Elastic scattering and breakup reactions of the proton drip-line nucleus 8 B on 208 Pb at 238 MeV

PHYSICAL REVIEW C 103, 024606 (2021) Elas ic sca e ing and b eakup eac ions o he p o on d ip-line nucleus 8Bon 208Pb a 238 MeV K. Wang ,1Y. Y. Yang,1,2,*A. M. Mo o,3,4V. Guima ães,5Jin Lei,6D. Y. Pang,7F. F. Duan,1J. L. Lou,8J. C. Zamo a,5 J. S. Wang,9,1,2Z. Y. Sun,1H. J. Ong,1,2,10 X. Liu,11 S. W. Xu,1J. B. Ma,1P. Ma,1Z. Bai,1Q. Hu,1X. X. Xu,1,2Z. H. Gao,1 G. Yang,1,2S. Y. Jin,1,2Y. H. Zhang,1,2X. H. Zhou,1,2Z. G. Hu,1,2and H. S. Xu1,2 (RIBLL Collabo a ion) 1CAS Key Labo a o y o High P ecision Nuclea Spec oscopy, Ins i u e o Mode n Physics, Chinese Academy o Sciences, Lanzhou 730000, China 2School o Nuclea Science and Technology, Uni e si y o Chinese Academy o Sciences, Beijing 100080, China 3Depa amen o de FAMN, Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain 4Ins i u o In e uni e si a io Ca los I de Física Teó ica y Compu acional (iC1), Apa ado 1065, 41080 Se illa, Spain 5Ins i u o de Física, Uni e sidade de São Paulo, Rua do Ma ão, 1371, São Paulo 05508-090, São Paulo, B azil 6Is i u o Nazionale di Fisica Nuclea e, Sezione di Pisa, La go Pon eco o 3, 56127 Pisa, I aly 7School o Physics and Beijing Key Labo a o y o Ad anced Nuclea Ma e ials and Physics, Beihang Uni e si y, Beijing 100191, China 8School o Physics and S a e Key Labo a o y o Nuclea Physics and Technology, Peking Uni e si y, Beijing 100871, China 9School o Science, Huzhou Uni e si y, Huzhou 313000, China 10Resea ch Cen e o Nuclea Physics, Osaka Uni e si y, Iba aki, Osaka 567-0047, Japan 11Key Labo a o y o Radia ion Physics and Technology o he Minis y o Educa ion, Ins i u e o Nuclea Science and Technology, Sichuan Uni e si y, Chengdu 610064, China (Recei ed 25 Oc obe 2020; e ised 9 Decembe 2020; accep ed 13 Janua y 2021; published 3 Feb ua y 2021) Elas ic sca e ing and b eakup angula dis ibu ions o he weakly bound adioac i e nucleus 8Bon a 208Pb a ge a an inciden ene gy o 238 MeV, which co esponds o ou imes he Coulomb ba ie , ha e been measu ed a he HIRFL-RIBLL acili y (Ins i u e o Mode n Physics, Lanzhou). The da a ha e been analyzed using he op ical model and he con inuum disc e ized coupled channels (CDCC) o malism. The measu ed and calcula ed elas ic sca e ing angula dis ibu ions do no show any signi ican Coulomb ainbow supp ession. The angula dis ibu ion o he b eakup eac ion was measu ed o he i s ime a his ene gy. The angula dis ibu ion o he 7Be agmen s could be ep oduced conside ing elas ic plus nonelas ic b eakup con ibu ions, wi h he o me e alua ed wi h he CDCC calcula ions and he la e wi h he model o Ichimu a, Aus e n, and Vincen [Phys. Re . C 32, 431 (1985)]. The compa ison o he b eakup c oss sec ion o 8Bwi h ha o 11Be sugges s ha he Coulomb and cen i ugal ba ie s encoun e ed by he alence p o on may supp ess he b eakup c oss sec ion. DOI: 10.1103/PhysRe C.103.024606 I. INTRODUCTION Di ec nuclea eac ions induced by ligh weakly bound nuclei, such as 6,8He, 11Li, 11Be, 8B, and o he s, ha e been ex ensi ely in es iga ed bo h expe imen ally and heo e ically o s udy hei unusual ea u es. Among he di ec eac ions, elas ic sca e ing is he simples ye powe ul ool o p obe he ma e densi ies, su ace di usenesses, and e en clus e s uc- u es o hese nuclei [1–3]. Elas ic sca e ing is known o be a ec ed by s ongly coupled eac ion channels, which usually esul s in an enhancemen o he o al eac ion c oss sec ion and a depa u e om he expec