Observation of the 𝐽≤7/2 low-spin states in 213Fr populated in the electron capture of the 1/2− ground state of 213Ra

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Observation of the ≤7/2 low-spin states in 213Fr populated in the electron capture of the 1/2− ground state of 213Ra © Authors 2024 Published version Clisu, C.; Andreyev, A. N.; Nita, C. R.; Lica, R.; Naïdja, H.; Andel, B.; Antalic, S.; Berry, T. A.; Borge, M. J. G.; Cocolios, T. E.; Costache, C.; Cubiss, J. G.; De Witte, H.; Fraile, L. M.; Fynbo, H.; Gadelshin, V. M.; Granados, C.; Greenlees, P.; Heinke, R.; Huyse, M.; Lazarus, I.; Leimbach, D.; Marginean, N.; Marginean, R.; Marsh, B. A.; Mihai, C.; Mosat, P.; Nacher, E.; Negret, A.; Ovejas, J. D.; Page, R. D.; Pascu, S.; Perea, A.; Podolyak, Zs.; Pucknell, V.; Rahkila, P.; Rezynkina, K.; Rossel, R. E.; Sotty, C. O.; Stan, L.; Studer, D.; Tengblad, O.; Van Duppen, P.; Vedia, V.; Warr, N.; The IDS Collaboration Clisu, C., Andreyev, A. N., Nita, C. R., Lica, R., Naïdja, H., Andel, B., Antalic, S., Berry, T. A., Borge, M. J. G., Cocolios, T. E., Costache, C., Cubiss, J. G., De Witte, H., Fraile, L. M., Fynbo, H., Gadelshin, V. M., Granados, C., Greenlees, P., Heinke, R., Huyse, M., Lazarus, I., Leimbach, D., Marginean, N., Marginean, R., Marsh, B. A., Mihai, C., Mosat, P., Nacher, E., Negret, A., Ovejas, J. D., Page, R. D., Pascu, S., Perea, A., Podolyak, Zs., Pucknell, V., Rahkila, P., Rezynkina, K., Rossel, R. E., Sotty, C. O., Stan, L., Studer, D., Tengblad, O., Van Duppen, P., Vedia, V., Warr, N., The IDS Collaboration. (2024). Observation of the ≤7/2 low-spin states in 213Fr populated in the electron capture of the 1/2− ground state of 213Ra. Physical Review C, 110, Article 064315. https://doi.org/10.1103/physrevc.110.064315 2024 PHYSICAL REVIEW C 110, 064315 (2024) Observation of the J⩽7/2 low-spin states in 213Fr populated in the electron capture of the 1/2−ground state of 213Ra C. Clisu,1,2A. N. Andreyev,3,4C. R. Nita ,1,*R. Lica,1,5H. Naïdja,6B. Andel,7S. Antalic,7T. A. Berry,8M. J. G. Borge,5,9 T. E. Cocolios,10 C. Costache,1J. G. Cubiss,3,5H. De Witte,10 L. M. Fraile,11 H. Fynbo,12 V. M. Gadelshin,13 C. Granados,5 P. Greenlees,14,15 R. Heinke,13 M. Huyse,10 I. Lazarus,12 D. Leimbach,5,13,16 N. Marginean,1R. Marginean,1B. A. Marsh,5 C. Mihai,1P. Mosat,7E. Nacher,17 A. Negret,1J. D. Ovejas,9R. D. Page,18 S. Pascu,1A. Perea,9Zs. Podolyak,8 V. Pucknell,19 P. Rahkila,14,15 K. Rezynkina,10 R. E. Rossel,5C. O. Sotty,1L. Stan,1,2D. Studer,13 O. Tengblad,9P. Van Duppen,10 V. Vedia,11 and N. Warr20 (The IDS Collaboration) 1Horia Hulubei National Institute for Physics and Nuclear Engineering, RO-077125 Bucharest, Romania 2Department of Physics, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania 3School of Physics, Engineering and Technology, University of York, YO10 5DD, York, United Kingdom 4Advanced Science Research Center, Japan Atomic Energy Agency, Tokai-mura, Japan 5ISOLDE, CERN, CH-1211 Geneva 23, Switzerland 6Université Constantine 1, Laboratoire de Physique Mathématique et Subatomique (LPMPS), 1 Route Ain El Bey, 25000 Constantine, Algeria 7Department of Nuclear Physics and Biophysics, Comenius University in Bratislava, 84248 Bratislava, Slovakia 8Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom 9Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, E-28006 Madrid, Spain 10KU Leuven, Instituut voor Kern- en Stralingsfysica, Celestijnenlaan 200D, 3001 Leuven, Belgium 11Grupo de Física Nuclear EMFTEL & IPARCOS, Universidad Complutense de Madrid, 28040, Madrid, Spain 12Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark 13Johannes Gutenberg-University, Saarstraße 21, 55122 Mainz, Germania 14University of Jyvaskyla, Department of Physics, Accelerator Laboratory, P.O. Box 35(YFL), FI-40014 University of Jyvaskyla, Finland 15Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland 16Department of Physics, University of Gothenburg, Origovägen 6 B, 41296 Göteborg, Sweden 17Instituto de Fisica Corpuscular, CSIC - Universidad de Valencia, E-46980, Valencia, Spain 18Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 19STFC