High-K three-quasiparticle isomers in the proton-rich nucleus Nd129

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/ High-K h ee-quasipa icle isome s in he p o on- ich nucleus Nd129 ©2023 Ame ican Physical Socie y Published e sion Pe ache, C. M.; Uusi alo, J.; B iscoe, A. D.; Sulli an, C. M.; Joss, D. T.; Tann, H.; Ak as, Ö.; Alayed, B.; Al-Aqeel, M. A. M.; As ie , A.; Bad an, H.; Cede wall, B.; Dela osse, C.; E op ak, A.; Fa ie , Z.; Fo sbe g, U.; Gins, W.; G ahn, T.; G eenlees, P. T.; He, X. T.; Hee y, J.; Hil on, J.; Kalan an, S.; Li, R.; Jodida , P. M.; Julin, R.; Juu inen, S.; Leino, M.; Lewis, M. C.; Li, J. G.; Li, Z. P.; Luoma, M.; L , B. F.; McCa e , A.; Na haniel, S.; Ojala, J.; Page, R. D.; Paka inen, J.; Papadakis, P.; Pa , E.; Pa anen, J.; Paul, E. S.; Rahkila, P.; Ruo salainen, P.; Sandzelius, M.; Sa én, J.; Smallcombe, J.; So i, J.; Szwec, S.; Wang, L. J.; Wang, Y.; Wa ing, L.; Xu, F. R.; Zhang, J.; Zhang, Z. H.; Zheng, K. K.; Zimba, G. Pe ache, C. M., Uusi alo, J., B iscoe, A. D., Sulli an, C. M., Joss, D. T., Tann, H., Ak as, Ö., Alayed, B., Al-Aqeel, M.A. M., As ie , A., Bad an, H., Cede wall, B., Dela osse, C., E op ak, A., Fa ie , Z., Fo sbe g, U., Gins, W., G ahn, T., G eenlees, P. T., . . . Zimba, G. (2023). High-K h ee- quasipa icle isome s in he p o on- ich nucleus Nd129. Physical Re iew C, 108, A icle 014317. h ps://doi.o g/10.1103/PhysRe C.108.014317 2023 PHYSICAL REVIEW C 108, 014317 (2023) High-K h ee-quasipa icle isome s in he p o on- ich nucleus 129Nd C. M. Pe ache ,1,*J. Uusi alo,2,3A. D. B iscoe,3,2C. M. Sulli an,3D. T. Joss,3H. Tann,2,†Ö. Ak as,4B. Alayed,3 M. A. M. Al-Aqeel,3A. As ie ,1H. Bad an,2B. Cede wall,4C. Dela osse,2,‡A. E op ak,4Z. Fa ie ,1,§U. Fo sbe g,2, W. Gins,2T. G ahn,2P. T. G eenlees,2X. T. He,5J. Hee y,2,¶J. Hil on,2,†S. Kalan an,3R. Li,1P. M. Jodida ,1R. Julin,2 S. Juu inen,2M. Leino,2M. C. Lewis,3J. G. Li,6Z. P. Li,7M. Luoma,2B. F. L ,6A. McCa e ,3S. Na haniel,3J. Ojala,2 R. D. Page,3J. Paka inen,2P. Papadakis,8,** E. Pa ,3,†† J. Pa anen,2,‡‡ E. S. Paul,3P. Rahkila,2P. Ruo salainen,2 M. Sandzelius,2J. Sa én,2J. Smallcombe,3J. So i,9,§§ S. Szwec,2, L. J. Wang,7Y. Wang,5L. Wa ing,3F. R. Xu,10 J. Zhang,5 Z. H. Zhang,11 K. K. Zheng,6and G. Zimba2 1Uni e si é Pa is-Saclay, CNRS/IN2P3, IJCLab, 91405 O say, F ance 2Accele a o Labo a o y, Depa men o Physics, Uni e si y o Jy äskylä, FI-40014 Jy äskylä, Finland 3Oli e Lodge Labo a o y, Depa men o Physics, Uni e si y o Li e pool, Li e pool L69 7ZE, Uni ed Kingdom 4KTH Depa men o Physics, Royal Ins i u e o Technology, S-10691 S ockholm, Sweden 5College o Ma e ials Science and Technology, Nanjing Uni e si y o Ae onau ics and As onau ics, Nanjing 210016, China 6Key Labo a o y o High P ecision Nuclea Spec oscopy and Cen e o Nuclea Ma e Science, Ins i u e o Mode n Physics, Chinese Academy o Sciences, Lanzhou 730000, People’s Republic o China 7School o Physical Science and Technology, Sou hwes Uni e si y, Chongqing 400715, China 8Uni e si y o Jy äskylä, Depa men o Physics, P.O. Box 35, FI-40014 Jy äskylä, Finland 9Sodankylä, Geophysical Obse a o y Uni e si y o Oulu, FIN-99600 Sodankylä, Finland 10S a e Key Labo a o y o Nuclea Physics and Technology, School o Physics, Peking Uni e si y, Beijing 100871, China 11Ma hema ics and Physics Depa men , No h China Elec ic Powe Uni e si y, Beijing 102206, China (Recei ed 27 Feb ua y 2023; e ised 20 June 2023; accep ed 29 June 2023; published 19 July 2023) Th ee h ee-quasipa icle isome s, one a an exci a ion ene gy o 2.3 MeV wi h T1/2=0.48(4) μs, and wo sho e -li ed wi h unknown hal -li es a sligh ly lowe ene gies ha e been iden i ied in 129Nd using he MARA +JUROGAM 3 se up and he ecoil agging echnique. All h ee isome s p esen decay pa e ns cha ac e is ic o high-Kisome s. The known 6.7 s β-decaying isome p e iously assigned o he 5/2+le el is now assigned o he new 7/2−g ound s a e. A new low-spin 5/2+isome ic s a e wi h a hal -li e o a ew ens o nanoseconds has been iden i ied, while a p e iously known 2.6 s β-decay ac i i y was assigned o he band head o he ν1/2+[411] band. The