Sca e ing o 6He a ene gies a ound he Coulomb
ba ie
A.M. S´anchez-Ben´ı ez†, D. Esc igk, M.A.G. ´
Al a ez‡, M.V.
And ´es‡, C. Angulo+, M.J.G. Bo gek, J. Cab e a+,
S. Che ubini§, J.M. Espino‡, P. Figue a§, M. F ee ],
J.E. Ga c´ıa-Ramos†, J. G´omez-Camacho‡, M. Gulino§,
O.R. Kakuee¶, I. Ma el†, C. Me elco], A.M. Mo o‡,
J. Rahighi¶, K. Rusek†, D. Smi no *, O. Tengbladk, P. Van
Duppen*, V. Ziman]
†Depa amen o de F´ısica Aplicada, Uni e sidad de Huel a, E-21071 Huel a, Spain
‡Depa amen o de F´ısica A ´omica, Molecula y Nuclea , Uni e sidad de Se illa,
E-41080 Se illa, Spain
kIns i u o de Es uc u a de la Ma e ia, CSIC, E-28006 Mad id, Spain
¶Van de G aa Labo a o y, Nuclea Resea ch Cen e, AEOI, PO Box 14155-1339,
Teh an, I an
+Cen e de Reche ches du Cyclo on, Uni e si ´e ca holique de Lou ain, B-1348
Lou ain-la-Neu e, Belgium
* Ins i uu oo Ke n-en S alings ysica, Uni e si y o Leu en, B-3001 Leu en,
Belgium
]School o Physics and Space Resea ch, Uni e si y o Bi mingham, B15 2TT
B imingham, England
§INFN Labo a o i Nazionali del Sud and Sezione di Ca ania, I-95123 Ca ania, I aly
E-mail: [email p o ec ed]
Abs ac . We ha e measu ed elas ic c oss sec ions o he sca e ing o 6He a
ELab = 14,16,17,18,22 MeV on 208Pb in he angula anges o 20◦−64◦and
135◦−170◦. A signi ican amoun o 4He e en s is ound a ene gies well below he
Coulomb ba ie , ha becomes dominan abo e i . Op ical Model calcula ions ha e
been pe o med including a dynamic pola iza ion po en ial. Ve y la ge imagina y di -
useness pa ame e is needed in o de o desc ibe he expe imen al dis ibu ions.
PACS numbe s: 01.30.Cc; 13.75.-n; 24.10.H ; 25.10.+s; 25.60.Dz; 25.60.Gc; 25.60.Bx;
21.10.G ; 27.20.+n
Submi ed o: J. Phys. G: Nucl. Phys.
208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 2
1. In oduc ion
The in e es in s udying he elas ic sca e ing o 6He a ises om i s weakly bound na u e,
which signi ican ly a ec s he dynamics o he collision. This nucleus is known o ha e a
well de eloped 3-body s uc u e consis ing on an alpha pa icle and wo alence neu ons
weakly bound by less han 1 MeV [1, 2]. Coupling o he s a es om he con inuum may
play an impo an ole in he dynamics o he eac ion p ocess by means o long ange
eac ion mechanisms. In pa icula , we a e in e es ed in con inuum s a es coupled wi h
he g ound s a e o 6He by he dipole componen o he Coulomb ield o he a ge .
Tha is wha Coulomb dipole pola izabili y accoun s o , and i has been ound ha i
gi es ise o a signi ican educ ion o he elas ic c oss sec ions o o he sys ems [3, 4, 5].
In his pape we epo on measu emen s o elas ic sca e ing and alpha p oduc ion
c oss sec ions o 6He+208Pb a Coulomb ba ie ene gies. Due o he high Z alue o
a ge and he ela i ely low sca e ing ene gy, we expec impo an e ec s om he
Coulomb dipole coupling.
2. Expe imen
The expe imen was pe o med a he Cen e de Reche ches du Cyclo on a Lou ain-
la-Neu e, Belgium [6]. The bomba ding ene gies o he seconda y 6He beam we e 14,
16, 17, 18 and 22 MeV, wi h a cu en in ensi y on a ge o abou 5 ×106pps (106
pps o he 22 MeV beam). Accele a ed 6He ions we e sca e ed on a sel suppo ed
a ge wi h he ollowing iso opic composi ion: 208Pb 87(2)%, 207Pb 1.20(2)%, 206Pb
11.4(2)%. A a ge o 0.950 mg/cm2 hickness was used o each ene gy excep o 22
MeV, whe e beam in ensi y was lowe and a hickness o 2.080 mg/cm2was chosen.
Elas ic sca e ing c oss sec ions o a 12 MeV 4He beam om 208Pb was also measu ed o
no malize da a and o cancel sys ema ic e o s in he 6He+208Pb elas ic c oss sec ions.
