+~+~2C4.43 is specially analysed and interference effects due to the different 1 values involved in the decay are discussed.

1. - Introduction.

The knowledge of spins, parities and decay properties of the highly excited (20 MeV or more) collective :c-like-particle 160 states, strongly populated in

:c-particle transfer reactions or in (~, :c), (~, :c') elastic and inelastic processes,

is of importance in unders tanding the structure of the 160 nucleus; in fact, in

this energy region (1-~) highest-spin members of the posit ive-pari ty rotat ional

band (K-----0 +) based on the 0+-state at 6.052 MeV and of the negative-

(*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction. (**) According to the contract BT-II/12.766 between the CEN-Saclay and the CSFN/SM-Catania. (***) On leave from Pontificia Universidade Cat61ica do Rio de Janeiro, Brazil: (1) J. K]~LSON: Phys . ~ett . , 16, 143 (1965). (2) A. P. ZUK]~R, B. BUCK and J. M. Mc GRonY: Phys . l~ev. Left. , 21, 39 (1968). (a) V.Z. GOLDBERG, V. P. RUDAKOV and V. A. TIMOFEEV: ]~ad. F iz . , 19, 503 (1974).

293

2~4 A. CUNSOLO, A. FOTI, O. PAPPALARDO, G. RACITI, N. 8AUNIER, :ETC.

partly rotational band (K- ---- 0-) based on the 1--state at 9.6 MeV are ex- pected to lie. The many-particle nature of these bands has been well estab- lished by considerations based on the selectivity of the a-particle transfer reac- tions (4), on theoretical calculations (1.3) and on the analysis of the ~-particle reduced widths (5.6).

I t would be also interesting to investigate about the existence and the properties of the 160 states arising from the coupling of the ~6Ne rotational states with the 2+-state at 4.43 MeV of 1~C, as predicted in the framework of the weak-coupling model (3.7); note that these states are expected to decay preferentially to the first excited state of 12C. One candidate would be (7.8) the 11.09 MeV, 4+-state, having a [2 + | 2 +] structure; no evident indications have been found so far for 160 states with excitation energies around 15 MeV and 20 MeV, having, respectively, a [2 + | 4 +] or a [2 + | 6 +] character.

Thus, in order to have new information on the 160 states in the excitation energy range (16--25)MeV, we performed

i) measurements of the energy spectra of deuterons emitted at forward angles in the 12C(eLi, d)~eO reaction at E.~ ~ 34 MeV,

ii) measurements of the d-a angular correlations between the primary deuterons and the decaying a-particles.

In the angular-correlation experiments, the deuterons were detected at 01 ~ 0 ~ with respect to the incoming-beam direction. We chose this geometry because very simple angular-correlation patterns are expected in the case of direct-transfer process.

In the present work, sect. 2 will refer to the experimental apparatus and results, sect. 3 will be devoted to the analysis of the data with particular emphasis on the particle-particle angular-correlation method.

Effects on the shape of the correlation function due to the decay mecha- nism parameters will be treated in the appendix.

2. - Experimental procedures and results.

2"1. Deuteron energy spectra. - A eli+++ beam of 34 MeV was produced by the FN tandem VdG of CE~-Saclay; targets were self-supporting natural-12C

(4) K . P . ARTEMOV, V. Z. GOLDBERG, I. P. PETROV, V. P. RUDAKOV, I. N. SERIKOV and V. A. TI~Ol~E:Ev: Phys. Lett., 37B, 61 (1971). (5) A. ARI~A and S. YOSI~IDA: Nucl. Phys., 219 A, 475 (1974). (6) M. ICHIMURA, A. ARIMA, E. C. HALBERT and T. T:ERASAWA: ~Vucl. Phys., 204 A, 225 (1973). (~) A. ARIMA, H. HORIVCHI and T. SEBE: Phys. Lett., 24B, 129 (1967). (s) P . T . D~BEVEC, H. T. FORTUNE, R. E. SEGEL and J. F. To~N: Phys. t~ev. C, 9, 2451 (1974).

