AIP Con e ence P oceedings 1351, 29 (2011); h ps://doi.o g/10.1063/1.3608932 1351, 29
© 2011 Ame ican Ins i u e o Physics.
Recen applica ions o ou -body
Con inuum-Disc e ized Coupled-Channels
calcula ions o eac ions
Ci e as: AIP Con e ence P oceedings 1351, 29 (2011); h ps://doi.o g/10.1063/1.3608932
Published Online: 10 Augus 2011
Manuela Rod íguez-Galla do, and An onio M. Mo o
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Recen applica ions o ou -body
Con inuum-Disc e ized Coupled-Channels
calcula ions o 6He eac ions
Manuela Rod íguez-Galla do∗,† and An onio M. Mo o†
∗IEM, CSIC, Se ano 123, 28006 Mad id, Spain
†Dep o. FAMN, Uni e sidad de Se illa, Ap o. 1065, 41080 Se illa, Spain
Abs ac .
The ou -body con inuum-disc e ized coupled-channels app oach using a con inuum-bins
scheme o disc e iza ion o h ee-body p ojec iles, ha has been ecen ly de eloped, is p esen ed.
The o malism is discussed and applied o eac ions induced by he Bo omean nucleus 6He on
di e en a ge s (27Al, 64Zn, 120Sn, and 208Pb), wi h special emphasis on he ole o he Coulomb
couplings.
Keywo ds: Few-body sys ems. Di ec eac ions. Reac ions induced by uns able nuclei. Coupled-
channel and dis o ed-wa e models. Halo nuclei.
PACS: 21.45.- ,24.50.+g,25.60.- ,24.10.Eq,27.20.+n
INTRODUCTION
Exo ic nuclei ha e been objec o s udy in ecen yea s due o hei special p ope ies,
e y di e en om he nuclei o he s abili y alley. Among he exo ic nuclei, an
in e es ing case a e he so-called halo nuclei. These a e weakly-bound nuclei comp ising
a co e and one o wo alence neu ons o bi ing a dis ances la ge han he ypical
nuclea adii. In ecen yea s, la ge accele a o s ha e been buil a ound he wo ld o s udy
his kind o exo ic nuclei. Simul aneously, app op ia e eac ion heo ies ha e been also
de eloped o ex ac eliable in o ma ion om he expe imen al da a on exo ic nuclei.
The con inuum-disc e ized coupled-channels (CDCC) amewo k has been wide and
success ully used o yea s o analyze expe imen al da a on wo-body weakly-bound
nuclei using a h ee-body o malism ( ha is, wo-body p ojec ile plus a ge ). Recen ly,
he me hod has been ex ended o ou -body p oblems ( h ee-body p ojec ile plus a ge ),
wha allows o s udy eac ions wi h h ee-body weakly-bound nuclei, in pa icula ,
Bo omean nuclei. These nuclei has he special cha ac e is ic ha none o he h ee
bina y subsys ems is bound. This is he case o 6He(4He+n+n) o 11Li(9Li+n+n).
The CDCC me hod, o a h ee-body sca e ing p oblem, was de eloped in he 80s.
The basic idea o he me hod, explained in de ail in Re s. [1, 2], consis s in expanding
he s a es o he whole sys em (p ojec ile+ a ge ) in o he s a es o he p ojec ile. Fo
weakly-bound p ojec iles, he coupling o unbound s a es ( ha o m a con inuum) is el-
e an wi hin he eac ion dynamics. Then, we need o ea p ope ly he con inuum o he
p ojec ile. Fo his pu pose, in he s anda d h ee-body CDCC o mula ion, he con in-
uum spec um o he p ojec ile is unca ed a a maximum exci a ion ene gy
ε
max and he
XXXIII B azilian Wo kshop on Nuclea Physics
AIP Con . P oc. 1351, 29-38 (2011); doi: 10.1063/1.3608932
© 2011 Ame ican Ins i u e o Physics 978-0-7354-0908-8/$30.00
29
model space, om he b eakup h eshold o
ε
max, is hen di ided in o in e als, whe e
he numbe and posi ions o he in e als can depend on he p ope ies (e.g. esonan o
non- esonan ) o he con inuum o he sys em. Fo each such in e al, o ene gy bin, a
ep esen a i e squa e-in eg able s a e is cons uc ed as a linea supe posi ion o he wo-
body sca e ing s a es in he in e al. The me hod has been eno mously success ul in
he desc ip ion o elas ic and b eakup obse ables in eac ions in ol ing weakly-bound
wo-body p ojec iles [3, 4, 5] and has been ecen ly ex ended o include co e exci a ion
[6].
