PHYSICAL REVIEW C 94, 064620 (2016)
Elas ic sca e ing and b eakup o 11Be on deu e ons a 26.9AMeV
J. Chen,1J. L. Lou,1,*Y. L. Ye,1J. Rangel,2A. M. Mo o,3D. Y. Pang,4Z. H. Li,1Y. C. Ge, 1Q. T. Li,1J. Li,1W. Jiang,1
Y. L. Sun,1H. L. Zang,1Y. Zhang,1N. Aoi,5E. Ideguchi,5H. J. Ong,5J. Lee,6J. Wu,6H. N. Liu,6C. Wen,6Y. Ayyad,5
K. Ha anaka,5T. D. T an,5T. Yamamo o,5M. Tanaka,5T. Suzuki,5and T. T. Nguyen5
1School o Physics and S a e Key Labo a o y o Nuclea Physics and Technology, Peking Uni e si y, Beijing 100871, China
2Ins i u o de F´
ısica, Uni e sidade Fede al Fluminense, A enida Li o anea s/n, G agoa ´
a, 24210-340, Ni e ´
oi, Rio de Janei o, B azil
3Depa amen o de FAMN, Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain
4School o Physics and Nuclea Ene gy Enginee ing, Beijing Key Labo a o y o Ad anced Nuclea Ma e ials and Physics, Beihang Uni e si y,
Beijing 100191, China
5Resea ch Cen e o Nuclea Physics, Osaka Uni e si y, Osaka, Japan
6RIKEN (Ins i u e o Physical and Chemical Resea ch), 2-1 Hi osawa, Wako, Sai ama 351-0198, Japan
(Recei ed 31 Augus 2016; published 30 Decembe 2016)
The elas ic sca e ing and b eakup eac ions o he halo nucleus 11Be on deu e ons a an inciden ene gy o
26.9AMeV a e epo ed o he i s ime. Special a en ion has been paid o he de e mina ion and sub ac ion
o he p o on con amina ions in he deu e a ed polye hylene (CD2)n a ge (whe e D2deno es 2H2). The c oss
sec ions o elas ic sca e ing a e analyzed wi h he sys ema ic op ical po en ials o Daehnick e al. and DA1p,
as well as wi h single- olding po en ials, de i ed om he Jeukenne-Lejeune-Mahaux e ec i e nucleon-nucleon
in e ac ion. An ex ended e sion o he con inuum-disc e ized coupled-channels (XCDCC) o malism, including
dynamic co e exci a ion (DCX) e ec s, is applied o analyze he elas ic sca e ing and b eakup da a. Compa isons
o he ull XCDCC calcula ion wi h ha omi ing DCX e ec s indica e ha he co e exci a ion plays a ema kable
ole in ep oducing b eakup eac ions o 11Be +d.
DOI: 10.1103/PhysRe C.94.064620
I. INTRODUCTION
The in es iga ion o exo ic nuclei has con inuously de el-
oped since he ea ly 1980s hanks o he a ailabili y o a ious
ools o adioac i e beam p oduc ion, including in- ligh
agmen a ion, which p o ide e e inc easing accessibili y
o he nuclea landscape a om he β-s abili y line [1–3].
11Be was ex ensi ely s udied as a neu on-halo nucleus. I s
small one-neu on sepa a ion ene gy o 504 keV oge he wi h
he dominan s-wa e con igu a ion o he alence neu on
lead o a e y ex ended neu on-densi y dis ibu ion [4–6].
The pa i y in e sion o i s g ound s a e (1/2+) was p edic ed
by Talmi and Unna [7] and con i med by he expe imen al
measu emen o Albu ge e al. [8]. Nume ous measu emen s
and s uc u e calcula ions sugges ha he g ound s a e o
11Be con ains, in addi ion o he dominan 10Be(0+)+n(s1/2)
con igu a ion, a signi ican admix u e (∼20%) o co e exci ed
componen s, wi h he alence neu on p e e ably occupying
he d5/2o bi [9–11].
The sizable co e exci a ion componen s in he 11Be g ound
s a e play an impo an ole in ea u ing he 11Be s uc u e.
Fu he mo e, when conside ing he collision o 11Be on a
a ge , he coupling be ween he collec i e exci a ions and
he co e exci a ions would a ec he eac ion dynamics.
Bo h e ec s (s uc u e and dynamics) ha e been imple-
men ed in an ex ended e sion o he con inuum-disc e ized
coupled-channels (XCDCC) o malism p oposed by Summe s
e al. [12], and in a no- ecoil ex ended dis o ed wa e Bo n
app oxima ion (XDWBA) model [13]. Co e exci a ion was
*[email p o ec ed]
shown o ha e a signi ican e ec on he b eakup c oss sec ions
in calcula ions using he XCDCC model o he b eakup o
11Be on a p o on a ge a inciden ene gies o 63.7 [13–15] and
26.9AMeV [16]. These wo measu emen s con i med he co e
exci a ion e ec s a a ious inciden ene gies. Fu he mo e,
co e exci a ion was demons a ed o be impo an on a ious
igh ly bound a ge s, like 1H[13–15], 12C[11], 64Zn [17,18],
and 208Pb [11]. I is in e es ing o examine he co e exci a ion
e ec on he weakly bound a ge s, such as a deu e on a ge .
