Resonance neutron-capture cross sections of stable magnesium isotopes and their astrophysical implications

PHYSICAL REVIEW C 85, 044615 (2012) Resonance neu on-cap u e c oss sec ions o s able magnesium iso opes and hei as ophysical implica ions C. Massimi,1,2,*P. Koehle ,3S. Bis e zo,4N. Colonna,5R. Gallino,4F. Gunsing,6F. K ¨ appele ,7G. Lo usso,5A. Mengoni,8,9 M. Pigna a i,10 G. Vannini,1,2U. Abbondanno,11 G. Ae s,6H. ´ Al a ez,12 F. ´ Al a ez-Vela de,13 S. And iamonje,6 J. And zejewski,14 P. Assimakopoulos,15,†L. Audouin,16 G. Badu ek,17 M. Ba bagallo,5P. Baumann,18 F. Beˇ c ´ aˇ ,19 F. Belloni,11 M. Benne ,20 E. Be houmieux,6M. Cal iani,9F. Cal i ˜ no,21 D. Cano-O ,13 R. Capo e,8,22 C. Ca apic¸o,23,6 A. Ca illo de Albo noz,23 P. Cennini,9V. Chepel,24 E. Chia e i,9G. Co es,25 A. Cou u e,26 J. Cox,26 M. Dahl o s,9S. Da id,16 I. Dillmann,7R. Dol ini,27 C. Domingo-Pa do,28 W. D idi,6I. Du an,12 C. Ele he iadis,29 M. Embid-Segu a,13 L. Fe an ,16,†A. Fe a i,9R. Fe ei a-Ma ques,24 L. Fi zpa ick,9H. F ais-Koelbl,8K. Fujii,11 W. Fu man,30 I. Goncal es,23 E. Gonz´ alez-Rome o,13 A. Go e do ski,31 F. G amegna,32 E. G iesmaye ,8C. Gue e o,13 B. Haas,33 R. Haigh ,34 M. Heil,35 A. He e a-Ma inez,9F. He wig,36 R. Hi schi,20 M. Igashi a,37 S. Isae ,16 E. Je icha,17 Y. Kadi,9 D. Ka adimos,15 D. Ka amanis,15 M. Ke eno,18 V. Ke le o ,30 V. Kono alo ,29 S. Kopecky,38 E. Kossionides,39 M. K iˇ cka,19 C. Lampoudis,29,6H. Leeb,17 C. Lede e ,40 A. Lindo e,24 I. Lopes,24 R. Losi o,9M. Lozano,22 S. Lukic,18 J. Ma ganiec,14 L. Ma ques,23 S. Ma one,5T. Ma ´ ınez,13 P. Mas inu,32 E. Mendoza,13 P. M. Milazzo,11 C. Mo eau,11 M. Mosconi,7F. Ne es,24 H. Obe humme ,17 S. O’B ien,26 M. Oshima,41 J. Pancin,6C. Papach is odoulou,15 C. Papadopoulos,42 C. Pa adela,12 N. Pa onis,15 A. Pa lik,40 P. Pa lopoulos,43 L. Pe o ,6M. T. Pigni,17 R. Plag,7A. Plompen,38 A. Plukis,6A. Poch,25 J. P aena,22 C. P e el,25 J. Quesada,22 T. Rausche ,10 R. Rei a h,34 G. Rocke elle ,34 M. Rose i,44 C. Rubbia,27 G. Rudol ,18 J. Salgado,23 C. San os,23 L. Sa chiapone,9R. Sa men o,23 I. Sa idis,29 C. S ephan,16 G. Taglien e,5 J. L. Tain,28 D. Ta ´ ıo,12 L. Tassan-Go ,16 L. Ta o a,23 R. Te lizzi,5P. Vaz,23 A. Ven u a,44 D. Villama in,13 V. Vlachoudis,9 R. Vlas ou,42 F. Voss,7S. Wal e ,7H. Wendle ,9M. Wiesche ,26 and K. Wisshak7 (n_TOF Collabo a ion) 1Dipa imen o di Fisica, Uni e si ` a di Bologna, Bologna, I aly 2Is i u o Nazionale di Fisica Nuclea e, Bologna, I aly 3Oak Ridge Na ional Labo a o y, Physics Di ision, Oak Ridge, Tennessee 37831-6369, USA 4Dipa imen o di Fisica Gene ale, Uni e si ` a di To ino, To ino, I aly 5Is i u o Nazionale di Fisica Nuclea e, Ba i, I aly 6CEA/Saclay, IRFU, Gi -su -Y e e, F ance 7Ka ls uhe Ins i u e o Technology (KIT), Campus No d, Ins i u ¨ u Ke nphysik, Ge many 8In e na ional A omic Ene gy Agency (IAEA), Nuclea Da a Sec ion, Vienna, Aus ia 9CERN, Gene a, Swi ze land 10Depa men o Physics, Uni e si y o Basel, Swi ze land 11Is i u o Nazionale di Fisica Nuclea e, T ies e, I aly 12Uni e sidade de San iago de Compos ela, San iago de Compos ela, Spain 13Cen o de In es igaciones Ene ge icas Medioambien ales y Tecnologicas, Mad id, Spain 14Uni e si y o Lodz, Lodz, Poland 15Uni e si y o Ioannina, Ioannina, G eece 16Cen e Na ional de la Reche che Scien i ique/IN2P3-IPN, O say, F ance 17A omins i u de ¨ Os e eichischen Uni e si ¨ a en, Technische Uni e si ¨ a Wien, Vienna, Aus ia 18Cen e Na ional de la Reche che Scien i ique/IN2P3-IReS, S asbou g, F ance 19Cha les Uni e si y, P ague, Czech Republic 20Keele Uni e si y, Newcas le-unde -Lyme, S a o dshi e, Uni ed Kingdom 21Uni e sidad Poli ecnica de Mad id, Mad id, Spain 22Uni e sidad de Se illa, Se ille, Spain 23Ins i u o Tecnol´ ogico e Nuclea (ITN), Lisbon, Po ugal 24LIP-Coimb a and Depa amen o de Fisica da Uni e sidade de Coimb a, Coimb a, Po ugal 25Uni e si a Poli ecnica de Ca alunya, Ba celona, Spain 26Uni e si y o No e Dame, No e Dame, USA 27Uni e si ` a degli S udi Pa ia, Pa ia, I aly 28Ins i u o de F´ ısica Co puscula , CSIC-Uni e sidad de Valencia, Valencia, Spain 29A is o le Uni e si y o Thessaloniki, Thessaloniki, G eece 30Join Ins i u e o Nuclea Resea ch, F ank Labo a o y o Neu on Physics, Dubna, Russia 31Ins i u e o Physics and Powe Enginee ing, Kaluga egion, Obninsk, Russia 32Is i u o Nazionale di Fisica Nuclea e, Labo a o i Nazionali di Legna o, Padua, I aly 33Cen e Na ional de la Reche che Scien i ique/IN2P3-CENBG, Bo deaux, F ance 34Los Alamos Na ional Labo a o y, New Mexico, Los Alamos 87545, USA 35GSI Helmhol zzen um ¨ u Schwe ionen o schung GmbH, Da ms ad , Ge