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1
Di ec p ocesses o he sys ems 7Be,8B + 208Pb a
Coulomb ba ie ene gies
M Mazzocco1,2, N Keeley3, A Boiano4, C Boiano5, M La Comma a6,4,
A Lagni1, C Manea2, C Pa ascandolo4, D Pie ou sakou4,
C Signo ini1,2, E S ano1,2, D To esi1,2, H Yamaguchi7, D Kahl7,
L Acos a8,9, P Di Meo4, J P Fe nandez-Ga cia9, T Gloda iu10,
J G ebosz11, A Guglielme i12,5, Y Hi ayama13, N Imai7,13,
H Ishiyama13, N Iwasa14, S C Jeong13,15, H M Jia16, Y H Kim13,
S Kimu a14, S Kubono7,17, G La Rana18,4, C J Lin16, P Lo i2,
G Ma qu´ınez-Du ´an8, I Ma el8,19, H Miya ake13, M Mukai13,
T Nakao7, M Nicole o2, A Pakou20, K Rusek21, Y Sakaguchi7,
A M S´anchez-Ben´ı ez22,23, T Sa a10, O Sgou os20, V Souke as20,
F So amel1,2, E S ilia is24, L S oe10, T Te anishi25, N Toniolo26,
Y Wakabayashi17, Y X Wa anabe13, L Yang16,7, Y Y Yang27 and
H Q Zhang16
1Dipa imen o di Fisica e As onomia, Uni e si `a di Pado a, ia F. Ma zolo 8, I-35131
Pado a, I aly
2INFN-Sezione di Pado a, ia F. Ma zolo 8, I-35131 Pado a, I aly
3Na ional Cen e o Nuclea Resea ch, ul. And zeja So l ana 7, 05-400 O wock, Poland
4INFN-Sezione di Napoli, ia Cin ia, I-80126, Napoli, I aly
5INFN-Sezione di Milano, ia Celo ia 16, I-20133, Milano, I aly
6Dipa imen o di Fa macia, Uni e si `a di Napoli “Fede ico II”, ia D. Mon esano, I-80131,
Napoli, I aly
7Cen e o Nuclea S udy (CNS) - The Uni e si y o Tokyo, Wako B anch, 2-1 Hi osawa,
Wako, Sai ama 351-0198, Japan
8Depa amen o de F´ısica Aplicada, Uni e sidad de Huel a, Campus de El Ca men, E-21071
Huel a, Spain
9INFN-Sezione di Ca ania, ia San a Sofia 64, I-95123, Ca ania, I aly
10 NIPNE, 30 Reac o ului S ee , 077125 Magu ele, Romania
11 Ins i u e o Nuclea Physics Polish Academy o Science, ul. Radzikowskiego 152, 31-342
K ak´ow, Poland
12 Uni e si `a degli S udi di Milano, Dipa imen o di Fisica, Via Celo ia 16, I-20133 Milano,
I aly
13 KEK, Oho 1-1, Tsukuba, Iba aki 305-0801, Japan
14 Depa men o Physics, Tohoku Uni e si y, Sendai, Miyagi 980-8578, Japan
15 Ins i u e o Basic Science (IBS), 55, Expo- o, Yuseong-gu, 34126 Daejeon, Ko ea
16 China Ins i u e o A omic Ene gy, P. O. Box 275 , Beijing 102413, China
17 RIKEN, 2-1 Hi osawa, Wako, Sai ama 351-0198, Japan
18 Dipa imen o di Fisica, Uni e si `a di Napoli “Fede ico II”, ia Cin ia, I-80126, Napoli, I aly
19 Depa men o Physics, Uni e si y o Li e pool, Li e pool L69 7ZE, Uni ed Kingdom
20 Depa men o Physics and HINP, Uni e si y o Ioannina, 45110 Ioannina, G eece
21 Hea y Ion Labo a o y, Uni e si y o Wa saw, ul. Pas eu a 5a, 02-093 Wa saw, Poland
22 Nuclea Physics Cen e , Uni e si y o Lisbon, P-1649-003 Lisbon, Po ugal
23 Cen o de Es udios A anzados en F´ısica, Ma em´a icas y Compu aci´on (CEAFMC),
Depa men o In eg a ed Sciences, Uni e si y o Huel a, E-21071 Huel a, Spain
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24 Ins i u e o Accele a ing Sys ems and Applica ions and Depa men o Physics, Uni e si y
o A hens, A hens, G eece