Daresbury, Daresbury, Warrington WA4 4AD, United Kingdom 20Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany (Received 1 August 2024; accepted 26 November 2024; published 16 December 2024) A detailed level scheme of 213Fr126 following the EC/β+decay of the 1/2−213Ra parent ground state was built in an experiment performed at the ISOLDE Decay Station, CERN. The fragmented total βdecay strength favours the direct population of several low-spin (J⩽7/2) excited states. The analysis of the γ-singles spectrum and γ-γcoincidences allowed us to identify many new γ-ray transitions and excited states in 213Fr up to about 3.6 MeV excitation energy. The spins and parities of the newly established levels, on top of the (7/2− 1) state, were mainly assigned based on the systematics of the N=126 isotones and further compared with shell-model calculations. The level scheme displays a structural pattern, with several groups of states with negative parity, emerging from the well-defined, simple, π(h5 9/2), π(h4 9/2f1 7/2) configurations or from their configuration mixing. The strength of the E2 transitions within the multiplets is compared with shell-model theoretical calculations performed with the KHPE and H208 effective interactions. A new (3/2−) isomer with a half-life of 26(3) ns has been identified. An upper limit of 35 ps was determined for the half-life of the first excited state, 7/2−.The possibility of a mixed M1+E2 character is discussed for the 7/2− 1→9/2− gs decay in 213Fr, which leads to an l-forbidden nature of the πf7/2→πh9/2transition. DOI: 10.1103/PhysRevC.110.064315 *Contact author: [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN. 2469-9985/2024/110(6)/064315(15) 064315-1 Published by the American Physical Society C. CLISU et al. PHYSICAL REVIEW C 110, 064315 (2024) I. INTRODUCTION Nuclei in the proximity of shell closures are of interest since they represent a benchmark test for the shell-model calculations. These nuclei are of particular significance as they may provide insight into the role and manifestations of core polarization, pairing [1], and other types of residual interactions, such as the quadrupole interaction. With exactly N=126 neutrons and lying in the vicinity of Z=82, the low-energy excited states of 213Fr (Z=87) are expected to be dominated by spherical j5=(h5 9/2)J−proton configurations. Simple configurations were proposed for the 9/2− gs,the7/2− 1, and the 13/2+states in the odd-A,N=126 isotones [1–6]asπhn 9/2,πf1 7/2and πi1 13/2, respectively, where nare the extra protons above Z=82. The ground-state spin was determined by Coc et al. [7]tobe9/2−. The first two excited states, at 498 and 1105 keV, respectively, were observed in an α-decay study of the 29/2+isomer in 217At performed by Decman et al. [8]. They were tentatively assigned as Jπ= (7/2−) and (13/2)+based on the conversion coefficients of their corresponding transitions to the ground state. The spectroscopic information concerning the low-spin states is quite scarce. It can be accessed via β-decay spectroscopy of the Jπ=1/2−ground state of 213Ra [T1/2= 2.73(5) min.] [9], which has a 13(2)% electron capture (EC) +β+decay branch to 213Fr [10]. Information on the low-Jstates of 213Fr was originally reported by Maier [11]by combining the results obtained from the αdecay of 217Ac and the EC decay of 213Ra. Their obtained level scheme includes four excited states arranged in a 9/2− gs–7/2− 1–(7/2− 2)–(5/2− 1)– (3/2− 1) sequence up to an energy of 1170 keV. The 213Ra EC decay was also observed by Guttormsen et al. [12] where conversion electrons were detected with a superconducting electron detection system in coincidence with the francium Kαlines. They assigned the 175-, 195-, 208-, 218-, 227-, 257-, 317-, 339-, 400-, 475-, and 498-keV transitions to 213Fr. A second measurement performed by Pragati et al. [13]using a MINI-ORANGE spectrometer coupled with two HPGe detectors, identified the corresponding 399.7-, 498.0-, and 520.4-keV γrays from 213Fr. Neither experiment presents any information on their decay pattern, intensity values, or internal conversion coefficients (IC). Additionally, the 7/2− 1→9/2− gs transitions in 209Bi and 211At were deduced to have M1+E2 mixing ratios of δ= −0.62(6) [2,14] and −0.65(6) [15], respectively. It results that the M1 component accounts for 1/(1 +δ2)≈70% of the total strength. This transition must then have a sizable l-forbidden M1 character component since it breaks the rule of l=0. It was observed experimentally that the singleparticle orbits in the vicinity of major shell gaps having (n,l,j=l+1/2) and (n−1,l+2,j=l+3/2) quantum numbers develop a near degeneracy [16,17]. Several neutron transitions have been investigated nearby 208Pb [18] between h9/2↔f7/2,g7/2↔d5/2,f5/2↔p3/2and d3/2↔ s1/2orbits. An l-forbidden d5/2→g7/2M1 transition has also been found at lower masses, nearby Z=50 and N= 82, in 129Sn [19]. In 213Fr, the proton h9/2and f7/2orbits might be pseudospin partners and form a doublet. Given the encountered similarities with the N=126 isotones it is expected that this hidden symmetry could also be displayed in 213Fr. We report here on a detailed γ-ray spectroscopy study of 213Fr, populated in the EC/β+decay of 213Ra, produced at the ISOLDE facility. Section II contains the beam conditions and the experimental setup used in two separate runs. The first run was dedicated to a detailed spectroscopic study of 213Fr while the aim of the second run was to measure the half-life of the 7/2− 1excited state through the fast electronic timing technique. The γ-ray spectroscopy of 213Fr is presented in Sec. III A, the experimental log ft values for the EC/β+decay branches are presented in Sec. III B, the half-life measurements for the 1170-keV and the 498-keV excited states are presented in Secs. III C and III D, respectively. Section IV comprises two independent spherical shell-model descriptions of 213Fr within the j-j coupling scheme by using the KHPE and H208 effective interactions developed for a specific model space. Section Vcontains the interpretation of the experimental data integrating the theoretical description. II. EXPERIMENTAL SETUP The experiment was performed at the ISOLDE facility at CERN. A 1.4-GeV proton beam delivered by the PS-Booster was impinged on a 46 g/cm2UCxtarget, inducing through spallation reactions the production of 213Ra and its isobar 213Fr. In order to separate the strongly produced 213Fr contamination, CF4gas was added to the target unit, maintained at a high temperature (≈2000 ◦C), allowing the formation and extraction of the 213Ra 19F+molecular ions. They were subsequently extracted from the target unit. The General Purpose Separator (GPS) setting of A=232 led to the removal of the 213Fr contamination as it does not produce stable molecular fluoride ions. The radioactive beam was transported to the ISOLDE Decay Station (IDS) [20,21], where it was implanted on an aluminized Mylar tape. In the first run, the IDS consisted of four high-efficiency HPGe clover detectors positioned upstream with respect to the beam direction. Two detectors were equipped with a thin carbon epoxy window to detect low-energy x rays and γrays down to about 30 keV. The energy calibration was performed with a 152Eu standard spectroscopic source and extended up to 3 MeV by using the 1460.8- (40K), 1764.5- (214Bi), 2204.2- (214Bi), and 2614.5-keV (208Tl) natural background γrays. The array has 2.77(2) keV energy resolution and 3.30(7)% absolute detection efficiency measured for the 1408-keV transition in 152Eu. In the second run, a pair of conical 1.5×1.5×1.0” LaBr3(Ce) scintillation detectors, separated by 180◦,was added to the experimental setup. The characteristic energy and time resolutions were measured by using the coincident 463–1436-keV γrays following the β−decay of 138Cs implanted on the tape. The individual energy resolutions of the LaBr3(Ce) detectors were found to be 20.3(1) and 23.4(1) keV, respectively, at 463 keV. The time differences between the fast scintillators were measured by means of time-to- amplitude-converter (TAC) modules with a 50 ns range. The obtained time distribution for the subpicosecond (T1/2<1 ps) [22]2 + 1state gave a resolution measured as FWHM of 064315-2 