Spectroscopy of 46Ar by the (t,p) two-neutron transfer reaction

This is an elec onic ep in o he o iginal a icle. This ep in may di e om he o iginal in pagina ion and ypog aphic de ail. Au ho (s): Ti le: Yea : Ve sion: Please ci e he o iginal e sion: All ma e ial supplied ia JYX is p o ec ed by copy igh and o he in ellec ual p ope y igh s, and duplica ion o sale o all o pa o any o he eposi o y collec ions is no pe mi ed, excep ha ma e ial may be duplica ed by you o you esea ch use o educa ional pu poses in elec onic o p in o m. You mus ob ain pe mission o any o he use. Elec onic o p in copies may no be o e ed, whe he o sale o o he wise o anyone who is no an au ho ised use . Spec oscopy o 46A by he ( ,p) wo-neu on ans e eac ion Nowak, K.; Wimme , K.; Hellga ne , S.; Müche , D.; Bilds ein, V.; Di iken, J.; Else ie s, J.; Ga ney, L. P.; Ge nhäuse , R.; Iwanicki, J.; Johansen, J. G.; Huyse, M.; Konki, Joonas; K öll, T.; K ücken, R.; Lu e , R.; O landi, R.; Paka inen, Janne; Raabe, R.; Rei e , P.; Roge , T.; Sch iede , G.; Seidli z, M.; So lin, O.; Van Duppen, P.; Wa , N.; De Wi e, H.; Zielińska, M. Nowak, K., Wimme , K., Hellga ne , S., Müche , D., Bilds ein, V., Di iken, J., Else ie s, J., Ga ney, L. P., Ge nhäuse , R., Iwanicki, J., Johansen, J. G., Huyse, M., Konki, J., K öll, T., K ücken, R., Lu e , R., O landi, R., Paka inen, J., Raabe, R., . . . Zielińska, M. (2016). Spec oscopy o 46A by he ( ,p) wo-neu on ans e eac ion. Physical Re iew C, 93(4), A icle 044335. h ps://doi.o g/10.1103/PhysRe C.93.044335 2016 PHYSICAL REVIEW C 93, 044335 (2016) Spec oscopy o 46A by he ( ,p) wo-neu on ans e eac ion K. Nowak,1K. Wimme ,1,2,*S. Hellga ne ,1D. M¨ uche ,1V. Bilds ein,1,3J. Di iken,4J. Else ie s,4L. P. Ga ney,5,† R. Ge nh¨ ause ,1J. Iwanicki,6J. G. Johansen,7M. Huyse,4J. Konki,8,9T. K ¨ oll,10 R. K ¨ ucken,1,11 R. Lu e ,12 R. O landi,13 J. Paka inen,8,9R. Raabe,4P. Rei e ,14 T. Roge ,4G. Sch iede ,10 M. Seidli z,14 O. So lin,15 P. Van Duppen,4N. Wa ,14 H. De Wi e,4and M. Zieli´ nska6 1Physik-Depa men E12, Technische Uni e si ¨ a M¨ unchen, D-85748 Ga ching, Ge many 2Depa men o Physics, The Uni e si y o Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 3Depa men o Physics, Uni e si y o Guelph, Guelph, On a io, N1G 2W1, Canada 4KU Leu en, Ins i uu oo Ke n- en S alings ysica, B-3001 He e lee, Belgium 5Oli e Lodge Labo a o y, Uni e si y o Li e pool, Li e pool L69 9ZE, Uni ed Kingdom 6Hea y Ion Labo a o y, Uni e si y o Wa saw, PL-02-093 Wa saw, Poland 7Depa men o Physics and As onomy, Aa hus Uni e si y, DK-8000 Aa hus C, Denma k 8ISOLDE, CERN, CH-1211 Gene a 23, Swi ze land 9Uni e si y o Jy askyla, Depa men o Physics, P.O. Box 35, FI-40014, Uni e si y o Jy askyla, Finland and Helsinki Ins i u e o Physics, P.O. Box 64, FI-00014 Uni e si y o Helsinki, Finland 10Ins i u ¨ u Ke nphysik, Technische Uni e si ¨ a Da ms ad , D-64289 Da ms ad , Ge many 11Depa men o Physics and As onomy, Uni e si y o B i ish Columbia, Vancou e , B i ish Columbia, Canada V6T 1Z1 and TRIUMF, 4004 Wesb ook Mall, Vancou e , B i ish Columbia, Canada V6T 2A3 12Ludwig-Maximilians-Uni e si ¨ a -M¨ unchen, Schellings aße 4, D-80799 M¨ unchen, Ge many 13Ins i u o de Es uc u a de la Ma e ia, IEM-CSIC, Mad id E-28006, Spain 14Ins i u ¨ u Ke nphysik, Uni e si ¨ a zu K¨ oln, D-50937 K¨ oln, Ge many 15G and Acc´ el´ e a eu Na ional d’Ions Lou ds (GANIL), CEA/DSM - CNRS/IN2P3, B. P. 55027, F-14076 Caen Cedex 5, F ance (Recei ed 1 Ma ch 2016; published 27 Ap il 2016) S a es in he N=28 nucleus 46A ha e been s udied by a wo-neu on ans e eac ion a REX-ISOLDE (CERN). A beam o adioac i e 44A a an ene gy o 2.16 AMeV and a i ium-loaded i anium a ge we e used o popula e 46A by he 3H(44A , p) wo-neu on ans e eac ion. P o ons emi ed om he a ge we e iden i ied in he T-REX silicon de ec o a ay. The exci a ion ene gies o s a es in 46A ha e been econs uc ed om he measu ed angles and ene gies o ecoil p o ons. Angula dis ibu ions o h ee inal s a es we e measu ed and based on he shape o he di e en ial c oss sec ion an exci ed s a e a 3695 keV was iden i ied as Jπ=0+. The angula di e en ial c oss sec ion o he popula ion o di e en s a es a e compa ed o calcula ions using a eac ion model employing bo h sequen ial and di ec ans e o wo neu ons. Resul s a e compa ed o shell-model calcula ions using s a e-o - he-a e ec i e in e ac ions. DOI: 10.1103/PhysRe C.93.044335 I. INTRODUCTION Among he magic numbe s which desc ibe he shell s uc u e o a omic nuclei, 28 is he i s main shell gap c ea ed by he spin-o bi in e ac ion. The 1 7/2o bi al ge s lowe