His o ically, he deu e on, as a ypical weakly bound
nucleus, is o g ea impo ance in nuclea eac ion s udy.
Mos di ec nuclea eac ions, such as s ipping, ans e , and
pickup, we e i s s udied wi h deu e on beams due o hei
easy access by accele a o s. Deu e on-induced eac ions ha e
been one o he mos powe ul spec oscopic ools o ex ac
s uc u e in o ma ion o s able nuclei. These s udies can be
ex ended o he case o uns able nuclei, using expe imen s
in in e se kinema ics. Fo uns able p ojec iles close o he
d ip lines, he desc ip ion o hese eac ions is, howe e ,
challenging because one has o ea coupling a ising om
bo h he p ojec ile and a ge b eakup. The measu emen o
hese kinds o da a, along wi h he modi ica ion o ela ed
eac ion o malisms o desc ibe hem, is he e o e a opic o
imely in e es o eliably ex end he spec oscopic s udies wi h
deu e ons o egions a om he s abili y line.
In his wo k, we p esen he da a o elas ic sca e ing and
b eakup o 11Be, o he i s ime, on a deu e on a ge a
26.9AMeV. The beam ene gy was chosen conside ing he
alidi y o bo h b eakup and ans e eac ion mechanisms,
he a ailabili y o he beam, he e ec i e de ec ion o ecoil
ligh cha ged pa icles a la ge angles, and he complemen
o he p e ious b eakup eac ion wo k a highe ene gy [19]
2469-9985/2016/94(6)/064620(8) 064620-1 ©2016 Ame ican Physical Socie y
J. CHEN e al. PHYSICAL REVIEW C 94, 064620 (2016)
and ans e eac ion expe imen s a lowe ene gies [20,21].
The pape is o ganized as ollows. In Sec. II we p esen
he de ails o he expe imen , and he da a analysis. Special
a en ion is paid o he de e mina ion and sub ac ion o
he p o on con amina ions in he (CD2)n a ge (whe e D2
deno es 2H2). In Sec. III we show an op ical model analysis
o he elas ic sca e ing da a in e ms o phenomenological
op ical po en ials. In Sec. IV he angula dis ibu ions o
elas ic sca e ing and b eakup a e compa ed wi h he XCDCC
calcula ions, and he impo ance o he co e exci a ion e ec
is also discussed. Finally, in Sec. Vwe summa ize he main
esul s o his wo k.
II. EXPERIMENTAL RESULTS
The expe imen was pe o med on he EN-cou se beam line
a he Resea ch Cen e o Nuclea Physics (RCNP), Osaka
Uni e si y, Japan [22]. The p ima y beam 13Ca 60AMeV
impinged on a hick 9Be a ge o p oduce a seconda y beam o
11Be, which was sepa a ed and pu i ied by he elec omagne ic
sepa a o . The beam in ensi y and pu i y o 11Be was app oxi-
ma ely 1 ×104pa icles pe second and 95%, espec i ely. The
momen um sp ead was limi ed, by a sli a he dispe sion plane,
down o P/P=1% o educe he ene gy sp ead o he beam.
The beam spo size on he physical a ge is less han φ20 mm.
The expe imen al se up can be ound in Re . [16], and
only de ec o s ele an o he elas ic sca e ing and b eakup o
11Be +da e desc ibed he e. Telescopes TELE0 and TELE1
we e employed o de ec he p ojec like iso opes and he
ecoil ligh pa icles, espec i ely. TELE0, comp ising a
double-sided silicon s ip de ec o (DSSD) wi h a hickness
o 1000 μm and wo la ge su ace silicon de ec o s (SSDs)
1500 μm hick, was ins alled a a ound 0◦ ela i e o he
beam di ec ion. TELE1 is composed o a 300-μm DSSD, a
1500-μm SSD, and a laye o ou CsI(Tl) c ys als ead ou
by pho odiodes. The ac i e a ea and s ip wid h o each DSSD
is 62.5 ×62.5 mm2and 2 mm, espec i ely. The dis ance
be ween he cen e o he a ge and TELE0 (TELE1) is 200
(170) mm. A (CD2)n a ge wi h a hickness o 4 mg/cm2
was moun ed as he physical a ge , oge he wi h a ca bon
ilm (12 mg/cm2) and also a (CH2)n oil (4 mg/cm2)used
o backg ound measu emen s. The (CD2)n a ge hickness
is op imized in o de o ha e enough ecoil deu e on yield
while e aining good esolu ion o exci a ion ene gies in 11Be
deduced om he ecoil deu e ons. Ta ge s we e il ed 15◦ o
es ic he ene gy loss o he ecoil ligh pa icles in he a ge .
