Testing microscopically derived descriptions of nuclear collectivity : Coulomb excitation of 22Mg

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ Tes ing mic oscopically de i ed desc ip ions o nuclea collec i i y : Coulomb exci a ion o 22Mg © 2018 The Au ho s. Published by Else ie B.V. Funded by SCOAP3. Published e sion Hende son, J.; Hackman, G.; Ruo salainen, Panu; S obe g, S.R.; Launey, K.D.; Hol , J.D.; Ali, F.A.; Be nie , N.; Ben ley, M.A.; Bow y, M.; Caballe o-Folch, R.; E i s, L.J.; F ede ick, R.; Ga nswo hy, A.B.; Ga e , P.E.; Jigmeddo j, B.; Kilic, A.I.; Lassen, J.; Measu es, J.; Mueche , D.; Olaizola, B.; O'Sulli an, E.; Pae kau, O.; Pa k, J.; Smallcombe, J.; S ensson, C.E.; Wadswo h, R.; Wu, C.Y. Hende son, J., Hackman, G., Ruo salainen, P., S obe g, S.R., Launey, K.D., Hol , J.D., Ali, F.A., Be nie , N., Ben ley, M.A., Bow y, M., Caballe o-Folch, R., E i s, L.J., F ede ick, R., Ga nswo hy, A.B., Ga e , P.E., Jigmeddo j, B., Kilic, A.I., Lassen, J., Measu es, J., . . . Wu, C.Y. (2018). Tes ing mic oscopically de i ed desc ip ions o nuclea collec i i y : Coulomb exci a ion o 22Mg. Physics Le e s B, 782, 468-473. h ps://doi.o g/10.1016/j.physle b.2018.05.064 2018 Physics Le e s B 782 (2018) 468–473 Con en s lis s a ailable a ScienceDi ec Physics Le e s B www.else ie .com/loca e/physle b Tes ing mic oscopically de i ed desc ip ions o nuclea collec i i y: Coulomb exci a ion o 22Mg J. Hende son a,b,∗, G. Hackman a, P. Ruo salainen c, S.R. S obe g a,1, K.D. Launey d, J.D. Hol a, F.A. Ali e, , N. Be nie a,g, M.A. Ben ley h, M. Bow y a, R. Caballe o-Folch a, L.J. E i s a,i, R. F ede ick a, A.B. Ga nswo hy a, P.E. Ga e , B. Jigmeddo j , A.I. Kilic , J. Lassen a, J. Measu es a,i, D. Mueche , B. Olaizola a, , E. O’Sulli an a, O. Pae kau a, J. Pa k a,g,2, J. Smallcombe a, C.E. S ensson , R. Wadswo h h, C.Y. Wu b aTRIUMF, Vancou e , BC V6T 2A3, Canada bLaw ence Li e mo e Na ional Labo a o y, Li e mo e, CA 94550, USA cDepa men o Physics, Uni e si y o Jy äskylä, FIN-40014 Finland dDepa men o Physics and As onomy, Louisiana S a e Uni e si y, Ba on Rouge 70803, USA eDepa men o Physics, College o Educa ion, Uni e si y o Sulaimani, P.O. Box 334, Sulaimani Ku dis an Region, I aq Depa men o Physics, Uni e si y o Guelph, Guelph, ON N1G 2W1, Canada gDepa men o Physics and As onomy, Uni e si y o B i ish Columbia, Vancou e V6T 1Z1, Canada hDepa men o Physics, Uni e si y o Yo k, Hesling on, Yo k, YO10 5DD, Uni ed Kingdom iDepa men o Physics, Uni e si y o Su ey, Guild o d, GU2 7XH, Uni ed Kingdom a i c l e i n o a b s a c A icle his o y: Recei ed 13 Sep embe 2017 Recei ed in e ised o m 1 Ma ch 2018 Accep ed 23 May 2018 A ailable online 31 May 2018 Edi o : V. Me ag Keywo ds: 22Mg 22Ne Ab ini io Collec i i y Coulomb exci a ion Many-body nuclea heo y u ilizing mic oscopic o chi al po en ials has de eloped o he poin ha collec i i y migh be s udied wi hin a mic oscopic o ab ini io amewo k wi hou he use o e ec i e cha ges; o example wi h he p ope e olu ion o he E2ope a o , o al e na i ely, h ough he use o an app op ia e and manageable subse o pa icle–hole exci a ions. We p esen a p ecise de e mina ion o E2 