ed in ene gy compa ed o he 1 5/2o bi al c ea ing his gap wi hin he N=3 majo oscilla o shell. The e olu ion o he shell gap a 28 nucleons, bo h as a unc ion o neu on and p o on numbe , is in luenced by he na u e o he spin-o bi in e ac ion. On he neu on- ich side o he alley o s abili y, i was shown ha o he e ms in he nucleon in e ac ion also play a ole in de e mining he size o he N=28 shell gap [1]. *Co esponding au ho : [email p o ec ed] †P esen add ess: School o Enginee ing and Compu ing, Uni e si y o he Wes o Sco land, Paisley, PA1 2BE, Uni ed Kingdom. Published by he Ame ican Physical Socie y unde he e ms o he C ea i e Commons A ibu ion 3.0 License. Fu he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he published a icle’s i le, jou nal ci a ion, and DOI. Th ee-body o ces ha e been success ully employed along he Ca iso opic chain (Z=20) o desc ibe he high exci a ion ene gy o he i s 2+s a e in 48Ca and he inc ease o he N=28 gap be ween N=20 and 28 mic oscopically [2]. E olu ion o he gap be ween he neu on sd shell and he 1 7/2 o bi al along he N=28 iso ones is in luenced by he cen al and enso in e ac ion be ween p o ons and neu ons [3]. Below 48Ca a a ie y o ea u es can be seen in he low-lying exci a ions o he N=28 iso ones. These a ise om he sub le in e play o he o ces, he b eakdown o he N=28 shell closu e, and he p o on subshell closu es a Z=16 (sul u ) and 14 (silicon). The B(E2; 2+ 1→0+ gs) alue o 46A (Z=18) was measu ed using Coulomb exci a ion a in e me- dia e ene gies [4–6] as well as ex ac ed om he measu ed li e ime [7] gi ing con lic ing esul s. The alue de e mined in he Coulomb exci a ion expe imen s (B(E2; 2+ 1→0+ gs)= 39(8) e2 m4[4], 44(6) e2 m4[5], and 54(5) e2 m4[6]) poin s o a mode a e de o ma ion and collec i i y in 46A consis en wi h he expec a ion o a semimagic nucleus. This is suppo ed by ime-dependen Ha ee-Fock-Bogoliubo calcula ions [8] ha link he inc ease in collec i i y wi h espec o 48Ca o a 2469-9985/2016/93(4)/044335(10) 044335-1 Published by he Ame ican Physical Socie y K. NOWAK e al. PHYSICAL REVIEW C 93, 044335 (2016) quenching o he N=28 shell gap. Shell-model calcula ions on he o he hand a o he esul o a la ge B(E2) alue as de e mined by he li e ime measu emen (B(E2; 2+ 1→ 0+ gs)=114+67 −32 e2 m4[7]). The neu on single-pa icle ene gies o he 2p3/2,2p1/2, and 1 5/2o bi als in 47A ha e been ex ac ed om a (d,p) ans e eac ion and compa ed o 49Ca he N=28 shell gap is educed by 330(90) keV [9]. Mass measu emen s also show a s ong gap a N=28 [10] and he sepa a ion ene gies a e well desc ibed by calcula ions using he SDPF-U [11] and SDPF-MU [12] e ec i e in e ac ions. Below 46A he nucleus 44Sexhibi s a low-lying exci ed 0+ s a e [13] which was in e p e ed as a sign o shape coexis ence. Measu emen s o o he low-lying s a es [14]aswellas con igu a ion mixing calcula ions sugges an e osion o he N=28 shell closu e a he han shape coexis ence [15]. 42Si has a e y low i s exci ed s a e [16] and he R4/2 a io indica es well-de eloped de o ma ion [17]. Shell-model calcula ions p edic ha his nucleus is obla e in i s g ound s a e [11,12]. The single-pa icle s uc u e o 46A and i s neighbo s was s udied in se e al expe imen s. Spec oscopic ac o s ex ac ed om neu on emo al eac ions om 46A o 45A ga e consis en esul s bo h in ans e [18] and knockou eac ions [19]. These expe imen s show ha he g ound s a e o 46A is domina ed by a 7/2con igu a ion. Spec oscopic ac o s ex ac ed om he s udy o he N=27 iso ope 45A by a one-neu on (d,p) ans e eac ion also ag ee wi h shell-model esul s [20]. These esul s sugges ha he N=28 shell gap is s ill p onounced in 46A . E en hough he i s exci ed s a e in 45A Jπ=3/2−is loca ed only a 542 keV, he spec oscopic s eng h is la ge o he second exci ed 3/2− s a e a 1416 keV. The low 3/2− 1s a e has likely a complica ed s uc u e, in ol ing also p o on exci a ions [20] and can he e o e no be ega ded as a sign o a educed shell gap. The B(E2; 2+ 1→0+ gs) as de e mined by in e media e beam ene gy Coulomb exci a ion is somewha small [4–6], a esul in disag eemen wi h he shell-model calcula ions [11,12,21] as well as calcula ions using he gene a o coo dina e me hod wi h he Gogny D1S in e ac ion [22]. The la e calcula ions p edic a coexis ence o sphe ical and de o med s a es a low exci a ion ene gy. The collec i e wa e unc ion calcula ed o bo h he 0+ gs and 0+ 2s a es show a mix u e o obla e and p ola e componen s, on a e age his leads o a sligh ly obla e 0+ gs and p ola e 0+ 2a ∼2.75 MeV [22]. A ela i ely low-lying exci ed 0+s a e is also p edic ed by