STUDY OF SOME 160 STATES AT HIGH EXCITATION ~NERGY 9-95

[ I I I ) 1 t I I I

+ co

I

i

co

~ c,J

i i 1

:3

8

+ Lo

uo

i 0 = 5 ~

Lab

= 7 ~

= 9 . 5 ~

= 1 1 ~

[ I., I l l I I I I 1 ! l I - I~"'i] 2/) ;)2 20 18 16 1L+ 12

IB 0 Eexc (MeV)

Fig. 1 . - Deuteron energy spectra from the 12C(6Li, d)160 reaction (E,LL= 34MeV) compared at the same 160 excitation energy scale for different angles. The data are shown normalized to the same area.

2 9 6 A. CUNSOLO, A. FOTI, G. PAPPALARDO, G. RACITI, .N. SAUNIER, E T C .

foils w i t h a t h i c k n e s s of 50 to 150 [zg/cm2; d e u t e r o n ene rgy s p e c t r a were meas -

u r e d f rom Oi, b = 4 ~ to O~, b = 25 ~ in s t eps of a b o u t 1 ~ us ing a t r i p l e AE1AE2 E t e l e scope of Si de t ec to r s . T h e ove ra l l e n e r g y r e s o l u t i o n was a b o u t 100 keV.

F i g u r e 1 shows t h e d e u t e r o n e n e r g y s p e c t r a r e c o r d e d a t 5~ 7 ~ 9.5 ~ a n d 11 ~

a n d d i s p l a y e d in t h e 160 e x c i t a t i m l e n e r g y scale. F o u r p r o m i l m n t p e a k s a re

e v i d e n t a t 16.30 MeV, 20.9 MeV, 21.8 MeV a n d 23.4 MeV.

foccLI, surfcLce

target

to spectrometer

Fig. 2. - Exper imenta l appara tus used for tlw deuteron-a-par t ic le correlation s tudy: a) vert ical section, b) horizontal scction.

S T U D I ~ OF SOME 180 STATES AT HIGI I E.~CITATION ENERGY 2 ~ 7

The 16.30 MeV s ta te is the k n o w n 6 + m e m b e r of the K-~ ---- 0 + ro ta t iona l

b a n d (4.5.9). The spin and p a r i t y of the 20.9 MeV 7- - s t a t e have beeu ussigned (4)

in ~n an~,~ular-correlatioa e xpe r i m e n t ; these results and its ~-decay reduced

wid ths (~,6) suggest t h a t this level is a m e m b e r of the K~ ~ 0 - ro t a t iona l band.

The 21.8 MeV level r epor t ed here was also observed (~o) in a recent 38 MeV

(~Li, t) expe r imen t al~d it p r o b a b l y corresponds to the s t ruc tu re a t 22.1 MeV

observed ia a 36.5 MeV (6Li, d) expe r imen t (11).

The 23.4 MeV s t ruc tu re has beclt observed ia a (TLi, t) expe r imen t (~o)

a t E* ~ 23.2 MeV a nd more recent ly a t E* - - 23.6 MeV in ~ 40 MeV (6Li, d)

expe r imen t (~2).

2"2. Deuteron-c<-particle angular-correlation experiments. - The deuterons

were de tec ted ut O~ ---- (0 • 2) dega'ees by us ing a B r o w a - B u e e h u e r magne t i c

60

50

4o

30

8 20

10

~ r = 2 O n s

. . .

P �9 Ill I . . . .

100 200 300 400 500 r(ns)

1 n 6 16 ~ ig . 3. - T y p i c a l t i m e spec t rum for the d-~ coincidences, for the reac t ion "C( L i , d) Oeo.9 --~ - * ~ ~-12C~, w i t h O~ ..... ~- 104.5 ~

(9) G. BASSA.~I, G. PAPPALARDO, •. SAt;_~n:~ and B. M. TRAOR~': Phys. Left., 34 B, 612 (1971). (lo) 3[. E. COBERX, D. J. PI~Axo a11d P. D. PAI{K~R: Phys. Rev. C, 14, 491 (1976). (al) A. A. 0GLOBI.IN :iH Nuclear Reaclio~t. lnduced by Heavy Ions, Proceedings o/the In- ternational Con]erenee o] Heidelberg, 1969, edited by R. Boc~ and W. R. I IEmxo (Am- sterdam, 1970), p. 231. (~-) R. 1). A. ARTEMOu V. Z. GOLDBERG, 1. ~P. P~TROV, V. I ). ]{UDAKOV, I. N. SERIKOV and V. A. TIMOFEEV: Yad. Fiz., 23, 489 (1976).

2 9 8 A. CUNSOLO, A. FOTI, O. I~APPALARDO, G. RACITI, N. SAUNIER, ETC.