ed beha io o o dina y nu- clei, such as he supp ession o he oscilla o y pa e n in he case o F esnel sca e ing. The na u e o hese channels can be e y di e en depending on he s uc u e o he colliding nuclei. Whe eas in he case o s able, well bound nuclei cou- *Co esponding au ho : [email p o ec ed] plings o collec i e exci a ions o he p ojec ile and/o a ge nuclei (such as quad upole and oc upole couplings) play a ma- jo ole [4–6], in he case o weakly bound nuclei o he modes gain ele ance, such as ans e and b eakup modes, due o he e y low binding ene gies and ex ended spa ial dis ibu ions o he alence pa icles in hese nuclei [7]. Fo 11Li and 11Be he b eakup can be conside ed mainly esponsible o he la ge o al eac ion c oss sec ions [8–11], while o 6,8He he ans e eac ion is mainly esponsible o he enhancemen o o al eac ion c oss sec ions [12–16]. Mo eo e , he la ge b eakup and ans e c oss sec ions o ligh weakly bound nuclei ha e a signi ican impac on o he eac ion channels such as usion and elas ic sca e ing [17–19]. Fo weakly bound nuclei in he p o on- ich side, such as 8B, he si ua ion is less clea . Wi h a sepa a ion ene gy o Sp=0.136 MeV, 8Bis a p o on halo nucleus, which has a clus e con igu a ion o an ine 7Be co e and a alence p o- on occupying he p-wa e o bi al. The spa ial ex ension and clus e con igu a ion o he 8Bnucleus a e a he impo an 2469-9985/2021/103(2)/024606(7) 024606-1 ©2021 Ame ican Physical Socie y K. WANG e al. PHYSICAL REVIEW C 103, 024606 (2021) o desc ibing he elas ic and b eakup eac ion channels. The s uc u e o his nucleus is also e y impo an in as ophysics since he adioac i e cap u e 7Be(p,γ)8B eac ion plays a majo ole in he p oduc ion o high-ene gy neu inos in he s anda d sola model [20–22]. The i s measu emen o he 8Bma e adius, which yielded a oo -mean-squa e ( ms) alue o R ms =2.38(4) m, was based on he in e ac ion c oss sec ions [23]. This alue is ac ually smalle han he es ima e R ms =1.23 ×A1/3=2.46 m, expec ed o o dina y nuclei, based on elec on sca e ing [24]. Mo e ecen ly, he ma e adius o 8Bwas deduced o be R ms =2.58(6) m, ia he elas ic p o on sca e ing on 8Bin in e se kinema ics a an ene gy o 0.7 GeV/u[25]. Assuming ha 8Bis well desc ibed by a 7Be co e plus a alence p o on, his adius was de e - mined o be a combina ion o co e and alence adii as R2 ms = 7/8×R2 C+1/8×R2 , wi h RC=2.25 m and R =4.24 m. This expe imen clea ly e idenced a halo s uc u e o his nucleus. Due o i s low binding ene gy, one would expec a decou- pling o he alence p o on and a subsequen enhancemen o he b eakup p obabili y. The ac ual e ec has been ound, howe e , o be much milde han in he case o neu on halo nuclei and weakly dependen on he a ge nucleus. Fo he 8B+12C eac ion [26] he e ec o he b eakup channels was ound o be negligible, and no enhancemen o o al eac ion c oss sec ion wi h espec o mo e bound sys ems was ob- se ed. Fo 8B+27Al [27], some enhancemen o he o al eac ion c oss sec ion was epo ed, al hough he F esnel peak emained. Fo he 8B+58Ni eac ion [28,29], he au ho s ind also an enhancemen o he o al eac ion c oss sec ion, which was explained as a combined e ec o he p o on b eakup and he eac ions induced by he 7Be co e, wi h no indica- ion o p o on ans e . Finally, in he ecen measu emen o 8B+208Pb a Elab =50 MeV an eno mous o al eac ion c oss sec ion was deduced om elas ic sca e ing. Mo eo e , he F esnel peak was comple ely supp essed. Howe e , CDCC (con inuum disc e ized coupled