Double charge-exchange reactions and the effect of transfer

1 Con en om his wo k may be used unde he e ms o heC ea i eCommonsA ibu ion 3.0 licence. Any u he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he i le o he wo k, jou nal ci a ion and DOI. Published unde licence by IOP Publishing L d 1234567890 ‘’“” Con e ence on Neu ino and Nuclea Physics (CNNP2017) IOP Publishing IOP Con . Se ies: Jou nal o Physics: Con . Se ies 1056 (2018) 012029 doi :10.1088/1742-6596/1056/1/012029 Double cha ge-exchange eac ions and he e ec o ans e J A Lay1,†, S Bu ello2, J I Bellone2,3, M Colonna2and H Lenske4 wi hin he NUMEN p ojec 1Dp o. de F´ısica A ´omica, Molecula y Nuclea , Uni e sidad de Se illa, Se illa, Spain 2Is i u o Nazionale di Fisica Nuclea e, Labo a o i Nazionali del Sud, Ca ania, I aly 3Dipa imen o di Fisica e As onomia, Uni e si di Ca ania, I aly 4Ins i u ¨u Theo e ische Physik, Uni e si y o Giessen, Giessen, Ge many E-mail: †[email protected] Abs ac . The e is a ecen ly enewed in e es on he s udy o single and double cha ge exchange eac ions wi h hea y ions. We epo he e a p elimina y heo e ical s udy o double cha ge exchange eac ions in e ms o wo successi e cha ge exchanges in 2nd o de Dis o ed Wa e Bo n app oxima ion. This allows us o include he e ec o he di e en ans e channels in an app oxima e way. E idences show ha he cha ge exchange p ocess is dominan . The ollowing one in impo ance is he combina ion o one single cha ge exchange, one neu on pick-up and one p o on s ipping. This pa icula p ocess calls o u he in es iga ion. 1. In oduc ion Nuclea eac ions a e one o he mos impo an ools o un a el he na u e o he in e ac ion be ween neu ons and p o ons inside he a omic nucleus. In p inciple, we can ex ac a lo o in o ma ion by making collide a nucleus o in e es wi h a ligh ion o wi h a hea y ion. In he la e case, he heo e ical desc ip ion o he eac ion is la gely mo e in ol ed, since we ha e o deal wi h he nucleon-nucleon in e ac ion o wo di e en many-body sys ems. In spi e o his ex a di icul y, we ind in he li e a u e di e en cases in which we ha e imp o e ou unde s anding o ce ain p oblems hanks o pa icula cha ac e is ics no a ailable wi h ligh nuclei. As an example, we can ci e he s udy o b eakup o halo nuclei unde ex eme elec ic ields supplied by a hea y a ge [1] o he sea ch o he Gian Pai ing Resonance, whe e a la ge Q- alue is needed and only eachable wi h a hea y p ojec ile [2]. Fo he case o cha ge exchange eac ions, we can s udy he single cha ge exchange (SCE) in he nucleus o in e es wi h bo h ligh and hea y ions. Howe e , pe o ming double cha ge exchange (DCE) wi h ligh ions p esen s ce ain di icul ies like dealing wi h he measu emen and econs uc ion o he ajec o y o h ee di e en inal p ojec ile pa icles as we would ha e wi h a ligh ion like 3He o . We can use hea y ions o a oid such p oblems since bo h he a ge -like and p ojec ile-like p oduc s o he eac ions will be bound in mos o he cases. In addi ion, he inal c oss sec ion o double cha ge exchange will depend on he Fe mi and Gamow Telle esponse o bo h he nucleus o in e es ( he a ge ) and he hea y ion used as expe imen al p obe in he eac ion. By choosing ca e ully a hea y ion wi h a la ge Fe mi o Gamow Telle esponse, we can inc ease he inal c oss sec ion, helping o he ex ac ion o he pa icula esponse o he nucleus o in e es . 