25 Depa men o Physics, Kyushu Uni e si y, Mo ooka 744, Fukuoka 819-0395, Japan
26 INFN-LNL, iale dell’Uni e si `a 2, I-35020, Legna o (PD), I aly
27 Ins i u e o Mode n Physics, Chinese Academy o Sciences, 509 Nanchang Rd., Lanzhou
730000, China
E-mail: [email p o ec ed]
Abs ac . The elas ic sca e ing p ocess o he nuclea eac ions induced by he Radioac i e
Ion Beams 7Be and 8B on a 208Pb a ge was measu ed o he fi s ime in he ene gy
ange a ound he Coulomb ba ie . Ex ensi e heo e ical calcula ions wi hin he amewo k
o he op ical model we e pe o med. An excellen ag eemen be ween expe imen al da a
and heo e ical p edic ions was achie ed o he eac ion 7Be + 208Pb, while a comp ehensi e
unde s anding o he eac ion dynamics induced by he mo e exo ic p ojec ile 8B is s ill a o
be eached. P edic ions o he c oss sec ion o he b eakup o bo h sys ems will also be gi en.
1. In oduc ion
The eac ion dynamics induced by ligh weakly-bound nuclei in he ene gy ange a ound he
Coulomb ba ie is a qui e in e es ing esea ch opic in p esen -day nuclea physics. These
s udies was o iginally mo i a ed by he expec a ion ha he peculia p ope ies o many ligh
exo ic nuclei, such as halo s uc u e, neu on skin s uc u e o e y weak binding ene gy,
could magni y he s ong enhancemen o nea -ba ie usion c oss sec ion obse ed in collisions
be ween s able nuclei. Despi e ea lie measu emen s, i was soon ealized ha he unusual
ea u es o exo ic nuclei end o inc ease he o al eac ion p obabili y a he han he usion
c oss sec ion. The in es iga ion hen mo ed o y o shed some ligh on which eac ion channels
we e mainly esponsible o he enhancemen o he o al eac ion p obabili y, whe he his e ec
was mainly ela ed o ans e channels o o he b eakup p ocess. Se e al e iew a icles ha e
been w i en o e he pas 15 yea s on his opic [1, 2, 3, 4, 5, 6, 7, 8, 9].
These s udies a e usually e y complica ed and ypically su e o low s a is ical accu acy. In
ac , hese exo ic p ojec iles a e gene ally adioac i e and sho -li ed, he e o e we need i s a
nuclea eac ion be ween s able nuclei o occu , in o de o p oduce he adioiso opes, and hen
a sui able de ice o selec and pu i y he seconda y beam. As a consequence, Radioac i e Ion
Beams nowadays a ailable s ill ha e a he low in ensi ies. Thus, he i s se ies o expe imen s
pe o med wi h exo ic beams in he ene gy ange a ound he Coulomb ba ie a e ypically
add essed o he in es iga ion o he mos p obable eac ion mechanism, i.e. he elas ic sca e ing
p ocess. The analysis o he elas ic sca e ing angula dis ibu ion wi hin he amewo k o he
op ical model can p o ide a i s indica ion abou he o e all eac i i y o an exo ic p ojec ile
and (possible) modi ica ion on he shape he expe imen al da a wi h espec o he heo e ical
p edic ions o he sca e ing p ocess can gi e some hin s on he magni ude o c oss sec ions o
o he nuclea p ocesses and hei in luence on he sca e ing channel.
2. Expe imen s
2.1. P oduc ion o he seconda y beams
Bo h Radioac i e Ion Beams used in hese s udies we e p oduced by means o he in- ligh
echnique.
