LETTER%] AL NUOVO CIMENTO VOL. 38, N. 3 17 Settembre 1983

nO-17N Analog States via the 14C(6Li, t) and lac(6Li, s~[e) Reactions.

A. CuNs0L0, A. ~0TI, G. ]M]~, G. PAPPALAIr and G. RACITI

Istituto Nazioqmle di ~isica Nucleate - Sezione di Catania, Italia Laboraforio Nazionale del Sud Centre Siciliano di ~isica Nucleate e di Struttura della Materia lstitulo dipartimentale di Iqsica dell' Universith - Corse Italia 57, 95129 Catania, Italia

N. SAV~I~R

D~partement de Physique NucMaire; Centre d'Etude Nucl~aire de Saclay Boite Postale 2, 91190 Gi/ sur Yvette, I~rance

(ricevuto il 9 Giugno 1983)

PACS. 25.70. - Heavy-part icle- induced reactions and scattering.

Summary. - The reactions 14C(SLi, t) '70 and 14C(eLi, 3Hc)lTN are investigated at E ( ~ L i ) - - 3 4 M e V . Energy spectra and angular distributions of tritons and 3He- particles are measured and spectroscopic factors are obtained through a I-IF and E F R - I ) W B A analysis of the data. The T = ~ analog pairs in the x~O-l~N nuclei are identified from the comparison of these data.

Recently it has been shown (1) tha t the strong transitions observed in the l~C(eLi, t)*~O reaction, at 34 MeV bombarding energy, proceed through a direct-transfer of a three-nucleon cluster. However, this reaction is not isospin selective because both '/' ---- { and T = ~ 'TO states can be populated.

On the other hand, it is well known (.~,3) that the parallel investigation of the (~Li,atie) and {eLi, t) reactions induced on the same target nucleus, provides a means to identify analog states in the residual isobar nuclei. Therefore, in order to identify analog states in 170 and '~N nuclei, and so T = ~ states in '70, it scented worthwile studying the *4C(eLi, t )n0 and '4C(eLi, aI[e)l:N reactions at E(eLi) = 34 MeV.

(1) A. CUNSOLO, 2k. FOTI, G. ]MM/~, G. P&PPALARDO, G. RACITI a n d N. SAU~IE~: Phys. Rev. C, 24, 2127 (1981). (a) 1~. G. ]3INGHAM, H . T. FORTUNE, J . D. GARRETT a n d 1%. MIDDLETON: Phys. Rev. l~tt., 26, 1448 (1971); J . D. GARRETT, I[ . G. BL~OrIAM, H . T. FO~TU~'E a n d R. MIDDLETON: Phys. l{ev. C, $, 682 (1972). (*) H . G . BINGHAM, ~N[. L. ]=/ALBERT, D. C. I[ENSLEY, E. NEWMAN, K . %V. KEMPER a n d L. A. C~ARL- TON: Phys. Rev. C, 11, 1913 (1975).

87

8~ A. CUNSOLO, A. FOTI, G. IMM~, G. PAPPALARDO, ETC.

Up to now the identif ication of 7' = ~- analog states in aT.N-~70 nuclei has been done s imply on the basis of the exc i tat ion energies (see, for example , the ~()(d, ~He) and ~s()(d,t) reactions comparison of ref. (~), snd the ] 6 0 + n reaction s tudy of ref. (~)).

400

300

200

100

40o

0 600

~50(10.48)

I 700

s o

I I [ 800 900 1000

r

2 + c~

co

1100

~'~N (10.69)

I I

300 J ~"

i I co

2O0 i ~t

", !', ii

1 0 0 - ,

o ( r * I 1 740 840 940

,,4

if)

r i i 1040 1140 1240

channel, n u m b e r

F i g . 1. - S p e c t r a of the - '4C('Li, t ) t ' O ( u p p e r I)art.) a n d 2 'C("Li , ~ / e )~TN ( l o w e r part) react ions , meas - ured at, 01,~b = 5 ~ .

( ' ) G. I~[AInLE, K . T . b l x o P F L E , 1 ). DOLL, H. IIRENI<R a n d J . WAONER: Nucl. Phys. A, 280, 97 (1977) . (~) ]". HINTERBERGER, t J, VON I{OS.~EN, S. ClI.]ICJ'ACI~% (~. SC]IMALZ, D. ERBE a n d 13. LEUGER$: Nucl. Phys. A, 352, 93 (1981) .

170-17N ANALOG STATES VIA TIIE 14C(~SLi, t ) AND l aC(6Li , S I Ie ) REACTIONS 8 9

In the present work we search supporting evidence for analog T ~ ~ states location in the 1~0-~7N nuclei starting from the comparison of tri ton and ZHe spectra and of both the angular distributions shapes and absolute values of the a4C(6Li, t) and ~4C(SLi, 3IIe) reactions. The experimental procedures have been already described in ref. (x). Typical tr i ton and aIIe-particlc spectra are shown in fig. 1, where the energy scales are shifted in order to align known analog states in ~70 with their parent states in ~TN (4.s).