he shell-model calcula ions a a ound 3 MeV (see Fig. 6). Expe imen ally, exci ed s a es beyond he 2+ 1s a e we e obse ed in in-beam expe imen s. In a p o on inelas ic sca e ing expe imen [23] a candida e o a3 −s a e a 4982 keV and se e al unassigned s a es a ound 4 MeV we e ound. Candida es o 0+ 2,2 + 2, and 4+ 1s a es we e ound in agmen a ion eac ions [24]. The 0+ 2s a e was loca ed a 2710 keV and en a i ely assigned only based on he obse a ion o a 1140-keV ansi ion in coincidence wi h he 2+ 1→0+ gs ansi ion and he compa ison o calcula ions. F om shell-model calcula ions in Re . [24] using he in e ac ion o e e ence [25] he0 +g ound s a e is domina ed by a 0p-0h con igu a ion. The i s exci ed 0+s a e on he o he hand has a2p-2hs uc u e wi h wo neu ons p edominan ly loca ed in he 2p3/2o bi al abo e N=28. In his wo k he s uc u e o low-lying s a es in 46A was s udied by a ( ,p) wo-neu on ans e eac ion in in e se kine- ma ics. Two-neu on ans e eac ions a e an excellen ool o s udy he na u e o 0+s a es caused by neu on exci a ions. The angula dis ibu ion o p o ons om he eac ion is indica i e o he ans e ed angula momen um o he eac ion. The e o e, 0+s a es can be iden i ied unambiguously. Fu he mo e, he c oss sec ion o he wo-neu on ans e eac ion depends on he de ails o he wa e unc ions o he s a es in ol ed, allowing o p ecise es ing o heo e ical models. II. EXPERIMENTAL SETUP The expe imen was pe o med a he REX-ISOLDE acil- i y a CERN [26]. Radioac i e 44A nuclei we e p oduced by impinging he 1.4-GeV p o on beam om he PS boos e on o a hick u anium ca bide (UCx) a ge . To educe con amina ion om ca bon dioxide CO2a he same mass numbe 44 he p ima y a ge was hea ed be o e he expe imen . A gon as a noble gas is ola ile, eme ging easily om he hick a ge ma e ial h ough a cooled ans e line o emo e less ola ile con aminan s. A o ced elec on beam induced a c discha ge (FEBIAD) ion sou ce [27] was used o achie e a high ioniza ion e iciency o he 1+cha ge s a e o 44A . A e accele a ion o 30 keV he beam is sen h ough he high esolu ion sepa a o (HRS). The HRS p o ides su icien esolu ion o disc imina e be ween 44A +and he emaining CO+ 2. Doubly cha ged 88K 2+could no ully be sepa a ed and emained in he low ene gy beam. A e mass sepa a ion, a adio equency quad upole coole and bunche we e employed o imp o e beam emi ance. Ions we e hen accumula ed and bunched in he REX ap o 60 ms be o e anspo a ion o he elec on beam ion sou ce REX EBIS o cha ge b eeding. Fo he 44A ions a maximum in he cha ge s a e dis ibu ion a q=+13 was achie ed in 59-ms cha ge b eeding ime. Be o e accele a ion in he REX linea accele a o he ions a e sepa a ed by hei mass o cha ge a io A/q. The cha ge s a e dis ibu ion o 88K is su icien ly di e en such ha an A/q selec ion o 3.3846 p o ided a clean beam o he expe imen . Selec ing a cha ge s a e o q=+13 also elimina ed con amina ion om he 22Ne bu e gas used in he EBIS. The ions we e accele a ed by he REX LINAC consis ing o an RFQ, an IH s uc u e, h ee se en-gap esona o s ollowed by a nine-gap esona o . Fo he p esen expe imen he beam ene gy was limi ed o 2.16 AMeV, o a oid usion eac ions wi h he a ge ca ie ma e ial, he e o e he nine-gap esona o was no used. The 44A beam a an a e age in ensi y o 2 ×105/s was hen sen o he expe imen al s a ion whe e i impinged on a i ia ed i anium oil. The a ge i sel is a 4.5-mm wide s ip o i anium oil wi h a hickness o 0.5 mg/cm2. The i anium is loaded wi h i ium a an a omic a io o 1.3 i ium a oms pe i anium a om, co esponding o an e ec i e i ium hickness o 36 μg/cm2. The a ge was he same one used in Re . [28] and he decay o he i ium had educed he e ec i e hickness since i s p oduc ion in Oc obe 2010. Ligh eac ion pa ne s eme ging om he a ge we e de ec ed and iden i ied using he T-REX silicon de ec o a ay [29]. The a ay consis s o wo boxes o 140-μm hick silicon s ip de ec o s o measu e 044335-2 SPECTROSCOPY OF 46A BY THE ( ,p) TWO- . . . PHYSICAL REVIEW C 93, 044335 (2016) he ene gy loss o ligh pa icles backed by 1-mm hick unsegmen ed silicon de ec o s o o al ene gy measu emen . In he mos backwa d di ec ion a double-sided annula silicon s ip de ec o was moun ed. The de ec o s co e 65% o he solid angle a ound he a ge . Recoil p o ons, deu e ons, and i ons om elas ic and inelas ic sca e ing as well as ans e eac ion channels a e iden i ied by hei cha ac e is ic ene gy loss in he hin i s laye o he de ec o s ack h ough he E-Eme hod. In backwa d di ec ion he ene gy o p o ons is no su icien o punch h ough he i s laye o silicon, howe e , he second laye can be