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THE SUCCESS OF THE DISTORTED WAVE
METHOD AT VERY HIGH INCIDENT ENERGY
J. Barrette, B. Berthier, J. Gastebois, A. Gillibert, R. Lucas, J. Matuszek, M.
Mermaz, A. Miczaika, E. van Renterghem, T. Suomijarvi, et al.
To cite this version:
J. Barrette, B. Berthier, J. Gastebois, A. Gillibert, R. Lucas, et al.. THE SUCCESS OF THE
DISTORTED WAVE METHOD AT VERY HIGH INCIDENT ENERGY. International Conference
on Heavy Ion Nuclear Collisions in the Fermi Energy Domain, 1986, Caen, France. pp.C4-179-C4-182,
�10.1051/jphyscol:1986421�. �jpa-00225787�
THE SUCCESS OF THE DISTORTED WAVE METHOD AT VERY HIGH INCIDENT ENERGY
J . BARRETTE, B . BERTHIER, J . GASTEBOIS, A. GILLIBERT, R. LUCAS,
J. MATUSZEK, M.C. MERMAZ, A. MICZAIKA, E . VAN RENTERGHEM,
T. SUOMIJARVI, A. BOUCENNA*, D. DISDIER*, L. KRAUS*, I . LINCK* , B. LOTT*, V. RAUCH*, R. REIBMEISTER*, F . SCHEIBLING",
J . C . SENS*, N. SCHULTZ*, C. GRUNBERG** a n d W. MITTIG"*
Service de Physique N u c l 6 a i r e , K&trologie Fondamentale, CEN-Saclay, F-91191 Gif-sur-Yvette Cedex, France
'CRN, BP 20 CR, F-67037 Strasbourg, France "GUNIL, BP 5 0 2 7 , F-14044 Caen, France
Résumé - Les réactions de transfert direct d'un proton et d'un neutron
in-duites par un faisceau de
1 60 de 793 MeV bombardant une cible de
2 0 8P b sont
largement expliquées par deux règles de sélection contenues dans le
formalis-me de la Méthode des ondes distordues.
Abstract - The one-proton and one-neutron d i r e c t surface t r a n s f e r r e a c t i o n s induced by 793 MeV 1 60 incident energy beam bombarding a 2 0 8Pb t a r g e t nu-c l e u s , are widely explained by two s e l e nu-c t i o n r u l e s nu-contained in the Distorted Wave Method formalism.
One-nucleon t r a n s f e r reaction induced by a 793 MeV 1 60 beam bombarding a 2 0 8Pb t a r -get has been studied a t the GANIL f a c i l i t y using an energy-loss magnetic spectrome-t e r in order spectrome-to evidence spectrome-two s e l e c spectrome-t i o n r u l e s concerning s i n g l e - p a r spectrome-t i c l e s spectrome-t a spectrome-t e popu-l a t i o n s f o r various spins j f = Xr ± 1/2. The f i r s t s e popu-l e c t i o n r u popu-l e t e popu-l popu-l s us : as the incident energy i n c r e a s e s , the strongly excited s t a t e s are the ones having a large o r b i t a l angular momentum Xf ( r e f . / l / ) . This i s due to the increase of angular momen-tum mismatch between the entrance and e x i t grazing p a r t i a l waves as the incident energy i n c r e a s e s . Then l a r g e t r a n s f e r angular momentum i s needed in order to assure the proper balance between grazing wave angular momenta. The second s e l e c t i o n rule says t h a t s t a r t i n g , in the p r o j e c t i l e , from an i n i t i a l s i n g l e p a r t i c l e s t a t e of spin j.j = *i ± 1/2 the favored final s i n g l e - p a r t i c l e s t a t e has a l s o a j f = Xe ± 1/2 spin, i . e . no i n t r i n s i c spin f l i p during the t r a n s f e r process. In t h e present measurement of 2 0 8P b (1 60 ,1 5N )2 0 9B i and 2 0 8P b (1 60 ,1 50 )2 0 9P b r e a c t i o n s , the strongly excited final s t a t e s w i l l be j f = Xr - 1/2 s i n c e t h e i n i t i a l s i n g l e p a r t i c l e s t a t e has a l p l / 2 configuration in the 1 66 p r o j e c t i l e . This s e l e c t i o n r u l e i s explained by the schema-t i c diagram of Fig. 1 : schema-the facschema-t schema-t h a schema-t schema-the schema-t r a n s f e r r e d nucleon has, in addischema-tion schema-to i schema-t s
i n i t i a l i n t r i n s i c nucleon v e l o c i t y , the v e l o c i t y of the p r o j e c t i l e , makes, i t can be captured by the t a r g e t only i f the a l g e b r a i c sum of these two speeds matches best the final i n t r i n s i c nucleon v e l o c i t y in the residual nucleus. Calculations based on the one-step Distorted Wave Born Approximation (DWBA) has to contain n a t u r a l l y these two high incident energy selection r u l e s .