2 1234567890 ‘’“” Con e ence on Neu ino and Nuclea Physics (CNNP2017) IOP Publishing IOP Con . Se ies: Jou nal o Physics: Con . Se ies 1056 (2018) 012029 doi :10.1088/1742-6596/1056/1/012029 Nowadays, he e is a la ge expe imen al in e es on double cha ge-exchange eac ions wi h hea y ions which has gi en o igin o di e en campaigns mainly a he adioac i e beam acili ies o RCNP a Osaka and RIKEN in Japan [3, 4] and a he LNS-INFN o Ca ania in I aly [5, 6]. The o me ones a e ocused on s udying he Gamow-Telle esponse o nuclei and in he p oduc ion o exo ic nuclei h ough double cha ge exchange eac ions. The la e is de o ed o he s udy o double cha ge-exchange eac ions in connec ion wi h he neu inoless double-be a decay. In he p esen con ibu ion we will ocus in one o he eac ions pe o med a he LNS-INFN: 15 MeV/A 18O p ojec iles impinging on a 40Ca a ge [5]. A e he double cha ge-exchange we will measu e 18Ne and 40A in di e en s a es. He e, we do no conside any di ec p ocess leading om he ini ial o he inal coun e pa s. This means ha he nucleus-nucleus in e ac ion canno change wo cha ges ac ing only once. Such a possibili y is unde in es iga ion [7]. The e o e, he double cha ge-exchange is p oduced by a pa o he e ec i e nucleus-nucleus in e ac ion able o change one cha ge a a ime bu ac ing wice, hus being called a second o de p ocess. The inal si ua ion can be eached also h ough di e en combina ions o neu on pick- up, p o on s ipping, and single cha ge-exchange p ocesses. Any o hese so-called compe ing p ocesses is o a highe o de han he double cha ge-exchange, so ha his la e p ocess should domina e. None heless, a low bomba ding ene gies, he di e ences can be oo small o neglec he con ibu ion o he compe ing p ocesses. In any case, i we manage o con ol hem we can ha e access o a complemen a y s uc u e in o ma ion o he nucleus conside ed which can be o g ea in e es when s udying double-be a decay candida es. The s udy o he compe i ion be ween cha ge exchange wi h hea y ion and he co esponding ans e a di e en bomba ding ene gies has only been p ope ly done o he case o single cha ge-exchange [8]. In single cha ge-exchange, he ans e consis s o one neu on (p o on) pick-up ollowed by a one p o on (neu on) s ipping (o ice e sa) wha means ha can be sol ed in e ms o 2nd o de Dis o ed Wa e Bo n App oxima ion (DWBA). Fo double cha ge-exchange we can ha e ans e channels in ol ing ou pa icles, which means he need o a 4 h o de DWBA. Non-o hogonali y be ween p io and pos ep esen a ion in asn e gene a es a non-o hogonali y con ibu ion. This e m, oge he wi h simul aneous and succesi e con ibu ions, con ibu es cohe en ly o he inal o al c oss sec ion. Full 2nd o de DWBA including simul aneous, succesi e and non-o hogonali y e ms has been ecen ly ully implemen ed, helping us o calcula e exac c oss sec ions o hese cases, whe eas o 4 h o de DWBA he e is no implemen a ion ye o he co esponding non-o hogonali ies. The e o e, ou pu pose is o p elimina y asses he impo ance o he di e en con ibu ions in o de o s udy he possibili y o ex ac ing he desi ed esponse om he expe imen al da a. We will es ima e he ans e con ibu ion o he 18O + 40Ca eac ion a 15 MeV/A and we will compa e wi h he double cha ge-exchange expe imen al da a om [5]. 