80C

60C . . j

{::

g 40 r o "d

20

30

2O

o .c o (J

10

a)

I I I , I ,

20 100

b)

./ 0 0 O

~ 0 �9 �9

o t I 4

~..~.........~euterons

180 260 340 channels

a, 1

. . .

�9 �9 O t O 0 0 0

! ! ! 6 8

a-part icle energy (MeV)

0 0 0 0 I

10

, I 420

Fig. 4. - Curve a) energy spectrum from the PSD 1 detector (the continuous back- ground is a t t r ibuted to the diffused eLi ions); curve b) coincidence a-particle energy spectrum for the l~C(eLi, d)16021.8-->:r reaction at O=lab-----96.7 ~ (spurious coinci- dences have been substracted).

STUDY OF SOME 160 STATES AT HIGH EXCITATION ENERGY 2 9 9

spec t rometer equipped with a (50 X 14) m m ~ posit ion-sensit ive detec tor (PSD 1)

in its focal plane. The effective thickness of the PSD 1 was 1070 ~m and its surface was

pro tec ted b y a gold screen of 170 m g / c m ~ effective thickness, to p reven t damages

f rom direct Li beam. The solid angle subtended b y the spec t rometer was /2 ---- 4.5 -10 -4 sr.

0.2

o 0.1

30 60 90 120 ~(olegrees)

Fig. 5. - d-a angular correlation from the Is0 16.3 MeV state for decay to the g.s. of 1~C, E%i= 25 MeV, O d = 0~ the theoretical curve W(D1, D~) is a calculation with eq. (6) for 121------ (Od= O, ~Od= 0), t2~--~ (0~, ~0~ ~).

Coincident ~-particles were detected b y a second PSD 2, 300 [~m thick, placed in the scat ter ing chamber a t 80 m m f rom the t a rge t ; a grid of 13 slits (2 • 12) m m ~ wide and 1 m m spaced was placed in f ront of the PSD 2 detector. The thickness of the 12C ta rge t was (308 =L 20) ~g/em ~ or (155 i 20) Fg/cm ~ depending on the i i tvest igated level. The geometr ical a r rangement is shown in fig. 2.

A t ime compensat ion m e t hod was used in order to el iminate the fluctua-

t ions of the pulse rise t ime (18). The e lementa ry informat ion corresponding

to t ime, energies and posit ions was stored for off-fine analysis.

Al though the overall t ime resolution was 40 ns, i t could be reduced to (15--25) ns, when a single slit was selected (as shown in fig. 3). F igure 4a)

shows the energy spec t rum of particles reaching the PSD 1; only the deu-

(13) j . p. FOUAN and J. P. PASSERIEUX: Natl . Inst . Meth., 62, 327 (1968).

3 0 0 A. CUNSOLO, A. FOTI, G. PAPPALARDO, G. RACITI, N. SAUNI~R, :ETC.

terons have been accomlted for successive processing. Figure 4b) shows a typical m-particle coincident er~ergy spectrum. An angula.r corrol&tion ranging from O=,,b : 35 ~ to :100 ~ in steps of about 2 ~ was obtained in three runs.

0.3

0 . 2 - - t

o t ~

! i i i

0.1 ~ ' ,

' ',

o 30 60 90

e (cLegrees)

;i i a

ilt I

120

0.3

0.2 t c o

li

o v

0.1

F i g . 6 . - T h i s f i gu re is a s fig. 5, b u t fo r i h e 1~O 20.9 M c V s t a t e , E , L ~ : 3 2 McV, O n = 0 ~

t h e o b t a i n e d Z 2 w~lucs a r c Ze(7 - ) : 19.8, Z2(9 ' ) : 26.1. I ' = 7 - , . . . . . 2 ' : 9 - .

To test exper imental arrangement , we have preliminarily performed angular- correlation measurements of a-particles emi t ted from the known 16.30 MeV 6+-state and corresponding to the decay towards the ]2C,,; the results are shown

in fig. 5 together with the DWBA theoretical prediction (see subsect. 3"1). Our exper iment agrees with the 64 spin and par i ty assignment for this

state. Figures 6, 7 and 11 show the experimental results, normalized to the theoret ical curves, relative to the m-decay from the 20.9 MeV and 21.8 MeV levels; the errors on the exper imental points are the statistical ones.