An al e na i e o ea he con inuum o he p ojec ile is o use a Pseudo-S a e (PS)
basis. This p ocedu e consis s in diagonalizing he Hamil onian o he sys em in a
unca ed disc e e basis and aking he posi i eene gy eigens a es as ep esen a i eo he
con inuum. The e a e many PS me hods in he li e a u e. Wi hin he CDCC amewo k,
di e en bases ha e been used like complex- ange Gaussian [7], T ans o med Ha monic
Oscilla o (THO) [8], and Lag ange [9].
In he pas decade he CDCC amewo k has been ex ended o ou -body p oblems.
Due o he di icul ies in calcula ing he ue con inuum o a h ee-body p ojec ile and
making bins, he CDCC was i s ex ended using PS bases like complex- ange Gaussian
[10, 11] and THO [12, 13]. Mos ecen ly, he binning p ocedu e has been de eloped
[14], p o iding mo e s able esul s o hea y a ge s.
In his wo k we p esen some ecen calcula ions o elas ic and b eakup obse ables,
o di e en eac ions induced by he Bo omean nucleus 6He, ob ained using he ou -
body CDCC o malism wi h he binning p ocedu e. In Sec ion II we explain he o mal
aspec s o he me hod. In Sec ion III we show he obse ables ob ained o he di e en
eac ions conside ed. Sec ion IV is he summa y and conclusions.
FOUR-BODY CDCC FORMALISM
To desc ibe he h ee-body g ound and exci ed con inuum s a es o he p ojec ile we
make use o a hype sphe ical ha monics (HH) expansion basis [15]. This in ol es use
o he one adial and i e angula hype sphe ical coo dina es,
ρ
,
α
,bx,by, ob ained om
he no malized Jacobi coo dina es~x,~y(see Fig. 1) o he h ee bodies [15, 13]. No e ha
he e a e h ee di e en Jacobi se s. The quan um numbe se ,
β
, ha de ines each h ee-
body channel [13] a e he hype momen um K, he o bi al angula momen a lxand lyin
coo dina es~xand~y, hei o al~
l=~
lx+~
ly, he o al spin Sxo he pa icles associa ed wi h
coo dina e~x, and he in e media e summed angula momen um ~
jab =~
l+~
Sx. I he spin
o he hi d pa icle, I, is assumed ixed hen he o al angula momen um is ~
j=~
jab +~
I
wi h p ojec ions
µ
. No e ha , o each con inuum ene gy
ε
and o al angula momen um
j, he e will be as many independen solu ions o he h ee-body sca e ing p oblem, as
he numbe o ou going channels
β
conside ed. These solu ions can be chosen as he
incoming channels
β
′, bu any o hogonal combina ion o hese could be equally alid.
Based on hese o al angula momen um eigens a es, Y
β
j
µ
(Ω)[13], whe e Ω≡
(
α
,bx,by), he bin wa e unc ions a e de ined as
φ
bin
nj
µ
(~x,~y) = ∑
β
Rbin
n
β
j(
ρ
)Y
β
j
µ
(Ω),(1)
30
000000
000000
000000
000000
000000
000000
000000
111111
111111
111111
111111
111111
111111
111111
x
y
R
2
1
3 a ge
p ojec ile
FIGURE 1. (Colo online) Rele an coo dina es o he sca e ing o a h ee-body p ojec ile by a
s uc u eless a ge .
whe e he label nincludes e e ence o he ene gy in e al o he bin [
κ
1,
κ
2], as well as
o he se o quan um numbe s
β
′. The unc ions Rbin
n
β
j(
ρ
)in Eq. (1) a e he associa ed
hype adial wa e unc ions,
Rbin
n
β
j(
ρ
)≡Rbin
[
κ
1,
κ
2]
β
′
β
j(
ρ
) = 2
p
π
N
β
′jZ
κ
2
κ
1
d
κ
e−i
δβ
′j(
κ
)
β
′j(
κ
)R
ββ
′j(
κ
,
ρ
),(2)
whe e
κ
=p2m|
ε
|/¯
his he momen um associa ed o he con inuum ene gy
ε
,
R
ββ
′j(
κρ
)a e he con inuum hype adial wa e unc ions wi h
δβ
′j(
κ
) hei sca e ing
phase shi , and
β
′j(
κ
)is a weigh unc ion wi h N
β
′ji s no maliza ion cons an . No e
ha o each jand h ee-body ene gy bin we mus cons uc wa e unc ions o all
allowed incoming channels
β
′. Fu he , as is explici in Eq. (1), o each nwe mus also
cons uc Rbin
n
β
j(
ρ
) o all allowed ou going channels
β
.