many 36Depa men o Physics and As onomy, Uni e si y o Vic o ia, Vic o ia, B i ish Columbia, Canada 044615-1 0556-2813/2012/85(4)/044615(15) ©2012 Ame ican Physical Socie y C. MASSIMI e al. PHYSICAL REVIEW C 85, 044615 (2012) 37Tokyo Ins i u e o Technology, Tokyo, Japan 38EC-JRC-IRMM, Geel, Belgium 39NCSR, A hens, G eece 40Uni e si y o Vienna, Facul y o Physics, Vienna, Aus ia 41Japan A omic Ene gy Resea ch Ins i u e, Tokai-mu a, Japan 42Na ional Technical Uni e si y o A hens, A hens, G eece 43Pˆ ole Uni e si ai e L´ eona d de Vinci, Pa is La D´ e ense, F ance 44ENEA, Bologna, I aly (Recei ed 9 Janua y 2012; e ised manusc ip ecei ed 22 Feb ua y 2012; published 20 Ap il 2012) We ha e measu ed he neu on cap u e c oss sec ions o he s able magnesium iso opes 24,25,26Mg in he ene gy ange o in e es o he sp ocess using he neu on ime-o - ligh acili y n_TOF a CERN. Cap u e e en s om a na u al me al sample and om samples en iched in 25Mg and 26Mg we e eco ded using he o al ene gy me hod based on C62H6de ec o s. Neu on esonance pa ame e s we e ex ac ed by a simul aneous esonance shape analysis o he p esen cap u e da a and exis ing ansmission da a on a na u al iso opic sample. Maxwellian-a e aged cap u e c oss sec ions o he h ee iso opes we e calcula ed up o he mal ene gies o 100 keV and hei impac on s-p ocess analyses was in es iga ed. A 30 keV he new alues o he s ella c oss sec ion o 24Mg, 25Mg, and 26Mg a e 3.8±0.2 mb, 4.1±0.6 mb, and 0.14±0.01 mb, espec i ely. DOI: 10.1103/PhysRe C.85.044615 PACS numbe (s): 26.20.Kn, 28.20.Np, 29.30.Hs, 21.10.Hw I. INTRODUCTION The slow neu on-cap u e p ocess (sp ocess) [1–4]ins a s is esponsible o he o igin o abou one hal o he elemen al abundances beyond i on ha we obse e oday. In his p ocess mos o he neu ons a e p o ided by he 13C(α, n)16O eac ion and by he 22Ne(α, n)25Mg eac ion. Mos o he p oduced neu ons a e cap u ed by ligh species in compe i ion wi h 56Fe, ha is he main seed o s-p ocess nucleosyn hesis on hea y elemen s. Among ligh neu on poisons, 25Mg and 26Mg may ha e a ele an impac on neu on balance, and hei neu on- cap u e c oss sec ions need o be known wi h high p ecision, in o de o ob ain obus s-p ocess calcula ions. Addi ionally, hese esul s yield some cons ain s o he ye poo ly known 22Ne(α, n)25Mg c oss sec ion by s udying he s a es o he 25Mg +ncompound nucleus. Ano he aspec o he cap u e c oss sec ion o he s able magnesium iso opes is ela ed o he open ques ion o he p oduc ion o he adioiso ope 26Al in he cosmos. The sensi i i y s udy o Iliadis e al. [5] has demons a ed ha he c oss sec ion o he 24Mg(n, γ ) eac ion is impo an o he o igin o 26Al, because i s main p oduc ion mechanism in massi e s a s is s ongly a ec ed by he unce ain ies o se e al c oss sec ions, including ha o 24Mg(n, γ ). The cap u e c oss sec ions o he Mg iso opes in cu en nuclea da a lib a ies exhibi de iciencies in he esol ed es- onance egion (RRR), in pa icula conce ning he assignmen o esonance spins. The espec i e e alua ions a e based on he Japanese E alua ed Nuclea Da a Lib a y (JENDL) 3.2 [6] e sion, which adop ed he B ookha en Na ional Labo a o y compila ion [7]in heRRR. Because he ene gy ange o in e es o s-p ocess empe a u es is sligh ly la ge han he one co e ed by he e alua ion, Koehle [8] ecen ly eanalyzed *[email p o ec ed] †Deceased. exis ing da a [9] o de i e an imp o ed se o esonance pa ame e s. His analysis included e y high esolu ion da a o he o al c oss sec ion ob ained wi h a me allic sample o na u al Mg and high- esolu ion cap u e da a measu ed wi h an en iched 25Mg sample, bo h om expe imen s a he Oak Ridge Elec on Linea Accele a o (ORELA) neu on ime-o - ligh acili y [10]. Al hough he e alua ion o Re . [8] is mo e accu a e han ha in Re . [6], he e a e h ee p oblems [11] wi h he o me wo k (Re . [8]). Fi s , he sca e ing wid hs gi en in Tables I and II o Re . [8] a e ac ually nand no gn, whe e gis he s a is ical spin ac o . Second, and mo e impo an ly, he sample hickness used in he ansmission analysis was 10% oo small. Thi d, he ansmission da a used in ha analysis we e oo much a e aged nea he 475-keV esonance, so he quo ed pa ame e s o ha esonance a e no e y accu a e. P e ious expe imen s comp ise a se ies o neu on ime- o - ligh (TOF) measu emen s on na Mg as well as on en iched samples. Typically, hese expe imen s co e ed only a limi ed ene gy egion, and cap u e da a we e aken wi h la ge de ec- o s, less sui ed o cap u e c oss-sec ion s udies on iso opes in he mass egion o Mg, whe e he c oss sec ions a e by a domina ed by he elas ic-sca e ing channel. While he mos abundan