used o disc imina e p o ons om elec on om βdecay o beam pa icles acciden ally s opped in he chambe . The e iciency and accep ance o he a ay was modeled using a GEANT4 [30] simula ion o he se up [29]. The silicon a ay is su ounded by he MINIBALL ge manium de ec o a ay [31]. MINIBALL consis s o 24 high pu i y ge manium c ys als, each six old segmen ed o imp o ed g anula i y, allowing o be e Dopple co ec ion o de ec ed γ ays. Ene gy and e iciency calib a ions we e pe o med using s anda d calib a ion sou ces. III. DATA ANALYSIS Ligh , cha ged ecoil pa icles, p o ons, i ons, and deu e ons we e iden i ied using he ene gy loss E and o al kine ic ene gy Emeasu emen s in he wo laye s o he T-REX silicon de ec o s. Fo pa icles s opped in he E laye addi ional kinema ic cu s ha e been applied. In labo a o y backwa d di ec ion bo h p o ons and deu e ons ha e kine ic ene gies below he iden i ica ion h eshold; hey a e s opped in he i s laye , and he e o e no pa icle iden i ica ion is possible. Howe e , he kine ic ene gy o deu e ons ollowing he ( ,d) eac ion is e y low. The e o e, a condi ion on sca e ing angle and pa icle ene gy can be used o elimina e deu e ons in he spec um. The spec um in Fig. 1shows he exci a ion ene gy o 46A econs uc ed om he p o on angle and kine ic ene gy. In addi ion o a s ong popula ion o exci ed s a es a ound 5 MeV (see below o de ails) h ee peaks a e obse ed in he exci a ion ene gy spec um. They co espond o he g ound s a e o 46A , he known i s exci ed 2+s a e a 1554 keV, and a p e iously unknown s a e a an exci a ion ene gy o 3660(60) keV. Figu e 2shows he Dopple co ec ed γ- ay ene gy spec um o 46A assuming a sca e ing angle o 0◦in he labo a o y sys em o 46A . The ansi ions a 1554, 2318, 2518, and 2707 keV ha e been p e iously obse ed [23,24]. A ansi ion a 1153 keV, co esponding o he decay o he p e iously assigned 0+ 2 s a e [24] was no obse ed. Newly obse ed a e he ansi ions a 2141 and 3590 keV. The s a is ics a e no su icien o a γ-γ coincidence analysis, bu he analysis o he exci a ion ene gy spec um shows ha all ansi ions eed he i s exci ed s a e and no o he s a e below 4 MeV was obse ed in Fig. 1.Fig- u e 3shows he exci a ion ene gy o 46A econs uc ed om he p o on angle and kine ic ene gy measu ed in coincidence wi h he s onges γ- ay lines obse ed in Fig. 2. The spec a ha e been i ed wi h a Gaussian unc ion, and he esul ing mean exci a ion ene gy ag ees wi h he one (MeV) exc E 1−012 coun s / 40 keV 0 5 10 15 20 25 (a) ° > 150 lab ϑ (MeV) exc E 1−012 345 345 coun s / 40 keV 0 5 10 15 20 25 30 (b) ° > 120 lab ϑ FIG. 1. Exci a ion ene gy o 46A econs uc ed om he p o on angle and kine ic ene gy. The da a a e i wi h an exponen ial unc ion ep esen ing he con inuum o highly exci ed s a es and Gaussian unc ions co esponding o s a es in 46A . (a) Shows he mos backwa d angles in he labo a o y sys em, whe e he esolu ion is bes . (b) Also includes mo e o wa d angles, whe e he known 2+ s a e a 1554 keV is mo e p onounced. Because he exci a ion ene gy esolu ion depends s ongly on he sca e ing angle, he i is only used o ex ac he mean posi ion o he peaks, no he c oss sec ion. de e mined om he sum o γ- ay ene gies wi hin he e o . Figu e 3(a) shows ha he main con ibu ion o he 2+s a e comes om indi ec eeding h ough exci ed s a es be ween 3 and 6 MeV. A ga e on he 2141-keV ansi ion e eals a single s a e a an exci a ion ene gy o 3670(100) keV [Fig. 3(b)]. This s a e co esponds o he p e iously discussed s a e o Fig. 1a 3660(60) keV. F om he sum o γ- ay ansi ion ene gies he exci a ion ene gy o his s a e is de e mined o 3695(4) keV. (keV) γ E 500 1000 1500 2000 2500 3000 3500 coun s / 10 keV 1 10 2 10 1554(1) 2141(3) 2318(3) 2518(2) 2707(2) 3590(3) FIG. 2. Dopple co ec ed γ- ay ene gy spec um measu ed in coincidence wi h ecoil p o ons iden i ied in T-REX. All p o on angles ha e been included. T ansi ions a e labeled by hei ene gy in keV. The g een a ow indica es 3695 keV, whe e a di ec g ound-s a e decay o he p oposed 0+s a e would be loca ed. 044335-3 K. NOWAK e al. PHYSICAL REVIEW C 93, 044335 (2016) (MeV) exc E 0 123456 coun s / 200 keV 0 5 10 15 20 25 30 (a)ga e 1554 keV (MeV) exc E 0 123456 coun s / 200 keV 1− 0 1 2 3 4 5 6 7(b)ga e 2141 keV (MeV) exc E 0 123456 coun s / 200 keV 0 2 4 6 8 10 12 (c)ga e 2707 keV (MeV) exc E 0123456 coun s / 360 keV 0 2 4 6 8 10 (d)ga e 3590 keV FIG. 3. Exci a ion ene gy o 46A econs uc ed om he p o on angle and kine ic ene gy ga ed on se e al γ- ay ansi ions. All p o on angles a e aken in o accoun . Random backg ound was sub ac ed. Exci a ion ene