Much of the study of the structure of atomic nuclei cen ters on the interplay between individual nucleons and the emergent collective behavior caused by the strong inter action between them. Quadrupole-deformed shapes are one of the emergent phenomena. Among these, axiallysymmetric prolate (cigar-like) shapes are observed more frequently than oblate (disk-like) shapes [1,2]. In addi tion, axially-asymmetric (triaxial) shapes are important in some regions of the nuclear chart, including the Ge-Kr mass region (Z = 32 -36) [3][4][5][6][7][8][9][10][11][12]. In some of the nuclei in this region, both axially symmetric and asymmetric shapes appear to coexist at comparably low excitation energies and lead to complex quantum-state mixing [13 15]. The delicate interplay between the different config urations influences several experimental observables con nected to the quadrupole degree of freedom and, further more, causes rapid shape changes observed with both isospin and spin [16][17][18][19][20][21][22].
In addition to quadrupole excitations, octupole excita tions are observed throughout the nuclear chart [23][24][25][26]. Due to the presence of the 2p3/2 and 1g9/2 orbitals for both protons and neutrons around the Fermi surface, en hanced electric octupole B(E3) transition strengths are expected for the neutron-deficient Ge, Se and Kr iso topes. Previous experimental studies established that the low energy octupole state (LEGS) fragments into two or more Jn = 3-states with the B(E3; 3-^ 0+) strengths summing up to approximately 15 Weisskopf units (W.u.) [27][28][29][30][31][32]. However, 70,72Ge are notable ex ceptions as a very sudden B(E3; 3-^ 0+) strength * mspieker@fsu.edu increase to around 30 W.u. is observed [28,30,32]. Chuu et al. were able to describe this B(E3) strength increase in the Ge isotopes with the Interacting-Boson-Model plus Interacting-Boson-Fermion-Model approach (IBM+IBFM); however, without considering shape coex istence [33]. In their study, they attributed the sudden in crease in octupole collectivity to a maximum contribution of the collective f-boson configuration to the total wave function. The contribution of the f5/2 -g9/2 fermionpair configuration turned out to be negligibly small at N = 40. Interestingly though, the sudden strength in crease is not observed for the N = 40 isotone 74 Se [31]. When comparing to the other isotonic chains, there also appears to be nothing particularly special about proton number Z = 32 in terms of octupole collectivity [27]. This questions previous conclusions about a simple ori gin of enhanced octupole collectivity at N = 40 drawn in, e.g., Refs. [33][34][35]. Instead, the idea that octupole collectivity is more sensitive to quadrupole distortions in the Ge-Kr region than in other mass regions might be correct [36]. Up to now, the sharp difference in octupole collectivity between 70,72Ge and the rest of the nuclei in this region has remained a puzzle. Shape coexistence and strong configuration mixing generally complicate the theoretical description of octupole strengths (see, e.g., the remarks in [37]). To more systematically approach this challenge, first exploratory calculations within the framework of the configuration-mixing sdf IBM mapping approach, which is based on microscopic self-consistent mean-field calculations employing universal energy den sity functionals and takes shape coexistence explicitly into account, have recently been performed [38]. In ad dition to enhanced strength for 72Ge, B(E3; 3-^ 0+) strengths of around 30 W.u. have been predicted in the rare isotopes 74,76Kr.
In this work, we report on measurements of the pre-viously unknown B(E3; 3,r ->• 0^) strengths in the rare isotopes 72Se (Z = 34) and 74-76Kr (Z = 36), which are the N = 38 and N = 40 isotones of 70,72Ge. To measure the octupole strengths in these nuclei, inelas tic proton scattering experiments in inverse kinematics were performed. Inelastic proton scattering has proven to be a very powerful tool to study the fragmentation of the LEGS among a few to several excited 3~ states for different structures of the ground state [31,[39][40][41], In combination with data available for stable nuclides, the new data clearly show that a simple picture of enhanced octupole correlations around the octupole magic number N = 40 cannot be claimed.