iso ope 24Mg has been in es iga ed se e al imes [12–15], he e a e ew neu on da a o 25,26Mg. Because he esonance-domina ed cap u e c oss sec ions o all h ee Mg iso opes a e ela i ely small, he measu emen s can be s ongly a ec ed by a ious kinds o backg ound and exhibi , he e o e, a he la ge disc epancies. Fo ins ance, spin and pa i y o he i s neu on esonance in 25Mg +nha e been epo ed as Jπ=3+[16], 3−[17], and 2+[18] bu was assigned as 2− in he JENDL e alua ion, al hough he pa i y assignmen o Re . [18] is consis en wi h an independen 26Mg(γ,n)25Mg expe imen [19]. Conce ning 26Mg +n eac ion, he obse ed di e ences be ween he only TOF da a om Re . [9] and ac i a ion expe imen s by Moh e al. [20,21] a e consis en wi h he 044615-2 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) TABLE I. Cha ac e is ics o he Mg samples. Sample Iso opic abundance (%) To al A eal densi y ID 24Mg 25Mg 26Mg mass (g) (a oms/b)a na Mg 78.7 10.13 11.17 5.2393 0.03415 25Mg 3.05 95.75 1.20 3.1924 0.01234 26Mg 2.46 1.28 96.26 3.2301 0.01219 aA eal densi y o he Mg iso opes. di ec adia i e cap u e (DRC) componen [22] ha is no co e ed by he TOF echnique. Fo his pa , he he mal cap u e c oss sec ion epo ed in Re . [23] p o ides an addi ional cons ain o no maliza ion o he 1/ slope o he c oss sec ion ( being he neu on eloci y). In iew o he unce ain and incomple e c oss-sec ion da a o he Mg iso opes, which may be due o he neu on sensi i i y o p e ious expe imen s, a se o cap u e measu emen s was pe o med a n_TOF o upda e he (n, γ ) c oss sec ions o 24,25,26Mg. In hese measu emen s pa icula ca e was de o ed o minimizing sys ema ic unce ain ies due o sca e ed neu- ons. In addi ion, en iched samples we e used o imp o e he assignmen o some doub ul esonances. The expe imen and he p ocedu e o he da a educ ion a e desc ibed in Secs. II and III, espec i ely. The esonance analysis is discussed in Sec. IV and he co esponding s ella c oss sec ions a e gi en in Sec. V. The as ophysical implica ions a e illus a ed in Sec. VI and he conclusions a e in Sec. VII. II. EXPERIMENT The cap u e expe imen was pe o med a n_TOF, he neu on ime-o - ligh acili y a CERN [24], which p o ides a whi e neu on spec um om he mal o abou 1-GeV neu on ene gy. Neu ons a e p oduced in a massi e lead a ge by a pulsed 20-GeV p o on beam om he CERN/PS accele a o complex. This spalla ion neu on sou ce is cha ac e ized by he high in ensi y o 7 ×1012 p o ons pe pulse, a sho pulse wid h o 6 ns, a low epe i ion a e o 0.4 Hz, and a long ligh pa h o 185 m. Two collima o s a e p esen in he neu on beam. They p o ide a nea ly symme ic Gaussian-shaped beam p o ile a he sample posi ion, wi h an ene gy-dependen s anda d de ia ion, which is abou 0.77 cm a low neu on ene gies. A ull desc ip ion o i s cha ac e is ics and pe o mance can be ound in Re s. [25,26]. The backg ound le el is kep low, in he expe imen al a ea, hanks o se e al massi e conc e e and i on shieldings and by means o a s ong sweeping magne . A. Cap u e appa a us The cap u e appa a us consis ed o wo C62H6liquid scin illa o s. The deu e a ed benzene liquid scin illa o s used in he p esen measu emen consis ed o cylind ical cells 127.3 mm in diame e and 78 mm in leng h wi h an ac i e olume o abou 1000 cm3. Deu e a ed benzene was chosen o i s e y small neu on sensi i i y. The neu on sensi i i y o FIG. 1. (Colo online) Ske ch o sample change and de ec o s in he expe imen al a ea a a ligh pa h o 185 m (D deno es deu e ium, 2H). he de ec o s was u he minimized by coupling a hin ca bon- ibe cell di ec ly o he EMI 9823QKA pho omul iplie s [27]. The de ec o s we e placed pe pendicula o he beam, 9.2 cm ups eam om he sample cen e in o de o educe he backg ound due o sca e ed pho ons. This geome ical con igu a ion also allowed us o educe he e ec s o he angula dis ibu ion om p ima y neu on cap u e γ ays ollowing neu on cap u e in =1p-wa e esonances. The se up o he sample-de ec o geome y is ske ched in Fig. 1. The o al ene gy de ec ion me hod in combina ion wi h he pulse heigh weigh ing echnique (PHWT)[28] was used o his expe imen . The neu on luence a he sample posi ion, abou 185 m om he neu on sou ce, was measu ed wi h a well-calib a ed 6Li-based neu on moni o [29]. I is an in-beam de ec o , consis ing o a 6Li deposi (300 mg/cm2and 6 cm in diame e ) on a Myla oil and ou o -beam silicon (6 ×4cm 2) de ec o s measu ing he pa icles om he 6Li(n, α)3H eac ion. The moni o was loca ed abou 3 m ups eam o he sample posi ion. The de ec o signals we e eco ded using as digi ize s wi h a sampling a e o 500 Msamples/s[30]. This con igu a ion made i