s eng h in 22Mg and i s mi o 22Ne by Coulomb exci a ion, allowing o igo ous compa isons wi h heo y. No-co e symplec ic shell-model calcula ions we e pe o med and ag ee wi h he new B(E2) alues while in-medium simila i y- eno maliza ion-g oup calcula ions consis en ly unde p edic he absolu e s eng h, wi h he missing s eng h ound o ha e bo h isoscala and iso ec o componen s. The disc epancy be ween wo mic oscopic models demons a es he sensi i i y o E2s eng h o he choice o many-body app oxima ion employed. ©2018 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3. 1. In oduc ion Recen de elopmen s in many-body nuclea heo y ha e seen a g ea ad ance in he numbe o nuclei accessible o mic oscop- ically de i ed heo e ical models – including hose cons uc ed in an ab ini io amewo k [1–15]. As hese models inc easingly each egions o he nuclea landscape inaccessible o expe imen , i is essen ial ha hei pe o mance is sc u inized in de ail us- ing less-exo ic sys ems whe e high-p ecision expe imen al da a *Co esponding au ho . E-mail add ess: [email p o ec ed] (J. Hende son). 1P esen add ess: Physics Depa men , Reed College, Po land OR, 97202, USA. 2P esen add ess: Depa men o Physics, Lund Uni e si y, 22100 Lund, Sweden. a e a ailable. The sd-shell lies be ween he adi ional shell-model p o on and neu on magic numbe s o 8 and 20 and is an ideal labo a o y o es ing new models. The egion con ains examples o many phenomena ound ac oss he nuclea landscape, anging om α-clus e ing [16] and Bo omean-nuclei [17], o shell e o- lu ion [18] and high deg ees o collec i e de o ma ion [19]. In pa icula , he sd-shell p o ides an excellen oppo uni y o in- es iga ions o collec i i y h ough he p obing o fi s -exci ed 2+ s a es in mid-shell e en–e en nuclei, which a e ypically domi- na ed by collec i e deg ees o eedom. By p obing ansi ions o such s a es in mi o nuclei, one is addi ionally sensi i e o cha ge- dependen e ec s in he in e ac ion. His o ically, he phenomenological shell model has p o ed a success ul ool in he modeling o his mass egion, wi h em- pi ically fi in e ac ions ypically well- ep oducing expe imen al h ps://doi.o g/10.1016/j.physle b.2018.05.064 0370-2693/©2018 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3. J. Hende son e al. / Physics Le e s B 782 (2018) 468–473 469 da a [20]. A pa icula limi a ion in he model, howe e , lies in he ep oduc ion o nuclea collec i i y – he bulk mo ion o many nu- cleons – and especially he elec ic-quad upole (E2) s eng h com- monly associa ed wi h i . As he shell model begins wi h an as- sump ion o sphe ici y, collec i e E2 s eng h is gene a ed h ough a cohe en sum o many small-ampli ude mul i-pa icle mul i-hole (mp–mh) exci a ions. A model space and in e ac ion ha achie e good ep oduc ion o le el ene gies does no necessa ily ep oduce ansi ion s eng h. This s eng h is o en unde p edic ed as he inclusion o a sufficien ly la ge numbe o mp–mh exci a ions is in p ac ice un easible. The ypical app oach is o explici ly com- pensa e o his missing physics h ough an a ificial infla ion o he nucleon cha ges wi h phenomenological e ec i e cha ges. I is he e o e o conside able