:Note (fig. 4b)) the impor tant de-excitation of the 21.8 MeV 160 level towards

the (2 +) 4.43 MeV 1~C state.

STUDY OF SOME 160 STAT~8 AT t I I G I I EXCITATION ENERGY S 0 1

I n all cases, the scat ter ing angle O1 = Od is given in the centre-of-mass

f rame of the to ta l sys tem, ~vhile the angle O~ = O~ of the ~-partiele emi t t ed in the disintegrat ion process is defined in the recoil nucleus centre-of-mass frame. They are bo th defined with respect to the b e a m direction.

0.3

o

0.2

0.1

30 V V

60 90 120 e (cLegrees)

Fig. 7. -- This figure is anah)gous with fig. 5, but for the 160 21.8 MeV state, E,LI == 34 ~IeV, O d ~ 0%

3. - Analys is o f the data.

The general theory of angular correlations (1~) has been main ly applied to y-y r~y exper iments and more recent ly to part icle-y exper iments (15).

(1~) S. DEVONS and L. J. B. GOLDFARB: Handbuch der .Physics, edited by S. FLfiG~E, Vol. 42 (Berlin, 1957), p. 362. (15) F. RYBICKI, T. TAM~r~A and G. R. SATCtIL:ER: .LV~/~I. Phys., 146A, 659 (1970).

20 - I I N u o v o G i m e n t o A .

302 A. CIYNSOLO, A. FOTI, G. PAPPALARDO, G. RACITI , 1~. SAUNIER, :ETC.

Particle-particle angular-correlation measurements, which h~ve been used initially for spin assignments (1~), have been extended in the last few years to nuclear properties and reaction mechanism studies (~7,18).

In the present analysis, no interference is assumed between the ejectile a' and the disintegration fragments of the recoil nucleus A ' (see fig. 8 for defini- tions). Therefore, the formalism described in ref. (~8) can be used and the correlation function W ( ~ , Q~) corresponding to the detection of the ejectile ~t Q~(O~---- 0, ~ ~ 0), is writ ten as

~ I w 2 (x) w(o, oc 2 2 ,

r tr~lm

where m~,, m~., m~. are, respectively, the mangetic substates of the recoil nucleus and of the disintegration fragments.

A(c~, cd) 4r(cW)A II

i a ~

! A

J

]?

St f?

CJ

L~ srt ]7I ~??

! t t _ _ Art

Fig. 8. - Scheme of the studied reaction with the notation used in the present work.

As is well known (19), in cases in which the sum of the spins I ~ - i - ~ i' does not exceed �89 the angular correlation depends only upon the properties of the states in the residual nucleus. If I + i ~ - i ' > �89 the population of the magnetic substates P~,,(0) depends on the primary process and can be evaluated (is) for different reaction mechanisms.

The disintegration amplitude J -~ : e(f22) describes the de-excitation process of the recoil nucleus having a definite spin I ' to two other nuclei with spin i"

(16) j , A . KUEHN:ER: Phys. •ev., 125, 1650 (1962). (17) A. STRAZZ~I~I: Nuovo Cimento, 34A, 229 (1976). (18) E. F. Dlk SILYEIRA: contribution to the X I V Meeting on Nuclear Physics, Bormio, January 18-24, 1976. (19) A. E. LIT~_ER~.AND and A. J. F~Gvsso~: Can. Journ. Phys., 39, 788(1961).

S T U D Y O F S O M E 1 6 0 S T A T E S A T n I G H : E X C I T A T I O N E N E R G Y

and I", and can be expanded, in the channel spin representation, as

(2)

303

m~srni.kw~2] $"~$s ~"m/s

( F i '~ ml" mi,, Is" m~.)"

�9 (l" s" ms. m~. [I' m,,) ~gv~:,. Y ~ " ( n , ) .

From inspection of (1) and (2), it follows that

i) the spectroscopic information on the decay of the state having a 1 t . spin I ' into the channel {I', s", l"} is contained in the decay amplitudes J . , . ,

if) contributions from different m,, add incoherently;

iii) for each magnetic substate m,,, the shape of the corresponding partial-correlation function does not depend on the reaction mechanism.