The experiments were performed at the Coupled Cy clotron Facility of the National Superconducting Cy clotron Laboratory (NSC-L) at Michigan State Univer sity [42] at secondary beam energies corresponding to proton energies of around 100 MeV in the center-of-mass frame. At these energies, both proton and neutron con tributions to the wave function are probed almost equally [43]. The secondary 76Kr (79% purity), 74Kr (51% pu rity) and 72Se (6 % purity) beams were produced from a 150 MeV/u 78Kr primary beam in projectile fragmen tation on a 308-mg/cm2 thick 9 Be target. The A1900 fragment separator [44], using a 240-mg/cm2 A1 degrader, was tuned to select the fragments of interest in flight us ing two separate magnetic settings. For the magnetic set ting centered on 74Kr, the secondary 72Se beam was part of the cocktail beam. All three secondary beams could be unambiguously distinguished from the other components in the cocktail beam via the time-of-ftight difference mea sured between two plastic scintillators located at the exit of the A1900 and the object position of the S800 anal ysis beam line. Downstream, the NSC-L/Ursinus Liquid Hydrogen (LH2) Target was located at the target posi tion of the S800 spectrograph. The projectilelike reac tion residues entering the S800 focal plane were identi fied event-by-event from their energy loss and time of flight [45].
The CRETIN A y-ray tracking array [47,48] was used to detect 7 rays emitted by the reaction residues in flight (v/c % 0.4). Eight CRETIN A modules, containing four, 36-fold segmented HPGe detectors each, were mounted in the north half of the mounting shell to accommodate the LH2 target. Event-by-event Doppler reconstruction of the residues' y-ray energies was performed based on the angle of the y-ray emission determined from the main interaction point in the Ge crystal and including trajec tory reconstruction of the residues through the S800 spec trograph [48]. Fig. 1 shows the experimental Dopplercorrected, in-beam y-ray spectra for 72Se and 74,76Kr together with the corresponding spectra simulated with UCGRETINA [46]. For the simulation, the known experi mental kinematics, target thickness, setup geometry and Data are shown in black. GEANT4 simulations performed with UCGRETINA [46] are presented in blue. A prompt background consisting of two exponential functions was included in the simulation. As an example for the yy coincidences placing the 3j) state in ,4I<r, the inset in the middle panel shows the coin cidence spectrum when gated on the 1953-keV, 37 2/ y-ray transition. A clear coincidence with the 456-keV, 2/ Oj7 y-ray transition is observed. y-ray detection efficiency were used as inputs. Pressure differences across the Kapton entrance and exit windows of the LH2 cell cause them to bulge outwards. To de termine the target thickness, this effect was taken into account and its contribution quantified by simulating the kinetic-energy distribution of the outgoing beam with the procedure described in [49]. An areal density of 69(3) mg/cm2 was determined. Assuming the population of different excited states in the reaction, the experimental y-ray yields were determined by fitting a superposition of the simulated y-decay spectra of individual excited states to the experimental spectrum. For each excited state, y-decay branching was explicitly taken into account if known from previous experiments [50][51][52][53][54]. The y-decay intensities were varied within the reported uncertainties. As y-ray cascades are included in the simulation, the obtained yields are corrected for observed feeders. The yields are used to calculate the inelastic proton scatter ing cross sections to excited states in 72Se and 74-76Kr by normalizing them to the number of incoming beam particles and the number of target nuclei. For the 2^ states of 72Se and 74-76Kr, the (p,p') cross sections are 17(4) mb, 28(5) mb and 43(2) mb, respectively. For the 37 states of 74-76Kr and the 3-7 state of 72Se, they are 4.6(8) mb, 5.9(3) mb and 13(3) mb. Stated uncertainties include statistical uncertainties, the stability of the sec ondary beam composition, uncertainties coming from the choice of software gates and the target thickness.
To calculate reduced transition probabilities B(EA) from deformation parameters (A = 2, 3,4,...), reaction calculations were performed with the coupled-channels program CHUCK3 [55] using the global optical-model pa rameters of [56]. Only single-step excitation was con sidered. As described in Refs. [27,41,57], the de formation parameters can be calculated by scaling the theoretical cross sections to the experimentally de termined ones. For the 21h states, deformation param eters of /J2 = 0.40 ± 0.02 (stat.) ± 0.03 (sys.) for 76Kr, /?2 = 0.35 ± 0.06 (stat.) ± 0.02 (sys.) for 74Kr, and /?2 = 0.26 ± 0.06 (stat.) ± 0.02 (sys.) for 72Se were de termined. Systematic uncertainties stem from the theo retically expected variation of the cross section over the LH2 target thickness. Within uncertainties, the fB val ues for the Kr isotopes are in excellent agreement with the adopted values of 0.3920(66) and 0.363(9) [57], re spectively. For 72 Se, the value agrees with the adopted value of 0.215(5) within uncertainties. For 74,76Kr, the inferred B(E2; 2\ -> 0),7) values are shown in Fig. 2(a) including data for the Kr isotopes between N = 34 and N = 50. As can be seen, the (p, p') data confirm the trend of a decreasing B(E2) strength when passing N = 40 (A = 76) and agree with the strengths determined with other probes [21,22,[57][58][59], validating both the reaction calculations and feeding correction.
