Elas ic sca e ing o 9Li on 208Pb a ene gies
a ound he Coulomb ba ie
M. Cube o∗,†, J.P. Fe nández-Ga cía∗∗,‡,J.A.Lay
∗∗, L. Acos a§,
M. Alco a∗, M.A.G. Al a ez∗∗,‡, M.J.G. Bo ge∗, L. Buchmann¶,
D. G. Dige , B. Ful on, H. O. U. Fynbo††,D.Gala iz
‡‡,
J. Gómez-Camacho‡,∗∗, I. Ma el§,A.M.Mo o
∗∗, I. Mukha§§, T. Nilsson¶¶,
A.M. Sánchez-Bení ez§, A. Sho e ¶, O. Tengblad∗and P. Walden¶
∗Ins i u o de Es uc u a de la Ma e ia, CSIC, E-28006 Mad id, Spain.
†CICANUM, Uni e sidad de Cos a Rica, Apdo. 2060, San José, Cos a Rica.
∗∗Depa amen o de FAMN, Uni e sidad de Se illa, Apdo. 1065, E-41080 Se illa, Spain.
‡Cen o Nacional de Acele ado es, A da. Thomas A. Edison, E-41092, Se illa, Spain
§Depa amen o de Física Aplicada, Facul ad de Ciencias, Uni e sidad de Huel a, Spain.
¶TRIUMF, V6T2A3 Vancou e B.C., Canada.
Depa men o Physics, Uni e si y o Yo k, YO10 5DD Hesling on, Yo k, U.K.
††Depa men o Physics and As onomy, Uni e si y o Aa hus, DK-8000, Å hus, Denma k.
‡‡Cen o de Física Nuclea da Uni e sidade de Lisboa, 1649-003 Lisbon, Po ugal.
§§Ins i u o de Física Co puscula , CSIC-Uni e sidad de Valencia, Spain.
¶¶Fundamen al Physics, Chalme s Uni e si y o Technology, S-41296 Gö ebo g, Sweden.
Abs ac . We ha e s udied he dynamical e ec s o he halo s uc u e o 11Li on he sca e ing on
hea y a ge s a ene gies a ound he Coulomb ba ie . This expe imen was pe o med a ISAC-
II a TRIUMF wi h a wo ld eco d in p oduc ion o he pos -accele a ed 11Li beam. As pa o
his s udy we epo he e on he i s measu emen o he elas ic c oss sec ion o he co e nucleus,
i.e. 9Li on 208Pb, a ene gies a ound he Coulomb ba ie . A p elimina y op ical model analysis
has been pe o med in o de o ex ac a global op ical po en ial o desc ibe he measu ed angula
dis ibu ions.
Keywo ds: Elas ic sca e ing, la ge angula co e age, halo nuclei, DSSSD de ec o s
PACS: [25.60.Bx,25.70.Bc]
The a ailabili y o uns able adioac i e beams accele a ed a di e en ene gy egimes
ha e open up new physics oppo uni ies based on he in e play o nuclea s uc u e
and eac ion dynamic e ec s. In pa icula he disco e y o he halo nuclei has b ough
enewed in e es in he modeling o nuclea eac ions since o he e y loosely bound
sys ems he eac ion model should include he coupling be ween he bound s a es and
he con inuum. The ac ha he sys em is loosely bound gi es ise o an inc ease in
he b eakup c oss sec ion, p opo ional o he educ ion o binding ene gy, bu also
changes in o he obse ables including elas ic sca e ing due o he dis o ion (dipole
pola izabili y) o he loosely bound p ojec ile in he p esence o he s ong elec ic ield
o a hea y a ge .
The pu pose o ou wo k was o s udy he eac ion o halo nuclei on he s ong
Coulomb ield o he a ge a ene gies a ound he Coulomb ba ie o assess he ele an
eac ion mechanisms. A 208Pb a ge was chosen due o i s double magic cha ac e and
i s high Z numbe (Z=82). The la ge Z gua an ees ha 11Li - lead sca e ing would be
F on ie s in Nuclea S uc u e, As ophysics, and Reac ions
AIP Con . P oc. 1377, 338-340 (2011); doi: 10.1063/1.3628405
© 2011 Ame ican Ins i u e o Physics 978-0-7354-0937-8/$30.00
338
domina ed by Ru he o d sca e ing i 11Li was a no mal compac nucleus. The ac ha
i is a halo nucleus esul s in depa u es om Ru he o d sca e ing and his de ia ion
can shed ligh on he nuclea halo. To isola e he halo e ec i is c ucial o de e mine he
dynamic beha iou o he co e, 9Li, in he same condi ions. The ene gies we e chosen
such ha he absolu e ene gy o he 9Li agmen s and he 11Li agmen s we e he same.
We epo he e on he elas ic sca e ing o 9Li on 208Pb a ene gies below (24.0
MeV), a ound (29.4 MeV) and abo e (33.0 MeV) he Coulomb ba ie . An op ical model
analysis has been pe o med wi h he aim o ex ac ing an o e all op ical po en ial o
he h ee measu ed ene gies. Al hough simila s udies ha e been done o 6He (see [1]
and e e ences he ein) and o 9Li on 208Pb well abo e he Coulomb ba ie [2], his is
he i s measu emen o he sca e ing o he wo-neu on halo nucleus 11Li and i s co e,
9Li, a ound he Coulomb ba ie .