gies ex ac ed om Gaussian i s ag ee wi h he sums o γ- ay ansi ion ene gies. Simila ly, we place s a es a 4255(4) and 5144(4) keV which decay by 2707- and 3590-keV ansi ions o he i s exci ed s a e. Fo he ansi ions a 2318 and 2518 keV he s a is ics is no su icien o de e mine he eeding le el om p o on-γ FIG. 4. Le el scheme o 46A as de e mined in his wo k. A ows indica e he obse ed γ- ay ansi ions; hei wid h co esponds o he ela i e in ensi y. (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(a)0 keV (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(b) SDPF-MU SDPF-U EPQQM 1554 keV (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(c)3695 keV FIG. 5. Angula dis ibu ion o p o ons om he wo-neu on ans e eac ion o 46A . (a) G ound s a e o 46A ; (b) i s exci ed 2+ s a e; (c) exci ed 0+ 2s a e. Lines ep esen he heo e ical calcula ions using he DWBA eac ion model desc ibed in Sec. IV B using ampli udes calcula ed wi h h ee di e en shell-model e ec i e in e ac ions, SDPF-MU ( ed, dashed), SDPF-U (g een, solid), and EPQQM (blue, do -dashed). coincidences p ecisely, howe e , hey a ise om s a es a ound 4 MeV. These ansi ions a e placed on op o he 2+s a e. The esul ing le el scheme o 46A is shown in Fig. 4. This le el scheme is consis en wi h he one ob ained om he p o on inelas ic sca e ing expe imen [23]. Because (p,p) does no popula e he exci ed 0+s a e di ec ly, and a wo- neu on ans e eac ion o a 3−s a e is no expec ed, he wo expe imen s a e complemen a y and in good ag eemen . In 044335-4 SPECTROSCOPY OF 46A BY THE ( ,p) TWO- . . . PHYSICAL REVIEW C 93, 044335 (2016) 0 + 0 1506 + 2 2928 + 0 3464 + 43510 + 0 3587 + 2 3649 + 33946 + 04046 + 4 4051 + 2 SDPF-NR 0 + 0 1594 + 2 3328 + 0 3529 + 43643 + 33775 + 23900 + 04125 + 0 4222 + 14236 + 2 SDPF-U 0 + 0 1443 + 2 3495 + 03741 + 43790 + 23891 + 34027 + 44075 + 04366 + 14533 + 0 SDPF-MU 0 + 0 1904 + 2 3098 + 0 3876 + 03978 + 24172 + 14295 + 2 4830 + 4 EPQQM FIG. 6. Calcula ed le el schemes o 46A using a ious e ec i e in e ac ions in he shell model [11,12,21,25]. addi ion o he s a es shown in Fig. 4 he exci a ion ene gy spec um (Fig. 1) indica es ha se e al o he s a es abo e 4- MeV exci a ion ene gy ha e been popula ed. The le el densi y inc eases wi h exci a ion ene gy and many indi idual s a es a e popula ed wi h small c oss sec ions, he e o e disc e e lines we e no iden i ied. Because he beam in ensi y luc ua ed du ing he ex- pe imen , he luminosi y was de e mined using he elas ic sca e ing o i ons. These da a we e also used o cons ain he op ical model pa ame e s o he DWBA analysis. The angula dis ibu ions we e ob ained by ga ing on he exci a ion ene gy (Fig. 1) and co ec ing o he geome ical accep ance o he T-REX a ay [29]. Figu e 5shows he angula dis ibu ion o p o ons om he wo-neu on ans e eac ion o he g ound s a e and exci ed s a es o 46A a 1554 and 3695 keV. To a oid sys ema ic unce ain ies da a om he annula de ec o a backwa d angles we e excluded because o an un esol ed p oblem wi h he ime-dependen e iciency o i s mul iplexed eadou [29]. The compa ison wi h he DWBA calcula ions (Sec. IV B) show ha p o ons om he ans e eac ion o he g ound s a e o 46A ollow he calcula ed di e en ial c oss sec ion wi h he cha ac e is ic L=0 minimum a a sca e ing angle ϑcm ∼20◦. The angula dis ibu ion co esponding o he popula ion o he 2+s a e displays a shallow maximum a ound ϑcm ∼30◦, indica i e o he o bi al angula momen um ans e o L=2. The di e en ial c oss sec ion o he newly obse ed exci ed s a e a 3695 keV shows he same end as he g ound s a e. This cha ac e is ic L=0 shape as well as he γdecay only o he 2+s a e and no di ec ly o he g ound s a e, and he somewha la ge wo-neu on ans e eac ion (see Sec. IV B) indica e a spin and pa i y Jπ=0+ o hiss a e. IV. THEORETICAL CALCULATIONS Fo he heo e ical calcula ion o he wo-neu on ans e eac ion c oss sec ion bo h nuclea s uc u e and eac ion inpu s a e equi ed. Shell-model calcula ions a e employed o ob ain he spec oscopic ampli udes (A) o one-neu on ans e s eps as well as wo-nucleon ampli udes (TNA) o he di ec pai ans e . In Sec. IV B he dependence o he di e en ial c oss sec ion on he op ical model pa ame e s and he in luence o he wo eac ion p ocesses a e analyzed. A. Shell-model calcula ions To ge insigh s in he unde lying s uc u e causing he la ge c oss sec ion o he i s exci ed 0+s a e shell-model calcu- la ions ha e been pe o med using he code NUSHELLX [32]. The model space comp ises he sd shell o he p o ons and he p shell o he neu ons. Th ee s a e-o - he-a e ec i e in e - ac ions ha e been compa