channels) calcula ions we e no able o ep oduce hese da a, a esul ha was in e p e ed by he au ho s as due o he limi a ions o he desc ip ion o 8B as an ine 7Be co e plus a alence p o on in which possible co e exci a ions a e igno ed [30]. B eakup obse ables, such as angula dis ibu ions o emi ed agmen s, a e e en mo e sensi i e o he 8Bcon- igu a ion as compa ed o he elas ic sca e ing angula dis ibu ions. Some measu emen s o angula dis ibu ions o he b eakup p ocess ha e been pe o med o 8B+58Ni a 25.75 MeV [31–35]. The inclusion o he p o on halo s uc u e o 8Bin o he calcula ions is essen ial o accoun o he b eakup c oss sec ion [31]. Fu he CDCC calcula ions o he 7Be agmen angula dis ibu ions showed ha he 8B s uc u e (size) is esponsible o he o e all scaling o he b eakup c oss sec ion while he p o on- a ge po en ials a ec he o e all shape by p oducing an enhancemen a backwa d angles [32,33]. In Re . [35], he 58Ni(8B,7Be) b eakup an- gula dis ibu ions we e compa ed wi h CDCC calcula ions using wo di e en s uc u e models o he 8Bnucleus. By scaling he calcula ed c oss sec ions o ep oduce he da a, spec oscopic ac o s and ANC alues we e de e mined, yield- ing o he la e C2=0.543 ±0.027 m−1, independen ly o he choice o he 7Be +ppo en ial model. Angula dis ibu- ion measu emen s o he 7Be agmen om 8Bb eakup on 208Pb ha e also been pe o med a deep sub-ba ie ene gies (≈30 MeV) and b eakup dominance was obse ed, which e idenced ha he di ec eac ion channel is dominan a his ene gy egion o halo nuclei on hea y a ge s [36]. In p e ious s udies, ou g oup epo ed he elas ic sca e - ing da a o he 8B+na Pb eac ions a ene gies a ound h ee imes he Coulomb ba ie bu wi hou any b eakup obse - ables [37,38]. In his case, no s ong b eakup coupling e ec in he angula dis ibu ions was epo ed. This is a a iance wi h he 11Be +208Pb eac ion, whe e a s ong supp ession o he F esnel peak was obse ed a a simila bomba d- ing ene gy [39]. This esul sugges s ha he Coulomb and cen i ugal ba ie s expe ienced by he p o on halo may sup- p ess he b eakup couplings e ec s [40,41]. In his pape , we p esen new esul s o he 8B-b eakup eac ion on a 208Pb a ge a an ene gy a ound ou imes he Coulomb ba ie . The angula dis ibu ion o he inclusi e 7Be agmen s was ob ained, which is he i s measu emen o his obse able a his ene gy ange. Elas ic and nonelas ic b eakup compo- nen s ha e been compu ed using he CDCC and he model o Ichimu a, Aus e n, and Vincen , espec i ely, and hei sum compa ed wi h he measu ed inclusi e c oss sec ion. Elas ic sca e ing angula dis ibu ions o 3He, 7Be, and 8Ba e also analyzed o shed ligh on he eac ion dynamics. II. EXPERIMENT AND DATA ANALYSIS The expe imen was ca ied ou a he Na ional Labo a o y o Hea y Ion Resea ch o he Ins i u e o Mode n Physics. Seconda y 7Be and 8B adioac i e beams we e p oduced by agmen a ion o a p ima y 59.7 MeV/u12C6+beam om he Hea y-Ion Resea ch Facili y in Lanzhou (HIRFL) on a 2528-μm- hick 9Be p oduc ion a ge [42,43]. The p ima y beam had an a e age in ensi y o abou 130 enA. The 7Be and 8Bp ojec ile-like agmen s we e sepa a ed by hei magne ic igidi y (Bρ) and deli e ed by he Radioac i e Ion Beam Line in Lanzhou (RIBLL) [44,45] o he sca e ing chambe . The a e age in ensi ies o 7Be and 8B adioac i e beams we e 6500 and 550 pps, wi h pu i ies o 57.6% and 4.9%, espec- i ely. A 500-μm- hick aluminum pla e was placed a he i s momen um-dispe si e ocal plane (F1) o RIBLL as a deg ade . A 317-μm- hick silicon de ec o (SD) was