Fo deu e ons elas ically sca e ed o 81.5◦, co esponding o
he minimum de ec ion angle in he cen e -o -mass sys em
(16.5◦) o 11Be, he ecoil deu e on ene gy is 3.3 MeV while
i s ene gy loss in he a ge is abou 1.19 MeV, assuming he
eac ion poin a he middle o he il ed a ge , which is good
enough o mee he de ec ion and esolu ion equi emen s.
In coincidence wi h he ecoil ligh pa icles, he esidual
agmen s we e iden i ied wi h E −Eme hod. 10Be is well
sepa a ed om 11Be as shown in he pa icle iden i ica ion
(PID) spec um in Fig. 1. The di e en ial c oss sec ions o
he 11Be +delas ic sca e ing and b eakup can be ex ac ed
om he ecoil deu e ons in coincidence wi h 11Be and 10Be,
espec i ely.
E (MeV)
120 140 160 180 200 220 240 260 280 300
E (MeV)
55
60
65
70
75
80
85
90
11Be
10Be
FIG. 1. The PID using da a aken by TELE0 in coincidence wi h
ligh pa icles measu ed by TELE1.
Figu es 2(a) and 2(b) illus a e ene gies e sus angles o
he ecoil ligh pa icles (p o on and deu e on) measu ed by
TELE0 in coincidence wi h 11Be and 10Be de ec ed by TELE1,
espec i ely. The ene gy losses o deu e ons in he a ge we e
co ec ed o he deduced exci a ion ene gy spec a in Fig. 2,
assuming a eac ion poin a he middle o he a ge . A cu
o labo a o y angles smalle han 80◦was applied due o
he ene gy de ec ion h eshold o he ecoil ligh pa icles.
Mos e en s lie along he kinema ic cu es o he 11Be +d
elas ic (solid cu e) and inelas ic sca e ing (dashed and do ed
cu es), bu a small po ion o e en s dis ibu e a ound he
kinema ic lines o 11Be +p(do -do -dashed cu e). The eason
is ha he deu e a ed compounds a e usually con amina ed
by some hyd ogen componen , whose con ibu ions should
be sub ac ed om he expe imen al da a o 11Be sca e ed
om he (CD2)n a ge . In addi ion, hese e en s could also
66 70 74 78
0
5
10
15
20
25
30
E (MeV)
E (MeV)
(a)
66 70 74 78
0
5
10
15
20
25
30
(b)
(a)
Be + d
11
Be + p
11
s ipping
1.78 MeV
3.41 MeV
FIG. 2. Plo o ene gy s angle o he ecoil ligh pa icles in
coincidence wi h (a) 11Be and (b) 10Be o (CD2)n(colo pale es) and
(CH2)n(black do s and iangles) a ge s. The calcula ed kinema ic
loci o he elas ic sca e ing o 11Be +dand 11Be +pa e shown as
solid and do -do -dashed cu es in (a), while ha o he 11Be +d
inelas ic sca e ing o he 1.78- and 3.41-MeV esonances o 11Be
a e ep esen ed as dashed and do ed cu es in (b), espec i ely. The
do -dashed line s ands o he kinema ic cu e o he n-delas ic
sca e ing.
064620-2
ELASTIC SCATTERING AND BREAKUP OF 11Be ON . . . PHYSICAL REVIEW C 94, 064620 (2016)
65
70
75
80
85
012345678
65
70
75
80
85
012345 678
(a) (b)
Be + d
11
Be + p
11
1.78 MeV
3.41 MeV
s ipping
FIG. 3. Angula co ela ion spec a o he ecoil ligh pa icles
and he elas ic sca e ed (a) 11Be, and (b) 10Be om he b eakup
eac ion, espec i ely, on he impu e (CD2)n a ge . The de ini ions
o kinema ic cu es a e he same as hose in Fig. 2. The a ea ma ked
by do ed cu es in (a) shows he cu applied o he calcula ion o
p o on con amina ions. The black do -dashed ci cle in (b) ep esen s
he a ea o he 1ns ipping eac ion om 11Be by he (CD2)n a ge .
be obse ed on he angula co ela ion spec a o he ecoil
ligh pa icles and 11Be [see do -do -dashed cu e in Fig. 3(a)].
Conside ing ha he Ru he o d c oss sec ion o 11Be +pis
abou ou imes la ge han ha o 11Be +da he same
labo a o y angles, we could in e ha he 11Be +pelas ic
sca e ing c oss sec ion is much la ge han ha o 11Be +d.
As a esul , e en i he hyd ogen con amina ion is small
in he (CD2)n a ge , i s in luence should no be igno ed,
especially in he small cen e -o -mass angles o 11Be o la ge
labo a o y angles o deu e ons [see Fig. 3(a)], whe e he
sca e ed p o ons a e mixed wi h deu e ons. This e ec can be
emo ed by sub ac ing he (CH2)n a ge expe imen al da a
om he (CD2)nda a as long as we know he ac ion o p o on
con aminan in he (CD2)n a ge .