ed, SDPF-U [11], SDPF-MU [12], and EPQQM [21]. The SDPF-MU and SDPF-U in e ac ions a e cons uc ed om h ee ing edien s. Bo h use he USD [33] e ec i e in e ac ion o he sd p o on-p o on ma ix elemen s. The neu on-neu on in e ac ion in he p shell is based on he KB3 [34] ma ix elemen s o he SDPF-U in e ac ions and he GXPF1B [35] in e ac ion o SDPF-MU, espec i ely. The sd- p c oss-shell p o on-neu on ma ix elemen s a e aken om G-Ma ix [36] o SDPF-U in e ac ion and om VMU [3] in he case o SDPF-MU. The SDPF-U in e ac ion di e s om he olde e sion, SDPF-NR [25], in ha expe imen al in o ma ion on N=21 and po assium nuclei was used o cons ain he monopole pa s. Fo he p esen calcula ion he e sion o Z>14 nuclei was chosen. The EPQQM e ec i e in e ac ion is based on pai ing plus quad upole-quad upole o ces wi h a monopole e m [37]. I was buil o consis en ly desc ibe nuclei be ween Ca and Si [21]. The calcula ed le el schemes o 46A a e shown in Fig. 6. Addi ionally we also ep esen he calcula ions wi h he o iginal SDPF-NR [25] in e ac ion, which was p e iously [24] used o assign spin and pa i y 0+ o a p oposed s a e a 2710 keV. The le el scheme calcula ed wi h he SDPF-U and SDPF-MU in e ac ions a e e y simila , while he EPQQM calcula ion p edic s a highe ene gy o he i s 2+and 4+s a es. The i s exci ed 0+s a e is ound a lowe exci a ion ene gy. The wo-neu on ans e eac ion can p oceed ei he by a successi e ans e o wo single neu ons o by a one-s ep di ec ans e o a neu on pai . To compa e he esul ing wo- neu on ans e c oss sec ion, he spec oscopic ampli udes A o he 44A +n|45A and 45A +n|46A s eps as well as wo-nucleon ampli udes TNA o he di ec one-s ep ans e o 044335-5 K. NOWAK e al. PHYSICAL REVIEW C 93, 044335 (2016) A 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 A (a) 45 - 1 7/2 - 1 3/2 - 2 3/2 - 1 1/2 - 2 1/2 - 3 1/2 - 1 5/2 - 2 5/2 A 2− 1− 0 1 2 (b) + gs 0 7/2 ⊗ - 1 7/2 3/2 p⊗ - 1 3/2 3/2 p⊗ - 2 3 /2 1/2 p⊗ - 1 1/2 1/2 p⊗ - 2 1/2 1/2 p⊗ - 3 1/2 5/2 ⊗ - 1 5/2 5/2 ⊗ - 2 5/2 SDPF-MU SDPF-U EPQQM A 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 (c) + 1 2 7/2 ⊗ - 1 3/2 3/2 p⊗ - 1 7/2 7/2 ⊗ - 1 7/2 A 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1 1.2 (d) + ex 0 7/2 ⊗ - 1 7/2 3/2 p⊗ - 1 3/2 3/2 p⊗ - 2 3 /2 1/2 p⊗ - 1 1/2 1/2 p⊗ - 2 1/2 1/2 p⊗ - 3 1/2 5/2 ⊗ - 1 5/2 5/2 ⊗ - 2 5/2 FIG. 7. Calcula ed spec oscopic ampli udes (A) o he ans e o s a es in 45A (a), and om a ious s a es in 45A o he g ound s a e (b), he 2+ 1s a e (c), and he i s exci ed 0+s a e (d) o 46A . a pai ha e been calcula ed. Figu e 7shows he spec oscopic ampli udes calcula ed in he shell model using he h ee di e en e ec i e in e ac ions. Only s a es which ha e a calcula ed spec oscopic ac o C2S=A2>0.05 a e included in he igu e. The c oss sec ion o a single-neu on ans e eac ion such as he 3H(44A , d) eac ion o s a es in 45A depends only on he squa e o he ampli ude; he phase has no e ec . The calcula ion wi h he SDPF-U e ec i e in e ac ion p edic s wo 5/2−s a es wi h signi ican spec oscopic ac o s, which a e bo h included in he calcula ion. Because o he high exci a ion ene gy, he wo-s ep ans e eac ion c oss sec ion h ough hese s a es is negligible. Fo he calcula ion o he wo-neu on ans e eac ion, howe e , he ela i e signs ma e s. All he ampli udes depic ed in Figs. 7(b)–7(c), o a gi en e ec i e in e ac ion, in e e e o con ibu e o he sequen ial ans e c oss sec ion. The wo-nucleon ampli udes a e shown in Fig. 8. Simila o he spec oscopic ampli udes he ela i e phase o he ampli udes con ibu ing o he c oss sec ion o one s a e de e mines he in e e ence. B. Reac ion model The wo-neu on ans e eac ion c oss sec ions and an- gula dis ibu ions we e calcula ed using he FRESCO DWBA code [38]. Op ical model pa ame e s o he incoming, in e - media e, and ou going channel we e aken om global i s o i ons [39–41], deu e ons [39,42], and p o ons [39,43,44]. The global pa ame e se o Re . [39] is he one which is ex ended o he lowes p ojec ile ene gies, he e o e his pa ame e se is conside ed as he base line o a compa ison. The nume ical alues o he pa ame e s a e lis ed in Table I. TNA 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 (a) + gs 0 2 ) 7/2 (1 2 ) 5/2 (1 2 ) 3/2 (2p 2 ) 1/2 (2p TNA 0.1− 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (b) + ex 0 2 ) 7/2 (1 2 ) 5/2 (1 2 ) 3/2 (2p 2 ) 1/2 (2p TNA 0.1− 0 0.1 0.2 0.3 0.4 (c) + 1 2 2 ) 7/2 (1 ) 5/2 )(1 7/2 (1 ) 3/2 )(2p 7/2 (1 2 ) 5/2 (1 ) 3/2 )(2p 5/2 (1 ) 1/2 )(2p 5/2 (1 2 ) 3/2 (2p ) 1/2 )(2p 3/2 (2p SDPF-MU SDPF-U EPQQM FIG. 8. Calcula ed wo-nucleon ampli udes (TNA) o he ans- e o he g ound s a e (a), he i s exci ed 0+s a e (b), and he 2+ 1 s a e (c). To es ima e he e ec o he po en ial pa ame e s, calcula- ions ha e been pe o med wi h di e en combina ions. The esul o he wo-neu on ans e eac ion o he g ound s a e o 46A is shown in Fig. 9 o selec ed po en ials. Wi h he excep ion o he pa ame e se in ended o highe deu e on ene gies (Ed>12 MeV) [39] all pa ame iza ions ag ee in hei shape. The bigges impac on he shape, as well as he in eg a ed c oss sec ion ha e changes in he in e media e 45A +d channel. Because he da a a e no su icien o i he elas ic sca e ing o i ons and p o ons o ob ain cons ain s on he pa ame e s, and o he elas ic deu e on channel no da a ha e been measu ed, in he ollowing he op ical po en ial pa ame e s a e ixed o he alues lis ed in Table I. Wi hin he angula ange co e ed by he silicon de ec o a ay, he calcula ed angula dis ibu ion o elas ic sca e ed i ons ag ees wi h he obse a ion. TABLE I. Pa ame e s o he op ical model om Re . [39]. 44A + 45A +d46A +p V(MeV) 162.73 102.26 59.14 ( m) 1.17 1.05 1.20 a( m) 0.75 0.86 0.72 WV(MeV) 23.85 WD(MeV) 17.23 12.78 i( m) 1.40 1.43 1.32 ai( m) 0.84 0.66 0.66 VSO (MeV) 2.5 7.0 6.2 SO ( m) 1.20 0.75 1.01 aSO ( m) 0.72 0.50 0.75 C( m) 1.30 1.30 1.25 044335-6 SPECTROSCOPY OF 46A BY THE ( ,p) TWO- . . . PHYSICAL REVIEW C 93, 044335 (2016) (deg)ϑ 0 20 40 60 80 100 120 140 160 180 (mb/s )Ω/dσd 3− 10 2− 10 1− 10 1Pe ey Va ne p Li FIG. 9. Angula dis ibu ion o p o ons om he wo-neu on ans e eac ion o he g ound s a e o 46A . The solid ed line ep esen s he calcula ion wi h he pa ame e s shown in Table I.Fo compa ison we show calcula ions wi h he p o on pa ame iza ion om [44] (blue, dashed) i on op ical model pa ame e s om [40] (g een, do -dashed). Spec oscopic one- and wo-nucleon ampli udes a e aken om he shell-model calcula ion using he SDPF-MU [12] e ec i e in e ac ion. As al eady indica ed abo e, he wo-neu on ans e eac- ion can p oceed wo ways, as a sequen ial ans e h ough he in e media e (45A +d) sys em o as a simul aneous di ec ans e o a neu on pai . Bo h p ocesses con ibu e o he c oss sec ion and hei in e e ence de e mines he o al c oss sec ion. Fo he calcula ions p esen ed in his pape he ollowing model was adop ed. Fo he in e media e 45A nucleus he g ound s a e was es ablished as Jπ=7/2− om ans e [20] and knockou eac ions [19]. The i s exci ed s a e is 3/2−[24]. In he d(44A , p) eac ion, h ee o he L=1 s a es ha e been obse ed [20]. Based on he shell-model calcula ions in Sec. IV A wo 3/2−and h ee s a es wi h Jπ=1/2−a e expec ed o be popula ed s ongly [Fig. 7(a)]. The eac ion model includes s a es wi h calcula ed spec oscopic ac o s la ge han 0.05. The hi d 1/2−s a e has no expe imen ally obse ed equi alen , he e o e he exci a ion ene gy o his le el is se o 3619 keV, he esul o he shell-model calcula ion using he SDPF-MU e ec i e in e ac ion [12]. Shell-model calcula ions also p edic a 5/2−s a e wi h a signi ican spec oscopic ac o ; o his he ene gy alue o he L=3 candida e om ans e eac ions [20], 4.8 MeV, is adop ed. The le el lies e y closely o he neu on sepa a ion ene gy o 45A (Sn=5.169 MeV), he e o e i is supp essed by he ( ,d) eac ion (Q alue −1088 keV) and ans e h ough i is negligible. Fo he second s ep o he eac ion, he (d,p) ans e o s a es in 46A ; he ansi ions om all le els in 45A which ha e a subs an ial spec oscopic ac o calcula ed (C2S>0.05) a e included in he eac ion model. Figu e 10 shows he pa hs included in he calcula ion o he eac ion o he exci ed 0+ 2s a e in 46A . All spec oscopic ampli udes a e implemen ed wi h hei espec i e phase. The sequen ial ans e was calcula ed using “pos -pos ” couplings [38,45]; i o he combina ions o “p io ” and “pos ” couplings a e used, he magni ude and shape o he di e en ial c oss sec ion a ies 0 keV + 0 0 keV - 7/2 542 keV - 3/2 1416 keV - 3/2 1876 keV - 1/2 2510 keV - 1/2 3619 keV - 1/2 4800 keV - 5/2 0 keV + 0 1554 keV + 2 3695 keV + 0 A + 44 A + d 45 A + p 46 FIG. 10. Reac ion model employed in he analysis. Fo he i s s ep o he sequen ial ( ,d)(d,p) wo-neu on ans e eac ion (blue a ows) se e al s a es in 45A ha e been conside ed as in e media e s a es. Expe imen al candida es o he heo e ically calcula ed s a es wi h spec oscopic ac o s la ge han 0.05 ha e been aken om he d(44A , p) measu emen o Re . [20]. The igu e shows as an example he channels o he second s ep o which a spec oscopic ac o la ge han 0.05 was calcula ed wi h he SDPF-MU in e ac ion [12] o he exci ed 0+ 2s a e. See ex o de ails. less han i di e en pa ame iza ions o he op ical model