placed a he ou h ocal plane (F4) o measu e he ene gy loss (E) o he agmen s o pa icle iden i ica ion pu pose du ing he beam uning, and emo ed om he beam line du ing he uns. Two plas ic scin illa o s we e placed a he second (F2) and ou h (F4) ocal planes o RIBLL as ime-o - ligh (ToF) de- ec o s. A comple e pa icle iden i ica ion was enabled using a combina ion o he ime-o - ligh , ene gy loss, and magne ic igidi y. The ske ch o he de ec o se up is shown in Fig. 1.Two double-sided silicon s ip de ec o s (DSSDs), segmen ed in o 16 ho izon al and 16 e ical s ips o 3 mm wid h on each side, we e used o p o ide he p ecise posi ion and di ec ion o he inciden beam pa icles. The DSSDs, wi h hicknesses o 87 μm(Si A) and 74 μm(Si B), espec i ely, we e placed 1516 and 714 mm away om he 208Pb a ge , as indica ed in Fig. 1. 024606-2 ELASTIC SCATTERING AND BREAKUP REACTIONS OF … PHYSICAL REVIEW C 103, 024606 (2021) FIG. 1. Ske ch o he de ec o se up. Two DSSDs (SiAand SiB) we e placed ups eam om he a ge o measu ing he beam po- si ion. The eac ion p oduc s we e de ec ed wi h wo elescopes, symme ically moun ed a ound he beam axis, which we e composed o wo DSSDs, a silicon de ec o , and an a ay o CsI(Tl) c ys als. The a ge consis ed o an 8.26-mg/cm2- hick sel -suppo ing oil, made by he e apo a ion me hod. The ene gies o he seconda y beams a he cen e o he a ge we e abou Elab =175 MeV o 7Be and Elab =238 MeV o 8B, wi h an o e all ene gy esolu ion o 1.6%. The de ec ion se up was comp ised o wo E-E elescopes, named TelR and TelL. These de ec o s we e used o measu e he eac ion p oduc s. Each elescope was made up o a hin DSSD, a silicon de ec- o , a hick DSSD, and a CsI(Tl) c ys al a ay. The hin DSSDs (301 and 142 μm hick) wi h 32 s ips on each side and an ac i ea eao 64mm×64 mm we e used as Ede ec o s in he elescopes. The silicon de ec o s ha e hicknesses o (TelR) 1528 and (TelL) 1535 μm and we e used o measu e he esidual ene gy o he sca e ed and b eakup 8Band 7Be pa icles. Addi ionally, hick DSSDs, wi h 32 s ips on each side, a sensi i e a ea o 64 mm ×64 mm, and hicknesses o 1004 and 998 μm, espec i ely, we e used as he Ede ec o s o measu ing p o ons o any o he ligh pa icles, while he CsI a ays se ed as he Ede ec o s. Bo h CsI a ays we e composed o 16 (4 ×4) CsI(Tl) c ys als, and each c ys al uni has an ac i e a ea o 21 mm ×21 mm. These wo elescopes we e moun ed 272 mm downs eam om he a ge , co e ing a pola angula ange om 3◦ o 20◦in he labo a o y ame wi h a esolu ion o abou 0.4◦. The de ec o s we e calib a ed wi h he elas ically sca e ed 1H,4He, 6Li, 7Be, and 8Bpa i- cles. Du ing he expe imen , he empe a u e o he de ec ion sys em was kep a −20 ◦C wi h a chilling sys em ha used an alcohol solu ion o he cooling cycle. Typical wo-dimensional pa icle iden i ica ion spec a a - e he ToF cu s o he 7Be and 8Bp ojec iles on a 208Pb a ge a e shown in Fig. 2. Owing o he supe b esolu ion o ToF signals, which is be e han 5 ns ( ull wid h a hal maximum), he pa icles in he seconda y beam a e well sepa a ed. I can be seen ha no elas ic sca e ed 7Be and 8Bbeams a e mixed wi h he 7Be p oduc s coming om b eakup e en s. The bes app oach o clea ly iden i y and isola e he elas ic b eakup componen would be o measu e he 7Be and p o on agmen s in coincidence, as pe o med in Re s. [20,21]. Howe e , due o he limi ed co e age o he de ec o se up, he coincidence measu emen was no possible and only he 7Be agmen , om he 8Bb eakup, was measu ed in