Expe imen al Se -up, Analysis Me hod and Resul s
The expe imen was pe o med a TRIUMF. The adioac i e beams o 9Li and 11Li
p oduced in a Ta a ge we e anspo ed o he ISAC-II acili y o pos accele a ion. The
de ec ion sys em con ained 4 pa icle elescopes a ound he sca e ing a ge co e ing
he ollowing angles: T1: 10◦-40
◦, T2: 30◦-60
◦, T3: 50◦-100◦and T4: 90◦- 140◦.The
choice o he angles co e ed by he elescopes was de e mined by he beha iou expec ed
o he di e en ial c oss sec ion o elas ic sca e ing o he halo nucleus 11Li acco ding
o a coupled-channels calcula ion which includes bo h nuclea and Coulomb couplings
o he con inuum. The a ge hickness was 1.45 mg/cm2 o 2.67 and 3.27 MeV/u 9Li
beam ene gies and 1.9 mg/cm2 o 3.27 and 3.67 MeV/u 9Li beam ene gies. The a ge
was il ed 75◦wi h espec o he beam axis.
Elas ic e en s we e selec ed in he wo-dimensional plo , he ΔE e sus E mass
spec a. A clea iden i ica ion o he elas ic peak, bo h in he 9Liandin he11Li sca e ing
da a is achie ed. Da a we e analyzed i s assuming ha he de ec o s T1 and T2 we e a
he posi ion de e mined by he geome ical measu emen s and he beam cen e ed in he
Pb a ge . This allowed o an assignmen o he sca e ing angle o each pixel o he
DSSSD de ec o s. Due o he close geome y o he se up inal uning o he geome y
was needed o assu e a la beha iou o he elas ic c oss sec ion di idied by Ru he o d
a o wa d angles.
The ex ac ed di e en ial elas ic c oss sec ions shown in Fig. 1 ha e been compa ed
wi h op ical model (OM) calcula ions in which he p ojec ile- a ge in e ac ion has been
pa ame ized wi h a s anda d Woods-Saxon shape, wi h eal and imagina y pa s. Due o
he lack o p e ious expe imen al da a o 9Li sca e ing on hea y a ge s in his ene gy
egime, we conside ed ini ially he po en ial epo ed in Re [3], which ep oduces he
elas ic sca e ing da a o he 7Li+208Pb eac ion a 33 MeV. This pa ame iza ion uses
a common geome y o he eal and imagina y pa s, wi h adius 0= i=1.3 m and
di useness a0=ai=0.65 m (labeled “se 1” in Fig. 1). This geome y was ound o be
inadequa e o desc ibe he p esen da a, so we ha e pe o med a
χ
2bes – i analysis in
which he po en ial pa ame e s we e allowed o a y in o de o minimize he
χ
2 o he
da a a 3.27 and 3.67 MeV/u da a, o which we expec a la ge sensi i i y wi h espec o
339
0 50 100 150
θc.m. (deg)
0
0.5
1
1.5
(dσ/dΩ)/(dσR/dΩ)
9Li+208Pb (1.45 mg/cm2 a ge )
9Li+208Pb (1.9 mg/cm2 a ge )
OM: se 1
OM: se 2
E=3.27 MeV/u
P elimina y
0 50 100 150
θc.m. (deg)
0.5
1
1.5
(dσ/dΩ)/(dσR/dΩ)
OM: se 1
OM: se 2
9Li+108(1.9mg/cm2)
P elimina y
E=3.67 MeV/u
FIGURE 1. Measu ed di e en ial elas ic c oss sec ions o he 9Li+208Pb eac ion a Elab=3.27 MeV/u
(le panel) and 3.67 MeV/u ( igh panel). The solid and dashed lines a e he op ical model calcula ions
desc ibed in he ex .The la ge F esnel in e e ence shown by he da a a he highes ene gy (3.67 MeV/u)
equi es u he in es iga ion.
he nuclea po en ial. As a esul o his analysis, we ob ained he alues: V0=15.1 MeV,
0=1.15 m, a0=0.95 m, W=58.7 MeV, i=1.19 m, and ai=0.51 m (labeled “se 2”
in Fig. 1). This analysis should be conside p elimina y, since bo h he expe imen al
and heo e ical analyses a e in p og ess. A mo e de ailed analysis will be p esen ed
elsewhe e.
SUMMARY AND OUTLOOK
The elas ic sca e ing o a exo ic 9Li beam on a 208Pb a ge has been measu ed a h ee
di e en ene gies, 2.67, 3.27 and 3.67 MeV/u. Fo he lowes ene gy, which is below
he nominal Coulomb ba ie , he ex ac ed c oss sec ion is consis en wi h an almos
pu e Ru he o d sca e ing. Fo he wo o he ene gies, he measu ed angula dis ibu ion
ollows he Ru he o d o mula o sca e ing angles up o 45◦. The da a o hese wo
ene gies ha e been compa ed wi h op ical model calcula ions. Ini ially, we conside ed
he op ical model po en ial de i ed in Re . [3] om he analysis o he elas ic sca e ing
o 7Li by 208Pb a Coulomb ba ie ene gies. This po en ial p o ed o be inadequa e
o desc ibe he p esen da a. Wi h he idea o ex ac ing a global op ical po en ial o
he measu ed ene gies, we pe o med a bes – i analysis o he da a s a ing om he
abo e men ioned po en ial, bu allowing he dep h and geome y o a y. The esul ing
po en ial p o ides a easonably good o e all ag eemen o he h ee angula dis ibu ions.
Al hough a mo e e ined analysis is s ill o be done, his kind o po en ials will be an
essen ial ing edien o he ew-body calcula ions ha will be e en ually pe o med o
he 11Li+208Pb elas ic and b eakup da a measu ed in he same expe imen .
REFERENCES
1. A. M. Sánchez-Bení ez e al., Nucl. Phys. A 803, 30 (2008).
2. N. K. Skobele , Z. Phys. A 341, 315 (1992).
3. I. Ma el e al., Nucl. Phys. A 582, 357 (1995).
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