a e used. Fo he di ec one-s ep ans e wo-nucleon ampli udes (TNA) a e calcula ed. The esul s o he wo componen s and hei in e e ence is shown in Fig. 11. Fo all h ee s a es he wo-s ep p ocess domina es he c oss sec ion, howe e , he in e e ence o one- and wo-s ep eac ion ampli udes is c i ical o he magni ude and shape o he di e en ial c oss sec ion. Fo he g ound s a e he di ec ans e has a la ge in luence han o he exci ed 0+ 2s a e, because wo-s ep eac ions a e inhibi ed by he eac ion Q alue. In he case o he 2+s a e he di ec ans e alone is abou wo o de s o magni ude smalle han he sequen ial one, and he e o e plays a mino ole. V. DISCUSSION While shell model p edic s a la ge B(E2; 2+ 1→0+ gs) alue (105 e2 m4calcula ed wi h he SDPF-U in e ac ion) o 46A han obse ed in Coulomb exci a ion, he wo-neu on ans e c oss sec ion seems o be well ep esen ed. The calcula ion wi h he SDPF-U e ec i e in e ac ion [11] gi es a be e ep esen a ion o he c oss sec ion o he 2+ 1s a e when s anda d op ical model pa ame e s a e used (see Fig. 5). E en i di e en se s o pa ame e s a e used, he angula di e en ial c oss sec ion using he ampli udes calcula ed wi h he SDPF-U e ec i e in e ac ion ep oduces he da a bes . Expe imen ally he c oss sec ion o he popula ion o he g ound and i s exci ed 0+s a es a e simila in mag- ni ude. Neu on emo al eac ions om he g ound s a e o 46A [18,19] showed ha i is domina ed by 0p-0h con igu a ions wi h all alence neu ons in he 1 7/2o bi al ( 7/2)8. The s uc u e o he wo 0+s a es is e y di e en . This can be seen by looking a he con ibu ion o di e en 044335-7 K. NOWAK e al. PHYSICAL REVIEW C 93, 044335 (2016) (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(a) ull di ec only wo-s ep only (a) + gs 0 keV 0 (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(b) + 1 1554 keV 2 (deg)ϑ 0 20 40 60 80 100 120 140 160 180 ( m b/ s ) Ω /d σ d 3− 10 2− 10 1− 10 1(c) + 2 3695 keV 0 FIG. 11. Calcula ed di e en ial c oss sec ion o he wo-neu on ans e o he g ound s a e (a), he 2+ 1s a e (b), and he i s exci ed 0+s a e (c) in compa ison wi h expe imen al da a. The SDPF-U e ec i e in e ac ion was used o calcula e he one- and wo-nucleon ampli udes. G een do -dashed lines ep esen he esul including only he di ec wo-nucleon ans e ; blue dashed lines he wo-s ep p ocess h ough s a es in 45A . The solid ed lines include he in e e ence o bo h con ibu ions. neu on pa icle-hole con igu a ions o he o al wa e unc ion shown in Fig. 12. The g ound-s a e neu on con igu a ions calcula ed wi h di e en e ec i e in e ac ions a e e y simila wi h a ound 50% 0p-0hand a ound 20% o 1p-1hand 2p-2hexci a ions o he 2p3/2o bi al. The con igu a ion o he exci ed 0+ 2s a e is domina ed by pa icle-hole exci a ions. He e a s iking neu on ampli ude (%) 0 10 20 30 40 50 60 (a) + gs A 0 44 6 ) 7/2 ( 1 ) 3/2 (p 5 ) 7/2 ( 2 ) 3/2 (p 4 ) 7/2 ( 4 ) 3/2 (p 2 ) 7/2 ( 2 ) 5/2 ( 4 ) 7/2 ( 2 ) 1/2 (p 4 ) 7/2 ( neu on ampli ude (%) 10 20 30 40 50 60 (b) + gs A 0 46 SDPF-MU SDPF-U EPQQM neu on ampli ude (% ) 0 10 20 30 40 50 60 (c) + ex A 0 46 8 ) 7/2 ( 1 ) 3/2 (p 7 ) 7/2 ( 2 ) 3/2 (p 6 ) 7/2 ( 3 ) 3/2 (p 5 ) 7/2 ( 4 ) 3/2 (p 4 ) 7/2 ( 2 ) 5/2 ( 6 ) 7/2 ( 1 ) 1/2 (p 1 ) 5/2 ( 6 ) 7/2 ( 1 ) 1/2 (p 1 ) 3/2 (p 6 ) 7/2 ( 1 ) 1/2 (p 2 ) 3/2 (p 5 ) 7/2 ( 2 ) 1/2 (p 6 ) 7/2 ( FIG. 12. Calcula ed wa e unc ions o he g ound s a e o 44A (a) and wo 0+s a es in 46A , (b) o he g ound s a e, and (c) o he i s exci ed 0+s a e. Only he la ges neu on componen s a e shown. di e ence be ween he h ee e ec i e in e ac ions can be seen. In calcula ions wi h he SDPF-MU in e ac ion [12] ( 7/2)8 emains he la ges componen ; 2p-2h,3p-3h, and 4p-4hexci a ions o he 2p3/2o bi al con ibu e abou 50%. The EPQQM calcula ions p edic a s ongly mixed wa e unc ion, wi h many componen s wi h signi ican ampli udes. In e es ingly, he 0p-0hcomponen is absen . Fo he SDPF-U in e ac ion a la ge componen o ( 7/2)6(p3/2)2is domina - ing he wa e unc ion. The e olu ion in collec i i y below 48Ca was a ibu ed o he enso componen o he nuclea in e ac ion [12]. The monopole componen o he enso in e ac ion causes a educ ion o he spli ing be ween he 1 7/2and 2p3/2o bi als esul ing in a educ ion o he N=28 shell gap. In 46A jus wo p o ons below he doubly magic 48Ca he si ua ion is unclea . The s onges among he T=0 c oss-shell monopole e ms is he a ac i e ν1 7/2-π1d3/2, he e o e a educed occupa ion o he p o on 1d3/2o bi al will cause ising o he ν1 7/2wi h espec o he 2p3/2 o bi al compa ed o 48Ca and educe he N=28 shell gap. We ha e pe o med calcula ions wi hou he c oss-shell enso 044335-8