Two 5 mm collima o s we e used o p o ide good beam de ini ion and o educe
ame sca e ing e en s. The ou going pa icles we e de ec ed by h ee a ays o
de ec o s, LEDA (used in s anda d and LAMP con igu a ions) and DINEX. Figu e
3 shows a schema ic lay-ou o he expe imen al se up.
LEDA silicon s ip de ec o s (SSD) a e desc ibed in [7]. DINEX de ec o a ay (see
igu e 1) consis s o ou 90◦ci cula silicon elescopes, o hickness 40µm ( on ) and
500µm (back). The on de ec o is a single sided SSD de ec o , a so called CD- ype
s ip de ec o [8]. DINEX de ec o a ay was able o achie e a good iden i ica ion o
4He and 6He e en s wi h an adequa e angula esolu ion (see igu e 2). LEDA, LAMP
and DINEX de ec o a ays co e h ee di e en angula anges (see igu e 3): LEDA
5◦−12◦wi h an angula esolu ion o 0.5◦, LAMP 20◦−64◦wi h an angula esolu ion
o 3◦, and DINEX 135◦−170◦wi h an angula esolu ion o 5◦. The solid angle co e ed
by LEDA+LAMP+DINEX a ays was 33% o 4π. Co ec ions o beam alignmen and
e iciency o he elec onic chain we e also e alua ed and included in he inal analysis.
As an example he elas ic c oss sec ion di ided by he Ru he o d c oss sec ion ob ained
208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 3
a 18 and 22 MeV a e shown in igu e 4, and he alpha p oduc ion c oss sec ion a he
ene gy o 22 MeV is shown in igu e 5.
The LAMP egion includes he onse o Ru he o d sca e ing egime a lowe
angles, p o iding us he needed e e ence expe imen al poin s o a global no maliza ion.
The e o e he analysis o he da a om LEDA egion is edundan , whe eas implies
addi ional non i ial co ec ions due o he high a e o de ec ed pa icles.
3. Analysis
We ca ied ou an op ical model (OM) analysis o he expe imen al da a using he code
ECIS [9]. In he calcula ions he e ec s o he dipole couplings o he s a es in he
con inuum we e included by means o a dynamic dipole pola iza ion po en ial (DDPP)
[10]. I s Coulomb pa was calcula ed explici ly om he heo e ically p edic ed B(E1)
ene gy dis ibu ion [11]. In he analysis we used a Coulomb adius o RC= 9.29 m.
Fo he nuclea po en ial we ha e chosen Woods-Saxon adial o m ac o s o bo h eal
and imagina y pa s wi h a adius R =Ri= 10.07 m [12]. We made a i o he 22
MeV dis ibu ion by means o ou -pa ame e sea ch. The dep hs and di usenesses o
he nuclea po en ial we e a ied in he sea ch, wi h he s a ing alues aken om [12].
The ene gy o 22 MeV is abo e he Coulomb ba ie so he calcula ions a e expec ed o
be sensi i e o he pa ame e s o he nuclea po en ial.
The alue o he imagina y di useness ob ained a 22 MeV (ai=2(1) m) i s well
he da a also a lowe ene gies. This e y la ge alue sugges s he p esence o he s ong
nuclea componen o he DDPP. The Coulomb componen was explici ly included in he
calcula ions. This esul is in acco dance wi h p e ious expe imen al wo ks [12, 13, 14].
Solid cu es in igu e 4 a e OM calcula ions using ai=2.21 m. Only he dep hs
we e a ied in he sea ch o he ene gy o 18 MeV. In o de o see he e ec o he
la ge imagina y di useness and he sensi i i y o he esul , OM calcula ions we e also
pe o med wi h a ixed and mo e s anda d alue o ai=0.819 m. This alue was used
in [15] o he sca e ing o 6Li on 208Pb. The esul o his calcula ion is shown in igu e
4 (do ed cu es). The la ge imagina y di usseness ob ained o 6He dumps oscilla ions
in he egion o he Coulomb ainbow.
P elimina y coupled channels calcula ions we e pe o med o he ene gy o 22
MeV, assuming a simple di-neu on model o 6He. The couplings wi h he s a es
om he con inuum we e included by means o con inuum - disc e ized coupled -
channels (CDCC) echnique.The OM calcula ions wi h ai=2.21 m (solid cu e) and
CDCC calcula ions (dashed cu e) i he expe imen al da a equally well, al hough a
in e media e sca e ing angles hey lead o qui e di e en esul s. This calls o new
expe imen al da a in his angula ange.
In o de o ackle he p ocess o neu on ans e o he a ge , ano he app oach was
adop ed assuming ha he de ec ed alpha pa icles a backwa d angles we e p oduced
ia he ans e o a ully co ela ed di-neu on clus e o ei he he a ge bound s a es
o con inuum s a es, he la e accoun ing o he b eakup con ibu ion. Bo h p ocesses
208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 4
we e ea ed using he p io o m o he DWBA ampli ude. The calcula ed angula
dis ibu ions o he alpha pa icles a e compa ed wi h he expe imen al da a in igu e
5.