The 8B expe imen was pe o med wi h he CRIB acili y [10, 11], loca ed inside he RIKEN
campus in Japan. We s a ed wi h a 11.2 MeV/u 6Li3+ p ima y beam wi h an a e age in ensi y
o abou 1 pµA impinging on a 8-cm long gas a ge , illed wi h 3He gas a a p essu e o abou
1 ba and kep a c yogenic empe a u e. The 8B was hen selec ed and pu i ied by means o
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he ion-op ical elemen s o CRIB and impinged on a 2.2 mg/cm2 208Pb a ge wi h an ene gy
o 50 ±1 MeV, an a e age in ensi y o 104pps and a pu i y a ound 20%.
The 7Be expe imen was ca ied ou a he Labo a o i Nazionali di Legna o (LNL, I aly),
whe e he adioac i e ion beam was p oduced wi h he acili y EXOTIC [12]. In his case, we
used a 7Li3+ beam wi h an ene gy o 48.8 MeV and an in ensi y o 50-60 pnA. The p ima y beam
was hi ing a 5-cm long gas a ge , illed wi h H2a a p essu e o abou 1 ba . The ou going
7Be seconda y beam was selec ed wi h he acili y EXOTIC and deli e ed wi h a in ensi y o
2-3 ×105pps and a nea ly 100-% pu i y on a 1 mg/cm2 208Pb a ge . Th ee di e en seconda y
beam ene gies we e ob ained by ope a ing he a ge a oom and c yogenic empe a u es and
by inse ing a 12.5-µm hick aluminum deg ade a a sui able posi ion along he beam line. The
7Be ene gies on a ge we e: 42.2±0.4 MeV, 40.5±0.4 MeV and 37.4±0.5 MeV.
2.2. De ec o se -up
In bo h expe imen s, six modules o he de ec o a ay EXPADES [13] we e employed o he
de ec ion o cha ged pa icles. Each module was composed by wo Double-Sided-Silicon-S ip-
De ec o s (DSSSDs), he inne one wi h a hickness o 43-57 µm, while he ou e one had a
hickness o 300 µm. Each DSSSD had an a ea o 64.0 mm ×64.0 mm and he on and back
sides we e segmen ed in o 32 e ical and ho izon al s ips, espec i ely. De ails on he elec onic
chains used o bo h de ec o s ages can be ound in [13].
The six modules o EXPADES we e a anged in a cylind ical con igu a ion a ound he a ge
posi ion ensu ing a solid angle co e age o abou 14 % o 4πs . A symme ical displacemen ,
co e ing he angula ange θlab = [52◦, 167◦], a ound he beam axis was chosen o he 7Be
expe imen . On he o he hand, o he 8B expe imen a sligh asymme ical a angemen o
he EXPADES modules was p e e ed in o de o enla ge he pola angle co e age θlab = [8◦,
166◦]. Mo e de ails on he de ec o geome y a e gi en in he ecen publica ion [14].
3. Resul s
3.1. Elas ic sca e ing and o al eac ion c oss sec ion
The i s s ep o he da a analysis was he e alua ion o he elas ic sca e ing angula
dis ibu ions o bo h sys ems and he ex ac ion, ia an op ical model i o he expe imen al
da a, o he o al eac ion c oss sec ions. All he s eps o he da a e alua ion and o he i ing
p ocedu e a e desc ibed in [14] and he e we discuss he esul s and he compa ison wi h simila
mass sys ems.
When compa ing di e en sys ems, bo h bomba ding ene gies and c oss sec ions need o he
no malize in o de o accoun o he di e en Coulomb ba ie and he di e en geome ical
size o he colliding nuclei. In doing ha , we used he o malism sugges ed by L.F. Can o
and collabo a o s [15]. This me hod was o iginally de eloped and wo ks p e y nicely o he
compa ison o usion c oss sec ion da a, bu can also be employed, paying some a en ion [16],
also o eac ion c oss sec ion da a. In ou case, we a e going o compa e eac ions induced by
p ojec iles wi h simila masses (in he ange A = 6-8) and all in e ac ing wi h he same a ge
nucleus (208Pb).