OBSERVATION OF THE J⩽7/2 LOW-SPIN … PHYSICAL REVIEW C 110, 064315 (2024) FIG. 1. (a) Singles energy spectrum obtained in the αand EC decay of 213Ra, where the 213Fr transitions are labeled in black, 209Rn in red and 209At in blue. The coincidence spectra gated with a particular γray are presented in (b) gate: 498 keV; (c) gate: 1300 keV; (d) gate: 521 keV; (e) gate: 562 keV. Inset to panel (a) The high-energy transitions seen in the singles spectrum extended up to 2200 keV. Inset to panel (b) The high-energy γ-ray transitions directly feeding the 498-keV state. The 2576-keV peak is coincident with 498- and 511-keV and represents the single escape peak of the 3088-keV transition. The (c), (d), and (e) gates show the statistics acquired in: the (942 →0 keV) 942-keV transition, the statistics in the 942-keV doublet and the (2632 →1690 keV) 942-keV transition, respectively. 231(5) ps. To correct any slight nonlinearity of the integration over the intensity range, a standard time calibrator was employed. The minimization of the energy dependence of the time response induced by the CFD modules was achieved by using implanted 138Cs. Both data sets were acquired in triggerless list mode with the NUTAQ digital acquisition system and a 100-MHz sampling time, operated using the MIDAS control program. Subsequently, the events were built using the GASPWARE analysis framework within a coincidence gate of 0.8 µs for the first run and 1 µs for the second run, allowing the data to be sorted into symmetric γ-γmatrices and also Eγ,Start–Eγ,Stop–Tcubes for the LaBr3(Ce) detectors. III. DATA ANALYSIS A. γ-ray spectroscopy In the first run, the continuous 213Ra 19Fbeam was implanted on the tape, which was moved every 20 s to reduce the contribution from the 209Rn decay (T1/2=28.5(10) min [23]). The absolute γintensity of the 110-keV transition from 209Rn [23] was used to estimate the total of 1.3(2) ×107213Ra nuclei decayed in a measurement time of 214 s. The singles γ-ray spectrum presented in Fig. 1(a) is dominated by the 213Ra decay products thus confirming the beam purity. A detailed level scheme was built based on the γ-γanaly- sis and the prior knowledge of the 498-keV, (7/2− 1)→9/2− gs, transition. The characteristic Fr x rays were used to distinguish between the 213Fr transitions from the EC/β+decay of 213Ra and other decay products. Figure 1(b) shows the energy spectrum gated on the 498-keV transition where the characteristic Kα,β lines of francium, together with a multitude of new γrays can be seen. The newly established level scheme was extended with 17 new excited states and 35 new transitions as presented in Fig. 2. Three γrays with Iγ<0.1 were only tentatively placed in the level scheme. Generally, the summing effects for coincident γrays were found to be negligible. The contribution for the intense 498–1142-keV pair of transitions gives ≈0.5% and raises up to ≈1.5–3 % when considering the coincidence between the intense low-energy transitions with 064315-3 C. CLISU et al. PHYSICAL REVIEW C 110, 064315 (2024) FIG. 2. The experimental level scheme of 213Fr obtained from 213Ra ground state EC/β+decay, extended on top of the previously known 7/2− 1state. The QEC,Qβ+and the ground state half-life are the evaluated values taken from Refs. [27]and[28], respectively. The EC branching ratio is the revised value given by Lorenz et al. [10]. The gating transitions from Fig. 1are presented in blue. The transitions with dashed line are tentative. The log ft and βfeeding values, the 1170-keV and the 498-keV state half-lives were obtained in this work, see Secs. III B–III D for details. The log ft values calculation and the 1u, 2u indices are detailed in Sec. III B. The energies of the states were obtained by performing a global minimization with GTOL [26]. The Iγlabels represent absolute values (see Table I). For the Group A and Group B bands intrinsic structure please see the text and Fig. 6. 