ansi ions depopula ing he high-Kisome s o low-lying s a es also es ablish he ela i e ene gies o h ee low-lying one-quasipa icle bands, leading o a new spin-pa i y assignmen o 7/2− o he g ound s a e o 129Nd. The pa ial hal -li es o he depopula ing ansi ions sugges spin-pa i ies 21/2+,19/2+, and 17/2+ o he h ee high-Kisome s. The p ope ies o he band buil on he 21/2+isome ic s a e sugges a one neu on- wo p o on con igu a ion. Based on he esul s o ex ensi e calcula ions wi h di e en models, we also assign one neu on– wo p o on con igu a ions o he 19/2+and 17/2+isome ic s a es. The assigned con igu a ions o he 17/2+and 21/2+isome ic s a es in ol e he π9/2+[404] o bi al, which is iden i ied in h ee-quasipa icle bands o p o on- ich A≈130 nuclei. DOI: 10.1103/PhysRe C.108.014317 *Co esponding au ho : pe [email protected]. †P esen add ess: Oli e Lodge Labo a o y, Depa men o Physics, Uni e si y o Li e pool, Li e pool L69 7ZE, Uni ed Kingdom. ‡P esen add ess: Uni e si é Pa is-Saclay, CNRS/IN2P3, IJCLab, 91405 O say, F ance. §P esen add ess: I u, CEA, Uni e si é Pa is-Saclay, F-91191 Gi - su -Y e e, F ance. P esen add ess: Depa men o Physics, Uni e si y o Yo k, Hes- ling on, Yo k YO10 5DD, Uni ed Kingdom; and Depa men o Physics, Lund Uni e si y, SE-22100 Lund, Sweden. ¶P esen add ess: Depa men o Physics, Uni e si y o Su ey, Guild o d, Su ey GU2 7XH, Uni ed Kingdom. I. INTRODUCTION Explo ing and ex ending he nuclea cha owa ds he limi s o s abili y is one o he main endea o s in nuclea **P esen add ess: STFC Da esbu y Labo a o y, Da esbu y, Wa - ing on WA4 4AD, Uni ed Kingdom. ††P esen add ess: GSI Helmhol zzen um ü Schwe ionen- o schung GmbH, 64291 Da ms ad , Ge many. ‡‡Deceased. §§P esen add ess: Radia ion and Nuclea Sa e y Au ho i y in Fin- land Jokiniemenkuja 1, 01370 Van aa, Finland. P esen add ess: Helsinki Ins i u e o Physics, Uni e si y o Helsinki, FIN-00014 Helsinki, Finland. 2469-9985/2023/108(1)/014317(13) 014317-1 ©2023 Ame ican Physical Socie y C. M. PETRACHE e al. PHYSICAL REVIEW C 108, 014317 (2023) s uc u e. Expe imen s de o ed o he s udy o ex emely p o on- ich nuclei by employing adioac i e and s able-ion beams, as well as powe ul se ups composed o ecoil mass spec ome e s o p ojec ile agmen sepa a o s, wi h high- e iciency a ays o de ec ion o γ ays and cha ged pa icles a he en ance and a he ocal plane o he spec ome e s. A wide ield o in es iga ion emains ye unexplo ed wi h s able p ojec ile- a ge combina ions using newly de eloped ins umen s which ha e much highe sensi i i y. Such s udies wi h s able-ion beams ha e been ecen ly pe o med wi h he MARA +JUROGAM 3 se up [1–3]in heA≈120 mass egion, e ealing ex emely ich band s uc u es in he ligh 119,120Ba and 118,119Cs nuclei, and phenomena unexpec ed in his mass egion, like shape coexis ence, chi al bands, o oc upole co ela ions [4–9]. The p esen expe imen , de o ed o he s udy o nuclei wi h Z>56, epo s he disco e y o h ee high-Kisome s, one low-spin isome , and a new spin-pa i y assignmen o he g ound s a e in 129Nd. F om he compa ison o he expe i- men al da a wi h con igu a ion-cons ained po en ial ene gy su aces (CC-PES) [10], p ojec ed shell model (PSM) [11], and pa icle numbe conse ing c anked shell model (PNC- CSM) [12] calcula ions, we assign one neu on– wo p o on con igu a ions o he high-spin isome s, wo o hem in ol ing he π9/2+[404] o bi al. These a e he i s epo ed mul i- quasipa icle high-Kisome s in ol ing he π9/2[404] o bi al in A≈130 nuclei, which p e iously we e only obse ed in one-quasipa icle bands close o he g ound s a e o odd-e en and odd-odd nuclei like he neighbo ing P nuclei (see, e.g., [13]), and in odd-e en nuclei jus abo e he Z=50 closed shell [[14–21]. No high-Kisome s a e known in he well- s udied Nd nuclei wi h N⩽73 [22–27], while high-Kisome s wi h spins 8−and 7−buil on wo-neu on con igu a ions a e known in N=74 and N=72 iso opes, espec i ely (see, e.g., [28]). The 129Nd nucleus was p e iously in es iga ed using he 92Mo(40Ca,α2pn) usion-e apo a ion eac ion [29] and he βdecay o 129Pm [30]. Fou o a ional s uc u es obse ed up o e y high