2. Double cha ge-exchange and mul inucleon ans e c oss sec ions On one hand, we only conside double cha ge exchange as a second o de cha ge exchange, so ha he o m ac o s needed o he eac ion calcula ion a e hose o he eac ions: 18O+40Ca →18F+40K and 18F+40K→18Ne+40A . Fo he calcula ion o such o m ac o s we can ely on a double olding p ocedu e o a esidual nucleon-nucleon in e ac ion and he co esponding ansi ion densi ies o a ge and p ojec ile. On he o he hand, co esponding ans e con ibu ions mus be conside ed. The o malism o mul inucleon ans e in DWBA has been known o se e al decades bu only ecen ly we ha e s a ed o calcula e second o de DWBA ans e due o i s compu a ional demands. Fo he case o double cha ge exchange we deal wi h he ans e o wo p o ons and wo neu ons. Tha would mean he need o a 4 h o de DWBA which has no implemen a ion ye . Since ou pu pose is o es ima e he o de o magni ude and i s ela i e impo ance wi h espec o he 3 1234567890 ‘’“” Con e ence on Neu ino and Nuclea Physics (CNNP2017) IOP Publishing IOP Con . Se ies: Jou nal o Physics: Con . Se ies 1056 (2018) 012029 doi :10.1088/1742-6596/1056/1/012029 cha ge-exchange, we can app oxima e he ull c oss sec ion by he one ob ained conside ing a second o de DWBA wo-neu on ans e o he g ound s a es o 16O+42Ca ollowed by a second o de DWBA wo-p o on ans e o he inal p oduc s 18Ne+40A . We ha e o add he e he possibili y o ha ing one neu on and one p o on ans e ollowed by a single cha ge exchange and ice e sa. This p ocess is o hi d o de . The e o e, e en hough i can be agains ou in ui ion o mix wo di e en esponses o nuclei, i could be la ge han he ull ou h o de ans e . The s uc u e inpu needed o he ans e a e he di e en o e laps be ween he di e en a ge -like p oduc s in he di e en ini ial, in e media e and inal si ua ions conside ed. The same eads o he p ojec ile like ones. Fo he sake o comple eness, hese o e laps should be p o ided by he same s uc u e calcula ion p o iding ansi ion densi ies o he cha ge exchange calcula ion. Howe e , hey a e usually app oxima ed by he o e lap ob ained wi h single pa icle wa e unc ions mul iplied by he co esponding spec oscopic ac o . An al e na i e op ion is o look o di e en spec oscopic ac o s ex ac ed om expe imen al ans e eac ions on he conside ed nuclei. The las ing edien o calcula ing he eac ion c oss sec ion a e he op ical po en ial be ween he di e en coun e pa s o he ini ial, in e media e, and inal si ua ions. All o hem can be ob ained again by a double olding p ocedu e wi h he co esponding cen al densi ies o p ojec ile-like and a ge -like nuclei. Finally, he o al c oss sec ion is he cohe en sum o all hese con ibu ions. The e o e, we canno neglec he p ocesses whose c oss sec ions a e small when compu ed sepa a ely. All o hem in e e e and, h ough his in e e ence, hei inal impac on he o al c oss sec ion can be la ge han expec ed. 3. P elimina y Resul s In o de o ackle he 18O + 40Ca eac ion a 15 MeV/A we combine wo p og ams HIDEX [9] and FRESCO [10]. Wi h HIDEX we calcula e he single cha ge exchange o m ac o by olding QRPA ansi ion densi ies o he di e en nuclei wi h he Lo e and F aney nucleon- nucleon in e ac ion [11]. We app oxima e he 18F+40K→18Ne+40A pa by using he same o m ac o s as in he i s single cha ge exchange, i.e. 18O+40Ca →18F+40K. Howe e , including all he cha ge exchange s eng h o all possible mul ipola i ies wi hin FRESCO is e y demanding compu a ionally, so ha in his p elimina y app oach we ha e cons ain ou sel es o he mul ipola i y leading o he g ound s a es o he in e media e coun e pa s: 18F(1+) and 40K(4−). Then we inc ease he o al s eng h o his speci ic pa o he o al esponse o he nuclei in o de o be o he o de o he expe imen al c oss sec ion a ze o deg ees. In his way he esul should be app oxima e bu s ill ep esen a i e o he s eng h o he double cha ge exchange p ocess