064315-4 OBSERVATION OF THE J⩽7/2 LOW-SPIN … PHYSICAL REVIEW C 110, 064315 (2024) the characteristic Fr x rays. The area of the identified summing peaks was used to correct the absolute intensities. The Eγ< 600 keV transitions were assumed to have E/ML=1,2 multipolarity. For the states from Group A and Group B, see Fig. 2, only M1, E2 multipolarities were considered. For the transitions observed in the conversion electron spectra from Ref. [12,13], the E1 multipolarity was excluded due to a very low conversion coefficient [of α(E1) =10−1–10−2for Eγ<600 keV], see Table I. Our work confirmed the 213Fr level scheme reported by Maier [11] and placed the 175-, 317-, 339-, 400-, and 520-keV transitions assigned to 213Fr by Guttormsen et al. [12] and Pragati et al. [13]. The 195-keV, 208-keV, and 218-keV transitions reported by Guttormsen et al. in their Fig. 11 [12], with CEKenergies of 94, 106, and 116 keV, have not been observed in this work. A possible explanation resides in the fact that 213Ra decays via two competing processes, 87(2)%(α)209Rn and 13(2)%(EC/β+)213Fr, see Fig. 4 of Ref. [10]. The αdecay strongly populates the 3/2− 1→1/2− 1→5/2− gs sequence in 209Rn where the 3/2−state subsequently decays via a 104.8–110.3-keV cascade and a 214.9 keV crossover transition [2]. The Kα2of francium and Kα1of radon have similar energies, of 83.23 keV and 83.78 keV [24]. Thus, it is expected that the Kαlines to be coincident with the conversion electrons (CE) from both 213Fr and 209Rn nuclei. Therefore, the CEs with energies of 94, 106, and 116 keV observed in Fig. 11 of Ref. [12] might actually correspond to the CEL(110 keV), CEM(110 keV), and CEK(215 keV) in 209Rn. Since there is an order of magnitude difference between the evaluated conversion coefficients of the 104.8- and 110.3-keV transitions, αk(104.8 keV; M1)/αk(110.3 keV; E2) =7.5(18)/0.362(5) [2], only the 110.3-keV transition is expected to contribute to the γdecay. The highest four excited states in the range E= 2.9–3.6 MeV can only be populated via the EC decay as Qβ+=2.9 MeV. The 3587- and 2877-keV states decay through rather high-energy transitions of 3088 keV and 2379 keV, respectively, directly to the (7/2−)1state, see Figs. 1(b) and 2. The 3380-keV state decay path is made through the 2210–227–942-keV sequence of γrays to the ground state. The 2950-keV state has several decay paths. Based on γ-γ coincidences, the most intense transitions form the 575–734– 1143–498-keV and 400–909–1143–498-keV cascades. Figure 1(c) shows that the 1300-keV transition feeding the 1170-keV state, is coincident with the 227–942-keV cascade and the 1128-keV γray. The γ-γanalysis and the energy balance for the 1170-keV state establishes that there exists a link between the 1170-keV and the 1128-keV states through the low-energy 42-keV γray. Therefore, the 42–1128-keV and the 227–942-keV cascades are parallel to each other. It should be noted that the energy of this transition has been deduced from the energy difference of the 1170- and 1128- keV excited states, while the intensity value quoted in Table I for the 42-keV transition has been deduced relative to the 227-keV transition and by considering that Iγ+IC(42) ≈ Iγ(1128) when observed in coincidence with the 1300-keV γ ray. The deduced total intensity Iγ+IC(42) was 3.2(10)%, see Table I. Although no peak was observed above the background at 42 keV, an upper limit of Iγ(42) <0.4% was estimated. Thus, the conversion coefficient has a lower limit of α(42) > 7. The existence of a 942-keV γ-ray doublet can easily be inferred by comparing Figs. 1(c)–1(e). The 521-keV and the 562-keV transitions are parallel, with similar intensities, see Table I, both depopulating the 1690-keV state. The 562-keV transition bypasses the 1170-keV state by feeding directly the 1128-keV level, and consequently, cannot be coincident with the 942-keV transition feeding the ground state. Therefore, the low 942-keV intensity seen in Fig. 1(e) is due to the contribution given by the higher-lying transition found to decay from the 2632-keV state. The spectrum presented in Fig. 1(d) shows the total 942-keV intensity since the 521-keV transition is coincident with both, while the spectrum in Fig. 1(c) includes only the contribution from the low-lying transition. B. Log ft estimates Considering that the