I ollows ha o include a la ge numbe o
β
′channels is a se e e compu a ional
challenge, and ha i is desi able o es ablish a hie a chy o he con inuum s a es ac-
co ding o hei impo ance o he eac ion dynamics. In so doing, we may be able o
desc ibe sca e ing obse ables using only a selec ed se o s a es, he numbe o hem
depending on he eac ion unde s udy. To his end, we make use o he eigens a es o
he mul i-channel h ee-body S-ma ix [16], o eigenchannels (EC), as ollows. (i) Fo
each jand con inuum ene gy
ε
, he S-ma ix in he
β
basis is diagonalized o ob ain
i s EC, enume a ed by
γ
, hei co esponding eigen alues exp[2i
δγ
j(
κ
)] and eigenphases
δγ
j(
κ
). (ii) The magni udes o hese eigenphases a e used o o de he EC. I has been
shown [14] ha hose EC wi h la ges phase shi s a e he mos s ongly coupled in he
eac ion dynamics, and hus a hie a chy o s a es can be es ablished by such an o de ing.
This leads o he possibili y o a unca ion in he numbe nec o EC included and es ing
o he con e gence wi h espec o his numbe .
The bin s a es gi en in Eq. (1) a e a disc e e ep esen a ion o he s a es o he h ee-
body p ojec ile. F om hem, he ou -body wa e unc ion o he p ojec ile- a ge sys em,
schema ically depic ed in Fig. 1, is o med as
ΨJM(~
R,~x,~y) = ∑
nj
µ
LML
φ
bin
nj
µ
(~x,~y)hLMLj
µ
|JMiiLYLML(b
R)1
R J
Lnj(R),(3)
whe e ~
Ris he coo dina e om he a ge o he cen e o mass o he p ojec ile, Lis
he o bi al angula momen um o he p ojec ile- a ge ela i e mo ion and Jis he o al
31
angula momen um, ~
J=~
L+~
j. The adial unc ions J
Lnj(R)sa is y he sys em o coupled
equa ions
−¯
h2
2m d2
dR2−L(L+1)
R2+
ε
nj −E J
Lnj(R)+ ∑
L′n′j′
iL′−LVJ
Lnj,L′n′j′(R) J
L′n′j′(R) = 0,
(4)
whe e m is he educed mass o he p ojec ile- a ge sys em. The coupling po en ials
VJ
Lnj,L′n′j′(R)a e hen
VJ
Lnj,L′n′j′(R) = hLnjJM|b
Vp (~ 1,~ 2,~ 3)|L′n′j′JMi,(5)
whe e he ke |LnjJMideno es he unc ion ΦJM
Lnj(b
R,~x,~y)gi en by
ΦJM
Lnj(b
R,~x,~y) = ∑
µ
ML
φ
bin
nj
µ
(~x,~y)hLMLj
µ
|JMiYLML(b
R).(6)
To calcula e hese coupling po en ials, a mul ipole expansion o he p ojec ile- a ge
in e ac ion is de eloped. The p ocedu e is analogous o ha o a h ee-body p oblem
epo ed in Re . [4]. We assume ha he p ojec ile- a ge in e ac ion is he sum o he
in e ac ions o each pa icle o he p ojec ile wi h he a ge , Vk (~ k)wi h k=1,2,3.