spin ha e been iden i ied in Re . [29], and con igu a ions ha e been assigned based on he mea- su ed B(M1)/B(E2) a ios, aligned angula momen a, band c ossings and signa u e spli ing, and c anked shell model calcula ions. A 2.3 s isome was iden i ied by bomba ding a 96Ru a ge wi h a 36A beam and using helium-je as ape anspo sys em o measu e he βdecay o 129Pm [30]. II. EXPERIMENTAL DETAILS AND RESULTS In he p esen wo k, highly exci ed 129Nd nuclei ha e been p oduced using he 58Ni(78K ,α2pn) usion-e apo a ion e- ac ion. The 78K beam was p o ided by he K130 Cyclo on a he Uni e si y o Jy äskylä, Finland. The a ge was a 750 µg/cm2 hick sel -suppo ing oil o en iched 58Ni. Two expe imen s ha e been pe o med. One wi hou JUROGAM 3 o sea ch o β-delayed p o on emi e s, las ing o 10 d wi h se e al beam ene gies be ween 340 MeV and 370 MeV, and a second one las ing 4 d, in which JUROGAM 3 was added and he beam ene gy o 364 MeV was op imized o he p oduc ion o 129Nd. The in- ligh double- ocusing ecoil mass sepa a o MARA [1,31] was uned o mass 133 o he low beam ene gies (hal o he beam ime), allowing he obse a ion o mass 129 which ully o e lapped wi h mass 133 due o an A/qambigui y. The ligh ime o he ecoils om a ge o he implan a ion poin is ≈450 ns. A he a ge posi ion, he pa icle de ec o a ay JYUTube consis ing o 96 sepa a e scin illa o de ec o s wi h SiPM (silicon pho omul i- plie ) eadou s was used o cha ged pa icle iden i ica ion. In he second expe imen in which he beam ene gy o 364 MeV was op imized o 129Nd, he MARA sepa a o was uned o mass 129, wi h he aim o sea ch o he p omp γ ays which eed he isome ic s a es in 129Nd using he ecoil ga ed isome agging echnique. P omp γ ays we e de ec ed a he a ge posi ion using he JUROGAM 3 ge manium-de ec o a ay consis ing o 24 Eu oball clo e [32] and 15 Eu ogam Phase I- ype [33] escape-supp essed de ec o s, wi h an e iciency o ≈5% a 1.3 MeV. The clo e de ec o s we e a anged symme - ically ela i e o a plane pe pendicula o he beam di ec ion (12 a 75.5◦and 12 a 104.5◦), while he Phase I de ec o s we e placed a backwa d angles wi h espec o he beam di ec ion ( i e a 157.6◦and en a 133.6◦). JYU ube was no in use. The usion-e apo a ion esidues we e sepa a ed as a unc- ion o A/qand iden i ied using he MARA sepa a o . A he ocal plane a posi ion-sensi i e mul iwi e-p opo ional coun e (MWPC) was used o ob ain A/qspec a. Pa o he ime a double-mass sli sys em was used o allow only wo cha ge s a es o a gi en mass o be anspo ed in o he im- plan a ion de ec o , a 300 µm hick double-sided-silicon-s ip de ec o (DSSD) placed 40 cm behind he MWPC. Behind he DSSD a second laye o silicon de ec o s (500 µm hick) is used o e o punch- h ough e en s. The ime o ligh (ToF) be ween he MWPC and DSSD is eco ded. The ToF and he ecoil ene gy deposi ed in he DSSD we e used o dis inguish be ween usion ecoils and sca e ed beam. Fi e clo e ge ma- nium de ec o s su ounding he MARA ocal-plane de ec ion sys em we e used o de ec γ ays emi ed om long-li ed isome ic s a es and daugh e s o he βdecays o he implan ed ecoils. All de ec o signals we e eco ded by he igge less o al da a eadou (TDR) da a acquisi ion sys em, and ime s amped by a global 100 MHz clock, which allowed he es- ablishmen o bo h empo al and spa ial co ela ions be ween ecoils and e en s ob ained wi h he emaining de ec o s o he ocal plane and o he JUROGAM 3 a ays [2,34]. The da a we e so ed in o coincidence γγ ma ices and γγγ cubes, and analyzed using he GRAIN [35] and RADWARE [36,37] packages. In he i s pa o he analysis new delayed ansi ions in coincidence wi h low-lying ansi ions al eady known in he one-quasipa icle bands o 129Nd we e iden i ied a he ocal plane. Then in he second pa , γ-, and ecoil-ga ed p omp spec a measu ed in JUROGAM 3 we e cons uc ed o iden i y ansi ions abo e he isome s. The mul ipola i ies and he mixing a ios o he newly iden i ied γ- ay ansi ions we e es ablished based on angula co ela ions da a. Figu e 1shows a pa ial le el scheme o 129Nd, wi h he p e iously known bands [29] d awn in black, and he new ansi ions d awn in ed. Th ee high-Kisome