In the ease of the ~2C(6Li, d)~60--~ 12C+:r reaction, i " ~ 0, then s" is unique and equal to I". Thus eq. (1) becomes

(3) [l"I"m m I ' m ~if*: Y~l"(12~)l ~ I / '~ ~ ~" 1"] I '] I l"

w(o, n~) = ~p=, , (o) 5 ~"~"

Notice that the following normalization has been introduced (18):

I" The decay amplitude Zf,,,~. in eq. (3) can be expressed in the form

(4) 1 a ~,, .(Fe,') ~ J ~ ' ~ - ~ ( r ~ exp [ - i~.~.],

where 1,1' and 2"~,,',. are positive quantities which represent, respectively, t h e total level width and the partial width corresponding to the decay into the channel {I' I"l"). Thus the differential cross-section for the sequential process can be expressed as

(5) d~a(f2, = O, D~) do- .

- - (0) ~ W(O, ~ ) . d~r d~22 d~21 1

The detailed expressions for If~,, and the phase ~.~. depend obviously on the

3 0 4 A. CUNSOLO, A. FOTI, G. PAPPALARDO, G. RACITI , N. SAUNIER, ETC.

m e c h a n i s m of t h e d e c a y a n d in t h e R - m a t r i x a p p r o a c h (2o) a re g i v e n b y

= 2P .r

~nd

w h e r e Yz" is t h e spec t ro scop i c a m p l i t u d e for t h e d i s i n t e g r a t i o n ~O ~' -+ ~2C~'+a,

P t . is t h e p e n e t r a b i l i t y a n d Or,, is t h e h a r d - s p h e r e s c a t t e r i n g p h a s e shif t .

0 60 120 180 (92 (degrees)

Fig. 9. - The DWBA correlation function W(/21, •2) in the reaction plane for the d) 02t.s(a ) Cg~ reaction, E~T.i = 34 MeV. The deuteron is emi t ted in the direc- 12C(~Li ' is 6+ 12

t ion ~21(O 1, ~1 = 0) ~nd the ~-particle is emi t ted in the direction /22(02, ~2 = ~). The used DWBA parameters have been taken from ref. (is). Notice tha t the curves cor- responding to emission of the deuteron at forward angles are just shifted when O 1 increases.

(no) E. P. WIGNEn and L. EISEZ~BUND: Phys. Rev., 72, 29 (1947); M. A. PRESTON: Physics o/ the Nucleus (Reading, Mass.), p. 494; R. G. THOMAS: Prog. Theor. Phys., 12, 253 (1954).

STUDY OF SOME 160 STATES AT H I G H EXCITATION- ENERGY 3 0 5

The va l id i ty of eq. (3) is restr ic ted to the cases in which the ejectile is

detected in the b e a m direction. I t can be shown (is) that~ a t forward angles for

O~, the correlat ion funct ion is shifted of an amoun t which is sensitive to the

120"

%

60.

~I I I I I 0 60 120

02 (cLegrees)

!

180

Fig. 10. - The correlation function WDw~A(01, 03) for the 12C(6Li, d)16021.8(~)6+ 12C4.432+ reaction. The calculation of the decay of the 21.8 MeV 1sO state into the 4.43 MeV 1~C have been described in the text. See fig. 9 for other comments. E6~= 34 MeV.

angular m o m e n t a involved ii1 the process. J u s t as an i l lustration, the evolut ion of the correlation function, when O1 increases, is shown in fig. 9 and 10,

respect ively, for the decay of the 21.8 MeV 1~O sta te into the 12CB and into the 12a 2+ states. Tile calculations were carried out in the f r amework of the ~ 4 . 4 3

DWBA, described elsewhere (is).

3 0 6 A. CU1NSOLO, A. FOTI , G. P A P P A L A R D O , O. RACITI , N. SAUNIER, ETC.

3"1. ~20~ t rans i t ions . - I f we consider the ~-decay toward the ~ : C , ex- pression (3) simplifies to ( I " ~ O, l" is unique and equal to I ' )

m i n i m 1 , w ( o , ~ , ) = E, p, , , , (o) I t , , ,=, , ( ~ ) 1 ~ .

Figures 5, 6 and 7 show the calculations of expression (6), under the hypothesis

t h s t only p0(0) contr ibutes for the ~-decay of the 16.30 MeV, 20.9 MeV and

21,8 MeV sta tes into the t2C~.

The spin ass ignment can be made b y comparison between exper imenta l snd theoret ical results; the 6 + value (see ref. (4)) is confirmed for the 16.30 MeV known level. For the 20.9 MeV previously repor ted as a 7- (ref. (4)), the cor-

re lat ion funct ion exhibits a complex shape, bu t indicates clearly a negat ive par i ty .