conversion coefficients for the lowenergy transitions in 213Fr are expected to be significant, it is generally difficult to obtain the log ft values and the individual branching ratios for the βdecay when there is poor knowledge of the spins, parities, transition multipolarities, and intensities. As the spin difference between the ground states of 213Ra and 213Fr is 4¯h, the ground state to ground state EC/β+ decay is negligible. The log ft values presented in Fig. 2are calculated with the LOGFT CALCULATOR [29] considering the shape factor for the second forbidden nonunique transitions calculated as firstforbidden unique (1u), while the first-forbidden nonunique is calculated as an allowed βtransition, as recommended by Turkat et al. [30]. The total γ+IC intensity to the ground state should equal the EC/β+decay branching ratio of 13(2) % and the absolute transitions intensities, presented in Fig. 2. The relative Iγvalues presented in Table Iare obtained by multiplying with the 0.066(10) factor. The higher-lying states in the daughter nucleus are expected to be restricted to have rather low Jvalues, due to the βdecay selection rules and absence of γfeeding from higherlying states, see the detailed discussion presented in Sec. V. The highest excited state, located at 3587 keV, has IEC = 0.22(5)% and log ft =5.32(11). The latter value corresponds to a presumably first-forbidden nonunique βtransition if one compares it with the available experimental data [30]for Z⩾80 heavier nuclei, see Fig. 3. Also, an allowed transition cannot be excluded. Thus, the Jbetween the 213Ra (g.s.) and the 213Fr (3587-keV state) is expected to be of 0, ±1¯hunits. The unique deexcitation path of the 3587-keV state through the 3088-keV γray directly to the 7/2− 1state but not to the ground state, correlated with the Jπ=1/2−ground state of 213Ra, indicates that it can be assigned a tentative value of Jπ=(1/2+,3/2+). The half-lives of the states decaying via Eγ>3MeV,M2orE3 [(1/2+,3/2+)→7/2− 1] transitions have single-particle values of the order of T1/2<170 ps. The 2950-keV excited state decays mainly via low-energy transitions that have significant conversion coefficients, thus accurate EC intensities could not be calculated. However, using the γ-ray intensities, a IEC ≈4.6(10)% can be assigned to the EC feeding, resulting in a value of log ft ≈5.15(10). It 064315-5 C. CLISU et al. PHYSICAL REVIEW C 110, 064315 (2024) TABLE I. Properties of the excited states of 213Fr: the excitation energy, E, the assigned spin and parity, Jπ,theγ-ray energy for the decaying transitions, Eγ, the corresponding γ-ray intensity relative to the 498-keV transition considered to have Iγ=100, Iγ,theγ-ray multipolarity assumption, the conversion coefficient, αtot, and the total γ+IC intensity are listed. The αtot was taken as the average of the minimum and maximum of the assumed multipolarity [25], with the uncertainty set to half their difference. Relative intensities were extracted from the γ-peak intensities in the singles spectrum. Iγand Iγ+IC intensities include the summing effect corrections. The spins and parities were assigned based on the comparison with the shell-model calculations (see Sec. IV), except where otherwise stated. The errors in Eγare statistical. The energies of the excited states were obtained after a global minimization with GTOL software [26]. EJ πEγIγcMultipolarity αtot Iγ+IC [keV] [keV] % % 498.3(1) 7/2−d498.3(1) 100(6) M1(+E2) 0.165(2) 116.5(70) 942.4(1) (7/2−)e444.4(1) 1.0(1) (M1,E2) 0.137(88) 1.1(1) 942.4(1) 34.8(12) 34.8(12) 1128.1(1) (5/2−)e1128.0(1) 35.2(12) 35.2(12) 1169.8(1) (3/2−)e41.8(2)a6.9(17) 6.9(17) 227.4(1) 17.1(5) (E2) 0.353(5) 23.1(7) 671.4(1) 1.4(2) 1.4(2) 1641.0(1) (3/2−)e1142.7(1) 105(6) 105(6) 1690.4(1) (1/2−)e520.5(1) 7.0(3) (M1,E2) 0.090(57) 7.6(5) 562.2(1) 6.8(3) (E2) 0.0281(4) 7.0(3) 1728.4(1) (5/2−)e1230.0(1) 7.3(7) 7.3(7) 1728.5(1) 3.1(2) 3.1(2) 1825.1(1) (5/2−)e1326.7(1) 5.4(2) 5.4(2) 1825.1(1) 7.6(5) 7.6(5) 1866.6(1) 738.6(1) 7.8(8) 7.8(8) 2374.9(1) 684.4(1) 1.8(2) 1.8(2) 733.8(1) 38.0(16) 38.0(16) 1205.1(1) 0.9(1) 0.9(1) 2469.5(1) 779.1(1) 3.1(1) 3.1(1) 