Fo each pai po en ial, an app op ia e Jacobi se is chosen so ha he co esponding
coo dina e~ kdepends only on he ec o s ~
Rand ~yk. Assuming ha he po en ials a e
cen al, he coe icien s o he mul ipole expansion a e gene a ed as
Vk
Q(R,yk) = 1
2Z+1
−1Vk( k)PQ(zk)dzk,(7)
whe e PQ(zk)is a Legend e polynomial, Qis he mul ipole o de and zk=b
~yk·b
~
Ris he
cosine o he angle be ween~ykand ~
R. So, he coupling po en ial can be exp essed as
VJ
Lnj,L′n′j′(R) = ∑
Q
(−1)J−jˆ
Lˆ
L′L Q L′
0 0 0 W(LL′jj′,QJ)FQ
nj,n′j′(R),(8)
whe e he adial o m ac o FQ
nj,n′j′(R)is
FQ
nj,n′j′(R) = (−1)Q+2j−j′ˆ
jˆ
j′(2Q+1)∑
ββ
′
3
∑
k=1∑
β
k
β
′
k
N
ββ
kN
β
′
β
′
k(9)
×(−1)lxk+Sxk+j′
abk−jabk−Ik
δ
lxkl′
xk
δ
SxkS′
xk ˆ
lyk ˆ
l′
yk ˆ
lkˆ
l′
kˆ
jabk ˆ
j′
abk lyk Q l′
yk
0 0 0 
×W(lkl′
klykl′
yk;Qlxk)W(jabk j′
abklkl′
k;QSxk)W(jj′jabk j′
abk;QIk)
×Z Z(sin
α
k)2(cos
α
k)2d
α
k
ρ
5d
ρ
Rbin
n
β
j(
ρ
)
ϕ
lxklyk
Kk(
α
k)Vk
Q(R,yk)
ϕ
lxkl′
yk
K′
k(
α
k)Rbin
n′
β
′j′(
ρ
),
32

wi h
β
kbeing he se o quan um numbe s in he k’ h Jacobi sys em whe e he po en ial
does no depend on xk, and
β
being he se in he Jacobi sys em in which he s a es
o he p ojec ile a e calcula ed. The ma ix elemen s N
ββ
k ans o m he hype angula ,
angula and spin pa s o he wa e unc ions om one Jacobi se o ano he . Thei explici
exp ession as a unc ion o he Raynal-Re ai coe icien s is de eloped in Re . [17]. No e
ha Eqs. (8) and (9) a e comple ely gene al, and do no depend on he na u e o he
basis.
APPLICATION TO 6HE+TARGET REACTIONS
We apply he o malism o he p eceding sec ion o se e al eac ions induced by he
Bo omean halo nucleus 6He. The eac ions conside ed, o which elas ic expe imen al
da a exis , a e 6He+27Al a 11 MeV, 6He+64Zn a 13.6 MeV, 6He+120Sn a 17.4 MeV,
and 6He+208Pb a 22 MeV. No e ha each a ge has a mass app oxima ely wice ha
o p e ious a ge and he ene gies in he labo a o y ame a e nea he Coulomb ba ie .
So, a s udy o his se o eac ions can gi e us a insigh on he ole o he Coulomb
in e ac ion as he mass o he a ge inc eases.
He e we use he same s uc u e model o he h ee-body sys em 6He, as in Re s. [12,
13, 14]. The nucleus is ea ed as a h ee-body sys em o an ine
α
pa icle co e and wo
alence neu ons. A no able p ope y o 6He is ha none o i s bina y sub-sys ems bind,
while he h ee-body sys em has a single bound s a e wi h binding ene gy o 0.973 MeV
and o al angula momen um j
π
=0+. I s low-lying con inuum spec um is domina ed
by a na ow j
π
=2+ esonance, 0.825 MeV abo e h eshold. The Hamil onian includes
wo-body po en ials plus an e ec i e h ee-body po en ial. The 6He g ound-s a e and
con inuum wa e unc ions a e gene a ed using he codes FACE [17] and STURMXX
[18]. The maximum hype momen um used was Kmax =8. The pa ame e s o he h ee-
body in e ac ion a e adjus ed o ep oduce he g ound-s a e sepa a ion ene gy and ma e
adius and he esonance ene gy ( o j=1−and 2+s a es). The calcula ed g ound s a e
ene gy was 0.953 MeV and he oo mean squa ed ( ms) adius was 2.46 m (assuming
a ms adius o 1.47 m o he
α
pa icle).
The coupled-channels equa ions we e sol ed using he code FRESCO [19], ha eads
he coupling po en ials ex e nally. We included in he calcula ion he s a es wi h angula
momen um j=0+, 1−, 2+and he p ojec ile- a ge in e ac ion mul ipole couplings wi h
o de Q=0,1,2. The agmen - a ge in e ac ions we e ep esen ed by op ical po en ials
which ep oduce he elas ic sca e ing a he app op ia e ene gy. The po en ials used
a e om he global pa ame iza ion o Koning and Dela oche [20] o he n+ a ge
subsys ems. Fo he 4He+ a ge subsys ems he choice depends on he a ge , being
om [21] o 27Al, [22] o 64Zn, [23] o 120Sn, and [24] o 208Pb. Fo all hese
eac ions we ha e ound con e gence including only he i s ou h EC and disc e izing
he con inuum in o 6 and 9 bins, o each EC, o j=0+,2+and j=1−, espec i ely. The
maximum ene gy o 6He included a ies om 6 MeV o 6He+27Al and 6He+64Zn o 7
MeV o 6He+120Sn, and 8 MeV o 6He+208Pb.