TABLE I. -- Analog pairs in 170 and ~7N and relative spectroscopic ]actors.

14C(nLi, t)170 E* (a) (MeV)

Jn cLq_. l02 (b) C2~. 103 (b)

set I set I I

12.99 -'~- 4.8 5.4

13.6 -~-+ 21.3 27.5

14.76 �89 s .s J0.5

14.76 9- 4.3 4.0 2

15.2 ~+ 25.6 32.7

16.3 ~.+ 4.4 5.1 2

x4C(6Li, aIIe)XTN E* (a) (MeV)

j n (a) C~q. 10 a (b) C2S. 103 (b)

set I set I I

1.91 5- 13.6 15.2 2

2.53 3 + 53.2 71.1

3.63 ~- 25.9 31.3

3.63 -~-- 16.1 15.2

4.01 a+ 75.6 104.6 2

9+ 12.9 14.8 5.17 -2-

C2S(eLi ' 3ile) (c)

CLS'(6Li, t)

C2S(q,i, SHe) (~

C2S(eLi, t)

set I set II

2.8• 2.8•

2 . 5 t0 .3 2 .6 t 0 .4

2 .9 t0 .2 2 . 9 t 0 . 2

3.7• 3.710.5

2 .9 t0 .2 3.2•

2 .9 t0 .2 2 .9 t 0 .2

(a) Ref . (,). (5) E s t i m a t e abso lu te unce r t a in t i e s ~ 2 5 % (due to s t a t i s t i c a l er rors (N 4-10%)

u n c e r t a i n t y ( ~ =k20 %)). (c) Th~ quo ted errors come f rom s t a t i s t i c a l er rors only.

and abso lu te -va lue

(') F. AJZENBERG-SELOVE" N~ff~~ P~t~8. A, 375, 1 (1982).

90 .~. CUN$OLO, A. I , ' O T I , G. IMM~2, G. PAPt'ALA/~DO, ETC.

The select;ivity show,t in these spectra is evidence for a dominant direct reaction m~elmnism also for the ~('(6Li, atIc) reaction, and ~tlh)ws a qu,ditative identification of ~malog stat,~, in aT0 ~nd tTN. 11~ p~rtieular, in agreement with previous suggestions (4.6), amfiog p~tir.~ are located at (1.91 :-12.99) .~[eV, (2.53--13.6) .~IcV, (4.01+15.2) McV and (5.17-:-16.3)MeV cxcitaHon energy ill 17N-~(), respectively. In addition the ~0 state at 14.76 ~[cV seems to have his eountcrp'/rt in the 3.63 31eV ~N level and then

10 ~

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10~

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101

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"--.... f

Fig. 2. - Coml)ari,~on of the a n g u l a r d i s t r i bu t ions of the ana log s t a t e s in 1~N-170, p o p u l a t e d in the ~*C(6Li, SIlc)~:N (open circles) and l~C(qA, t)~70 (full circles) reac t ions a t E ( 6 L i ) = 34 MeV. a) (3.63<- -- l i . 7 6 ) MeV, ,]'~= (7/2, 9/2)- ; b) (2.53 : 13.6) MeV, ,1 ~ - 5- /2; e) ( I . 9 1 . 1 2 . 9 9 ) MeV, J ' ~ 5- /2 ; d) (5.17 -:-16.3) MeV, J'~ - 9- /2 ; c) (4.01 :-15.2) McV, J ~ = 3+/2. The e x p e r i m e n t a l *l ie po in t s h a v e been mu l t i p l i ed by 1/3 (see t ex t ) . The c u r v e s ((lashed for the O M P set I a n d full for t he O M P set I f ) r e p r e s e n t the incoheren t s u m of tile I-IF and E F R - D W B A cross-sec t ions for t tm two reac t ions , nor- real ized to the e x p e r i m e n t a l da ta of the "C(6Li, t) reac t ion . N o t e t h a t for the ( 1 4 . 7 6 . 3 . 6 3 ) M e V pa i r the full cu rve r e p r e s e n t the ca lcu la t iou wi ih l = 3 a n d the do t -da she d one is the ca lcula t ion wi th l = 5, bo th wi th t h e O M P sot ][I.

I I I 40 60

170-17N ANALOG STATES VIA THE ~4C(6Li,t) AND ~'C(SLi, SHe) REACTIONS 9 1

it could be a T ~ ~ state. The excitation energies, the spins and the parities of the mentioned analog pairs are reported in table I.