The 2257-keV, 37 state of 76Kr was previously ob served in several experiments including the (p,t) exper iment of [60]. No excited 3~ states were known in 74Kr prior to this work. The first two excited 3~ states of 72Se at 2406 keV and 2434 keV, respectively, were ob served in a number of experiments [50,61]. However, for none of the three nuclei, B(E3) strengths were previ ously measured. In this work, the well-known 1834-keV, 3]f -> 21h 7-ray transition in 76Kr is prominently observed (see Fig. 1). The = 37 state of 74Kr is newly assigned based on the striking similarity of its 1953-keV, 37 -> 2\ 7-ray transition to the corresponding one in 76Kr (also see Fig. 1). 77 coincidences confirm the placement and establish the 74Kr, = 37 state at 2409(3) keV (see in set in Fig. 1). Reduced transition strengths B(E3; 37 -> Oj7) of 15.0 ± 0.9(stat.) ± 1.8(sys.) W.u. for 76Kr and 13 ± 2(stat.) ± 2(sys.) W.u. for 74Kr were determined, respectively. As can be seen in Fig. 2(b), they match the rather constant B(E3; 37 -> Oj7) values of around 15 W.u. observed in the stable Kr isotopes [29]. The excitation-energy systematics in the Kr isotopes are pre sented in Fig. 2(c). Interestingly, rather than the 37 state, the 37 state is the most strongly populated 3~ state in 72Se (see 1572-keV, 37 -> 2\ 7-ray transition in the bottom panel of Fig. 1). A significantly larger B(E3; 37 -> Oj7) strength of 32 ± 7(stat.) ± 4(sys.) W.u. is determined. For the 37 state, only an upper limit of B(E3; 37 -> Oj7) < 4.5 W.u. can be reported. In agreement with newer experiments on 72Se [52,54], the 37 -> Oj7 ground-state branch is not observed. Note that in 74-76Kr, the 37 -> Oj7 7-decay branch was also not observed and, thus, not considered for the calculation of the experimental (p,p') cross sections.
Given that the 37 state is more strongly populated than the 37 state in 72Se, it is worth noting that Ref. [29] established a pronounced variation of the B(E3; 37 -> 0^) strength with neutron number in the stable Kr iso topes. This was linked to the emergence of quadrupole deformation possibly fragmenting the strength. The data are shown in Fig. 2 (b). When inspecting Figs. 2 (a) and (b), it is apparent that the B(E3; 3T -> 0^) follows the B(E2; 2^ -> 0^) strength increase. There is a caveat though. In the stable isotope 78Kr, the 3-7 is not the one reported in [29]. There exists a lower-lying 3~ state at 2678 keV [50], which was most likely not observed in (p,p') because of its small B(E3) strength [see Fig. 2 (c)]. The fragmentation of the B(E3) strength appears, thus, nontrivial as quadrupole deformation begins to mani fest. The observations made for 72Se support this point. For the Kr isotopes, we will consequently use the nota tion 37(pp') for the second 3~ state observed in (p,p') and carrying non-negligible B(E3) strength. In unsta ble 76Kr, the situation is comparable to 78Kr. Matsuki et al. reported a possible 3~ state at 2601 (15) keV [60], which they observed in the 78Kr(p, f)76Kr reaction. In a follow-up publication, they presented a firmly identi fied 3~ state at 2872 (15) keV as the 37 candidate [29]. We do not observe any resolved 7 rays in our spectra, which could be attributed to the population of the 2872-keV state in (p,p'). Its B(E3) strength must either be small or its 7-decay behavior be very complex, i.e., the yield be shared between several 7-decay branches. Both scenarios may prevent its detection. A JT = 3" assign ment is possible for a state at 2581 keV though. Previ ously, Giannatiempo et al. had argued for a = 2+ assignment based on the state's 7-decay behavior and the deduced log (ft) value [51]. The log (ft) =7.1 value is, however, exactly the same as for the known 37 state in 76Kr. The corresponding feeding intensity is also low suggesting a forbidden decay from the J7r = 1" parent ground state of 76 Rb. Furthermore, the 7 decays to the 21 (i7 = 78%) and 4^ (/7 = 22%) states