ic s a es ha e been iden i ied, wi h exci a ion ene gies o 1893, 2109, and 2284 keV, and spin-pa i y assignmen s o 17/2+,19/2+, and 21/2+, espec i ely, discussed in he ollowing. The p omp -delayed γγ coincidence spec um o Fig. 2, ob ained 014317-2 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) FIG. 1. Pa ial le el scheme o 129Nd showing he isome and i s decay owa ds he low-lying s a es. The new ansi ions a e d awn in ed, while ansi ions epo ed in he p e ious wo k o Zeidan e al. [29] a e indica ed in black. The le els wi h isome ic cha ac e a e d awn wi h hick lines. Exci ed le els in Band 1 up o ene gies simila o he highes ones obse ed in Band 5 a e included o compa ison. The Nilsson con igu a ions assigned o he bands in Re . [29] a e also indica ed. The inse shows a zoom o he low-spin pa o Bands 3 and 4. by ga ing on he 848-keV ansi ion depopula ing he 2284- keV, 21/2+s a e and on he 551-keV ansi ion o Band 4 de ec ed a he MARA ocal plane, shows a se ies o p omp ansi ions which ha e been g ouped in he newly obse ed Band 5. Spec a o delayed ansi ions measu ed a he MARA ocal plane, ob ained by ga ing on ansi ions depopula ing he 21/2+isome ic s a e and p esen ing ansi ions in he lowe pa o he known one-quasipa icle bands a e shown in Fig. 3. A singles γ- ay spec um, and a p ojec ion o he γγ ma ix measu ed wi h he ge manium de ec o s a he ocal plane o he MARA sepa a o a e shown in Fig. 4. They gi e an o e all iew o he ela i e in ensi y o he ansi ions depopula ing he isome s, wi h he 848-keV ansi ion being he s onges . Figu e 5shows wo ocal plane spec a ob ained om he γγ ma ix by ga ing on he 175- and 391-keV ansi ions which depopula e he 21/2+isome o he lowe -lying 19/2+ and 17/2+isome s, espec i ely. The nonobse a ion o he ansi ions depopula ing he 17/2+isome in he spec um ga ed by he 175-keV ansi ion indica es he missing 216-keV connec ing ansi ion be ween he 19/2+and 17/2+isome s, gi ing hus suppo o he assignmen o e y di e en con ig- u a ions o he wo isome s. The expe imen al in o ma ion on he ansi ions depopula - ing he h ee high-Kisome s is gi en in Table I. The hal -li e o he 21/2+isome ic s a e has been ex ac ed om he summed ime spec a be ween he DSSD and he ge - manium de ec o s a he ocal plane o MARA, by ga ing on he s ong and clean 848- and 551-keV ansi ions. A alue o 014317-3 C. M. PETRACHE e al. PHYSICAL REVIEW C 108, 014317 (2023) TABLE I. Ene gies (Eγ), spin and pa i y assignmen s (Iπ i→Iπ ), ela i e in ensi ies (Tγ), and mixing a ios (δ)o heI=1 ansi ions in Band 5 abo e he Kπ=21/2+isome , as well as he Weisskop hind ance ac o s logFWo he ansi ions depopula ing he 21/2+isome . Eγ(keV)aIπ i→Iπ Tγbδlog FW Band 5 250.6 (23/2+)→(21/2+) 100 0.32(7) 274.0 (25/2+)→(23/2+) 61(3) 0.43(16) 297.7 (27/2+)→(25/2+) 38(3) 0.32(6) 321.5 (29/2+)→(27/2+) 33(3) 0.38(13) 345.2 (31/2+)→(29/2+) 19(3) 368.1 (33/2+)→(31/2+) 20(3) 391.1 (35/2+)→(33/2+) 11(2) 413.5 (37/2+)→(35/2+) 14(2) 432.3 (39/2+)→(37/2+)5(2) 523.9 (25/2+)→(21/2+) 31(4) 571.7 (27/2+)→(23/2+) 32(4) 619.2 (29/2+)→(25/2+) 37(4) 666.7 (31/2+)→(27/2+) 42(4) 713.8 (33/2+)→(29/2+) 40(4) 758.7 (35/2+)→(31/2+) 39(4) 804.7 (37/2+)→(33/2+) 37(4) 844.1 (39/2+)→(35/2+) 31(4) 890.4 (41/2+)→(37/2+) 38(4) 937(2) (43/2+)→(39/2+)<10 959(2) (45/2+)→(41/2+)<10 978(2) (47/2+)→(43/2+)<10 1018(2) (49/2+)→(45/2+)<10 Decay ou om he 21/2+isome 175.3 (21/2+)→(19/2+) 15(2) 1.56(7) 391.0 (21/2+)→(17/2+) 20(2) 3.29(8) 536.7 (21/2+)→19/2+3(1) 7.70(2) 796.0 (21/2+)→17/2+6(1) 5.62(18) 847.8 (21/2+)→17/2+49(3) 4.47(5) 1049.8 (21/2+)→19/2−7(1) 10.50(9) Decay ou om he 19/2+isome 565.8 (19/2+)→21/2−24(2) 671.7 (19/2+)→17/2+19(2) 954.5 (19/2+)→15/2+22(2) 1138.4 (19/2+)→17/2−35(2) Decay ou om he 17/2+isome 659.4 (17/2+)→19/2−25(2) 739.8 (17/2+)→15/2+12(2) 822.9 (17/2+)→15/2−15(2) 924.5 (17/2+)→17/2−16(2) 1009.1 (17/2+)→13/2+10(2) 1183.5 (17/2+)→15/2−22(2) aThe unce ain y on he ansi ion ene gies is 0.2 keV o ansi ions below 1000 keV, and 0.5 keV o ansi ions abo e 1000 keV, excep when indica ed di e en ly. bRela i e in ensi ies co ec ed o e iciency, no malized o he in ensi y o he 