Based on he ac ha 11Be +pelas ic sca e ing di e en ial
c oss sec ions a e he same o p o ons in (CH2)nand impu e
(CD2)n a ge s, and he de ec o s (solid angles) a e he same
du ing (CH2)nand (CD2)n a ge expe imen s, he ollowing
equa ion can be es ablished:
ρH-CD2
ρH-CH2
=NSH-CD2
NSH-CH2
Nin-CH2
Nin-CD2
,(1)
whe e ρH-CH2(ρH-CD2), NSH-CH2(NSH-CD2), and Nin-CH2
(Nin-CD2) s and o he p o on a eal densi y (mg/cm2), he
elas ically sca e ed p o on numbe , and he incoming 11Be
beam pa icle numbe o he (CH2)n[(CD2)n] a ge , e-
spec i ely. Since he hickness o he (CH2)n a ge is known
(4.0 mg/cm2), he densi y o p o on con amina ions in he
(CD2)n a ge can be de e mined by he a io o he sca e ed
p o ons in (CH2)nand (CD2)n a ge s wi h he no malized
11Be pa icle numbe . In o de o calcula e ρH-CD2we applied
a cu (black do ed a ea) on Fig. 3(a) whe e he p o ons a e
clea ly sepa a ed om he deu e ons and mos e en s ollow
he kinema ic cu e o he 11Be +pangula co ela ions
(do -do -dashed cu e). Wi h his cu , he 11Be exci a ion
ene gy spec a a e deduced om ene gies and angles o he
p o ons measu ed om he (CH2)nand he con amina ed
(CD2)n a ge s. Finally, o he con amina ed (CD2)n a ge
wi h a o al hickness o 4.0 mg/cm2used in his expe imen ,
he a io o p o on and deu e on numbe is de e mined o be
9.5±0.6%. The e o 0.6% is ob ained om he s a is ics o
he sca e ed ligh pa icles numbe , and he incoming beam
pa icles numbe . The sys ema ic e o is es ima ed o be 1.2%
mainly esul ing om he di e en cu s in Fig. 3(a) and he
unce ain ies in a ge hickness.
In Sec. IV, he measu ed b eakup da a a e compa ed wi h
XCDCC calcula ions. Because his me hod p o ides only
he elas ic b eakup c oss sec ions, he con ibu ions om
o he eac ion p ocesses should be emo ed om he b eakup
expe imen al esul s. Simila ly o Re . [16], he coinciden
measu emen o he ecoil deu e ons and 10Be can help us
exclude he con ibu ions o 1ns ipping om 11Be using he
kinema ic condi ions. Some de ails can be seen in Figs. 2(b)
and 3(b). Fi s , he neu on s ipped om he 11Be p ojec ile by
he deu e on a ge would app oxima ely ollow he kinema ics
o he n-delas ic sca e ing, as shown by he black do -dashed
cu e in Fig. 2(b). Second, a e he 1ns ipping eac ion, he
esidual 10Be agmen s would be emi ed a ound 0◦ ela i e
o he beam di ec ion. A labo a o y angles smalle han 1.2◦,a
small ac ion o e en s a e clea ly sepa a ed om he angula
co ela ion cu es o he 11Be +dinelas ic sca e ing; see
black do -dashed ci cle a ea in Fig. 3(b). In p inciple, using
he coinciden measu emen , we could ba ely de ec he 10Be
om b eakup eac ion a angles smalle han 1.2◦due o he
ene gy h eshold o he ecoil ligh pa icles. The e o e, he
e en s in he black do -dashed ci cle in Fig. 3(b) should mainly
come om he 1ns ipping eac ion o 11Be. As a esul , a
cu o 10Be labo a o y angles la ge han 1.2◦was applied o
ex ac he b eakup c oss sec ions. O he p ocesses, such as
e apo a ion and abso p ion, can also be elimina ed using he
coinciden measu emen , because he low ene gy deu e ons
om hose eac ions would be emi ed a he smalle labo a o y
angles [16].
Figu es 4(a) and 4(b) display he exci a ion ene gy spec a
o he g ound s a e (g.s.) and he con inuum s a es o 11Be,
which a e deduced om ene gies and angles o he elas ically
and inelas ically sca e ed deu e ons in coincidence wi h 11Be
and 10Be, espec i ely. The backg ound con ibu ions a ising
om 12Cand 1Hha e been sub ac ed using he da a aken om
he ca bon and (CH2)n a ge s no malized o he same numbe
o beam pa icles and he equi alen ca bon and hyd ogen
componen as o he (CD2)n a ge . The ull wid h a hal
maximum (FWHM) o he exci a ion ene gy spec um o he
elas ic sca e ing is abou 2.3 MeV [Fig. 4(a)], esul ing om
he ene gy dispe sion o he 11Be beam, he ene gy losses and
s aggling o he ecoil deu e ons in he a ge s, as well as he
ene gy and angula esolu ion o TELE1. This alue ag ees
wi h he simula ion esul using he GEANT4 package [23].