possible o eco d he de ec o signals o e he en i e TOF in e al om ela i is ic neu on ene gies down o app oxima ely 1 eV. The e ec i e leng h o he ligh pa h, L=185.07 ±0.01 m, was calib a ed using he i s s-wa e esonances o Au as explained in Re . [31]. The TOF da a we e con e ed o neu on ene gy by En=mnc2⎡ ⎣ c c2−L  2−1⎤ ⎦,(1) whe e mnis he neu on mass and c he speed o ligh . The TOF in e al o a neu on  was de e mined by he ime be ween he s a signal, based on he e e ence signal p o ided by he p omp γ- lash γ, and he s op signal n(bo h 044615-3 C. MASSIMI e al. PHYSICAL REVIEW C 85, 044615 (2012) de ec ed in he C62H6de ec o s) acco ding o he ollowing:  = n− γ+L/c. B. Samples and measu emen s En iched samples o 25Mg and 26Mg we e bo owed om he Science-Technical Cen e “S able Iso opes” (Obninsk, Russia) in he o m o magnesium oxide powde . The powde was sealed in e y hin aluminum cans wi h o al masses o 350 mg. The en iched samples we e complemen ed by a me al disk o na u al magnesium. All samples we e 22 mm in diame e . The composi ion o he samples is lis ed in Table I.The speci ied impu i ies o he en iched samples included aces o Be, Sb, Fe, Al, Sn, Mn, Cu, Ca, Mo, Ni, Ag, and Pb [32]. F om he esonance shape analysis (RSA) o he cap u e da a, some aces o In we e ound in addi ion. The concen a ion o impu i ies was e i ied and i esul ed o be e y low. Fo ins ance, he mos impo an impu i ies (115In, 121,123Sb, 117Sn, and 95Mo) we e a he le el o ens o ppm. The mass o he samples was quo ed in he accompanying documen a ion wi h- ou unce ain ies. Fu he mo e, no in o ma ion was a ailable on he p ocedu e used o he p epa a ion, no on he inal homogenei y o he powde samples. Because MgO is highly hyg oscopic, he Mg con en migh ha e been o e es ima ed by he abso p ion o mois u e be o e he powde was sealed in he Al cans. Un o una ely, i was no possible o hea he samples o emo ing abso bed wa e as desc ibed in Re . [20]. In ac , he compa a i e analysis o he i s s-wa e esonance a 19.86 keV in he 25Mg(n,γ) c oss sec ion, which was obse ed wi h he en iched 25MgO sample and wi h he me allic na u al sample, p o ided clea e idence ha he quo ed 25Mg mass was o e es ima ed by abou 30% (see Sec. IV B). An al e na i e explana ion could be possible inho- mogenei ies o he sample, ela ed o he spa ial dis ibu ion o he powde inside he canning. Ne e heless, a p ocedu e desc ibed in he analysis sec ion allowed de e mina ion o he 25Mg mass wi h an unce ain y o app oxima ely 12%. Un o una ely, he same p ocedu e could no be applied o he 26Mg sample. The e o e, he c oss sec ion p esen ed he ein may be unde es ima ed by as much as 30% o his iso ope. Addi ional samples o Au, Pb, and C (all 22 mm in diame e ) ha e been used in he expe imen . The Pb and C (co esponding o an a eal densi y o 2.99 ×10−3a oms/b and 2.018 ×10−2a oms/b, espec i ely) disks we e used o de e mine a ious backg ound componen s. A gold sample, 0.25 mm in hickness (co esponding o an a eal densi y o 1.498 ×10−3a oms/b), se ed o no malize he cap u e da a ia he sa u a ed esonance echnique [33]. This echnique can be applied when he mac oscopic o al c oss sec ion is much la ge han uni y. In his pa icula case, all incoming neu ons, wi h ene gies in he icini y o he esonance ene gy, in e ac wi h he sample. The e o e, since all neu ons a e abso bed in he sample, he p obabili y o a cap u e e en in he sample is 1. The measu emen s wi h he di e en samples we e cycled e e y 2 days and hey we e in e spe sed wi h ene gy calib a ion o he scin illa o s. III. DATA REDUCTION The use o he PHWT, by which he TOF spec um is modi ied on he basis o he signal ampli ude, equi es a ca e ul ene gy calib a ion o he cap u e de ec o s in combina ion wi h p ope s udy o he de ec o esolu ion [34]. Du ing he en i e expe imen , he pulse heigh esponse o he C62H6de ec o s was calib a ed in egula in e als wi h s anda d sou ces, i.e., wi h 137Cs, 60Co, and a composi e 238Pu/C sou ce, which yields 6.13-MeV γ ays h ough he 13C(α,n)16O∗ eac ion. Da a we e aken wi h a digi ize h eshold co esponding o a deposi ed ene gy o abou 160 keV, bu a ixed h eshold o 200 keV was la e applied in he o -line p ocessing. By he use o as digi ize s o da a acquisi ion he dead ime could be educed o an e ec i e alue o less han 25 ns, ela ed o he pulse econs uc ion algo i hm. In he o -line e en p ocessing, we applied a ixed dead ime o 30 ns and used his alue in he calcula ion o he co ec ion due o coun ing- a e losses. When an e en was obse ed, all subsequen signals occu ing wi hin he dead ime o 30 ns in bo h de ec o s we e disca ded in o