In order to confirm this correspondence we have analysed the tr i ton and 3He angular distributions involving these ~v0-1%N anah)g states. The comparison of these data is shown in fig. 2, where the experimental 3I[e cross-sections have been multiplied by a factor ~,~ as required by the isospin argument that will be discussed later on. As can be noted, the shapes of the angular distributions of each analog-state pair arc very similar, thus giving a first confirmation of the suggested correspondence.

Morcover, iu order to extract more quanti tat ive information, we have analysed the angular distributions in the hypothesis that the contributions from the direct threc- nucleon transfer and from the statistical compound-nucleus reaction mechanism add incoherently (~). Thc statistical compound-nucleus cross-section has been estimat~ed by using the IIauser-Fcshbach (IIF) formalism 0). The direct cross-section was cvalu- ated in the exact finite-range distorted-wave Born approxiinalion (EFR-DWBA) frame- work (1), by assuming the tr 'msfer of a threc-uucleon cluster.

Thc optical-model parameters are thc samc successfully used in the previous analysis of the reported (1) 14(?(eLi ' t)170 reaction. In particular, we use the same 0MP in the exit channels of both (~Li, t) and (6Li, 3tle) reactions.

As shown in fig. 2, the general trend of the data is sufficiently well reproduced by the theoretical predictions, for both the used OMI' sets.

The comparison of the theoretical calculations with the data. allows the extraction of the C"S spectroscopic factors through thc relation

exp HF EFR DWBA

being C 2 the square of the isospin coupling Clebsh-Gordan coefficient. We note that thc calculatcd differential cross-sections result to be about the same for each pair of analog states populated in the two rc'lctions.

The extracted C2S values are reported in table I for the 1,wo different OMI ) sets. If charge-dependent cffccts are neglected, the three-mlclcon ,_~ spectroscopic strengths are expected to be the same for each pair of analog statcs. Then the ratio of the C2S f'~ctors, for the (6Li, t) and (GLi, aHe) reactions leading to anah)g final states, can be expressed simply as (7)

C" 8(eLi,~g_e) ~ < T, T~tt.I T, T.,} ~ C2S(eL, t) - , . . . . . . ' 2' (, I i T. t t t . [I ~ T,~}

where the brackets are Clebsh-Gordan coefficients for fin'~l states with isospin T~ = T~ t- t, being T~ the target nucleus isospin and t the isospin of the transferred cluster. Thus, the spectroscopic-factor values should be in the ratio ~ 3 when the T~ = { and t = �89 values are considered. The ratios of the obtained spectroscopic factors arc reported in table I and result to be close to the expected value of 3, for all the analysed lVN-170 pairs, independently of the choice of the OMP set.

In general, the sufficiently good fit of the angular distributions data and the de- monstrated correspondence between ~N-~O level pairs allows us to confirm previous (6)

( ' ) J . (JERNY a n d R. H. PEHL: Phys . Rev. Lett., 12, 619 (1964); J . C. IIARDY, l~. BKUNNKDER, J . CE~NY and J . J&NECKE: Phys . l~ev., 183, 854 (1969).

9 2 A. CUNSOLO, A. FOTI , G. IMM~;, G. PAPPALARDO, ETC.

spin and parity assignments and to correct the da r {+ suggestion (8) for the 13.6 MeV tT0 level. ~'or that coneel'rling the presently evidenced analog pair at (3.63--14.76) MeV, the data seem to be fitted assuming either l -- 3 or 1 : 5 t ransferred-angular-momentum v~lue, so hampering an unambiguous choice of the /-value and so of the spin value bctweell the reported (~) J.~ ~ {{, 9) - values for the 3.63 MeV ~TN state.

In conclusion, it appears that the ~4(7{eLi, t)170 and 14C(SLi, 3He)tTN reactions proceed predomin'lntly through a direct three-nucleon transfer mechanism. I t has been shown that a parallel investigation of the (eLi, SHe) and (~Li, t) reactions on a ~4C target rep- resent % powerful tool for determining isobaric analog states in the ~TN-~vO nuclei. This investig%tion is based on the, comparison of both f.hc energy spectra ~nd the spectro- scopic factors extracted by the an:tlysis of the me~tsured angular distributions in both ~he reae[ions. In particular the previously suggested(~6) (1.91-12.99)MeV, (2.53 :-13.6) MeV. (4.01 : 15.2) 5It.V and (5.17--16.3) MeV 17N-170 T =: .~- analog pairs are confirnled by the pre.~ent analysis and a farther level pair at (3.63--14.76)MeV is identiiied.

(*) A. CUNSOLO, A. FOTI, G. IMM~, G. I>APPALARDO, (~-. RACITI a n d N. SAUNIER: Phys. Letl. B, 124, 439 (1983).