he expe imen (inclu- si e b eakup). The angles o elas ic sca e ing and b eakup e en s we e de e mined by conside ing he inciden posi ion and di ec ion 15 20 25 30 E(MeV)Δ Be 7 (a) 100 150 200 250 E(MeV) 15 20 25 30 E(MeV)Δ B 8 B eakup e en s (b) FIG. 2. The calib a ed wo-dimensional E-Epa icle iden i i- ca ion spec a o he (a) 7Be and (b) 8Bp ojec ile nuclei ob ained by he TelR elescope, ga ed by hei co esponding ToF. The solid- ed- line ellipsoids ep esen he loci o he elas ic sca e ing e en s o 7Be and 8B. The dashed line ep esen s he band o 7Be (b eakup e en s), which ha e he same ToF as 8Bbu di e en ene gy. o he beam on he a ge p o ided by SiAand SiBand he hi posi ions in he elescopes TelR and TelL. Mon e Ca lo simula ions, aking in o accoun he de ec o geome y and he b oad and nonuni o m beam p o iles on he a ge , we e pe o med o e alua e he geome ical accep ance, and o de e mine he absolu e di e en ial c oss sec ion. Wi h his me hod, he sys ema ic e o s a ising om he measu emen s o he o al numbe o inciden beam pa icles, he a ge hickness, and he solid angles can be elimina ed. Mo e de ails on he p ocedu e o co ec o he he de ec o misalignmen , on he analysis o he con amina ion om pa icles sca e ed by SiAand SiB, and on he da a no maliza ion a e gi en in Re s. [37,46–49]. III. RESULTS AND DISCUSSION A global no maliza ion ac o [37] o he measu ed c oss sec ions was ex ac ed om he elas ic sca e ing o a 3He- beam con aminan a o wa d angles, whe e he σ/σRu h a io is close o uni y. The esul ing expe imen al elas ic sca e ing angula dis ibu ions, no malized o he Ru he o d sca e ing c oss sec ions o 3He +208Pb a Elab =55 MeV, 7Be +208Pb a Elab =175 MeV, and 8B+208Pb a Elab =238 MeV a e p e- sen ed in Fig. 3.As o 7Be and 8B, ypical F esnel di ac ion pa e ns can be seen in bo h dis ibu ions, which is consis en wi h he esul s ob ained o he elas ic sca e ing o 8B+na Pb a Elab =170 and 178 MeV epo ed in Re s. [37,38]. In a i s app oach, we pe o med an op ical model (OM) analysis o desc ibe he 7Be and 8Belas ic sca e ing da a using he code FRESCO [50] wi h he sys ema ic op ical po- en ial p oposed by Xu and Pang [51]. This is a global nucleus-nucleus po en ial cons uc ed wi h he single- olding model based on he B uyè es Jeukenne-Lejeune-Mahaux 024606-3 K. WANG e al. PHYSICAL REVIEW C 103, 024606 (2021) 510 15 20 θc.m. (deg) 0 0.3 0.6 0.9 1.2 σ/σR da a - 7Be+208Pb da a - 8B+208Pb da a - 3He+208Pb sys - 8B sys - 7Be FIG. 3. Elas ic sca e ing angula dis ibu ions o 3He +208Pb a Elab =55 MeV (black emp y diamond), 7Be +208Pb a Elab = 175 MeV (blue solid ci cle), and 8B+208Pb a Elab =238 MeV ( ed solid squa e) and compa isons wi h OM calcula ions. E o ba s a e due o he s a is ical unce ain y only. (JLMB) semi-mic oscopic nucleon-nucleus po en ial and which should ake in o accoun easonable nucleon densi y dis ibu ions o he colliding nuclei [51]. The p o on and neu on densi y dis ibu ions o he 7Be, 8B, and 208Pb nu- clei we e aken om Ha ee-Fock calcula ions wi h he SkX in e ac ion [52]. The ms adii o he p o on dis ibu ions we e 2.371, 2.537, and 5.441 m o 7Be, 8B, and 208Pb, espec i ely. This po en ial has a simple ene gy dependence o he po en ial pa ame e s and i is able o ep oduce he angula dis ibu ions o elas ic sca e ing and o al eac ion c oss sec ions o p ojec iles wi h a omic masses up o a ound A=40, including bo h s able and uns able nuclei, and a inciden ene gies up o abou 100 MeV/nucleon. The e- sul s o