de o elimina e coincidence coun ing. The dead ime co ec ion ne e exceeded 1%. A. Cap u e yield The cap u e yield Y(En), which ep esen s he p obabili y o a neu on o be cap u ed by he sample, can be deduced om he backg ound-sub ac ed coun s in he TOF spec um C(En) egis e ed by he C62H6a ay, C(En)=Y(En)(En)Aεc,(2) whe e (En) ep esen s he in ensi y o he neu on beam, A he sample a ea, and εc he e iciency o de ec ing a cap u e e en . In he PHWT, he p opo ionali y o he cap u e e iciency o he o al γene gy eleased in he cap u e e en εc∝ Ec, whe e Ecis he sum o he neu on sepa a ion ene gy and he kine ic ene gy (Ec=Sn+Kc.m.), is ob ained by a weigh ing unc ion, which modi ies he de ec ion e iciency so εcbecomes independen o he γcascade. The weigh ed coun a e spec um is CW(En)=NY(En)(En)Ec,(3) whe e he absolu e no maliza ion No he cap u e da a is ob ained by means o he sa u a ed esonance in Au a 4.9 eV. Since he Au disk was 0.25 mm in hickness, he a enua ion o he γ ays in he Au sample was conside ed as desc ibed in Re . [28]. The co esponding co ec ion o he no maliza ion cons an was o he o de o 1%. The measu ed cap u e yields a e shown in Fig. 2. B. Backg ound s udies The backg ound componen s ha e been de e mined by compa ison o he Mg cap u e yields wi h he espec i e yields measu ed wi h he Pb and C samples as illus a ed in Fig. 3. The main sou ce o backg ound in he keV egion is gene a ed by in-beam γ ays, which a e sca e ed om he 044615-4 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 10 102103104105106 na Mg(n,γ) 25Mg(n,γ) 26Mg(n,γ) Neu on ene gy (eV) Cap u e yield (in uni s o 102) FIG. 2. (Colo online) Cap u e yield o he na Mg(n,γ), 25Mg(n, γ), and 26Mg(n,γ) eac ions. sample and de ec ed by he cap u e se up. These γ ays a ise mainly om neu on cap u e on hyd ogen in he wa e mode a o su ounding he spalla ion a ge and a e esponsible o mos o he backg ound in he keV egion. This componen is mos p onounced in he yield o he Pb sample, which is pa icula ly sensi i e o in-beam γ ays due o high a omic numbe o lead. Acco dingly, he e ec o he C and Mg samples is much weake as illus a ed in Fig. 3. Ano he impo an backg ound is p oduced by sample- sca e ed neu ons, which a e cap u ed in he de ec ion se up and in su ounding ma e ials. This backg ound componen is s udied wi h he C sample ha can be conside ed as a pu e neu on-sca e e sample. The shape o he ca bon yield is e y simila o ha o 25Mg, because he non esonan elas ic c oss sec ion σn( he so-called po en ial sca e ing) is smoo h o bo h elemen s in his egion and he elas ic yield nσn(whe e nis he a eal densi y in a oms pe ba n) is simila o bo h samples. The compa ison o he wo componen s shows ha he o e all backg ound was domina ed by he e ec o sample- 10-5 10-4 10-3 1 10 102103104105106 25Mg + n na C + n na Pb + n Neu on ene gy (eV) Yield (no no malized) FIG. 3. (Colo online) Cap u e yield o he 25Mg +n eac ion oge he wi h he spec a o he C and Pb measu emen s. sca e ed neu ons. Since he backg ound displays a smoo h, non esonan beha io as a unc ion o ene gy, i was no sub ac ed bu was i ed in he esonance analysis. In his way, he unce ain y ela ed o he backg ound was included in he unce ain y o he esonance pa ame e s. IV. SIMULTANEOUS RESONANCE SHAPE ANALYSIS The p esen cap u e da a we e analyzed oge he wi h ansmission da a om ORELA [9], a ailable om he Expe imen al Nuclea Reac ion Da a (EXFOR) da abase [35], using he R-ma ix code SAMMY [36]. A simul aneous esonance shape analysis o cap u e and ansmission da a esul s in much mo e eliable esonance pa ame e s han can be ob ained h ough independen analyses o he a ious da a se s. Expe imen al e ec s due o neu on mul iple sca e ing in he sample, sel -shielding (i.e., shielding o he inne a oms in he sample by he ou e a oms close o he su ace), Dopple b oadening, and expe imen al esolu ion a e p ope ly aken in o accoun wi hin he SAMMY code. As shown in Eq. (3), he e iciency, and, hence, he calcula ed cap u e yield, is in e sely p opo ional o Ec. Howe e , only a single Sn( ypically chosen o be ha o he mos abundan iso ope in he sample) can be used in weigh ing he da a. The e o e, in he analysis o he cap u e da a, he abundances o he o he Mg iso opes in he sample mus be scaled acco ding o hei Sn alue. In pa icula , he neu on sepa a ion ene gies used we e 7.33, 11.09, and 6.44 MeV o 25Mg, 26Mg, and 27Mg, espec i ely. Resonance pa ame e s epo ed in Re . [8]we eusedas ini ial alues in he RSA, wi h he ollowing excep ions. An a e age eac ion wid h γ=3.5 eV was kep ixed o i cap u e da a when a esonance was no isible in he ansmission