4. Summa y and ou look
We ha e in es iga ed he elas ic sca e ing o 6He on 208Pb a bomba ding ene gies
ELab = 14,16,17,18,22 MeV in a wide ange o angles. A signi ican amoun o 4He
e en s is ound a ene gies well below he Coulomb ba ie , ha becomes dominan
abo e i .
Op ical model calcula ions including a dynamic dipole pola iza ion po en ial can
ep oduce p ope ly he da a, p o ided ha a e y la ge imagina y di useness is used.
Thus, Coulomb dipole pola izabili y accoun s only o pa o he abso p ion om elas ic
channel. Da a a 22 MeV can be equally well desc ibed by he CDCC calcula ions.
The ans e o 2n o he a ge and di ec b eak-up we e included simul aneously in a
di e en app oach, achie ing pa ially o ep oduce alpha p oduc ion c oss sec ion.
New sca e ing da a would be needed o ully unde s and he mechanism o 6He
in e ac ion wi h 208Pb in he icini y o he Coulomb ba ie .
Acknowledgmen s
The au ho s would like o hank he s a a he CYCLONE RIB acili y a he
Cyclo on Resea ch Cen e in Lou ain-la-Neu e, Belgium, o p o iding us wi h an
in ense and good quali y adioac i e beam. This wo k has been pa ially suppo ed by
he Spanish Di ecci´on Gene al de In es igaci´on, Ciencia y Tecnolog´ıa unde p ojec s
numbe FPA2000-1592-C03-02, FPA2002-04181-C04-02/04, he Belgian p og am P5/07
on in e uni e si y a ac ion poles o he Belgian-s a e Fede al Se ices o Scien i ic,
Technical and Cul u al A ai s, and he Eu opean Communi y-Access o Resea ch
In as uc u e ac ion o he Imp o ing Human Po en ial P og amme, con ac No
¯
HPRI-CT-1999-00110. A. M. S. B. acknowledges a esea ch g an om he Spanish
MCyT.
Re e ences
[1] Taniha a I, 1996 J. Phys. G: Nucl. Pa . Phys. 22 157-8
[2] Hansen P G and Jonson B, 1987 Eu ophysics Le e s 4409-14
[3] And ´es M V, G´omez-Camacho J and Naga ajan M A, 1995 Nucl. Phys. 583A 817-20
[4] Mo o A M and G´omez-Camacho J, 1999 Nucl. Phys. 648A 141-56
[5] Ma el I, G´omez-Camacho J, Rusek K e al ., 1998 Nucl. Phys. 641A 188-202
[6] Ve ie J, 1997 Nucl. Phys. 616A 97c-106c
[7] Da inson T, B and ield-Smi h W, Che ubini S, e al ., 2000 Nucl. Ins um. Me hods 454A 350-8
[8] Os owski A N, Che ubini S, Da inson T, e al ., 2002 Nucl. Ins um. Me hods 480A 448-55
[9] Raynal J, 1981 Phys. Re . 23C 2571-85
[10] And ´es M V, G´omez-Camacho J and Naga ajan M A, 1994 Nucl. Phys. 579A 273-84
208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 5
[11] Thompson I J, Danilin B V, E os V D, e al ., 2000 Phys. Re . 61C 24318
[12] Kakuee O R, Rahighi J, S´anchez-Ben´ı ez A M, e al ., 2003 Nucl. Phys. 728A 339-49
[13] Aguile a E F, Kola a J J, Nunes FM, e al ., 2000 Phys. Re . Le . 84 5058-61
[14] Aguile a E F, Kola a J J, Becche i F D, e al ., 2001 Phys. Re . 63C 061603-6
[15] Keeley N , Benne S J, Cla ke N M, e al ., 1994 Nucl. Phys. 571A 326-36

208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 6
Figu e 1. DINEX de ec o a ay.
Figu e 2. Mass spec um a E=
14 MeV, θlab = 161◦ob ained
wi h DINEX de ec o a ay.
Figu e 3. Ske ch o he
expe imen al se -up.
208Pb(6He,6He)208Pb@14,16,17,18,22 MeV 7
6He+208Pb
dσ / dσR
E = 18.0 MeV
0 50 100 150
0.0
0.5
1.0
1.5
θc.m. (deg)
E = 22.0 MeV
0 50 100 150
0.0
0.5
1.0
1.5
Figu e 4. Angula dis ibu ions o elas ic
c oss sec ion di ided by he Ru he o d
c oss sec ion compa ed wi h OM and CDCC
calcula ions.
100 120 140 160
θc.m. (deg)
1
10
100
1000
dσ/dΩ (mb/s )
He + Pb, 22 MeV
6208
Figu e 5. Angula dis-
ibu ion o alpha p oduc-
ion c oss sec ion com-
pa ed wi h DWBA calcu-
la ion.