I has been discussed o a long ime whe he , om he poin o iew o he eac ion dynamics,
he 7Be beha io would ha e esembled mo e ha o 6Li, which has a sepa a ion ene gy e y
simila (wi hin 100 keV) o ha o 7Be, o ha o i s mi o nucleus 7Li, wi h an analogue
nuclea s uc u e bu a sepa a ion ene gy 60% la ge . Ou s udy p o ides a i s answe o
his ques ion, a leas o he in e ac ion wi h a e y massi e a ge such as 208Pb, since he
h ee da a poin s we measu ed o he sys em 7Be + 208Pb ollow essen ially he end o he
eac ion 6Li + 208Pb [17]. This esul sugges s ha nuclea binding ene gy plays a majo ole
han nuclea s uc u e in collisions in ol ing weakly-bound nuclei, a leas in he ene gy ange
a ound he Coulomb ba ie .
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I we now add o he compa ison also he mi o nuclei o mass A = 8, i.e. 8Li [18]
and 8B, again in e ac ing wi h a 208Pb a ge , we obse ed in [14] ha , in bo h cases, he
”‘no malized”’ o al eac ion c oss sec ion da a a e enhanced wi h espec o egion o he g aph
whe e p ojec iles wi h mass A = 6-7 a e loca ed. A simple a gumen ela ed only o he p ojec ile
binding ene gy would no s and in his occasion, since he 8Li sepa a ion ene gy is exac ly in
be ween hose o 6Li/7Be and 7Li. The ac ual eason o he 8Li enhancemen has he e o e o
be sea ched elsewhe e and, mos likely, elies on he la ge p obabili y, i.e. c oss sec ion, o he
n-s ipping p ocess (leading o 7Li in he eac ion exi channel) o occu . Speci ic expe imen al
measu emen s o his p ocess a e he e o e needed in o de o con i m his scena io.
E en mo e s iking is he compa ison o 8B wi h all o he ligh p ojec iles. In ac , i s eac ion
c oss sec ion is enhanced by a ac o 3-4 wi h espec o ha measu ed o he eac ion induced
by i s co e 7Be. Following he analogies wi h he sys em 8+58Ni [19], he enhancemen should
be due o he ex emely weak binding ene gy o 8B (Sp= 137.5 keV) and consequen ly he e y
high p obabili y o his nucleus o b eak up while app oaching a a ge nucleus. To his ex end,
we pe o med ex ensi e Coupled-Channel calcula ions in o de o p o ide an es ima e o he
c oss sec ion o he b eakup p ocess 8B→7Be + p.
3.2. B eakup p ocess
Theo e ical calcula ions we e pe o med o bo h sys ems. Being bo h p ojec ile e y weakly-
bound, we desc ibed he b eakup p ojec ile by means o a disc e iza ion o he (con inuous)
ene gy spec um abo e he b eakup h eshold in bins equally spaced in he momen um space.
Also in his case, he p ocedu e adop ed o he calcula ions is ully desc ibed in [14] and he e
we summa ize he main de ails impo an o he subsequen discussion.
The 7Be nucleus was modelled using an 3He + 4He clus e olding model. In he calcula ions,
we included also he possibili y o exci e he 7Be i s exci ed s a e a 0.429 MeV (Jπ= 1/2−),
he wo l= 3¯h esonances a 4.57 (7/2−) and 6.73 (5/2−) MeV, he non esonan con inuum up
o mul ipola i y λ= 4 and up o an exci a ion ene gy o 9.88 MeV abo e he b eakup h eshold.