in e es o de e mine whe he mod- e n mic oscopically de i ed nuclea heo ies a e able o ep oduce he expe imen ally obse ed collec i i y in his egion wi hou he need o he phenomenologically de i ed co ec ions equi ed in he shell model. Accu a e calcula ion o collec i e E2s eng hs wi hou he use o e ec i e cha ges is cu en ly being pu sued wi hin se e al he- o e ical amewo ks. Fo example, he no-co e symplec ic shell model (NCSpM) has in ecen yea s de e mined B(E2) alues o nuclei wi hin he sd shell, wi hou eso ing o such phenomeno- logical co ec ions [21]. This model, hough no s ic ly ab ini io, p o ides he capabili y o each la ge shell-model spaces using a mic oscopic in e ac ion, while being in ag eemen wi h ab ini io symme y-adap ed no-co e shell-model [13](SA-NCSM) calcula- ions in smalle , mo e easible model spaces ha use he N2LOop chi al po en ial [22]. A sui e o ab ini io many-body echniques a e also able o pe o m calcula ions in he sd-shell wi h, o exam- ple, coupled-clus e (CC) [23], no-co e shell model (NCSM) [24] and in-medium simila i y- eno maliza ion-g oup (IM-SRG) [25,15] me hodologies demons a ing p omising esul s in e ms o le el- ene gy calcula ions. CC echniques ep oduced ansi ion s eng hs in sel -conjuga e 20Ne and 24Mg wi h p ecision compa able o he a ailable expe imen al da a [23]; howe e , his equi ed he use o e ec i e cha ges. Two p e ious measu emen s o he 2+ 1s a e li e ime in 22Mg ha e been epo ed esul ing in an e alua ed B(E2; 2+ 1→0+ 1)o 95 ±40 e2 m4[26–28]. The s able nuclide 22Ne has been well measu ed, wi h a p ecisely known li e ime yielding a B(E2; 2+ 1→ 0+ 1) alue o 46.72 ±0.66 e2 m4[28]. Fu he mo e, he diag- onal ma ix elemen , 2+ 1|E2|2+ 1, and hus he spec oscopic quad upole momen o he 2+ 1s a e, Qs(2+ 1)has also been mea- su ed in 22Ne, yielding an e alua ed alue o Qs(2+ 1) =−0.19 ± 0.04 b [29]. In his Le e we p esen a Coulomb-exci a ion mea- su emen o he A =22 mi o pai , 22Mg–22Ne, h ough which we ha e significan ly imp o ed he p ecision o he 22Mg B(E2)and Qs(2+) alues. This ep esen s he fi s measu emen o Qs(2+) in an e en–e en Tz=1 2(N−Z) =−1nuclide, whe e Z(N) is he numbe o p o ons (neu ons). The new da a a e now o sufficien quali y o es s a e-o - he-a mic oscopically de i ed heo e ical calcula ions. I is ound ha NCSpM p edic ions o his A =22 mi o pai a e in excellen ag eemen wi h expe imen al ansi- ion s eng hs. 2. Expe imen al de ails The fi s -exci ed 2+s a es in 22Mg and i s s able mi o 22Ne we e popula ed h ough Coulomb exci a ion in no mal kinema ics a he TRIUMF-ISAC-II acili y. 22Mg was p oduced using a 50 μA, 480-MeV p o on beam impinged on a SiC a ge coupled o an ion guide lase ion sou ce (IG-LIS) [30,31]. Wi h lase esonance ioniza ion and supp ession o isoba ic con amina ion om su ace ioniza ion a 22Na supp ession in excess o 106compa ed o he con en ional ho ca i y-lase ion sou ce was achie ed [32]. I was he e o e possible o accele a e a clean beam o 22Mg ions h ough he ISAC accele a o chain o he TIGRESS acili y [33]. Two 22Mg beam ene gies we e used o he p esen measu emen : 92.4 MeV and 83.4 MeV. Beam in ensi ies a TIGRESS we e main ained a ap- p