250.6 keV ansi ion o Band 5, and o 100% o he ansi ions depopula ing each o he h ee isome s. The ansi ion in ensi ies we e ob ained om a combina ion o he o al p ojec ion and ga ed spec a. T1/2=0.48(4) µs has been de e mined om he i o he ime spec um wi h wo exponen ial unc ions, he one wi h long hal -li e being necessa y o accoun o andom coincidences (see Fig. 6). Six ansi ions depopula ing he 21/2+isome ic s a e ha e been iden i ied: ou o 537, 796, 848, and 1050 keV o Bands 1, 3 and 4, and wo o 391 and 175 keV o he 17/2+and 19/2+isome ic s a es, espec i ely, which in u n decay o low-lying s a es o Bands 1 and 4 ia en ansi ions o 566, 659, 672, 740, 823, 924, 955, 1009, 1138, and 1183 keV (see Fig. 4). III. DISCUSSION A. Spin-pa i y and con igu a ion assignmen s o he isome s One o he key issues is he assignmen o spins and pa i ies o he obse ed isome s. This was done by analyzing he 014317-4 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) 0 200 400 600 800 1000 1200 0 1 2 937 978959 432 414 391 1018 890 846 805 759 714 667 619 572 525 368 346 321 298 274 Ene gy [keV] 251 Coun s (102) FIG. 2. Spec um o γ ays o Band 5 buil on he 21/2+isome ic s a e measu ed a he a ge posi ion o he JUROGAM 3 a ay, ob ained by employing he ecoil ga ed isome decay agging ech- nique on he 848-keV ansi ion depopula ing he isome and on he 551-keV ansi ion o Band 4 de ec ed by he ge manium de ec o s a he MARA ocal plane. obse ed decay ou pa e ns o he isome s, including he log F W[38] alues o he depopula ing ansi ions, he single- pa icle aligned angula momen um ix, kinema ic momen o ine ia J(1), and o al angula momen um on he o a ion axis Jxo he band buil on he 2284-keV isome ic s a e (see Fig. 7). In addi ion, he assump ion widely employed in he high-spin egion o well-de o med nuclei ha he spin inc eases wi h inc easing exci a ion ene gy is adop ed. 0 20 40 0 5 10 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 2 4 267 269 Nd X- ays (c) (b) 282 239 214 325 392 452 179 146 108 69 594 508 848 keV 551 (a) 360 265 479 418 524 220 198 162 130 439 796 312 537 keV Coun s (10 2 ) 292 259 Ene gy [keV] 1050 keV FIG. 3. γγ-coincidence spec a o he delayed ansi ions mea- su ed a he MARA ocal plane when ga ing on he (a) 848-keV, (b) 537-keV, and (c) 1050-keV ansi ions depopula ing he 21/2+ isome ic s a e. The 267- and 439-keV ansi ions in (b) a e due o he eeding by he delayed 796-keV ansi ion o he 17/2+le el o Band 3, which subsequen ly decays ia he 535-keV ansi ion, con amina ing hus he 537-keV ga e. 10 2 10 3 10 4 10 5 10 6 0 200 400 600 800 1000 1200 10 2 10 3 10 4 10 5 10 6 175, 178 391, 392 535, 537 1050 (b) Coun s (a) 848 Ene gy [keV] FIG. 4. (a) Singles γ- ay spec um and (b) p ojec ion o he γγ coincidence ma ix measu ed wi h he ge manium de ec o s a he MARA ocal plane, showing he ensemble o ansi ions depopula - ing he high-Kisome s and he s a es o Bands 1, 3, and 4 o 129Nd. The ene gies o he unlabeled ansi ions indica ed wi h ed lines a e gi en in he ex . Figu e 7shows he expe imen al single-pa icle aligned angu- la momen a o he bands buil on he 21/2+isome in 129Nd and on he 8−isome s in he N=74 nuclei, he kinema ic momen o ine ia J(1), and he o al angula momen um on he o a ion axis Jxo he one-quasipa icle Band 1 and o he h ee-quasipa icle Band 5 buil on he 2284-keV isome . Based on he lowes and highes spins o he s a es ed by he isome s, we concluded ha hei spins ha e o be be ween 17/2 and 21/2. The spin-pa i y o he 2284-keV isome ic s a e can be ei he 17/2±,19/2±,o 21/2+. The 17/2±and 19/2−assignmen s can be disca ded because hey would lead o ansi ions inc easing spin by 1¯h o he 17/2+assignmen (17/2+→19/2+ o Band 4 and 19/2+→21/2− om he 0 500 1000 1500 2000 0 200 400 600 800 1000 1200 0 500 1000 1500 ∗ 479 439 508 392 360 452 69 672 Nd X- ays (b) 550 418 239 214 198 179 162 130 146 740 659 1009 1183 566 955 Coun s 175 keV 1138 (a) ∗ 848 391 keV Coun s Ene gy [keV] FIG. 5. Focal plane spec a om γγ coincidences ga ed on he 175- and 391-keV ansi ions om he 21/2+isome , showing he depopula ing ansi ions o he 19/2+and 17/2+isome s o s a es o he Bands 1, 3, and 4. Con amina ing ansi ions a e indica ed wi h as e isks. 014317-5 C. M. PETRACHE e al. PHYSICAL REVIEW C 108, 014317 (2023) 0 100 200 300 400 500 600 700 800 1 Coun s (10 3 )/10 ns Time [10 ns] 5 T 1/2 =0.48(4)μs FIG. 6. Time spec um and i s i wi h wo exponen ials om which he hal -li e o he 21/2+isome ic s a e was de e mined. The spec um is ob ained wi h a s a gi en by he ecoils de ec ed in he DSSD, and he s op gi en by he 848-keV ansi ion depopula ing he isome and he 551-keV ansi ion o Band 4 de ec ed by he ge manium de ec o s a he MARA ocal plane. 