he OM calcula ions a e p esen ed in Fig. 3.As seen in he igu e, his po en ial ep oduces he da a qui e well, al hough i sligh ly o e es ima es he da a a he F esnel peak, pa icula ly o 8B+208Pb. The de i ed o al eac ion c oss sec ions a e 3253 and 3423 mb o 7Be +208Pb and 8B+208Pb, espec i ely, co esponding o almos he same educed c oss sec ions [53], namely, σ educed =σ o al/(A1/3 p+ A1/3 )2=52.95 and 54.50 mb o 7Be and 8Bp ojec iles, espec i ely. To explici ly in es iga e he impo ance o he b eakup channel and i s in luence on he elas ic sca e ing angula dis ibu ion o he 8B+208Pb eac ion, we ha e compa ed he measu ed da a wi h CDCC calcula ions. The 8B+208Pb eac ion was desc ibed using a s anda d h ee-body model in which he 8Bp ojec ile is ea ed as an ine 7Be co e plus a alence p o on (8B→7Be +p). Fo simplici y, he spin o he 7Be co e was igno ed. The p-7Be in e ac ion, equi ed o gene a e he 8Bg ound and con inuum s a es, consis ed o cen al and spin-o bi e ms wi h s anda d Woods-Saxon o ms and wi h he pa ame e s R0=2.391 m and a0=0.52 m, adop ed om Re . [54]. Fo he spin-o bi pa , he dep h was ixed o Vso =4.898 MeV whe eas o he cen al pa i was adjus ed o gi e he expe - 510 15 20 25 θc.m. (deg) 0 0.3 0.6 0.9 1.2 σ/σR da a - 8B+208Pb OM: sys - 8B CDCC CDCC: no con inuum FIG. 4. Elas ic sca e ing angula dis ibu ions o he 8B+208Pb eac ion a Elab =238 MeV. Expe imen al da a om he p esen expe imen (black squa es) a e compa ed wi h OM and CDCC cal- cula ions. E o ba s a e s a is ical only. imen al p o on sepa a ion ene gy o he g ound s a e o 8B (Sp=0.136 MeV). The g ound-s a e wa e unc ion ob ained wi h his po en ial has an ANC alue o C2=0.53 m−1, which is wi hin he ange o alues ex ac ed om di e en eac ions [35,55–59] and mic oscopic calcula ions [60–62]. Fo con inuum s a es, he same p+7Be po en ial was em- ployed. The con inuum was disc e ized using he pseudos a e (PS) me hod, which consis s o diagonalizing he p ojec ile Hamil onian in a basis o squa e-in eg able unc ions. In his wo k, we used he ans o med ha monic oscilla o (THO) basis, which is ob ained by applica ion o a local scale ans- o ma ion (LST) o he con en ional HO basis. In pa icula , we used he analy ical LST p oposed in Re s. [63,64]. The ange o he basis is con olled by he oscilla o leng h (b) and he pa ame e γ[64]. We ha e used b=1.6 m and γ=2 m −1/2, al hough his choice is no c i ical since he compu ed obse ables mus be independen o his choice i he basis is chosen la ge enough. The size o he basis is de e mined by he numbe o oscilla o unc ions (N), he maximum exci a ion ene gy (εmax), and he maximum o bi al angula momen um o he co e- alence mo ion (max). In he p esen calcula ions we used N=25, εmax =35 MeV, and max =3. Con e gence o elas ic sca e ing and b eakup c oss sec ions we e ensu ed by using a la ge enough model space. The CDCC calcula ions equi e also he p o on + a ge and 7Be + a ge op ical po en ials. Fo 7Be +208Pb,weused he sys ema ic single- olding po en ial o Re . [51] e alua ed a 208 MeV (7/8 o he inciden ene gy) whe eas o p+208Pb he sys ema ic global po en ial o Koning and Dela oche [65], e alua ed a 29.8 MeV (1/8 o he inciden ene gy), was used. The p ojec ile- a ge coupling po en ials we e gene a ed wi h he code THOX[66] and he coupled equa ions we e sol ed wi h he code FRESCO [50]. The calcula ed elas ic c oss sec ion is shown in Fig. 4.To highligh he e ec o he coupling o he b eakup channels, he single-channel calcula ion