Two egions o exci a ion ene gy o he con inuum s a es
we e selec ed due o he poo esolu ion. The i s one, anging
om 0.5 o 3.0 MeV, is cen e ed a ound he known 5/2+
esonance a Eex =1.778 MeV. The second egion, om 3.0
o 5.5 MeV, con ains o he highe ene gy esonan s a es, such
as he 3/2+s a e a Eex =3.41 MeV. The c oss sec ions o
he second egion could no be ex ac ed om he 11Be +p
b eakup eac ion in Re . [16] because he solid angle o TELE1
dec eases e y quickly as he exci a ion ene gy inc eases o
ha eac ion. Fo he 11Be +db eakup eac ion, simula ions
064620-3
J. CHEN e al. PHYSICAL REVIEW C 94, 064620 (2016)
E* MeV
-20246810
Coun s / 300keV
0
20
40
60
80
100
120
140
160
E* MeV
-4 -2 0 2 4 6 8 10
Coun s / 300keV
0
100
200
300
400
500
600
(a)
(b)
(
(
)
)
(s )
FIG. 4. Exci a ion ene gy spec um o (a) he g ound s a e and
(b) unbound exci ed s a es o 11Be deduced om he sca e ed
deu e ons in coincidence wi h 11Be and 10Be, espec i ely. The
backg ound con ibu ions a ising om 12Cand (CH2)nha e been
sub ac ed. The dashed cu e in (b) wi h he e ical axis on he
igh -hand side s ands o he solid angle o TELE1.
o he solid angle o TELE1 as a unc ion o exci a ion ene gy
(Eex) we e pe o med wi h he GEANT4 package, and he esul s
a e shown by he dashed line in Fig. 4(b) wi h he e ical
axis on he igh -hand side. The solid angle emains nea ly
a cons an om Eex =0–4.5 MeV, and dec eases abou 10%
om Eex =4.5–5.5 MeV. Fo Eex >5.5 MeV, he solid angle
dec eases quickly, so he b eakup c oss sec ions we e no
ex ac ed.
The di e en ial c oss sec ions o he 11Be +delas ic
sca e ing, as a a io o he Ru he o d c oss sec ions, a e
displayed in Fig. 5. The angula dis ibu ions o b eakup c oss
sec ions o he exci a ion ene gy in e als o 0.5<E
ex <
3.0 MeV and 3.0<E
ex <5.5 MeV a e displayed in Figs. 7(a)
and 7(b), espec i ely. The e o ba s a e pu ely s a is ics only
aking in o conside a ion he backg ound sub ac ion o ca bon
and p o on con amina ions in he (CD2)n a ge . The sys ema ic
e o is less han 10%, a ising om he unce ain ies in solid
angles (5%), he hickness o he a ge (2%), he cu s on he
h eshold and he pa icle iden i ica ion spec um measu ed by
TELE0 (4%), and he cu s applied on he exci a ion ene gy
spec a (5%). To moni o he possible deu e on leakage om
he (CD2)nplas ic a ge , we checked he de ec ed numbe
o ecoil deu e ons a he beginning and close o he end o
FIG. 5. Compa isons be ween he expe imen al di e en ial c oss
sec ions (as a a io o Ru he o d) and op ical model calcula ions o
he 11Be +delas ic sca e ing a 26.9AMeV. The do -dashed, do ed,
as well as dashed and solid cu es ep esen he calcula ions wi h
op ical po en ials o DA1p, Daehnick e al. [24], as well as he olding
po en ial gene a ed wi h he JLM nucleon-nucleon in e ac ion, wi h
ene gy-dependence pa ame e s o se I and se II, espec i ely.
he expe imen , espec i ely, o he same numbe o inciden
pa icles and he same a ge se up, and ound a change o less
han 2.0%. This de ia ion is wi hin he s a is ical unce ain y.
The e o e, he change o C/D a io in he a ge is negligible
o he p esen expe imen .
III. PHENOMENOLOGICAL OPTICAL MODEL ANALYSIS
In his sec ion, he measu ed elas ic sca e ing angula
dis ibu ion is analyzed in he amewo k o he op ical model
(OM). The e exis in he li e a u e se e al global deu e on
op ical model po en ials o deu e on sca e ing, such as
ha ob ained om he comp ehensi e analysis o Daehnick
e al. [24]. Howe e , p e ious analyses ha e e idenced ha
hese pa ame iza ions ail o p ope ly desc ibe he da a
when ex apola ed ou side hei ini ial domain o alidi y,
pa icula ly o ligh a ge s and a la ge sca e ing angles [25–
27]. Fo his eason, a new global deu e on po en ial, called
DA1p [28], was ecen ly de eloped, based on 67 se s o
expe imen al da a o deu e on elas ic sca e ing om 1p-shell
nuclei wi h inciden ene gies be ween 5.25 and 170 MeV. This
global po en ial is employed o he p esen da a.