and i s compa ison wi h he compe ing channel emains meaning ul. We use he same in e ac ion o calcula e he co esponding op ical po en ials. We include he o m ac o s and op ical po en ials in o FRESCO whe e we can add he di e en ans e con ibu ions. Fo his las pa , we ely on expe imen ally ex ac ed spec oscopic ac o s [12, 13, 14, 15] o he di e en cases. Only g ound s a es a e conside ed o e en-e en o odd-odd nuclei. Fo he odd-e en o e en-odd ones, we conside all he single pa icle le els in he icini y o he Fe mi ene gy. The e o e, all hese le els p o ide a la ge basis and we only lack o comple eness in he e en-e en and odd-odd nuclei. A inal ema k has o be done ega ding he choice o p io o pos in e ac ions o each s eps. We only conside he successi e pa o he ans e choosing pos in e ac ions o all he s eps. In o de o ha e he ull ans e c oss sec ion, we will need o conside he di e en non-o hogonali ies.The ans e leading o he same coun e pa s as DCE is a 4 h o de DWBA calcula ion. The co esponding non-o hoganli y e ms ha e no been implemen ed so a . A calcula ion including only succesi e e ms wi h pos in e ac ions, as he calcula ion p esen ed 4 1234567890 ‘’“” Con e ence on Neu ino and Nuclea Physics (CNNP2017) IOP Publishing IOP Con . Se ies: Jou nal o Physics: Con . Se ies 1056 (2018) 012029 doi :10.1088/1742-6596/1056/1/012029 he e, should be a good es ima ion and mus each he exac esul i ou basis is inc eased owa ds comple eness [10]. In o de o assess he ela i e impo ance o pu e ou pa icle ans e , he combina ion o ans e and a single cha ge exchange and he successi e double cha ge exchange, we ha e pe o med h ee di e en calcula ion. In he i s one we include all con ibu ions. In he second one, only cha ge exchange and he combina ion o cha ge exchange and ans e . Finally, in a hi d calcula ion, only cha ge exchange is included. We show he p elimina y esul s in able 1. When only double cha ge exchange is conside ed, we ge a di e en ial c oss sec ion o 18.3 µb/s a ze o deg ees. This alue is an 8% la ge han he calcula ion ha includes all possible compe ing channels. This las calcula ion is en i led o be he mos co ec one and he e o e his 8% can be unde s ood as he le el o accu acy ound when neglec ing he e ec o ans e . Howe e , i we conside he double cha ge exchange in combina ion wi h one-neu on and one-p o on ans e channels, he di e ence wi h espec o he ull calcula ion is educed o less han a 5%. Table 1. P elimina y calcula ions o he di e en ial c oss sec ion a ze o deg ees and he o al c oss sec ion o he di e en p ocesses conside ed. P ocesses conside ed dσ dΩ(0) (µb/s ) In eg a ed σ(µb) DCE only 18.3 0.060 DCE and (np ans e + SCE) 16.2 0.051 DCE and all ans e s conside ed 17.0 0.054 Expe imen al [5] 11.1 0.072 This educed di e ence is only p esen in he case o he di e en ial c oss sec ion a ze o deg ees. The angula dis ibu ion also changes depending on he p ocesses conside ed. In ac , he esul s o he o al in eg a ed c oss sec ions show a la ge di e ence as can also be ound in able 1. 