esul ing om he omission o he con inuum s a es in he CDCC calcula ion is also 024606-4 ELASTIC SCATTERING AND BREAKUP REACTIONS OF … PHYSICAL REVIEW C 103, 024606 (2021) 510 15 20 θlab (deg) 0 5000 10000 15000 dσ/dΩ (mb/s ) Exp. EBU (CDCC) NEB (IAV) To al: EBU + NEB 8B+208Pb @ 238 MeV FIG. 5. Expe imen al 7Be angula dis ibu ions om he 8B+208Pb eac ion a Elab =238 MeV (yellow ci cle) and compa isons wi h calcula ions. E o ba s a e s a is ical only. included (do ed line). The inclusion o he b eakup channels educes he F esnel peak and sligh ly inc eases he c oss sec- ion a la ge angles. These wo e ec s a e in he di ec ion o imp o ing he ag eemen wi h he da a, al hough some o e es ima ion o he F esnel peak is s ill isible. In addi ion o he elas ically sca e ed 8Bp ojec ile, he p esen expe imen allowed o a clea iden i ica ion o he p oduced 7Be agmen s, p esumably s emming om he b eakup and ans e p ocesses. B eakup c oss sec ions a e e y sensi i e o he p ojec ile s uc u e and can be used o in es iga e he in e play be ween nuclea s uc u e and e- ac ion dynamics. The e o e, in he ollowing, we analyzed his channel in de ail and compa ed i wi h he calcula ions. The angula dis ibu ion o hese 7Be agmen s has been ex ac ed and compa ed in Fig. 5wi h he CDCC p edic ion. The la e was compu ed by a sui able ans o ma ion o he CDCC b eakup ampli udes, using he o malism o Re . [67]. Besides he sys ema ic po en ial o 7Be +208Pb [51]used in his calcula ion, ano he wo di e en po en ials, namely, he complex Woods-Saxon po en ial [68] om he i ing o 7Be +208Pb da a in his expe imen and Cook’s op ical model po en ial [69], we e also es ed. The calcula ed b eakup c oss sec ions ba ely showed any di e ence, indica ing ha his obse able is weakly sensi i e o he choice o his po en ial e en o his ela i ely high ene gy. F om Fig. 5, i is seen ha he CDCC calcula ion ep oduces e y well he measu ed dis ibu ion (wi hin e o ba s) up o a sca e ing angle o ≈7◦, bu unde es ima es he da a a la ge angles. A his s age, i is wo h ecalling ha he CDCC me hod p o ides only he so-called elas ic b eakup (EBU) c oss sec ion, in which he p ojec ile dissocia es while he a ge emains in i s g ound s a e. Since he p esen expe imen is inclusi e wi h espec o he emo ed p o on, o he p ocesses can in p inciple con- ibu e o he 7Be p oduc ion, in which he p o on in e ac s nonelas ically wi h he a ge nucleus. These con ibu ions, ha we deno e globally as nonelas ic b eakup (NEB), can be e icien ly compu ed wi h he model p oposed by Ichimu a, Aus e n, Vincen (IAV) [70]. The IAV model has been e- cen ly e isi ed by se e al g oups [71–77]. The model has been success ully applied o weakly bound p ojec iles induced eac ions, such as o he exo ic 11Be p ojec ile on 208Pb a - ge [39]. The same po en ials used in he CDCC calcula ion we e also adop ed in he NEB calcula ion. The esul s o he NEB calcula ions a e also shown in Fig. 5.TheNEB dis ibu ion peaks a la ge angles as compa ed o he EBU dis ibu ion. When he NEB con ibu ion is added o he EBU, a a he good ag eemen wi h he da a is ob ained (solid line in Fig. 5). Thus, om he p esen analysis, we conclude ha mos o he inclusi e 7Be yield can be explained as due o an elas ic dissocia ion mechanism, bu wi h a small bu no negligible con ibu ion due o nonelas ic b eakup p ocesses. The b eakup angula dis ibu ion o 11Be →10Be +non a 208Pb a ge a 3.5 imes he Coulomb ba ie has also been ecen ly measu ed [39]. The in eg a ed b