oxima ely 1 ·104pps h oughou he expe imen . The 22Ne beam was p o ided by he offline ion-sou ce (OLIS) and accele a ed by he ISAC and ISAC-II accele a o s o a final ene gy o 54.8 MeV wi h a mean in ensi y o app oxima ely 5 ppA. The 22Mg (22Ne) beam was impinged on o a 97.6-% en iched, 2.6-mg/cm2(1.6-mg/cm2) hick 110Pd a ge wi hin he BAMBINO se up a he cen e o he TIGRESS a ay. Fo he p esen mea- su emen s BAMBINO consis ed o a pai o Mic on S3- ype sili- con de ec o s [34]co e ing angles o 20◦ o 49.4◦and 131.6◦ o 160◦in he labo a o y ame. Sca e ed beam-like pa icles we e de ec ed in he BAMBINO S3 de ec o s and γ- ays de-exci ing s a es popula ed in he beam- and a ge -like nuclei we e de ec ed wi h TIGRESS. TIGRESS was ope a ed in i s high-efficiency config- u a ion [35], wi h ou een HPGe clo e de ec o s a a a ge - o- de ec o dis ance o 11 cm. Da a we e acqui ed h ough he TI- GRESS digi al da a acquisi ion sys em [36]using a single hi in one o he silicon de ec o s as he expe imen al igge o he 22Mg po ion o he expe imen , and wi h a pa icle-γ igge o he highe - a e 22Ne beam. A iming signal om he lase ion sou ce was acqui ed wi h he expe imen al da a and made i possible o dis inguish p omp lase -ionized 22Mg om ime- andom su ace- ionized 22Na e en s. This me hod o con inuously moni o ing su - ace ionized con amina ion was e ified by pe iodically edi ec ing he beam in o a B agg de ec o [37] and yielded a 22Na:22Mg a io o e he cou se o he expe imen o app oxima ely 2%. 3. Analysis Da a we e so ed using he in-house GRSISo [38]so wa e package, buil on he ROOT [39]da a analysis amewo k. Pa icle- ga ed γ- ay spec a we e Dopple co ec ed o beam-like and a ge -like sca e ing kinema ics on an e en -by-e en basis, de e - mined by he ajec o y o he de ec ed pa icle in he S3 de ec o s. Gamma- ay spec a, Dopple co ec ed o 22Mg, 22Ne and 110Pd a e shown in Fig. 1. Due o he highe beam ene gies used o he 22Mg beams, he ups eam S3 de ec o was excluded om he analysis as a esul o lying in an “unsa e” Coulomb exci a- ion egime, i.e. he dis ance o closes app oach was less han 5 m[40]. In he 22Mg analysis he da a we e spli in o six an- gula bins, while he 22Ne da a we e analyzed on a ing-by- ing basis o maximize sensi i i y. The da a we e co ec ed o o se s in he x- and y-di ec ions ela i e o he beam axis on he basis o asymme ies in he pa icle dis ibu ions on he S3 de ec o s. Addback was applied o he TIGRESS γ- ay spec a on he basis o he sub-c ys al segmen a ion wi hin he HPGe clo e de ec o s. Gamma- ay de ec ion efficiencies in TIGRESS we e de e mined us- ing 152Eu, 133Ba and 60Co sou ces. Efficiency-co ec ed 22Mg, 22Ne and 110Pd Coulomb exci a ion yields we e hen e alua ed using he GOSIA and GOSIA2 so wa e packages [41], allowing o simul aneous analysis o bo h beam- like and a ge -like exci a ion. As desc ibed in Re . [42], χ2su - ace dis ibu ions could hus be c ea ed o he 0+|E2|2+and 2+|E2|2+ma ix elemen s in bo h 22Ne and 22Mg, based on exci a ion ela i e o he well-known low-lying ma ix elemen s in 110Pd which we e included in he GOSIA analysis, wi h yields co ec ed o accoun o he deg ee o en ichmen o he a ge and he con