The calcula ions we e pe o med by using he coupled channel code F esco [20]. Fi s o all, we
ema k ha we we e able o ep oduce he expe imen al elas ic sca e ing angula dis ibu ion
wi hou any ee pa ame e , p o iding an addi ional con i ma ion o he alidi y o he adop ed
app oach. The calcula ions p edic a b eakup c oss sec ion o 20-38 mb in he ange o ene gies
co e ed by ou expe imen . These alues co espond app oxima ely o abou 10% o he o e all
eac ion c oss sec ion o he sys em 7Be + 208Pb, s ongly indica ing ha he b eakup p ocess
does no domina e he eac ion dynamics o his sys em, in a quali a i e ag eemen wi h ou
p e ious obse a ion o he eac ion 7Be + 58Ni [?]. We also had an addi ional con i ma ion
o his ou come om he p elimina y analysis o he p oduc ion c oss sec ion o he eac ion
p oduc s 3He and 4He. The hea ie iso opes is indeed 4-5 imes mo e abundan han he ligh e
coun e pa , sugges ing ha he e a e many o he eac ion channels (such as, o ins ance, n-
pickup o p-s ipping) open in his ene gy ange and leading o ex a-p oduc ion o 4He wi h
espec o 3He.
Mo ing now o 8B, we used a 7Be + pclus e olding model o desc ibe his e y exo ic
p ojec ile. To educe he compu a ion ime, 7Be was assumed o be spinless and ine and
he p o on o be in a pu e p3/2s a e. The non esonan con inuum up o a mul ipola i y
λ= 5 and up o an exci a ion ene gy o 11.7 MeV abo e he b eakup h eshold was included.
Due o assumed spinless na u e o 7Be, no 8B esonances we e conside ed in he heo e ical
calcula ions. The p edic ed di e en ial c oss sec ion o he elas ic sca e ing p ocess ailed o
ep oduce sa is ac o y he expe imen al da a, al eady indica ing ha ou model o desc ibe 8B
migh be oo simplis ic. Being he 8co e, i.e. 7Be, also a weakly bound nucleus, pe haps a
4-body app oach, including also he possibili y o co e exci a ion, should be mo e adequa e o
his eac ion.
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Ne e heless, coupled channel calcula ions p edic an ex emely la ge b eakup c oss sec ion
o a ound 600 mb, which co esponds o mo e han 50% o he o al eac ion c oss sec ion.
We a e p esen ly wo king o ex ac he angula dis ibu ion o he 7Be eac ion p oduc . A
p elimina y e alua ion shows a di e en ial c oss sec ion s ongly peaked a o wa d angles, wi h
a la ge ail ex ending up o e y backwa d angles, in quali a i e ag eemen wi h he ea lie
obse a ions by V. Guima ˜aes and collabo a o s o he eac ion 8B + 58Ni [22, 23].
4. Ou look
The elas ic sca e ing p ocess o he sys ems 7Be, 8B + 208Pb has been measu ed o he i s
ime in he ene gy ange a ound he Coulomb ba ie . The expe imen al da a ha e been analyzed
wi hin he amewo k o he op ical model in o de o ex ac he o al eac ion c oss sec ion.
The 8B + 208Pb eac i i y esul ed o exceed by a hose epo ed o p ojec iles o masses in he
ange A = 6-8 and in e ac ing wi h he same a ge nucleus. Theo e ical calcula ions indica e
ha his enhancemen migh be due o he b eakup p ocess 8→7Be + pand we a e p esen ly
wo king o ex ac he expe imen al di e en ial c oss sec ion o he 7Be eac ion p oduc .
Acknowledgmen s
The 8B expe imen was pe o med a RI Beam Fac o y ope a ed by RIKEN Nishina Cen e
and CNS, Uni e si y o Tokyo. This wo k was suppo ed by he Polish Na ional Science Cen e
unde Con ac No. 2014/14/M/ST2/00738 (COPIN-INFN Collabo a ion), by JSPS KAKENHI
(Nos. 16K05369, and 19K03883) om he Minis y o Educa ion, Cul u e, Spo s, Science and
Technology (MEXT) o Japan and by he p ojec s: CONACyT LN-294537 and DGAPA-PAPIIT
IA103218.
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