4. Conclusions We ha e s udied he double cha ge exchange eac ion 18O + 40Ca→18Ne+40A a 15 MeV/A measu ed a he LNS-INFN [5] ocusing in he ela i e impo ance o he di e en compe ing channels, i.e. double cha ge exchange and he di e en possible ans e combina ions leading o he same inal nuclei. We ha e ound ha double cha ge-exchange is he leading p ocess since he e is only a di e ence o an 8% be ween he di e en ial c oss sec ion a ze o deg ees calcula ed including all p ocesses conside ed and he one calcula ed by conside ing only he double cha ge-exchange. This esul was as expec ed acco ding o he ac ha his p ocess is he lowes o de one conside ed. Among he p ocesses in ol ing ans e o pa icles, he combina ions o one single cha ge exchange, one p o on s ipping and one neu on pick up is he ollowing in impo ance. Conside ing his p ocess and he double cha ge-exchange we ob ain a di e en ial c oss sec ion a ze o deg ees jus a 5% di e en om he one ob ained including all p ocesses. Finally, he 4 h o de mul inucleon ans e is he lowes in impo ance. This is impo an since he e is no a comple e de i a ion and implemen a ion o he co esponding non- o hogonali y e ms needed o p ope ly calcula e his con ibu ion. This is also consis en wi h wha ound o he 20Ne + 116Cd eac ion [16] whe e di e en calcula ions o he ans e o wo neu on and wo p o ons p oduce s ongly supp essed c oss sec ions. 5 1234567890 ‘’“” Con e ence on Neu ino and Nuclea Physics (CNNP2017) IOP Publishing IOP Con . Se ies: Jou nal o Physics: Con . Se ies 1056 (2018) 012029 doi :10.1088/1742-6596/1056/1/012029 The combina ions o one single cha ge exchange, one p o on s ipping and one neu on pick up is a hi d o de p ocess. In o de o do a ull DWBA calcula ion one has o include non- o hogonali y e ms o he pa ha includes ans e . Howe e , hese non-o hogonali ies a e pa allel o hose o he second o de p ocess and i s de i a ion should be much simple han hose o he 4 h o de ans e . In any case, hese conclusions a e based on p elimina y, no comple e, calcula ions which should be jus ep esen a i e o he o de o magni ude. Fu he in es iga ions a e demanded in o de o co obo a e hese p elimina y esul s. Mo eo e , a ull de i a ion o he hi d o de p ocess a ising om he combina ion o ans e and cha ge exchange could be o g ea in e es in o de o imp o e accu acy when compa ing ou s uc u e models o neu inoless double- be a decay candida es wi h he double cha ge-exchange eac ion expe imen al da a. Ano he issue o in es iga e is whe he he choice o he hea y ion could educe e en mo e his ans e con ibu ion. As shown in [17], he c oss sec ion o ans e o a pa icle depends o he alignmen o i s spin wi h i s angula momen um in he ini ial and inal occupied o bi s. This ea u e is no seen in ans e wi h ligh ions since he pa icles ans e ed a e ini ially in s−o bi s. Howe e , he ele ance o he ans e can be e y di e en i we use a hea y ion wi h alence neu ons and p o ons occupying a spin-aligned o a spin-an ialigned o bi . Acknowledgmen s The esea ch leading o hese esul s ecei ed unding om Spanish Minis e io de Econom´ıa y Compe i i idad and FEDER unds unde P ojec No. FIS2014-53448-C2-1-P, by he Ayudas a Consolidaci´on de G upos om Jun a de Andaluc´ıa, 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. Re e ences [1] Pesudo V e al. 2017 Phys. Re . Le . 118 152502 URL h ps://link.aps.o g/doi/10.1103/PhysRe Le .118.152502 [2] Cappuzzello F e al. 2015 Na u e Communica ions 66743 [3] Kisamo i K e al. 2016 Phys. Re . Le . 116 052501 URL h ps://link.aps.o g/doi/10.1103/PhysRe Le .116.052501 [4] Takaki M e al. 2014 Hea y-Ion Double-Cha ge Exchange S udy ia a 12C(18O,18Ne)12Be Re- ac ion ol 6 p 02038 (P ep in h p://jou nals.jps.jp/doi/pd /10.7566/JPSCP.6.020038) URL h p://jou nals.jps.jp/doi/abs/10.7566/JPSCP.6.020038 [5] Cappuzzello F, Ca alla o M, Agodi C, Bond M, Ca bone D, Cunsolo A and Fo i A 2015 Eu . Phys. J. 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