A single- olding model (SFM) analysis was also pe o med
o he elas ic sca e ing da a using he Lane-consis en
B uy`
e es Jeukenne-Lejeune-Mahaux (JLM) model nucleon-
nucleon in e ac ion. Two se s o ene gy-dependen pa ame e s,
designa ed as JLM Se I [29] and JLM Se II [30], we e applied.
The nucleon densi y dis ibu ion o 11Be was calcula ed wi h
he Ha ee-Fock me hod using he SkX in e ac ion [31]. The
calcula ions om he JLM model, oge he wi h hose om
he sys ema ic op ical po en ials o DA1p and Daehnick e al.,
a e compa ed wi h he expe imen al angula dis ibu ions in
Fig. 5.
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ELASTIC SCATTERING AND BREAKUP OF 11Be ON . . . PHYSICAL REVIEW C 94, 064620 (2016)
AsshowninFig.5, he calcula ions wi h he DA1p po en ial
and he olding po en ial gene a ed wi h bo h JLM po en ials
show easonable ag eemen wi h he expe imen al di e en ial
c oss sec ions. By con as , he calcula ion wi h he Daehnick
e al. po en ial o e es ima es he da a. This migh indica e
ha he elas ic sca e ing o deu e ons on he weakly bound
nuclei could be ep oduced by he OM wi h po en ials specially
de eloped o he co esponding inciden ene gy and mass
egion, o by he SFM including he densi y o weak-binding
nuclei.
IV. XCDCC CALCULATIONS
In his sec ion we compa e he measu ed elas ic and
b eakup c oss sec ions wi h XCDCC calcula ions [12,15]. The
XCDCC me hod is a gene aliza ion o he s anda d con inuum-
disc e ized coupled-channels (CDCC) o malism which akes
in o accoun he e ec s o co e exci a ion in he s uc u e o
he p ojec ile, by including co e-exci ed componen s in he
p ojec ile s a es, and also in he dynamics o he eac ion,
by allowing co e exci a ions and deexci a ions du ing he
collision. In he p esen wo k, his is done by including
explici ly he de o ma ion o he 10Be co e, wi hin a collec i e
model.
The 11Be s uc u e is desc ibed by he pa icle- o o model
using he Hamil onian o Re . [32] (model Be12-b), comp ised
o cen al and spin-o bi pa s, wi h he usual Woods-Saxon
olume and de i a i e shapes, espec i ely. The cen al pa has
a ixed geome y (R0=2.483 m, a=0.65 m) and a pa i y-
dependen s eng h (Vc=−54.24 MeV and −49.67 MeV, o
posi i e and nega i e pa i y s a es, espec i ely). The spin-o bi
pa uses he same adius and di useness as he cen al pa and
a ixed s eng h Vso =8.5 MeV. Fo he 10Be co e, his model
assumes a pe manen quad upole de o ma ion β2=0.67, (i.e.,
δ2=β2R0=1.664 m). This model ep oduces he sepa a ion
ene gies o he wo bound s a es o 11Be as well as he posi ions
o he low-lying na ow 5/2+and 3/2+ esonances.
To calcula e he ene gies and wa e unc ions o 11Be we use
a pseudos a e (PS) me hod [15], which consis s in diagonaliz-
ing he Hamil onian o his composi e sys em in a con enien
basis o squa e-in eg able unc ions. In his wo k, we use
he ans o med ha monic oscilla o (THO) basis, which is
ob ained by applica ion o a local scaled ans o ma ion (LST)
o he adi ional ha monic oscilla o (HO) basis. The pu pose
o he LST is o ans o m he Gaussian asymp o ic beha io
in o an exponen ial o m, which is mo e con enien o he
desc ip ion o he bound s a es o he sys em. In pa icula ,
we use he analy ical LST p oposed in Re . [33], which was
al eady applied o 11Be in Re s. [15,16,34], and he pa ame e s
used in he p esen calcula ions a e simila o hose employed
in hose e e ences. The size o he basis is de e mined by
he numbe o oscilla o unc ions (N), he maximum o bi al
angula momen um o he co e- alence mo ion (), and he
numbe o co e s a es. In he p esen calcula ions we use
N=12 and max =3 and he i s wo s a es o he co e
( he g.s. and he i s exci ed s a e). Con inuum s a es wi h
o al angula momen um Jπ
p=1/2±,3/2±, and 5/2+we e
conside ed in he calcula ions. We e i ied ha using a la ge
alue o No highe alues o Jpdid no change app eciably
he calcula ed obse ables. Fu he mo e, only eigen alues wi h
ene gies below 7 MeV we e e ained in he coupled-channels
calcula ions, since he e ec o highe eigen alues was ound
o be negligible.
The XCDCC calcula ions equi e also he alence- a ge
and co e- a ge in e ac ions. In XCDCC, he co e- a ge in e -
ac ion (10Be +din he p esen case) con ains noncen al e ms
which a e esponsible o he dynamic co e exci a ion (DCX)
mechanism o he co e du ing he collision. To gene a e his
po en ial, we s a om he DA1p pa ame iza ion in oduced
in he p e ious sec ions. This po en ial is de o med wi h a
quad upole de o ma ion leng h o δ2=1.9 m, and expanded
in mul ipoles, e aining he monopole and quad upole e ms.