da a. Spin-pa i y assignmen o esonances abo e 500 keV we e aken om known esul s o a neu on elas ic- sca e ing expe imen [13]. All esonances up o 700 keV we e included in he Rma ix. The a ailabili y o cap u e da a in he ull ene gy ange allowed us o assign he obse ed esonances o he espec i e iso opes in he i o he ansmission da a up o 700 keV. The RSA o he cap u e da a was limi ed o below abou 700-keV neu on ene gy, whe e inelas ic sca e ing s a s o in e e e. In he i ing p ocedu e, he esonance ene gy and he pa ial wid hs (nand γ) we e allowed o a y while spin and angula momen um we e kep ixed. The nuclea adii o 24Mg +nand 25Mg +nwe e allowed o a y in he i s o he ansmission da a as explained in Re . [8]. The esul s a e adii o 5.4 and 3.8 m o sand pwa es in 24Mg +n, espec i ely, and 5.1 m common o sand pwa es in 25Mg +n. Figu e 4 shows he quali y o he i o he ansmission da a. Pa ame e s o he esonances a nega i e ene gy we e changed wi h espec o he assump ions in Re . [6] o ep o- duce he he mal-neu on cap u e c oss sec ion epo ed in Re . [23]. Thei ene gy was aken om he le el scheme in Re . [37]. A. 24Mg +n esonances The cap u e yield conside ed o his analysis was ob ained om he na Mg +nmeasu emen . The p oblems desc ibed in 044615-5 C. MASSIMI e al. PHYSICAL REVIEW C 85, 044615 (2012) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 100 200 300 400 500 600 700 na Mg+nI SAMMY RSA Neu on ene gy (keV) T ansmission FIG. 4. (Colo online) na Mg +n ansmission da a ( ed symbols) and he SAMMY i (blue line). Sec. II B o he oxide samples do no apply o his me al sample. In Table II he esul s o he RSA a e epo ed oge he wi h he unce ain ies om he i ing p ocedu e. Examples o he i s a e gi en in Figs. 4and 5. In he p esen analysis, he 68.5-keV esonance, assigned o 24Mg in he li e a u e, has been ound o be a 26Mg esonance. Indeed, i was isible in he 26Mg(n, γ ) da a and wi h much educed size in he na Mg(n, γ ). Mo eo e , he doub ul esonance a 177 keV was con i med as belonging o 24Mg. The cap u e ke nels ωγ =gγn/(γ+n),(4) calcula ed om p esen esonance pa ame e s, a e compa ed o hose om Re . [9]inFig.6. In pa icula a ios o he cap u e ke nels as a unc ion o neu on ene gy and o he gn/ γ alues a e shown. I has been shown [38] ha some ke nels TABLE II. 24Mg +n esonance pa ame e s ex ac ed om he simul aneous R-ma ix analysis. The quo ed unce ain ies we e ob ained by he SAMMY i .Spinandpa i y omRe .[8]andRe .[13]. En(keV) J πγ(eV) n(eV) −100 0 0.5+13 3000 46.347 ±0.001 (1) (0.5−) 1.4 ±0.2 1.44 ±0.06 83.940 ±0.004 1 1.5−4.1 ±0.2 7607 ±4 176.67 ±0.01 (1) (0.5−) 3.5a0.4 ±0.2 257.182 ±0.001 (2) (1.5+) 1.8 ±0.1 20.9 ±0.5 267.48 ±0.01 1 0.5−7±3 83270 ±20 430.79 ±0.01 1 1.5−6.7 ±0.6 28180 ±20 475.359 ±0.004 2 2.5+1.2 ±0.2 13.9 ±0.5 498.285 ±0.004 1 1.5−0.25 ±0.1 752 ±2 551.04 ±0.03 (2) (2.5+)8±7 1.2 ±0.4 642.012 ±0.004 1 0.5−1.5 ±0.3 1459 ±8 659.95 ±0.01 0 0.5+(13 ±1) 17470 ±40 aAssumed eac ion wid h. See ex o de ails. 0 0.005 0.01 0.015 0.02 45 45.5 46 46.5 47 24Mg(n,γ)I SAMMY RSA (a) Incoming neu on ene gy (keV) Cap u e yield 0 0.05 0.1 0.15 260 280 300 24Mg(n,γ)I SAMMY RSA (b) Incoming neu on ene gy (keV) Cap u e yield (in uni s o 102) FIG. 5. (Colo online) Fi s o he cap u e yield o he 24Mg +n eac ion in di e en ene gy egions. om p e ious ORELA measu emen s o esonances ha ing la ge gn/ γwe e sys ema ically oo la ge, p esumably due o an unde es ima ion o he neu on-sca e ing backg ound (so-called neu on sensi i i y e ec ). The di e ences be ween he p esen cap u e ke nels and hose o Re . [9] do no appea o indica e his neu on sensi i i y e ec . B. 25Mg +n esonances The cap u e yield o 25Mg was ob ained om he spec um measu ed wi h he en iched oxide sample a e i s a eal densi y was scaled o ep oduce he esonance pa ame e s de e mined om he na u al Mg sample, whe e he i s s-wa e esonance in 25Mg +na 19.86 keV is well isola ed. Wi hou ha co ec ion, γ alues o 1.7 ±0.2 and 1.16 ±0.06 eV we e ound using he da a measu ed wi h he na u al and he en iched MgO sample, espec i ely. This disag eemen sugges ed ha he a eal densi y o he oxide sample was 27.5% oo high, indica ing a signi ican wa e con amina ion o he oxide sample. 