33
0 10 20 30 40 50 60
θc.m. (deg ees)
0
0.2
0.4
0.6
0.8
1
σ/σRu h
Expe imen al da a
No con inuum
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Al
0 20 40 60 80 100 120
θc.m.(deg ees)
0
0.2
0.4
0.6
0.8
1
σ/σRu h
Expe imen al da a
No con inuum
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Sn
0 30 60 90 120 150 180
θc.m. (deg ees)
0
0.2
0.4
0.6
0.8
1
σ/σRu h
Expe imen al da a
No con inuum
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Zn
0 30 60 90 120 150 180
θc.m. (deg ees)
0
0.2
0.4
0.6
0.8
1
σ/σRu h
Expe imen al da a
No con inuum
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Pb
FIGURE 2. (Colo online) Elas ic di e en ial c oss sec ion ( a io o Ru he o d) in he cen e o mass
ame o 6He+27Al a 11 MeV ( op le ), 6He+64Zn a 13.6 MeV ( op igh ), 6He+120Sn a 17.4 MeV
(bo om le ), and 6He+208Pb a 22 MeV (bo om igh ). The expe imen al da a a e aken om Re s. [25],
[22], [26], and [27] o 6He+27Al, 6He+64Zn, 6He+120Sn, and 6He+208Pb, espec i ely.
Elas ic sca e ing
In Fig. 2 we show he elas ic di e en ial c oss sec ion dis ibu ions o he eac-
ions conside ed. The yellow ci cles a e he exis ing expe imen al da a om Re s.
[25, 22, 26, 27]. The do ed blue lines a e he calcula ions wi hou including he con-
inuum. The black solid lines a e he ull ou -body CDCC calcula ions including bo h
nuclea and Coulomb in e ac ions. Finally he dashed ed lines a e he ull ou -body
CDCC calcula ions including only nuclea couplings (keeping he cen al Coulomb in-
e ac ion be ween he colliding nuclei). We can see ha in all he eac ions he ou -body
CDCC calcula ions, wi h Coulomb and nuclea in e ac ions, ep oduces ai ly well he
expe imen al da a. Only o he 6He+208Pb sys em, he expe imen al da a a backwa d
angles is somewha unde es ima ed by he calcula ion. We can also see he ele ance o
including he con inuum o ep oduce he expe imen al da a. Compa ing wi h he nu-
clea calcula ion we see ha he ole o he Coulomb in e ac ion is p ac ically negligible
o he ligh es a ge 27Al whe eas is c ucial o he hea ies a ge 208Pb.
B eakup
In Fig. 3 we p esen he b eakup di e en ial dis ibu ions as a unc ion o he cen e -
o -mass sca e ing angle. The black solid lines a e he ull ou -body CDCC calcula ions
34
0 10 20 30 40 50 60
θ (deg ees)
1
10
100
dσbu/dΩ (mb/s )
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Al
0 20 40 60 80 100 120
θc.m. (deg ees)
1
10
100
dσbu/dΩ (mb/s )
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Sn
0 30 60 90 120 150 180
θc.m. (deg ees)
1
10
100
dσbu/dΩ (mb/s )
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Zn
0 30 60 90 120 150 180
θc.m. (deg ees)
1
10
100
dσbu/dΩ (mb/s )
4b-CDCC: Nuclea +Coulomb
4b-CDCC: Nuclea
Pb
FIGURE 3. (Colo online) B eakup di e en ial c oss sec ion dis ibu ion in he cen e o mass ame
o 6He+27Al a 11 MeV ( op le ), 6He+64Zn a 13.6 MeV ( op igh ), 6He+120Sn a 17.4 MeV (bo om
le ), and 6He+208Pb a 22 MeV (bo om igh ).
TABLE 1. To al b eakup and eac ion c oss sec ions.
6He+27Al 6He+64Zn 6He+120Sn 6He+208Pb
σ
nuc+coul
eac (mb) 1661.7 1442.9 1495.9 1389.8
σ
nuc+coul
bu (mb) 187.09 97.06 161.85 266.28
σ
nuc
bu (mb) 166.71 56.15 67.44 70.84
including bo h nuclea and Coulomb in e ac ions and he dashed ed lines a e he ull
ou -body CDCC calcula ions including only nuclea couplings. He e we see ha he
Coulomb b eakup is no ele an o he ligh es a ge , whe eas ge s d ama ically im-
po an as he mass o he a ge inc eases.