The Fig. 2 shows the energy spectrum of the 2 0 8P b (2 60 ,1 5N ) 2 0 9Bi one-proton t r a n s f e r r e a c t i o n . The energy r e s o l u t i o n i s 215 keV FWHM. As a t low incident energy only the s i n g l e p a r t i c l e s t a t e s are populated. We can s e e , immediately from the second s e -l e c t i o n r u -l e t h a t the 2f5/2 s t a t e i s more strong-ly excited than the 2f7/2 one of same o r b i t a l angular momentum if = 3 . The lh9/2 l e v e l , and if - 5 s t a t e , i s also
JOURNAL
DE
PHYSIQUEFiy. I
ALLOW ED
s t r o n g l y populated. The l i 1 3 / 2 s t a t e population i s favored by the f i r s t selec- t i o n r u l e since i t involves
a l a r g e af = 6 f i n a l o r b i t a l
600
momentum b u t i t i s a l s oi n h i b i t e d by the second se- l e c t i o n r u l e since i t has a jf = ~f + 1/2 f i n a l spin.
For these two contradictory
reasons, i t has turned out
,
600
t h a t the l i l 3 / 2 - s t a t e cross I-section i s smaller than the
a
ground-state one. L e t us quote t h a t the mismatch be- tween the entrance and out- going grazing waves i s M. Angular d i s t r i b u t i o n s have been measured between 0' and 6" and a one-step DWBA ana-l y s i s has been performed
200
w i t h the code PTOLEMY /3/.The form f a c t o r parameters were taken from ref./2/. The o p t i c a l model parameters were obtained by i n t e r p o l a-
t i o n between a 1503 MeV 160
0
i n c i d e n t energy s e t /4/ and
1100
1125
1150
1175
1200
1225
a 312 MeV s e t /2/. These pa-
CHANNEL
rameters have the f o l 1 owi ng
values : V=W=50 MeV, r, = Fig. 2
1.105 fm, r = 1.085 fm and ao = a1 = b.750 fm. They
correspond t o a strong absorptive potential. This DUBA analysis reproduces q u i t e w e l l the r e l a t i v e i n t e n s i t i e s o f a l l the s i n g l e - p a r t i c l e s t a t e t r a n s i t i o n s as i t Can be judged from the spectroscopic f a c t o r s l i s t e d i n Table I.
One-proton spectroscopic factors of 208Pb(160,
?
!
O9Pbone-neutron t r a n s f e r reaction. Only single- particle s t a t e s are po- pul ated. According to the second selection rule the 29712 s t a t e i s more strongly popu- lated than the 29912 ground s t a t e , both are a = 4 t r a n s i t i o n s .
T R ~
most s t r o n g l y excited s t a t e i s the a ) All spectroscopic factors are normalized on the g.s. li1112 level which has t h e o r e t i c a l value ( s e e ref.151). an af = 6 orbitalmo-
mentum and i s a j =If-
112 state. The two selection rules favor t h i s direct transfer reaction. The lj15/2 s t a t e i s strongly favored by the f i r s t selection rule, Rf = 7 compared to a grazing wave angular momentum mismatch of 1M. B u t on the other hand population t o t h i s s t a t e i s inhibited by the second selection rule : jf = a f + 112.
State
lh9/2- 227/2- l i 1 3 / 2 + Zf5/2-
The one-neutron spectroscopic factors of Table I 1 are the results of the same DWBA aria.
lysis than the one performed for the one-proton transfer reaction. The agreement i s quite reasonable and shows once more that the one-step DWBA calculation i s able to reproduce f a i r l y we1 1 the re1 ative intensities governed by these two selection rules for high incident energy.
COO
V) I-f
8
200
0
1150
1175
1200
1225
1250
Fig. 3 E* (MeV) g.s. 0.896 1.608 2:822From t h e absolute cross section estimate and the success of these two selec- tion rules i t can be infer- red that the upper part of the transfer reaction energy domain has been reached and corresponds to twice the Fermi energy. (160,15N) 793 MeV 0.95 0.89 0.80 0.77 ( 1 6 0 , 1 5 ~ ) 312 MeV 0.95 0.81 0.73 0.72
CHANNEL
(3He,d) 20.3 MeV 0.95 0.63 0.45 0.71 heo or^^) 0.95 0.85 0.70 0.66JOURNAL DE PHYSIQUE
Table I1
One-neutron spectroscopic factors
a)
A l l spectroscopic factors are normalized onthe g.s. theoretical value see ref . / 5 / .
REFERENCES
/1/ Brink, D.M., Phys. Lett. 408 (1972) 37.
/2/ Olmer, C. e t a l . , Phys. R KC18 (1978) 205.
/3/ Macfarlane, M.H. and Pieper,
m.,
ANL-76-11 Rev. 1 Mathematics and computersUC-32 (1976).
/4/ Barrette, 3 .
,
this proceeding volume./5/ Ring, P. and Werner, E . , Nucl. Phys.
A211
(19731 198.(160,150) 793 MeV 0.89 0.53 0.54 0.67 ( d , p ) 20.0 MeV 0.89 0.92 0.62 1.13