828.4(1) 6.0(2) 6.0(2) 1299.7(1) 18.1(13) 18.1(13) 2549.8(1) 174.9(1) 1.2(2) (M1,E2) 1.9(10) 3.5(14) 724.8(1) 7.4(2) 7.4(2) 821.4(1) 6.1(2) 6.1(2) 908.7(1) 22.2(10) 22.2(10) 2611.1(1) 969.9(1) 4.0(2) 4.0(2) 920.8(1) 0.6(1) 0.6(1) 2632.4(1) 257.4(1) 1.0(1) (E1,M1,E2) 0.52(47) 1.5(5) 765.8(1) 2.6(4) 2.6(4) 942.2(2) 3.7(4) 3.7(4) 1462.4(3) 2.4(2) 2.4(2) 2744.7(1) 1103.7(1) 2.2(2) 2.2(2) 1574.9(1) 4.3(2) 4.3(2) 2800.0(1) 1109.4(1) 2.2(2) 2.2(2) 1159.2(1) 1.3(1) 1.3(1) 2877.1(1) 2378.7(1) 2.0(2) 2.0(2) 2949.8(1) (1/2+,3/2+)b317.3(1) 6.5(2) (M1,E2) 0.34(22) 8.7(14) 338.5(1) 4.2(4) (M1,E2) 0.28(18) 5.4(9) 400.0(1) 21.0(7) (M1,E2) 0.18(12) 24.8(26) 480.4(1) 4.2(1) (M1,E2) 0.11(7) 4.7(3) 574.9(1) 4.5(1) (E1,M1,E2) 0.06(5) 4.8(3) 1083.2(2) 0.8(2) 0.8(2) 1308.8(1) 5.7(2) 5.7(2) 3027.4(1) 1386.3(1) 1.7(1) 1.7(1) 3380.1(2) 2210.3(1) 0.6(1) 0.6(1) 3586.7(1) (1/2+,3/2+)b3088.3(1) 3.4(5) 3.4(5) aFor this transition, the intensity includes the total γ+IC value. bSpins and parities assigned in this work based on the arguments presented in Sec. III B, see text for details. cMultiply by 0.066(10) to obtain absolute intensities per 100 decays. dThe spins and parities of the g.s. and the first excited state are taken from Decman et al. [8] and confirmed by the present work. eDetermined by the SM calculations detailed in Sec. IV. 064315-6 OBSERVATION OF THE J⩽7/2 LOW-SPIN … PHYSICAL REVIEW C 110, 064315 (2024) FIG. 3. Experimental log ft values for allowed and first-forbidden EC/β+decays for Z⩾80. In the heavier mass region, the forbidden transitions compete with the allowed transitions making the forbidden transitions the dominant decay mode. The centroids of the log ft distributions for the first-forbidden EC/β+decays is 7.13(65) with slightly higher log ftC=7.54(70) for allowed EC/β+decays. The numerical data are taken from the compiled data of Turkat et al. [30]. must be noted that the population of this state exhausts about 36% of the EC decay. The log ft value is most likely indicating a first-forbidden nonunique transition and therefore a tentative Jπ=(1/2+,3/2+) value was assigned. C. Half-life determination of the 1170-keV state During the first run (see Sec. II for details), the 1170-keV state was found to be isomeric by measuring, with the HPGe detectors, the time distribution between the feeding 1300-keV and the deexciting 227-keV transitions. The half-life of the state was obtained through a two-step procedure, which included the energy correction of the time response and fitting the time distribution with an analytic function representing the convolution of the prompt time distribution with an exponential decay curve [31,32]. For this purpose, an Eγ,Start–Eγ,Stop–Tcube was built, where Tis the time stamp difference between any two HPGe crystals that detect a coincident pair of transitions, which populate and subsequently depopulate the state of interest. The time reference was chosen to be the average of the time stamps of the HPGe crystals in the event. The prompt distribution was constructed using a similar energy 1213– 245 keV Start-Stop pair from the 152Sm source to eliminate the energy dependence of the time response, see Fig. 4.The half-life of the 3−state at 1579 keV from 152Sm has an evaluated value of 72(6) fs [33] and it is negligible in comparison to the measured time resolution (FWHM) of the HPGe array of 43(1) ns for this pair of γrays. By fitting the 1170-keV state time distribution, presented in Fig. 4, with the convoluted function a half-life of 26(3) ns was obtained. Assuming an E2 character for the 227-keV transition (see Sec. IV), the strength becomes B(E2)=21(3) e 2fm4 [0.271(36) W.u.]