allow for a = 3~ assignment. This state might, thus, corre spond to the 2601-keV state reported by Matsuki et al., where the (p, t) angular distribution favors an l = 3 trans fer. We observe the population of the 2581-keV state in (p,p'). The (37) -> 21 and (37) -> 4^ transitions are highlighted in Fig. 1. As mentioned earlier, the 7-decay intensities reported in Ref. [51] were used for the UC-GRETINA simulation. Even though the spin-parity assign ment is tentative, the deduced B(E3; 37^,^ -> 0|) = 6.2 ± 0.7(stat.) ± 0.7(sys.) W.u. fits well into the systematics. For 74Kr, we observe a new 7-ray transition of 2062( 5) keV (see Fig. 1), which is in coincidence with the 456-keV, 21h -> 0], 7 transition. Thus, there is evi dence for a previously unobserved level at 2518 (5) keV. If this state is indeed a 3~ state, then this would estab lish two excited 3~ states within ~ 100 keV. We, thus, want to emphasize that the first two excited 3~ states of the N = 38 isotone 72Se are within 28keV [50]. The 2518-keV 7-ray yield corresponds to a B(E3; 37^,^ -> Oj7) = 4.3 ± l.l(stat.) ± 0.5(sys.) W.u., which is again in excellent agreement with the general trend seen in [27,[29][30][31][32]. For all nuclei but ,2Se, the strongest fragment is the 37 state. Theoretical pre dictions for the B(E3; 37 -> Oj7) strengths of ,2Ge, ,4Se, and ,4,,6Kr were added to panel (a) [solid symbols]. These were obtained with the recently introduced configuration-mixing sdf IBM mapping approach [38]. The color coding and cor responding symbols are the same for the experimental data and theoretical predictions. Additionally, predictions made within IBM+IBFM approach of Ref. [33] for the Ge isotopes were added to panel (a) [dashed line]. The blue and grey bands correspond to the 14(4) W.u. and 18(4) W.u. averages mentioned in the text. Fig. 2 (b). Interestingly, for both 74,76Kr and even though tentatively assigned, the B(E3; 37^,^ -> 0),7) strength agrees with the upper limit of 4.5 W.u. determined for the B(E3; 37 -» 0]7) strength in 72Se.
Based on our new data, we establish that the sudden B(E3) strength increase at N = 40 is exclusively ob served for 72Ge (Z = 32). For the N = 38 isotones, it is observed for 70Ge (Z = 32) and 72Se (Z = 34) but not for 74Kr (Z = 36). A simple picture of enhanced octupole correlations around the octupole magic number N = 40 can consequently not be claimed. The almost degener ate, low-lying 3~ states and the fact that -in contrast to 77772Ge, 74Se and 74-76Kr -the 37 state is the strongest fragment in 72 Se also suggest that two microscopic con figurations could cross beyond A = 74.
To obtain a clearer picture, the B(E3; 37 -» 0]7) of the strongest fragment and summed B(E3; 37 ->. 0),7) strengths in the Ge-Kr mass region are compiled in Fig. 3. Except for 72Se and 74,76Kr, the summed strengths were deduced from the available proton and alpha inelastic scattering experiments on the stable Ge, Se and Kr isotopes [29][30][31][32]. The data draw an intriguing picture of two distinct regions. The first region extends from the spherical N = 50 neutron shell closure all the way down to A = 74. In this region, weighted averages of B(E3) = 14(4) W.u. and B(E3) = 18(4) W.u. are determined from the data. The quoted uncertainties cor respond to the standard deviation. The new data on 74,76Kr, with their dominant prolate ground-state config uration [17], fit perfectly into this group. Then, the sud den jump of the B(E3) strength is observed at A = 72. The location of this "jump" coincides with the transition from a prolate to an oblate ground-state configuration at A % 72 [16,[18][19][20][21]. However, based on experimental data, triaxial configurations appear to be important at A = 72, too [10]. Most importantly, the "jump" is not observed at a fixed proton or neutron number as might be naively expected and, thus, seems to be more intimately connected to specific structure changes.