amina ion in he beam. Li e a u e 0+ 1|E2|2+ 1and 2+ 1|E2|2+ 1ma ix elemen s o 22Ne and 22Mg we e no included as expe imen al inpu s in he analysis. The le els and ansi ions 470 J. Hende son e al. / Physics Le e s B 782 (2018) 468–473 Fig. 1. Dopple -co ec ed γ- ay spec a o (a) 22Mg impinged on a 110Pd a ge a 92.4 MeV, (b) 22Ne impinged on a 110Pd a ge a 54.8 MeV. Dopple -co ec ed o 22Mg and 22Ne (black) and 110Pd ( ed). (Fo in e p e a ion o he colo s in he figu e(s), he eade is e e ed o he web e sion o his a icle.) Fig. 2. Le els and ansi ions in 22Mg (le ) and 22Ne ( igh ) included in he Coulomb exci a ion analysis. T ansi ions o which ma ix elemen s we e a ied in he χ2 minimiza ion a e indica ed by dashed a ows. Ene gy uni s a e keV. A ow wid hs co espond o ela i e b anching a ios. Fig. 3. χ2su aces in 22Mg de e mined h ough a compa ison o calcula ed Coulomb-exci a ion yields and expe imen al yields using GOSIA2 [41]. (a) To al χ2 su ace o he 0+ 1|E2|2+ 1and 2+ 1|E2|2+ 1ma ix elemen s. (b) As (a) bu wi hin he χ2 min +1(1σ) limi , demons a ing he p e e ence o a nega i e 2+ 1|E2|2+ 1 ma ix elemen . Fig. 4. χ2su ace a he χ2 min +1(1σ) limi o he 0+ 1|E2|2+ 1and 2+ 1|E2|2+ 1 ma ix elemen s in 22Ne. included in he analysis o 22Ne and 22Mg a e shown in Fig. 2. Figs. 3and 4show he o al and 1σχ 2su ace dis ibu ions plo - ed o 22Mg, and he 1σχ 2su ace o 22Ne, espec i ely. Based on hese analyses, alues o he ma ix elemen s we e ex ac ed and a e summa ized in Table 1alongside li e a u e alues, whe e a ailable, and heo e ical alues. J. Hende son e al. / Physics Le e s B 782 (2018) 468–473 471 Table 1 B(E2) alues and quad upole momen s o 22Ne and 22Mg as de e mined in he p esen wo k. Also shown a e li e a u e alues, whe e a ailable, including exci a ion ene gies. B(E2) alues co espond o B(E2; 2+ 1→0+ 1). Quo ed unce ain ies include sys ema ic unce ain ies a ising om he beam composi ion analysis, he 110Pd B(E2), he a ge composi ion and he γ- ay de ec ion efficiencies. Theo e ical alues a e included o he shell- model, IM-SRG and NCSpM me hodologies, wi h IM-SRG alues shown o wo in e ac ions. Shell-model alues we e calcula ed using e ec i e cha ges o eπ=1.36 and eν=0.45. Shell model IM-SRG NCSpM Expe imen 22Ne USDB EM1.8/2.0 N2LOOp This Wo k Li e a u e Re . E(2+)keV 1363 1657 1248 874 1274.54±0.01 [28] B(E2)e2 m448.97 20.0 18.5 50.8 47.06 ±0.62 46.72 ±0.66 [28] Qs(2+ 1)eb −0.139 −0.086 −0.096 −0.15 −0.215 ±0.012 −0.21 ±0.04 [43] −0.17 ±0.03 [28] 22Mg E(2+)keV 1363 1604 1201 874 1247.02±0.03 [28] B(E2)e2 m465.8 41.3 35.5 73.2 76.1±9.2 9.895.2±62.4 26.8[28] 268±201 183 [26] 64.6±34.2 16.6[27] Qs(2+ 1)eb −0.16 −0.13 −0.13 −0.18 −0.43±0.43 0.38 Fig. 5. Expe imen al B(E2; 2+ 1→0+ 1) alues o e en–e en, Tz=−1(a) and Tz=+1(b) mi o nuclei in he sd-shell, including he p esen alue o 22Mg. NCSpM calcula ions a e shown o he A =22, 26 and 30 mi o pai s and IM-SRG calcula ions a e shown wi h an e ol ed e ec i e E2ope a o bu wi h no u he adjus men o he nucleon cha ges. IM-SRG calcula ions a e shown o wo in e ac ions, N2LOOp and EM1.8/2.0. Also shown a e USDB shell model calcula ions o a numbe o common cha ge modi ying combina