However , some ambigu i ty exists between 7- and 9- spin assignments. I t mus t be no ted also for this ease the disagreement between exper imenta l and

10 -2

o lo-T

10 0

~'.X / / - . ",, ..-..'\ Ii..---. ,, \ :. / ' - \ ?"'" ',

30 60 120 150 180 90 O(~egrees)

Fig. 11. - Comparison between experimental points and the three different theoretical predictions for I ' = 4, 6, 8 ( , , , respectively) for the ~-deeay of the 21.8 MeV 1~0 state into the 4.43 MeV 2 + excited state of 12C, for t91= (@d= 0, 9d = 0), /22(0 a, 9~ = z), by using optical-model parameters (set I) reported in table I. The obtained % ~ values are Z~(4)=4.8, Z2(6)=3.4, 73(8)=6.3. E,I~=34MeV, Od=0 ~

S T U Y Y O F S O M E 1 6 0 S T A T E S A T H I G H E X C I T A T I O I q ] ~ N E R G Y 3 0 7

theoret ical vMues in the angular region around 60~ we note tha t our experi- menta l da ta are obtained in two independent measurements and this disagree- ment cannot be a t t r ibu ted to exper imental errors or normalizat ion effects. A 6 + spin and par i ty assignment can be made for the 21.8 MeV 160 state.

I t must be observed tha t the obta ined fits are quite sat isfactory; thus the most impor tan t contr ibut ion comes f rom the mz,----- 0 component in agreement with the predictions of the t ransfer of a zero-spin cluster in a direct or multi- step process if spin-orbit interact ion is neglected in bo th cases. I t is interesting to compare these results (po (0 )= 1) with the statistical-model predictions,

which are (for the 21.8 MeV level)

po(O) = 0 . 4 3 , p l (o ) - - p _ l ( o ) - - 0 . 2 0 , p,(O) - - p _ , ( o ) = 0 . 0 8 5 .

3"2. The :c-decay of the 21.8 MeV 6 + 1~0 state to the 4.43 MeV 2 + 12C state. -

In this case, the correlation funct ion (eq. (3)) is a coherent sum of the terms corresponding to the l "= 4, 6, 8 values.

10 0 i I I

^ o 10

" - . \ .r

"" "x\ 11 ~ - " ~ . ',, , , . ~ , ,,1'/,1 '"' '\" ,.,//'" �9 ',,,,

/ ,/....~ . , /.. �9 ', '~ # ' i .' '~l '" ~ ,,.#(" ""~ ',,

" i ~ / i , h' ".%. , I

i i t ' . ' \ ~. t i t

',," V:i ' ,7 ".,: ',,,,I \,,,I

10 I I I I I 30 60 90 120 150 180

(~ (clegrees) Fig . 12. - T h e o r e t i c a l c o r r e c t i o n f u n c t i o n W ( ~ 1, ~92) (eq. (3)) f o r t h e ca se of fig. 11 fo r I'---- 6 ; c u r v e s I ( . . . . . . ) a n d I I ( . . . . ) r e f e r , r e s p e c t i v e l y , to t h e t w o se t s I a n d I I of o p t i c a l p a r a m e t e r s e m p l o y e d ; t h e t w o c u r v e s A ( . . . ) a n d B ( - - . . . . ) a r e t h e i n - coherent s u m of d i f f e r e n t t e r m s of (3) w i t h d i f f e r e n t l ~ 4, 6, 8 v a l u e s a l l o w e d i n t h i s case , r e s p e c t i v e l y , f o r t h e t w o se t s I a n d I I . T h e Z a v a l u e fo r c u r v e I I is X2(6) = 7.6.

30~ A. CUNBOLO, A. FOTI, G. PAPPALARDO, G. RACITI, N. SAUNIER, :ETC.

T~aLE I . - Optical.model paramete~'s and penetrabilities used to compute Pl" and ~, in expression (3).