Predictions for the B(E3; 3-^ 0+) strengths of 72Ge, 74Se and 74-76Kr, obtained with the pioneering configuration-mixing sdf IBM mapping approach [38], were added to Fig. 3(a). Before discussing these pre dictions, it should be mentioned that the experimentally determined magnitude of the quadrupole moments Q2+ are well reproduced while for all nuclei but 74Kr the pre dicted signs disagree with the data. A similar observa tion was made in Ref. [20]. As the self-consistent meanfield results already predict pronounced oblate minima, this gets propagated to the mapped IBM wave functions. However, Ref. [38] also shows that the ground-state wave functions of all considered nuclei are strongly mixed with spherical 0p-0h, oblate 2p-2h and prolate 4p-4h config urations contributing. This highlights the complexity of this mass region. Still, for a more meaningful comparison in terms of octupole collectivity, a functional should be employed, which can reproduce the signs of the experi mental quadrupole moments as the correct ground-state structure is critical [37]. The consistent overprediction of the B(E3) strengths, with the exception of 72Ge, could consequently be an artifact of the incorrect and domi nantly oblate ground-state structure. Most 3-sdf-IBM wave functions are also predicted to be dominated by the oblate 2p-2h intruder configuration. More impor tantly though, the calculations show that enhanced octupole collectivity is indeed expected for the oblate con figuration. This qualitatively agrees with the significant B(E3) strength increase seen at A = 72, where oblate configurations start to strongly mix into or even domi nate the ground state wave function (see, e.g., the work of Refs. [8, 16-22, 62, 63]). For completeness, we added the IBM+IBFM results of Ref. [33] to Fig. 3(a). As the parameters are, however, explicitly fitted to the Ge isotopes, no clear microscopic information for the entire Ge-Kr mass region can be extracted. Considering the projected shell model calculations of Ref. [64], which pre dict a dominant two-quasiparticle (2QP) character for the lowest negative-parity rotational bands in the Kr iso topes, it is possible that for nuclei with A > 72 the con tribution of the f5/2 -g9/2 fermion-pair configuration to the total wave function increases and leads to decreased octupole collectivity as in the Ge isotopes. The inspec tion of the predicted structures reveals, however, that the 2QP Nilsson configurations in 72-76Kr originate from the spherical 2p3/2 and 1g9/2 orbitals, i.e., the octupolecollectivity driving orbitals [64]. While the experimental signature is clear, the theoretical picture in the Ge-Kr mass region remains a puzzle.
In summary, we have performed inelastic proton scat tering experiments in inverse kinematics on the rare iso topes 72Se and 74,76Kr to measure their B(E3) strengths. While significantly enhanced octupole strength of ~ 32 W.u. was established for 72Se (Z = 34, N = 38), much smaller strength of ~ 15 W.u. was observed for 74,76Kr (Z = 36, N = 38,40). Based on our new data, we estab lish that the sudden B(E3) strength increase at N = 40 is exclusively observed for 72 Ge (Z = 32). For the N = 38 isotones, it is observed for 70Ge (Z = 32) and 72Se (Z = 34) but not for 74Kr (Z = 36). The almost degener ate, low-lying 3-states and the fact that -in contrast to 70,72Ge, 74Se and 74,76Kr -the 3-state is the strongest fragment in 72Se also suggest that two microscopic con figurations could cross beyond A = 74. In combina tion with previously existing data, the new data clearly question a simple origin of enhanced octupole strengths around N = 40. Instead, the present work establishes two regions of distinct octupole strengths with a sud den strength increase around the A = 72 prolate-oblatetriaxial shape transitional point. Theoretical calcula tions performed in the framework of the configuration mixing sdf IBM mapping approach predict enhanced B(E3) strengths built on the oblate minimum in this mass region, but fall short on correctly describing the ground-state structure of the considered nuclei. Future experiments at next-generation rare isotope beam facil ities must test whether, as in 70Ge, enhanced octupole strengths can also be observed in the A = 70 isobars 70Se and 70Kr. To investigate how far the region of enhanced octupole collectivity extends, strengths should also be determined for the even lighter Ge, Se and Kr isotopes. To arrive at a sound understanding of the experimental data, more microscopic calculations, along the lines of Ref. [38] and which incorporate configuration mixing as well as triaxial degrees of freedom, are called for.