2109-keV isome ic s a e o Band 1), o 2¯h o he 17/2−and 19/2−assignmen s (15/2−→19/2+ om he 1893-keV iso- me ic s a e o Band 4), which a e unlikely in he de-exci a ion o high-spin s a es. The candida e con igu a ions o he emaining 19/2+ and 21/2+possible assignmen s can be es ablished om he analysis o he single-pa icle alignmen and c ossing equency o he band buil on he isome . As one can see in Fig. 7, Band 5 abo e he 2284-keV isome ic s a e consis s o wo comple ely degene a e signa u e pa ne s and has ix≈1.5¯h, indica ing he p esence o only high-o bi als in i s con igu a ion. The up bend a a o a ional equency o ¯hω≈0.35 MeV obse ed in all one-quasipa icle bands o 129Nd (see Fig. 6 o Re . [29] and in Fig. 7) and in he bands buil on he 8−isome s wi h wo-neu on con igu a ions o he N=74 iso ones, all a ibu ed o he alignmen o a pai o h11/2p o ons, is absen in Band 5. Wi h he (πh11/2)2alignmen being blocked, he con igu a ion has o in ol e one h11/2p o on o bi al, which can be ei he π5/2−[532] o π3/2−[541]. Fo Z=60 and ε2≈0.3, he Fe mi su ace is in he middle o he h11/2subshell whe e he π5/2−[532] Nilsson o bi al is closes in ene gy, being he e o e a o ed. To es ablish he o bi al occupied by he second p o on in he isome con igu a ion, we obse e ha J(1) o Band 5 is smalle han ha o Band 1 abo e he up bending, whe e wo o a ionally aligned h11/2p o ons a e p esen , sugges ing ha he second p o on occupies a high- o bi al, like π9/2+[404] o π5/2+[413], which by ha ing he angula momen a pe pendicula o he o a ion axis ha e iny con ibu ions o J(1). The neu on has o be placed in a nega i e-pa i y o bi al o ge he posi i e pa i y o he isome , which can only be ν7/2−[523]. We 0.2 0.4 0.6 h -ω (MeV) 0 4 8 12 16 Alignmen ix (h - ) 128Xe K=8 130Ba K=8 132Ce K=8 134Nd K=8 129Nd K=9.5 Kπ=8- bands in N=74 nuclei Kπ=21/2+ band in129Nd (a) 0 0.2 0.4 0.6 h _ω (MeV) 0 6 12 18 24 30 Jx 30 40 50 60 J(1) (h _2/MeV) Exp. Band 1 Exp. Band 5 (b) Band 1 ν7/2[523] (c) Band 1 ν7/2[523] Band 5 ν7/2[523] - π9/2[404] 5/2[532] Band 5 ν7/2[523] - π9/2[404] 5/2[532] FIG. 7. (a) Single-pa icle aligned angula momen a o he bands buil on he 21/2+isome in 129Nd and o he 8−iso- me s in he N=74 nuclei. The Ha is pa ame e s a e J(0) = 14¯h2MeV−1and J(2) =38¯h4MeV−3 o he N=74 isome s, and J(0) =38¯h2MeV−1and J(2) =15¯h4MeV−3 o he 21/2+isome in 129Nd; (b) expe imen al kinema ic momen s o ine ia J(1); (c) p o- jec ions on he c anking axis o he o al angula momen um Jx o Bands 1 and 5 o 129Nd. he e o e acknowledge wo candida es o he h ee- quasipa icle con igu a ion o he 2284-keV isome ic s a e, {ν7/2−[523] ⊗π(9/2+[404]5/2−[532])}21/2+and {ν7/2−[532] ⊗π(9/2+[404]3/2−[541])}19/2+. F om he analysis o he logF W alues o he depopu- la ing ansi ions one conclude ha bo h 19/2+o 21/2+ assignmen s nicely i s he sys ema ics o he E2, M1, and E1 ansi ions depopula ing high-Kisome s [38] o all 014317-6 HIGH-KTHREE-QUASIPARTICLE ISOMERS IN THE … PHYSICAL REVIEW C 108, 014317 (2023) 0.0 0.1 0.2 0.3 0.4 X = β2cos(γ+30) (a) 0.0 0.1 0.2 0.3 0.4 Y = β2sin(γ+30) FIG. 8. Calcula ions o he ν7/2−[523] ⊗π(9/2+[404]5/2−[532]) con igu a ion assigned o he 21/2+isome ic s a e: (a) Po en ial ene gy su ace calcula ed wi h he CC-PES model; (b) Compa ison be ween he expe imen al kinema ic momen o ine ia J(1) o Band 5 and he PNC-CSM calcula ions. (c) Compa ison be ween he expe imen al Band 5 and he PSM calcula ions, using de o ma ion pa ame e s ε2=0.35 and ε4=0.02 which bes ep oduce he band-head and le el ene gies. ansi ions