V % a W %, a, ro P, Ps Ps A~s., A~,.,

Sot I (a) 199.1 1.26 0.65 42.17 1.26 0.65 1.25 0.982 0.650 0.03 48.3 ~ 55.7 ~

Sot I I (~) 251.8 1.44 0.48 12.5 1.44 0.48 1.44 0.941 0.422 0.006 7.6 ~ 13.1 ~

Pt, represents the optical penetrability for the partial wave l". Aetfzl ~$s ' , [ --~z ' t | = ~t [ - ~z], where ~t, the usual real part of the optical-model phase shift. (a) N. BARON, R. F. LEONARD and W. N. STEWART: Phys. Rev. C, 4, 1159 (1971). (b) MAKOWSICA et el.: Institut of Nuclear Physics. Cracow, Poland, Report No. 735/PL (1970).

We assumed, in a first approach, ?t" constant and independent of l" and the computed expression (3) using the penetrabilities/~t, and the phase shifts ~,. given by the optical model.

To test the sensitivity of the correlation curve to the above parameters we have performed calculations using two independent sets of optical para- meters (see table I).

10

'~ 0 60 120 180 e 2 (cl.eg t e e s )

Tiff. 13. - Inf luence of t h e ra t io be tween two pa r t i a l w i d t h s (Fix:t[ and F~ot;)z' on t h e shape of t he cor re la t ion func t ion WDWBA(0; 0 , , r =) (eq. (A.1)). The spins of t he in i t ia l a n d t h e two final s t a t e s arc, respec t ive ly , 1 ' = 6, 1 ' = 2 a n d i " = 0. The orb i ta l angu la r m o m e n t a cons idered are l~ = 6 a n d l~ = 4. A~e4 is t aken to be 90 ~

STUDY OF SOME 160 STATES AT HIGH EXCITATION ENERGY 3 0 9

Figures 11 and 12 show the results of the calculations. F ro m these figures

it follows tha t

i) the assignment of I - = 6 + to the 21.8 MeV state is confirmed (see fig. 11);

ii) the incoherent sum (curves A) and B)~ fig. 12) of the terms of (3) rel- at ive to the l "= 47 6, 8 values, which is given by diagonal elements and repre- sents essentially the effects of the penetrabilities, is practically independent of the optical-model parameters at forward and backward angles O~ of the ~-particle;

\

Q)

\|

60-

0 60 120 180 @2(degrees)

Fig. 14. - Influence of the relative phase At-- ~1"~[-- ~z'% on the shape of the correla- tion function. The ratio Fgs/Fg4 is considered to be 1. See other comments in fig. 13.

310 A. C U N S O L O , A. F O T I , G. P A P I ' A L A R D O , G. R A C I T I , N . S A U N I E R , :ETC.

iii) the coherent mixture (curves I and II , fig. 12), i.e. the complete calculation of (3) shows an impor tan t dependence on the parameters at for- ward and backward angles 02.

The observed dependence arises essentially (see also fig. 13 and 14 in the appendix) f rom the difference in the phases, suggesting the importance of angular-correlat ion measurements at forward or backward angles 03, of the part icle emi t ted in the second process, in order to get information on these phases; it would also be interesting to test to which ex ten t the assumption of y~,, independent of l" is valid.

An analysis of this sensitivity is described in the appendix.

4 . - C o n c l u s i o n s .

This work has been carried out to investigate the properties of highly excited 1~O states which are selectively populated by the (6Li, d) react ion on 1~C. Moreover, as some of these states can decay strongly into the 4.43 MeV 2+-state of the 1~C, we have analysed the possibility of extending the usual angular-correlation method (19) of spin assignment to the decay to nonzero- spin states: A brief review of theory is presented.

Our exper imental angular-correlation measurements at O1 ~ 0 ~ confirm the spin assignment for the 16.3 MeV 6+-state and the 20.9 MeV 7--state. The spin determinat ion 6 + for the state at 21.8 MeV was done. The analysis indicates a ve ry weak populat ion of the magnetic substates m = • 1, in agreement with the DWBA or CCBA which predict exclusively a populat ion with m I, ----0, in case of absence of spin-orbit interaction.

A spin assignment for the 21.8 MeV level can also be obtained through the d-= correlation with the =-particles leading to the 2+-state of 1~C. The necessity of more than one l" fit to the correlation pa t t e rn does not favour (~) the prel iminary hypothesis ]12C2+ Q 2~ I (s.~l) tha t has been

suggested, concerning the s tructure of this level. However, a more rigorous i + theoretical t r ea tmen t of the Sz,, ~. amplitudes is necessary before drawing defi-

nite conclusions. I t is noticeable tha t the presence of two l" allows us to obtain an oscillatory

pa t te rn ; if only the lowest allowed l" is present, the oscillations are completely washed out. An illustration of the different factors which affect the shape

of the correlation funct ion is given in the appendix.