The la e one accoun s o he diagonal 2+→2+and o -
diagonal 0+→2+coupling po en ials among he conside ed
10Be s a es. To a oid double coun ing o he 10Be exci a ion,
all pa ame e s a e sligh ly adjus ed in o de o eco e he
o iginal desc ip ion o he 10Be +delas ic sca e ing da a.
In pa ame izing he n+dpo en ial one has o deal wi h he
complica ions a ising om he p esence o angula -momen um
and spin-dependen e ms, including enso o ces. Cu en
implemen a ions o he CDCC and XCDCC me hods do no
allow o hese kinds o in e ac ion, so we jus de i e a simple
cen al n+dpo en ial ep oducing some key ea u es o his
sys em. Fo ha , wo di e en p esc ip ions a e used in his
wo k. In ou i s p esc ip ion, he n+dpo en ial is calcula ed
as he olding o n+pand n+npo en ials wi h he g ound
s a e o he deu e on. Fo ha , he n+pand n+nin e ac ions
we e desc ibed wi h he po en ials o Man lie and Tjon [35]. In
ou second p esc ip ion, we pa ame ize he n+din e ac ion
using he simple Gaussian o m
Und ( )=VGexp[−( /a )2]+iWGexp[−( /aw)2],(2)
wi h ou pa ame e s VG,WG,a , and awadjus ed o ep oduce
he expe imen al elas ic sca e ing and eac ion c oss sec ions
o his sys em a En=27.5MeV[36]. The di e ences
be ween he 11Be +dobse ables calcula ed wi h hese wo
p esc ip ions will p o ide us wi h an idea o he sensi i i y o
hese obse ables on he choice o he n+din e ac ion. The
compu a ion o he coupling po en ials en e ing he XCDCC
coupled equa ions and he esolu ion o hese equa ions
we e done employing he o malism and codes de eloped in
Re . [15].
The calcula ed di e en ial c oss sec ions o he 11Be +d
elas ic sca e ing a e compa ed wi h he expe imen al da a in
Fig. 6. The solid and dashed lines a e he ull XCDCC cal-
cula ions wi h he wo p esc ip ions o he n+din e ac ion,
as indica ed by he labels. We ind a good ag eemen wi h he
da a o c.m. angles up o 30◦, and an unde es ima ion beyond
his angle. Fu he mo e, we see ha he wo p esc ip ions
o he n+din e ac ion lead o simila esul s, and hei
di e ences canno explain he obse ed disc epancy wi h he
da a a he la ges angles. We also include in his igu e he
XCDCC calcula ion omi ing he DCX mechanism (do ed
line). The sizable di e ence be ween his calcula ion and he
ull calcula ion a la ge c.m. angles indica es ha he DCX
has a clea impac on he elas ic sca e ing c oss sec ions o
his eac ion.
064620-5

J. CHEN e al. PHYSICAL REVIEW C 94, 064620 (2016)
FIG. 6. Expe imen al and calcula ed elas ic di e en ial c oss
sec ions, a io o Ru he o d, o he eac ion 11Be +da 26.9AMeV.
FIG. 7. Expe imen al and calcula ed b eakup c oss sec ions, as
a unc ion o he c.m. sca e ing angle, o he eac ion 11Be +da
26.9AMeV. The meaning o he lines is he same as in Fig. 6.The
inse in (a) ampli ies he egion con aining he expe imen al da a.
FIG. 8. Ene gy di e en ial c oss sec ion, as a unc ion o he
n-10Be ela i e ene gy, calcula ed wi h he XCDCC me hod. The solid
line is he ull XCDCC calcula ion, whe eas he dashed line is he
calcula ion omi ing he 10Be +dexci a ion mechanism. The a ow
indica es he exci a ion ene gy o he n+10Be(2+) h eshold.
The co esponding b eakup angula dis ibu ions a e com-
pa ed wi h he expe imen al da a in Fig. 7. The op and
bo om panels co espond o he exci a ion ene gy in e als
Ex=0.5–3.0 MeV and Ex=3.0–5.5 MeV o 11Be. The
meaning o he igu es is he same as in Fig. 6. We obse e
ha he wo p esc ip ions o he n+dpo en ial lead o
e y simila esul s, pa icula ly a he measu ed angles. I
becomes also appa en ha he maximum o he b eakup
c oss sec ion occu s a θc.m.≈10◦, which is ou side he ange
o he measu ed da a. Consequen ly, he conclusions on he
compa ison o he calcula ed and measu ed b eakup da a mus
be aken wi h he same cau ion because hey a e based on a
egion whe e he b eakup c oss sec ion is ela i ely small and
s uc u eless.