excep ing he 175- and 391-keV ones. The 391- keV ansi ion has highe hind ance o bo h E2 and M1 cha ac e s, whe eas he 175-keV ansi ion has highe hin- d ance only o M1 cha ac e . The high hind ances o hese wo ansi ions would be in ag eemen wi h he sys ema ics o he high-Kisome s only i K⩾3, which would lead o oo low spins o he isome s ha in u n would decay o le els wi h spins highe by mo e han 2¯h han ha o he ini ial s a es, and he e o e can be disca ded. To explain he logF W alues o he 175- and 391-keV ansi ions we ha e o in oke he p esence o addi ional hind ances, which can be induced by e y di e en con igu a ions o di e en de o ma ions o he isome s. In o de o u he in es iga e he con igu a ion o he 21/2+isome ic s a e, he mixing a ios o he I=1 and I=2 ansi ions depopula ing a gi en s a e o spin Io he band buil on he isome ha e been es ima ed om he ansi ion in ensi ies employing s anda d o mulas alid in he app oxima ion o an axially symme ic o a ing nucleus [39,40]: δ2 1+δ2=2K2(2I−1) (I+1)(I−1+K)(I−1−K) E5 1 E5 2 T2 T1 ,(1) gK−gR Q0 =0.933E1 δ(I2−1),(2) whe e δis he mixing a io, Eis he ansi ion ene gy in MeV, Tis he γ- ay ansi ion in ensi y, and Q0is in uni s o eb. The subsc ip s 1, 2 e e o I=1, 2 ansi ions, espec i ely. The |δ| alues can be es ima ed om Eq. (1) by assuming a ce ain K alue, whe eas he sign o δcan be ob ained om he analysis o he angula co ela ions o he emi ed γ ays. F om Eq. (1) one ob ains |δ|≈ 0.5. I he δ alues a e posi- i e, he (gK−gR)/Q0 alues a e also posi i e o a p ola e shape [41]. To es ima e gKwe can adop a smalle gy o- magne ic ac o o gR=0.3 han he o a ional app oxima ion gR=Z/A=0.46, as sugges ed by ha ecen ly obse ed ex- pe imen ally o he 8−high-Kisome in 130Ba, o which gR=0.278(15) has been ex ac ed ins ead o gR=Z/A= 0.43 [42]. We can also adop an in insic quad upole mo- men o Q0=5.5eb co esponding o an axially symme ic p ola e shape wi h a de o ma ion o β2=0.3, as sugges ed by he calcula ions. Wi h his adop ed alues, one ob ains a gy omagne ic ac o o gK≈0.3+0.11 δ≈0.53 o I=12.5. Ve y simila alues a e ob ained o highe spins. This has o be compa ed wi h calcula ed gK alues o di e en h ee- quasipa icle con igu a ions, which a e ≈0 o h ee-neu on con igu a ions, and ≈+1 o one neu on- wo p o on con ig- u a ions. One can he e o e conclude ha he con igu a ion in ol ing wo p o ons is a o ed. This conclusion is also sup- po ed by he mixing a ios ha could be ex ac ed o he 251- and 298-keV ansi ions o Band 5, which a e posi i e and a ound 0.36+23 −9(see Table I), in ai ag eemen wi h he es ima ed absolu e alues ex ac ed using he ela ions (1) and (2). Fo an obla e shape such a conclusion is no alid, bu , as will be discussed in he ollowing subsec ion, he obla e con igu a ion can be sa ely disca ded, because he calcula ed ene gy is oo high and no minimum o an obla e shape is calcula ed in he po en ial ene gy su aces. The spin-pa i y o he 1893-keV s a e is ixed as 17/2+ by he 391-keV popula ing ansi ion om he 21/2+iso- me and he 1009-keV depopula ing ansi ion o he 13/2+ s a e o Band 4 which ha e o be E2 o he wise one an- si ion would be I=1 and he o he one I=3 which is e y unlikely. The spin-pa i y o he 2109-keV s a e is ixed as 19/2+by he 955-keV ansi ion o he 15/2+s a e o Band 4, he 566-keV ansi ion o he 21/2−s a e o Band 1, and he 175-keV ansi ion om he 21/2+iso- me ic s a e. These assignmen s a e also in ag eemen wi h he esul s o he calcula ions desc ibed in he ollowing subsec ion. Ve y di e en con igu a ions ha e o be chosen o he 19/2+and 17/2+isome ic s a es, since no ansi ion has been obse ed be ween hem. This can be ealized i we adop he ν7/2−[523] ⊗π(5/2+[413]5/2−[532]) con ig- u a ion o he 17/2+isome ic s a e, which di e s by wo p o on and one neu on exci a ions om he ν5/2+[402] ⊗ π(9/2+[404]5/2+[413]) con igu a ion assigned o he 19/2+ isome ic s a e. Mo eo e , his con igu a ion is simila o he ν7/2−[523] ⊗π(9/2+[404]5/2−[532]) con igu a ion o he 21/2+isome ic s a e, om which i di e s by one p o on 014317-7 C. M. PETRACHE e al. PHYSICAL REVIEW C 108, 014317 (2023) TABLE II. Calcula ed ene