ions (eπand eνmodi ying he p o on and neu on cha ges, espec i ely). Finally, “ba e” USDB shell model calcula ions a e also shown, wi hou adjus men o nucleon cha ges. The e o band on he NCSpM alues co espond o he sp ead in B(E2) alues a ising om a ia ions o 5% in he model pa ame e s. 4. Discussion The de e mined B(E2; 2+ 1→0+ 1) alue in 22Mg is app oxi- ma ely 20% lowe han he e alua ed alue epo ed in he li - e a u e [28]. The p esen alue lies wi hin he 1σunce ain ies o he li e a u e alue bu is conside ably mo e p ecise. Taking a weigh ed a e age o he 22Mg li e a u e alues [26,27]and p esen alues yields B(E2; 2+ 1→0+ 1) =76.5±9.9 7.4e2 m4. Asymme ic un- ce ain ies we e combined using he me hod ou lined in Re . [44]. The ex ac ed 2+ 1E22+ 1ma ix elemen is nega i e, indica ing a p e e ence o p ola e de o ma ion. The 22Mg B(E2; 2+ 1→0+ 1) alue now has unce ain ies compa able o he o he Tz=−1nu- clei, as shown in Fig. 5in which he upda ed da a a e plo ed wi h heo y. Fo 22Ne good ag eemen is ob ained wi h he well-known li - e a u e ansi ion ma ix elemen s, confi ming he alidi y o he analysis. While ag eeing a app oxima ely he 2σlimi wi h he e alua ed 2+ 1|E2|2+ 1 alue, he p esen esul is in bes ag eemen wi h he alues ob ained in Re . [43]. The p esen 2+ 1|E2|2+ 1ma- ix elemen is mo e han a ac o o wo mo e p ecise han he e alua ed alues (see Table 1). Inco po a ing he p esen esul a new weigh ed a e age alue o 2+ 1|E2|2+ 1 =−0.283 ±0.015 eb is ob ained, co esponding o Qs(2+ 1) =−0.215 ±0.011 eb. Cou- pling he p esen esul wi h he li e a u e yields a new weigh ed a e age alue o B(E2; 2+ 1→0+ 1) =46.9 ±0.5e 2 m4. As shown in Fig. 5, he NCSpM ep oduces he A =22, 26 and 30 da a well. NCSpM calcula ions a e pe o med wi h a ha monic oscilla o equency, ¯ hω=15 MeV in a model space o 15 ma- jo shells. The calcula ions ag ee wi h ab ini io SA-NCSM esul s using he N2LOop whe e calcula ions a e easible [45] (e.g., o 22Mg in 9 shells, B(E2)s eng hs di e by 0.4%). We no e ha o achie e he con e ged B(E2) alues shown in Fig. 5, i is impo - an o include mp–mh exci a ions o e y high shells, as achie ed in he NCSpM [46]. Allowing o he modes heo e ical unce ain- ies esul ing om 5% a ia ions in he model pa ame e s shown in Fig. 5, he NCSpM p o ides excellen ag eemen wi h he expe - imen al B(E2)da a o bo h Tz=±1nuclei. 472 J. Hende son e al. / Physics Le e s B 782 (2018) 468–473 Also shown in Fig. 5a e calcula ions pe o med using he alence-space IM-SRG o malism [47,48,25,15]using a consis en ly e ol ed E2ope a o (see Re . [49] o de ails o he ope a o e o- lu ion) wi hou inco po a ing e ec i e cha ges. These calcula ions we e pe o med ab ini io using bo h he SRG- eno malized [50] 1.8/2.0 chi al in e ac ion [51–53] and he N2LOop in e ac ion wi h a ha monic oscilla o basis o ¯ hω=20 MeV, and wi h ope a o s unca ed a he wo-body le el. Clea ly, hese alues significan ly unde p edic he B(E2; 2+ 1→0+ 1)s eng h. I should be no ed, howe e , ha he IM-SRG calcula ions do p o ide a good quali- a i e desc ip ion o he E2 s eng h wi h inc easing mass. No e ha a ia ions in he heo e ical alues o he exci a ion ene gies eflec di e ences in he