(2~) M. AVRIL, ~. LEPAR:EUX, N. SAUNIER, A. FOWl, G. PAPPALARDO and A. STRAZZERI: J. Physique T~ett., 36, L-229 (1974).

S T U D Y O F S O M E 1 6 0 S T A T E S A T n I G H E X C I T A T I O N E N E R G Y 311

A P P E N D I X

Effects of the shape of the correlation function due to the decay mechanism parameters.

I f ~ sequential process is considered (see fig. 8), the correlation funct ion corresponding to the detect ion of the ejeetile at the beam direction is defined as

ml" 8"l"

where p,,,,(0) is the populat ion of the magnetic substate m~, of the recoil nu- cleus A' at $2~--~ 0 and the mat r ix elements ~J-~/,'~,,,(f2~) are defined by expression (2).

The ] ~ : c l ~ terms are direct ly re la ted to the par t ia l widths ]~z',,,t,, correspond- ing to the decay to these channels (see eq. (4)).

After some straightforward manipulat ions with the geometrical terms to introduce the decay funct ion

i t m

the correlation funct ion can be pu t in this form:

1 (A.~) W(O,~) = ~,,~P'~'(O) ~1,7~:,,,I""

�9 ~'~.r~,,(O~, ~,~) + '~ ~ i, ~, ~., , , . , , s"

I t can be seen from this expression tha t the phase ~,"L" of 5f~:z. has a ve ry sensitive effect on the shape of the angular correlation. The effects of the rela- t ive magni tude and of the relat ive phase of Sf~ c on W(0, s are shown, respec- t ively, in fig. 13 and fig. ]4, in which we have considered I ' ~ - 6 , i " = 0, s " = I " = 2 and contributions of l " = 4 and l " = 6.

Notice in these two figures tha t

i) the oscillations of the correlation funct ion are ve ry strong when [s << 15f~e] 2 (fig. 13), i.e. when the par t ia l width /~ 'c corresponding to the (~ s t re tch )> case (l"--~ I ' ~: s") is negligible with respect to tha t one corresponding to the ((adiabatic)> case (1"= I ' ) ;

6 o ii) the oscillations are completely washed out when 15f~el~<< [5f24[" (fig. ~3);

iii) the correlation funct ion in forward- and backward-O~ angular region is specially sensitive to changes in the relative phase A~ = ~:~'=2,c=~- ~:r-z.z'=4 (fig. 14).

312 A. CUN$OLO, A. FOTI, G. PAPPALARDO, G. RACITI, N. SAUNIER, ]"TC.

These f e a t u r e s come f r o m t h e g e o m e t r i c a l p r o p e r t i e s of t he d e c a y func- t i on ~,o ~-o.~;,;(0~, ~v~) which

I[ 1! ~60 i) osc i l l a t e s s t r o n g l y w h e n l~ = lz = I ' (e.g. in our ease ~2e~),

ii) does n o t osc i l l a te a t ~11 when l~"= 1.,": I ' -4-s" (e.g. ~-2,),a~

iii) has r e l a t i v e l y la rge v a l u e s in t h e f o r w a r d - a n d baekward-O~ reg ions a n d rc l '~ t ive ly s m a l l va lue s in t h e O2 i n t e r m e d i a t e r eg ion when l ~ - - I ' - A = s" a n d l~' = I ' (e.g. ~ ) .

�9 R I A S S U N T O

I1 metodo delle eorrelazioni angolari part ieel la-part ieel la ~ applicato alia re~rzione 12C(eLi, d)1eO--~+12C. Si determinano spin e parit/t di alcuni s ta t i del ~sO ad al ta energia di eccitazione, effettuando la misura delia correlazione angolare deuterone-alfa nel easo speeiale in cui il deuterone ~ rivclato a zero gradi (Ox-- 0~ L'analisi della curve di correlazione indiea ehe il meecanismo dominante ~ quello di un tr:~sferimento diret to. Si ~ analizzata in lnaniera part ieolare la eorrelazionc angolare eorrist)ondeute al deeadimento ~021.a-~-!-r'C~.~a e si sono discussi gli effetti di interferenza dovuti ai differenti valori di l permessi nel deeadimento.

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