No wi hs anding hese conside a ions, one can see ha
he ag eemen be ween he calcula ions and he da a is
e y easonable. Mo e in e es ing is he e ec o he DCX
mechanism, which can be in e ed om he compa ison o
he ull XCDCC calcula ion wi h ha omi ing his e ec
(do ed line). I is clea ly seen ha he omission o he DCX
gi es signi ican ly ewe b eakup c oss sec ions. The e ec is
pa icula y no iceable o he highe ene gy in e al [Fig. 7(b)],
o which he calcula ion igno ing he DCX mechanism clea ly
unde es ima es he da a. These e ec s a e quali a i ely simila
o hose ound o he p+11Be eac ions a 63.7AMeV [15]
and 26.9 MeV [16]. This ein o ces he idea ha he impo ance
o dynamic co e exci a ions is a gene al ea u e o 11Be
sca e ing on ligh a ge s.
To ge u he insigh in o hese esul s we in es iga ed he
b eakup c oss sec ions as a unc ion o he ela i e ene gy
(E el)o he11Be sys em, wi h espec o he n+10Be (g.s.)
b eakup h eshold. This is shown in Fig. 8. No e ha he
XCDCC me hod p o ides only a disc e e b eakup dis ibu ion,
co esponding o he b eakup c oss sec ion o each inal
pseudos a e. To ob ain a con inuous dis ibu ion, we con olu e
064620-6
ELASTIC SCATTERING AND BREAKUP OF 11Be ON . . . PHYSICAL REVIEW C 94, 064620 (2016)
his disc e e dis ibu ion wi h he 11Be con inuum (sca e ing)
s a es [37]. The solid line is he esul o such a con olu ion
o he ull XCDCC calcula ion. One can see e y clea ly
he wo na ow peaks a E el ≃1.15 MeV and E el ≃3MeV,
which co espond espec i ely o he low-lying 5/2+and
3/2+ esonances. Also no iceable is he sudden inc ease o
he c oss sec ion when he exci a ion ene gy c osses he
h eshold n+10Be(2+). Fo exci a ion ene gies abo e his
h eshold, he sys em can decay ei he o he 10Be g.s. o o
i s i s exci ed s a e (2+). We include also in his igu e he
calcula ion omi ing he DCX mechanism (dashed line). The
sizable educ ion o he c oss sec ion is appa en , pa icula ly
in he egion o he 3/2+ esonance, as we obse ed o he
co esponding angula dis ibu ions. These esul s show e y
clea ly he key impo ance o he DCX mechanism in he
11Be +d eac ion.
V. SUMMARY
We measu ed he elas ic sca e ing and b eakup eac ion
o 11Be on deu e ons o he i s ime a an inciden
ene gy o 26.9AMeV. The p o on con amina ion in he
(CD2)n a ge was de e mined by compa ing he p o on
elas ic sca e ing da a o 11Be on he (CD2)nand (CH2)n
a ge s. The measu ed elas ic sca e ing da a we e compa ed
wi h se e al op ical model calcula ions. We ound ha he
da a a e well desc ibed wi h a ecen ly de eloped deu e on
po en ial o 1p-shell nuclei (named DA1p), as well as wi h
single- olding po en ials gene a ed wi h he JLM nucleon-
nucleon in e ac ion. On he con a y, he global deu e on
po en ial o Daehnick e al. ailed o ep oduce he da a
sa is ac o ily.
An ex ended e sion o he XCDCC me hod, which
includes he DCX e ec s, was also applied o analyze he
elas ic and b eakup da a o 11Be +d. In he case o he elas ic
sca e ing, he ull XCDCC calcula ions including he DCX
mechanism easonably ep oduced he expe imen al c oss
sec ions. Fo he b eakup eac ion, he ull XCDCC calcu-
la ions signi ican ly inc ease he calcula ed c oss sec ions and
signi ican ly imp o e he desc ip ion o he expe imen al da a
wi h espec o he calcula ed esul s omi ing DCX e ec s. The
DCX e ec is pa icula ly no iceable o he highe exci a ion
ene gy in e al (Ex=3–5.5 MeV), o which he calcula ion
igno ing he DCX mechanism clea ly unde es ima es he da a.
These esul s con i m he ele ance o he DCX e ec s in he
sca e ing o weakly bound de o med sys ems on ligh a ge s.
ACKNOWLEDGMENTS
We g a e ully acknowledge he s a o he RCNP accel-
e a o g oup o p o iding he 13Cp ima y beam and he
s a o EN-cou se o assis ance and local suppo . This
wo k is suppo ed by he 973 P og am o China (G an No.
2013CB834402), he Na ional Na u al Science Founda ion o
China (G an s No. 11275001, No. 11535004, No. 11275011,
No. 11275018, and No. U1432247), and China Pos doc o al
Science Founda ion (G an No. 20100470133). A.M.M. is
pa ially suppo ed by he Spanish Minis e io de Econom´
ıa y
Compe i i idad, unde G an No. FIS2014-53448-C2-1-P. J.R.
was pa ially suppo ed by B azilian Minis e ios o Educa ion
CAPES and CNPq.
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