gies o he assigned con igu a ions o he h ee high-Kisome s. The con igu a ions a e gi en in e ms o Nilsson quan um numbe s. The shape pa ame e s (β2,γ) esul ing o m he CC-PES calcula ions, as well as he adop ed quad upole de o ma ions ε2 o he PNC-CSM and PSM calcula ions a e also indica ed. The app oxima e ela ion be ween β2and ε2is ε2≈0.95β2. IπEexp x(keV ) Con igu a ion CC −PES (β2,γ)PNC-CSM(ε2)PSM (ε2) 21/2+2284 ν7/2−[523]π9/2+[404]5/2−[532] 2605 (0.31,−4◦) 3272 (0.31) 2247 (0.35) 19/2+2109 ν7/2−[523]π9/2+[404]3/2−[541] 3016 (0.29,−6◦) 4973 (0.29) 3195 (0.35) 19/2+2109 ν5/2+[402]π9/2+[404]5/2+[413] 3210 (0.29,−8◦) 3992 (0.29) 2786 (0.35) 17/2+1893 ν7/2−[523]π5/2+[413]5/2−[532] 3044 (0.28,0◦) 2421 (0.28) 2836 (0.35) 17/2+1893 ν5/2+[402]π9/2+[404]3/2+[411] 2702 (0.30,9◦) 4658 (0.30) 3092 (0.35) exci a ion, being hus in ag eemen wi h he obse a ion o he connec ing 391-keV ansi ion. The 17/2+and 19/2+s a es a 1893 and 2109 keV, espec i ely, ha e decay pa e ns simila o hose o he 2284- keV 21/2+isome ic s a e, sugges ing high-Kcon igu a ions and isome ic cha ac e . Thei hal -li es could no be di- ec ly de e mined in he p esen expe imen . Fo es ima ing hei hal -li es, we analyzed he Weisskop hind ance ac o s log F W=log τγ τWo he depopula ing ansi ions (τγis he pa - ial γ- ay li e ime and τWis he Weisskop es ima e), which depend on he elec omagne ic cha ac e o he ansi ion and inc ease nea ly linea ly wi h K[38]. I was ound ha hey a e compa ible wi h high K alues anging be ween 3 and 4 o hal -li es o ens o nanoseconds, be ween 5 and 6 o hal -li es o a ew hund eds nanoseconds, and be ween 6 and 7 o hal -li es o a ew mic oseconds, gi ing suppo o hei high-Kna u e. By imposing ha he logF W alues o he depopula ing ansi ions a e in ag eemen wi h he sys ema ics [38], he bes ag eemen was ob ained o hal -li es be ween se e al nanoseconds and ens o nanoseconds o bo h iso- me s. The dec easing hal -li es o he h ee high-Kisome s 21/2+,19/2+, and 17/2+can be pa ially ela ed o hei inc easing ene gy ela i e o he y as line. The ansi ions om he isome o he p e iously known bands ix he absolu e ene gies o Bands 1, 3, and 4, and a he same ime con i m he ela i e ene gies o Bands 3 and 4 es ablished in Re . [29]. A new 406-keV E2 ansi ion om he 9/2+s a e o Band 3 o he 5/2+band-head o Band 4 has been iden i ied, which con i ms he assigned ela i e spins and posi i e pa i y o Bands 3 and 4 [29]. The p esen esul s p o ide e idence ha he g ound s a e o 129Nd is 7/2−, he band-head o Band 1, no 5/2+, he band-head o Band 4, as p esen ly adop ed by ENSDF [43]. We ound ha he 5/2+ band-head o Band 4 decays ia wo delayed ansi ions o 69 and 108 keV o he 3/2+s a e o Band 3 and he newly as- signed 7/2−g ound s a e, espec i ely. These ansi ions ha e been obse ed a he ocal plane o MARA in coincidence wi h he 848-keV ansi ion depopula ing he 21/2+isome ic s a e, and also in delayed coincidence wi h he ansi ions o Band 4 below he 19/2+s a e, he highes ed by depopula - ing ansi ions om he 21/2+isome ic s a e. Howe e , hey we e no obse ed in p omp coincidence wi h ansi ions o Band 4 abo e he 19/2+le el. This indica es ha he 5/2+ band-head o Band 4 is isome ic, wi h a hal -li e o a ew ens o nanoseconds. An indi ec con i ma ion o he isome ic cha ac e o he 108-keV, 5/2+s a e is he nonobse a ion o he 69-keV ansi ion in he p e ious expe imen o Zeidan e al. [29], in which only p omp coincidences we e measu ed. In he p esen expe imen we also used a hin a ge , bu unlike he Zeidan e al. expe imen [29], we we e able o obse e he delayed 69- and 108-keV ansi ions emi ed a he ocal plane o he MARA sepa a o due o he eeding o Band 4 by ansi ions om he long-li ed 21/2+isome ic s a e. The lowes s a es o Band 3 wi h spins 1/2+and 3/2+ ha e exci a ion ene gies o 17 and 39 keV, espec i ely. Thei decays o he 7/2−g ound s a e ia low-ene gy E3 and M2 ansi ions would be ex emely hinde ed, hey mos FIG. 9. Resul s o PSM calcula ions [11] o Bands 1, 2, 3, and 4 o 129Nd, adop ing ε2=0.29 and ε4=0.02 aken om Re . [45], in compa ison wi h he da a o his wo k and hose om Re . [29]. 014317-8