044615-6 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) 0 0.5 1 1.5 2 2.5 3 0 100 200 300 400 500 600 700 (a) Neu on ene gy (keV) Ke nel a io ( his wo k/Weigmann) 0 0.5 1 1.5 2 2.5 3 10 -2 10 -1 1 10 102103104 (b) gΓn/Γγ Ke nel a io ( his wo k/Weigmann) FIG. 6. Cap u e ke nel a ios o he p esen wo k o Weigmann [9] as unc ions o neu on ene gy (a) and gn/ γ alues (b) o 24Mg esonances. I he shape o a esonance is dis o ed by expe imen al e ec s, e.g., by Dopple and esolu ion b oadening, he emaining obse able is he cap u e ke nel (p opo ional o he a ea unde he esonance) and he a eal densi y o he sample [39]. Acco dingly, he RSA is sensi i e o ngγn/(γ+n). Because nγ o he 19.86-keV esonance, his quan i y educes o ngγ, and because he s a is ical spin ac o is known om p e ious measu emen s, he e ec i e a eal densi y ncan be de i ed ia RSA om he cap u e da a ob ained wi h he oxide sample. This p ocedu e is alid only i he esonance pa ame e s, and in pa icula he eac ion wid h, is kep ixed in he i . In his way, he e ec i e a eal densi y u ned ou o be (8.6±1.0) ×10−3a oms/b, whe e he 12% unce ain y is gi en by he unce ain y on γ. This adjus ed a eal densi y was used in he RSA o he en iched 25Mg sample. As shown in Fig. 7, he cap u e yield o he oxide sample can be ep oduced wi h he same accu acy ei he by i ing he eac ion wid h o he a eal densi y o he sample. On he con a y, he calcula ion o he yield 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15 20 25 30 25Mg(n,γ)I n=0.0118 a oms/b Γγ=1.7 eV n=0.0086 a oms/b Γγ=1.7 eV n=0.0118 a oms/b Γγ=1.16 eV Incoming neu on ene gy (keV) Cap u e yield (in uni s o 103) FIG. 7. (Colo online) The cap u e yield o he 25Mg(n, γ ) esonance a 19.86 keV. The da a measu ed wi h he oxide sample (symbols wi h e o ba s) a e clea ly o e es ima ed wi h he esonance pa ame e s ob ained om he me allic sample and he o iginally decla ed a eal densi y (black line). The esonance analysis wi h SAMMY shows ha he da a a e ep oduced ea ing he a eal densi y no he cap u e wid h γas ee pa ame e s (blue and g een lines, espec i ely). Consis ency wi h he esul ob ained wi h he me al sample equi es adop ing he educed a eal sample densi y. assuming n=0.01182 a oms/b (i.e., he o iginally decla ed alue) and γ=1.7 eV (de i ed om he me allic sample) does no ep oduce he da a. I is ob ious ha he esul s o he 19.86-keV esonance can be econciled only i he educed a eal densi y is adop ed o he en iched sample. The co esponding esul s o he RSA a e lis ed in Table III oge he wi h he unce ain ies om he SAMMY i s. Examples o he RSA analysis a e gi en in Figs. 4and 8. The pa ame e s o he 19.86-keV esonance de i ed om he me allic na Mg sample a e in ag eemen wi h hose o Re . [9]. Mo eo e , he spin and pa i y assignmen o his le el was con i med since he χ2/DOF (χ2is chi-squa ed and DOF is he numbe o deg ees o eedom) alue o he i (in he ene gy ange 15–30 keV) was 1.6 assuming Jπ=2+and 5.6 assuming Jπ=3+. The spin and pa i y o he 72.66 keV was con i med as well: he χ2/DOF alue o he i (in he ene gy ange 60–80 keV) was 4.6 assuming Jπ=2+and 7.9 assuming Jπ=3+. The pa i y o he 62.727-keV esonance was changed o nega i e acco ding o a ecen pho oexci a ion expe imen by Longland e al. [40]. The doub ul esonances a ≈102 and 107 keV we e ound o imp o e he quali y o he simul aneous RSA and a e, he e o e, included in Table III. Howe e , hey a ec he esonance pa ame e s o he la ge s wa e a 100.03 keV and cap u e da a wi h an en iched sample and e y high s a is ic a e equi ed o sol e his poin . The spin and pa i y o he 211.14-keV esonance was changed om 3− [8] o2 −, because he simul aneous RSA o he ansmission and cap u e da a we e mo e sa is ac o y. In pa icula , he χ2/DOF alue o he i (in he ene gy ange 200–220 keV) was 1.1 assuming Jπ=2−and 3.5 assuming Jπ=3−.Fo he esonances abo e 450 keV he la ge s a is ical unce ain ies p e en ed a meaning ul RSA o he cap u e da a. 044615-7 C. MASSIMI e al. PHYSICAL REVIEW C 85, 044615 (2012) TABLE III. 25Mg +n esonance pa ame e s ex ac ed om he simul aneous R-ma ix analysis, unce ain ies include he one om he sample mass. Spin and pa i y om Re . [8]. Resonances and alues in b acke s mus be conside ed wi h some cau ion. En(keV) J πγ(eV) n(eV) −154.25 0 2+6.5 30 000 19.86 ±0.05 0 2+1.7 ±0.2 2310 ±30 62.727 ±0.003 1a1+a4.1 ±0.7 28 ±5 72.66 ±0.03 0 2+2.5 ±0.4 5080 ±80 79.29 ±0.03 (0) (3+) 3.3 ±0.4 1560 ±80 81.117 ±0.001 0b(2)+3±2 0.8 ±0.7 93.60 ±0.02 (1) (1−) 2.3 ±2 0.6 ±0.2 100.03 ±0.02 0 3+1.0 ±0.1 5240 ±40 [101.997 ±0.009] [1] [2−] [0.2 ±0.1] [4 ±3] [107.60 ±0.02] [0]b[3+] [0.3 ±0.1] [2 ±1] 156.34 ±0.02 (1) (2−) 6.1 ±0.4 5520 ±20 188.347 ±0.009 0 (2)+1.7 ±0.2 590 ±20 194.482 ±0.009 (1) 4(−)0.2 ±0.1 1730 ±20 200.20 ±0.03 1b1−0.3 ±0.3 1410 ±60 200.944 ±0.006 (2) (2+) 3.0 ±0.3 0.7 ±0.7 203.878 ±0.001 (1) (2−) 0.8 ±0.3 2 ±1 [208.27 ±0.01] [1] [1−] [1.2 ±0.5] [230 ±20] 211.14 ±0.05 (1) (2−)d3.1 ±0.7 12400 ±100 226.255 ±0.001 (1) (1−)4±3 0.4 ±0.2 242.47 ±0.02 (1) (1−)6±4 0.3 ±0.2 244.60 ±0.03 1 1−c3.5 ±0.6 50 ±20 