We can see his ac mo e clea ly in Table 1 whe e he o al eac ion and b eakup c oss
sec ions oge he wi h he o al nuclea b eakup c oss sec ion a e shown. I is no iceable
he la ge dec ease o he nuclea b eakup c oss sec ion wi h espec o he nuclea plus
Coulomb b eakup c oss sec ion in he case o he hea ies a ge , whe eas bo h b eakup
c oss sec ions a e e y close o he ligh es a ge .1
1No e ha he o al eac ion and b eakup is la ge o he ligh es a ge since he ene gy o he eac ion
is well abo e he Coulomb ba ie wi h espec he o he h ee eac ions.
35
T i ial local pola iza ion po en ial
We ha e also ex ac ed om he ou -body CDCC calcula ions he so-called i ial
local pola iza ion (TLP) po en ial [28]. This is a local and L-independen po en ial
which ep esen s he o e all e ec o he b eakup channels on he elas ic sca e ing.
This po en ial is cons uc ed in such a way ha he one-channel calcula ion pe o med
wi h he po en ial Uba e( ) +UTLP( )gi es app oxima ely he same elas ic sca e ing as
he ull CDCC calcula ion. The ba e po en ial, Uba e( )is jus he sum o he agmen -
a ge in e ac ions con olu ed wi h he g ound s a e densi y o he 6He nucleus. Figu e 4
shows hese pola iza ion po en ials, due o Coulomb and nuclea in e ac ion wi h solid
black lines and nuclea wi h dashed lines, calcula ed o he di e en sys ems a di e en
ene gies.
The eal pa o he TLP po en ials is epulsi e (excep a e y sho dis ances whe e
he de ails o his po en ial a e p obably no meaning ul). This epulsi e componen is
mainly due o nuclea couplings [29, 30, 31]. Howe e , as he a ge mass inc eases he
eal pa s a s o exhibi a long- ange nega i e ail a dis ances la ge han he s ong
abso p ion adius. The e ec o his long- ange a ac i e ail is o educe he he heigh
o he ba ie o he ba e po en ial leading o an enhancemen o he abso p ion [32]. This
ail is known o a ise om dipole Coulomb couplings and is consis en wi h quali a i e
ea u es ound in ecen op ical model i s o he 6He+208Pb da a [29]. The imagina y
pa s o he TLP po en ials a e mos ly abso p i e. Bo h he eal and imagina y pa s
ex end o la ge dis ances, well beyond he s ong abso p ion adius. These ea u es a e
consis en wi h he indings o Mackin osh and Keeley [33] and Rusek [34].
The TLP ex ac ed om he calcula ion wi h only nuclea couplings does no show he
a ac i e ail o he eal pa , e idencing he Coulomb o igin o his ail. Besides, he
imagina y pa s o all he a ge s ha e a longe ange han in he calcula ion including
he Coulomb couplings. This e ec is la ge o he hea ies a ge and e y small o
he ligh es a ge .
SUMMARY AND CONCLUSIONS
We ha e p esen ed he ou -body CDCC o malism o s udy he eac ions induced
by h ee-body p ojec iles like he Bo omean nucleus 6He. To ea he h ee-body
con inuum o he p ojec ile we use a con inuum-bins scheme ha has been ecen ly
de eloped. The o malism has been applied o se e al eac ions o 6He wi h inc easing
mass a ge s: 6He+27Al a 11 MeV, 6He+64Zn a 13.6 MeV, 6He+120Sn a 17.4 MeV,
and 6He+208Pb a 22 MeV.
We ha e compa ed he elas ic c oss sec ion dis ibu ions calcula ed wi h he ou -
body CDCC wi h he exis ing expe imen al da a. In gene al, we ha e ound a good
ag eemen . We ha e compa ed he calcula ed dis ibu ions including Coulomb plus
nuclea couplings wi h hose pe o med including only nuclea couplings and we ha e
ound ha he ole o he Coulomb b eakup g ows d as ically om he ligh es o he
hea ies a ge . The same e ec is p esen in he b eakup angula dis ibu ions.
We ha e also p esen ed he TLP po en ials ex ac ed om he ou -body CDCC
calcula ions, wi h and wi hou Coulomb b eakup. Inclusion o Coulomb couplings has
36