. For A≈200 nuclei and Eγ≈200 keV, the FIG. 4. The time distribution (as black line histogram) obtained for the 1170-keV state in 213Fr using the 1300–227 keV Start-Stop pair of γrays. From the fit of the distribution (red line), a half-life of T1/2=26(3) ns was obtained. The prompt time distribution (grey shaded histogram) shows the τ=0 ns centroid used for the fit obtained using the 1213–245 keV from 152Sm as Start-Stop selections. The error on the half-life value results from the fit. The reduced χ2 test returned a value of 1.9. experimental B(E2) values between single- or multiparticle states generally fall below 1 W.u. [34]. D. Half-life determination of the 498-keV state In the second run, the time distribution presented in Fig. 5was obtained by considering the 1142–498-keV pair of FIG. 5. (a) The total LaBr3(Ce) energy projection from Eγ,Start– Eγ,Stop–Tcube. The labels represent the Start-Stop transitions, also shown in the energy HPGe spectrum of Fig. 1(a). Therefore, no contamination is expected to be included in the time distribution. (b) The double-gated time distribution obtained for the 498-keV state in 213Fr. The centroid shift analysis gives a half-life upper limit of 35 ps. 064315-7 C. CLISU et al. PHYSICAL REVIEW C 110, 064315 (2024) FIG. 6. The comparison between our partial experimental and the calculated 213Fr level schemes with the KHPE [36]andH208 [39] interactions. The relevant part of the experimental level scheme includes the states up to about 2 MeV excitation energy. See Table II for the detailed wave-function compositions. The values above each decay represent the energy (in keV) and the calculated E2and/or M1 transition probabilities (in units of e 2fm4and/or μ2 N). The seniority quantum number (ν), calculated with NATHAN [37], is indicated for each level. The colors indicate dominant configurations, as shown in the top-left corner. coincident transitions by using the LaBr3(Ce) subarray. The choice of the feeding-deexcitation γrays was based on their experimentally determined intensity balance, see Table Iand Fig. 1(a), combined with the selectivity of the LaBr3(Ce) detectors presented in Fig. 5(a). From the centroid shift analysis an upper limit of T1/2⩽35 ps has been obtained. A pure 7/2− 1→9/2− gs M1 transition has the strength with a lower limit of the order of 9 ×10−3μ2 N(≈5×10−3W.u.), while if a pure E2 multipolarity is assumed then B(E2) =526 e 2fm4 (≈7 W.u.). A detailed discussion regarding the possible E2 admixtures in this transition may be found in Secs. IV and V. IV. SHELL-MODEL CALCULATIONS Two independent shell-model (SM) calculations have been performed for 213Fr (see Fig. 6): within the jj-coupling scheme with the NUSHELLX code [35] by using the KHPE diagonalization space [36] and with NATHAN [37,38] code, by using the H208 [39,40] interaction. Standard effective charges were used in the evaluation of the transition probabilities: eν= 0.5e, eπ=1.5e for E2 transitions and gl π=1.,g s π=5.586, gl ν=0,and gs ν=−3.826 for the spin and orbital factors for M1 transitions. The configuration space for both interactions lies above the Z=82 and N=126 shell closures, and allows for the excitations of the 5 extra protons across the full π0h9/2(spe = −3799 keV), 1 f7/2(−2902 keV), 0i13/2(−2191 keV), 1 f5/2 (−977 keV), 2p3/2(−681 keV), 2p1/2(−166 keV) singleparticle orbits fixed in the Kuo-Herling effective interaction [36]. No neutron particle-hole excitations were considered above the Fermi level at N=126 for the H208 and KHPE effective interactions, since 208Pb is considered as closed core. No truncation was used in the calculations. Although the experimental energy level scheme seems more compressed than the calculated ones, overall, a good agreement is found between the KHPE model predictions and the experiment, see Fig. 6, with E=|Eexp −Eth|< 200 keV for the states from Group A. For Group B, E remains around 200–400 keV. The KHPE theoretical level scheme closely follows the group structure exhibited by the experimental one. The energy gap between the states belonging to Group A and Group B is (GroupB −GroupA)EXP ≈ 470 keV for the experimental level scheme. This gap is 064315-8 OBSERVATION OF THE J⩽7/2 LOW-SPIN … PHYSICAL REVIEW C 110, 064315 (2024) J. T. H. Dowie, T. J. Gray, T. Kibédi, B. P. McCormick, L. J. McKie, M. S. Rahman, M. Reece, N. J. Spinks, B. P. E. Tee, Y. Y. Zhong, and K. Zhu, Phys. Lett. B 823, 136738 (2021). [52] P. Hansen, Advances in Nuclear Physics,editedbyE.V.M. Baranger (Springer, Boston, 2004). [53] E. Caurier, M. Rejmund, and H. Grawe, Phys.Rev.C67, 054310 (2003). 064315-15