eakup c oss sec ion o 8Bin he p esen wo k (779 mb) is app oxima ely only one ou h o ha o 11Be (3632 mb). Conside ing ha he p o on sepa a ion ene gy o 8B(Sp=0.136 MeV) is much smalle han he neu on sepa a ion ene gy o 11Be (Sn=0.502 MeV), he ob ained smalle in eg a ed c oss sec ion indica es ha he Coulomb and cen i ugal ba ie s expe ienced by he alence p o on in he g ound s a e o 8Bmay supp ess he b eakup p obabili y. This in e p e a ion is suppo ed by he s udy o Re . [40], whe e calcula ions a e p esen ed o 8B-induced eac ions in which he alence p o on is eplaced by a neu on, esul ing in a much la ge c oss sec ion, simila o a neu on in 11Be a simila binding ene gy. IV. SUMMARY In summa y, new da a we e p esen ed o he elas ic sca - e ing and b eakup eac ions o 8Bon a 208Pb a ge a an inciden ene gy o Elab =238 MeV, which co esponds o ou imes he Coulomb ba ie . The elas ic sca e ing angu- la dis ibu ion, which is well ep oduced by op ical model and CDCC calcula ions, exhibi s he ypical Coulomb nu- clea in e e ence peak. This is a a iance wi h he case o he neu on- ich halo nucleus 11Be on he same a ge and a a simila ene gy [39], whe e a s ong supp ession o his in e e ence peak was obse ed. The ex ac ed educed o al eac ion c oss sec ion o 8B+208Pb is simila o ha o he 7Be +208Pb eac ion. The p esen wo k indica es ha he b eakup couplings e ec s, in he elas ic sca e ing o he 8B+208Pb sys em a highe ene gies, do no play an impo - an ole. In con as , a s ong supp ession in he 8B+208Pb elas ic sca e ing a ene gies close o he Coulomb ba ie was obse ed, hough he da a we e a he poo ly desc ibed by CDCC calcula ions [30]. This migh co obo a e he idea o he g adual dec easing o he b eakup couplings e ec s in he elas ic sca e ing o he 8B+208Pb sys em. Howe e , o be e in es iga e his issue, u he da a on elas ic sca e ing and b eakup o his sys em a di e en ene gies would be e y welcome. The angula dis ibu ion o 7Be agmen s was measu ed o he i s ime a his ene gy. The ex ac ed 7Be c oss sec ion could be mos ly accoun ed o by he CDCC calcula ions, he eby indica ing he dominance o he EBU mechanism. 024606-5 K. WANG e al. PHYSICAL REVIEW C 103, 024606 (2021) To es ima e he con ibu ion coming om NEB, addi ional calcula ions we e pe o med using he IAV model [70]. The NEB con ibu ion was ound o be ele an a angles a ound he g azing angle. The combined EBU +NEB esul desc ibes e y well he shape and magni ude o he da a. ACKNOWLEDGMENTS We would like o acknowledge he s a o HIRFL o he ope a ion o he cyclo on and hei iendly collabo a- ion. This wo k was inancially suppo ed by he Na ional Key R&D P og am o China (G an No. 2018YFA0404403), he Na ional Na u al Science Founda ion o China (G an s No. 11947203, No. 11775013, No. 11575256, and No. U1632138), and he You h Inno a ion P omo ion Associa- ion CAS (No. 2020411). V.G. and J.C.Z. would like o hank he São Paulo Resea ch Founda ion (FAPESP) (G an s No. 2016/17612-7 and No. 2018/04965-4) o he inan- cial suppo . A.M.M. is suppo ed by he Spanish Minis e io de Ciencia, Inno ación y Uni e sidades (including FEDER unds) unde p ojec FIS2017-88410-P and by he Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og am unde G an Ag eemen No. 654002. [1] L. F. Can o, P. R. S. Gomes, R. Donangelo, and M. S. Hussein, Phys. Rep. 424, 1 (2006). [2]N.Keeley,K.W.Kempe ,andK.Rusek,Eu . Phys. J. A 50, 145 (2014). [3] J. Kola a, V. Guima ães, and E. 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