fine de ails o he in e ac ions used. Fo compa ison phenomenological shell-model calcula ions we e pe o med using he USDB in e ac ion using NuShellX [54] wi h some o he common combina ions o e ec i e cha ge [20,54, 55]. The new da a indica e ha , while he phenomenological shell- model is able o ep oduce he A =22 case wi h a gi en choice o e ec i e cha ge, no single combina ion o e ec i e cha ges is able o ep oduce he en i e sd-shell, wi h no able de ia ions a Tz=−1, A =26 and Tz=+1, A =34. The o igin o he sho all in E2 s eng h om he IM-SRG calcula ions is no ye ully unde s ood, bu mus eside in he dis- ca ded e ms in ol ing h ee-body o highe -body ope a o s. Wo k in his di ec ion is cu en ly in p og ess. The na u e o he missing s eng h was assessed by no malizing he B(E2)da a acco ding o he a io o he heo e ical and expe imen al alues o he mi o pa ne . Fo example, a B(E2)s eng h o he p o on- ich mi o was p ojec ed as: B(E2)P oj. Tz=−1=B(E2)Theo y Tz=−1×B(E2)Exp Tz=+1 B(E2)Theo y Tz=+1 ,(1) This analysis was pe o med o bo h IM-SRG and shell-model cal- cula ions and he p ojec ed B(E2) alues we e compa ed wi h expe imen . I is ound ha , wi h he excep ion o mi o -pai s con aining a magic numbe , he IM-SRG esul s a e highly consis- en , o e -p ojec ing he p o on- ich s eng h by a ac o o app ox- ima ely 15% o he EM1.8/2.0 in e ac ion. I he missing s eng h we e pu ely isoscala , a common scaling be ween heo y and ex- pe imen would be expec ed o he Tz=+1 and Tz=−1mem- be s o he mi o pai . The common 15% disc epancy he e o e indica es ha he missing s eng h is no pu ely isoscala , and ha a non-negligible iso ec o componen mus also be inco po a ed. Shell-model calcula ions – bo h wi h and wi hou e ec i e cha ges – on he o he hand, exhibi no such consis en beha io in his analysis. 5. Conclusions In conclusion, we p esen an imp o ed measu emen o he low-lying E2 s eng h in he |Tz| =1, A =22 mi o pai . A fi s Coulomb-exci a ion measu emen o 22Mg has been pe o med, in- dica ing i s p ola e de o ma ion a he fi s -exci ed Jπ=2+s a e and significan ly imp o ing he unce ain y o he B(E2; 2+ 1→0+ 1) alue. This ep esen s he fi s spec oscopic quad upole momen measu emen o an e en–e en N<Znuclide. Compa ison wi h he s a e-o - he-a no-co e symplec ic shell model calcula ions, alida ed in smalle model spaces by he ab ini io SA-NCSM, show excellen ag eemen in he A =22, A =26 and A =30 cases wi hou a eliance on e ec i e cha ges. On he o he hand, he alence-space IM-SRG, p o ides good quali a i e ag eemen o he e olu ion o E2s eng h, bu d ama ically unde p edic s he ab- solu e alues. These ag eemen s p o ide some p omise o each- ing desc ip ions o enhanced collec i i y in sd-shell nuclei in he amewo k o he ab ini io heo y s a ing wi h chi al po en ials. The ailu e o he IM-SRG o ep oduce he da a in con as o he NCSpM demons a es he sensi i i y o E2 s eng h o he choice o many-body app oxima ion employed, which needs o be u he explo ed. Acknowledgemen s The au ho s would like o hank he TRIUMF beam deli e y g oup o hei e o s in p o iding high-quali y s able and adioac- i e beams. 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