245.552 ±0.002 (1) (1−) 2.3 ±2 0.5 ±0.2 253.63 ±0.01 (1) (1−) 3.1 ±2.7 0.1 ±0.1 261.84 ±0.03 (1) 4(−)2.6 ±0.4 3490 ±60 279.6 ±0.2 (0) (2+) 1.9 ±0.7 3290 ±50 311.57 ±0.01 (2) (5+) (0.84 ±0.09) (240 ±10) 362.04 ±0.02 2 4+c2.2 ±0.2 2020 ±40 387.57 ±0.04 (3) (5−)c(1.7 ±0.3) (8910 ±80) 423.43 ±0.01 1 (1−)c(20 ±10) (25 ±10) 451.24 ±0.06 (1) (3−)c(6.6 ±0.8) (3000 ±100) 514.88 ±0.03 (1) (2−) (8.6 ±0.8) (1800 ±100) 536.0 ±0.02 (1) (4−) (2.7 ±0.3) (840 ±40) aSpin and pa i y assignmen based on Re . [40]. bPa i y assignmen based on Re . [19]. cObse ed in 22Ne(α, n)25Mg eac ion. dSpin assignmen based on χ2. C. 26Mg +n esonances This analysis is based on he cap u e yield measu ed wi h he en iched 26MgO sample. The RSA esul s a e epo ed in Table IV oge he wi h he unce ain ies om he i ing p ocedu e. As indica ed by he cap u e yields in Fig. 2, he mass o he 26Mg sample seemed less a ec ed by adso p ion o mois u e. Ne e heless, his possibili y s ill implies a signi ican unce ain y, because none o he esonances could be seen wi h he na u al Mg sample. The e o e, he γ alues (and, co espondingly, he cap u e c oss sec ion) may be unde es ima ed by as much as 30%. I is wo h no ing ha cap u e ke nels ha e been es ima ed in Re . [21] on he basis o ac i a ion da a and a heo e ical calcula ion o he DRC componen . The ωγ alues o he 68.5- and 219.4-keV esonances a e gi en as 0.067 ±0.016 eV and 1.34 ±0.24 eV, espec i ely. In he p esen wo k we measu ed ωγ =0.09 ±0.02 eV o he 68.5-keV esonance and 2.17 ±0.12 eV o he 219.2-keV esonance. This disag eemen would e en be enhanced by a possible educ ion o he sample mass. Examples o he simul aneous RSA analysis a e gi en in Fig. 9. TABLE IV. 26Mg +n esonance pa ame e s ex ac ed om he simul aneous R-ma ix analysis. The quo ed unce ain ies we e ob ained by he SAMMY i . Spin and pa i y om Re . [8]. En(keV) J πγ(eV) n(eV) −60 0 0.5+3 2400 68.529 ±0.001 (1) (0.5−) 0.09a±0.02 48 ±2 219.395 ±0.002 2 1.5+1.10a±0.06 80 ±2 302.34 ±0.1 ±0.08 1 0.5−6.3a±0.9 61200 ±200 427.23 ±0.02 (0) (0.5+) 2.7a±0.5 90 ±20 438.59 ±0.09 (1) (0.5−) 3.4a±0.9 11900 ±200 500.50 ±0.01 (1) (1.5−) 0.48a±0.08 260 ±10 aValues may be unde es ima ed by as much as 30%. 044615-8 RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ... PHYSICAL REVIEW C 85, 044615 (2012) TABLE V. Maxwellian-a e aged cap u e c oss sec ions o 24,25,26Mg (in mb) o di e en empe a u es compa ed wi h he alues in he KADoNiS da abase [41]. The mal ene gy This wo k KADoNiS [41] (keV) Resonances DRC To al Resonances To al 24Mg(n, γ )25Mg 5 0.17 ±0.01 0.04 0.21 ±0.01 0.11 8 0.38 ±0.02 0.05 0.43 ±0.02 10 0.67 ±0.04 0.06 0.71 ±0.04 0.48 15 1.7 ±0.1 0.08 1.71 ±0.1 1.3 20 2.7 ±0.1 0.09 2.7 ±0.1 2.3 23 3.1 ±0.2 0.1 3.2 ±0.2 25 3.3 ±0.2 0.1 3.4 ±0.2 2.9 30 3.7 ±0.2 0.1 3.8 ±0.2 3.3 ±0.4 40 3.8 ±0.2 0.1 3.9 ±0.2 3.6 50 3.6 ±0.2 0.1 3.7 ±0.2 3.4 60 3.2 ±0.2 0.2 3.4 ±0.2 3.1 80 2.6 ±0.2 0.2 2.8 ±0.2 2.7 90 2.4 ±0.3 0.2 2.6 ±0.3 100 2.1 ±0.2 0.2 2.3 ±0.3 2.1 25Mg(n, γ )26Mg 5 3.5 ±0.4 0.02 3.5 ±0.4 4.8 8 4.9 ±0.6 0.03 4.9 ±0.6 10 5.1 ±0.6 0.03 5.1 ±0.6 5.0 15 4.9 ±0.6 0.03 4.9 ±0.6 5.5 20 4.6 ±0.4 0.04 4.6 ±0.4 6.0 23 4.5 ±0.6 0.05 4.6 ±0.6 25 4.3 ±0.6 0.05 4.4 ±0.6 6.2 30 4.0 ±0.6 0.05 4.1 ±0.6 6.4 ±0.4 40 3.4 ±0.6 0.06 3.5 ±0.6 6.2 50 2.8 ±0.5 0.07 2.9 ±0.5 5.7 60 2.4 ±0.4 0.08 2.5 ±0.4 5.3 80 1.8 ±0.3 0.09 1.9 ±0.3 4.4 90 1.5 ±0.2 0.1 1.6 ±0.2 100 1.3 ±0.2 0.1 1.4 ±0.2 3.6 26Mg(n, γ )27Mg 5 0.067a±0.002 0.02 0.087b±0.002 0.103 8 0.050a±0.001 0.02 0.070b±0.001 10 0.047a±0.001 0.03 0.077b±0.001 0.091 15 0.056a±0.003 0.03 0.086b±0.003 0.098 20 0.069a±0.005 0.04 0.109b±0.005 0.110 23 0.07a±0.01 0.04 0.11b±0.01 25 0.08a±0.01 0.04 0.12b±0.01 0.124 ±0.008 30 0.09a±0.01 0.05 0.14b±0.01 0.084 ±0.005 0.126 ±0.009 40 0.12a±0.01 0.06 0.18b±0.01 0.143 50 0.17a±0.02 0.06 0.23b±0.02 0.161 60 0.21a±0.02 0.07 0.28b±0.02 0.165 80 0.29a±0.04 0.08 0.37b±0.04 0.226 90 0.31a±0.05 0.09 0.40b±0.05 100 0.34a±0.05 0.09 0.43b±0.05 0.265 aValues may be unde es ima ed by as much as 30%. bValues may be unde es ima ed by as much as 20%. V. STELLAR CROSS SECTIONS A. Resonance con ibu ions The c oss sec ions de e mined using he esonance pa am- e e s in Secs. IV A,IV B, and IV C ha e been con olu ed wi h a Maxwellian neu on ene gy dis ibu ion o ob ain he ac ual s ella c oss sec ion (MACS). The esul s a e lis ed in he Table V o he mal ene gies be ween kT =5 and 100 keV, including he speci ic alues o he common s-p ocess si es, e.g., o kT =8 and 23 keV ela ed o He shell bu ning in low-mass AGB s a s and kT =25 and 90 keV o he case o co e He and shell C bu ning in massi e s a s. The alue 044615-9