Decay spectroscopy of exotic nuclei at RIBF

Neutron-rich nuclei around the doubly magic nucleus 132Sn and the double midshell nucleus 170Dy have been investigated by means of decay spectroscopy techniques with the EURICA setup at the RIBF facility at RIKEN. The nuclei of interest were produced by in-flight fission of a high-intensity 238U beam at 345 MeV/u. In this contribution, some selected topics are reported.


Introduction
Exotic nuclei far from the valley of β stability can serve as a good probe for studying new phenomena, such as neutron skin/halo structures and appearance/disappearance of magic numbers, which emerge with largely asymmetric values of the N/Z ratio.The advent of the third-generation in-flight fragment separator facility, the RI-Beam Factory (RIBF) at RIKEN [1], enables systematic investigations of such novel nuclear properties and allows for extension of our knowledge of nuclear structures towards the neutron and proton drip lines.In that occasion, γ-ray spectroscopy following the β decay is an effective tool for probing low-lying yrast and non-yrast states, from which key information on nuclear structure, such as shape transitions/coexistence and single-particle orbits, can be obtained.For the study of rare isotopes, especially when the nucleus of interest lies at the boundaries of availability for spectroscopic studies, isomeric decays are likely to be a more useful means than β decays to populate excited levels.The combined β-γ and isomeric-decay measurements using state-of-the-art detection systems at RIBF, which has the capability of providing the world's strongest RI beams, are at the forefront of exploration of exotic nuclei far from stability.
The RIBF was commissioned in 2007, with the adoption of a sequential acceleration system consisting of a linac injector (RILAC) and four ring cyclotrons (RRC-fRC-IRC-SRC), which can provide heavy-ion beams at 345 MeV/u.The primary-beam intensity increases year by year owing to the steady improvement of the accelerators and the related devices.For instance, the intensity of a 238 U beam was lower than 0.1 pnA when the facility was commissioned, but now it can be delivered with a stable intensity higher than 20 pnA.The first decay spectroscopy experiment at RIBF was carried out in 2009 with four Compton-suppressed Clover-type Ge detectors arranged around an active stopper system consisting of nine double-sided silicon-strip detectors (DSSSD) stacked compactly.A major aim of this work was the study of neutron-rich nuclei around Z = 40 and A = 110, where the shape transitions from prolate, via γ-soft, to oblate deformations are predicted to occur with increasing the number of neutrons.New results obtained include the observation of shape evolution in 106,108 Zr [2], a possible oblateshape isomer in 109 Nb [3], and a large-amplitude γ-soft dynamics in 110 Mo [4].These findings revealed the shapetransitional phenomena in this neutron-rich region for the first time.
Research opportunities for decay spectroscopy at RIBF can be expanded in the EURICA (EUROBALL-RIKEN Cluster Array) project [5].The main body of EURICA consists of 12 Cluster-type HPGe detectors, surrounding a highly segmented silicon stopper system named WAS3ABi [5].In addition to the normal EURICA setup, 18 LaBr 3 (Ce) detectors and plastic scintillators are installed for the fast-timing measurement of γ and β rays, respectively.The aim of EURICA is to pin down currently controversial subjects in nuclear physics and nuclear astrophysics, such as the evolution of shell structures that can lead to the appearance or disappearance of the spherical magic numbers, the effect of weak binding and pairing in largely diffused neutron densities, search for stable oblate, triaxial, and higher-order deformations at low excitation energy, and the decay properties of neutron-rich isotopes relevant to the r-process nucleosynthesis.A wide range of unstable nuclei on the Segre chart are within the scope of EURICA.In this report, some selected results of the EU-RICA experimental campaigns will be introduced, highlighting γ-ray spectroscopy of exotic nuclei in the vicinity of doubly magic 132 Sn and doubly mid-shell 170 Dy.   128 Pd ions.Four γ rays at ener-gies of 75, 260, 504, and 1311 keV have been unambiguously observed.These γ rays are found to be in mutual coincidence and exhibit consistent time behavior.Therefore, we conclude that they proceed through a single cascade originating from one isomeric state.A least-squares fit of the summed gated time spectra of the isomeric-decay transitions yields T 1/2 = 5.8(8) μs.The total internal conversion coefficient (α T ) for the 75-keV transition derived from a comparison with the 1311-keV γ-ray intensity is 2.6(17), which is consistent with the theoretical value of α T = 3.88 for an E2 multipolarity.Based on these arguments, the level scheme of 128 Pd is proposed as displayed in Fig. 2, where the spin and parity of the 5.8-μs isomeric state at 2151 keV is assigned as J π = 8 + .A transition strength of B(E2; 8 + → 6 + ) = 0.22(3) W.u. can be obtained from the measured half-life of the 2151-keV isomeric state.
Assuming that the excited states in 128 Pd are the same multiplet members (with seniority υ = 2, as will be discussed later), the half-life of the J π = 6 + state is estimated to be 22(3) ns from that of the 8 + isomer.Since this value is significantly shorter than the flight time of fragments from the production target to the implantation position (∼ 650 ns), there would be little 128 Pd ions remaining at this state during the flight.Hence, the observed intensities of the four cascade γ rays should depend only on the population of the 8 + isomeric state.
The excitation energies of the J π = 2 + − 8 + states in 128 Pd are comparable to those in 130 Cd [6].The constancy of level energies is characteristic of the seniority scheme, where seniority υ counts the number of nucleons that are not in pairs coupled to spin zero.In case of a n-particle (or n-hole) system in a single-j shell, the level energies with identical J π and υ are independent of n.Thus, the excited states in 128 Pd can be interpreted in terms of the υ = 2 configuration of the πg 9/2 subshell, which locates just below the Z = 50 shell gap.
A direct implication of the N = 82 shell closure can be corroborated from the behavior of the E2 transition strength for the 8 + → 6 + isomer decay in 128 Pd.The E2 matrix elements between υ = 2 states are close to zero near the middle of the valence shell in semi-magic nuclei, giving rise to seniority isomerism.For the N = 82 isotones, it turns out that the B(E2; 8 + → 6 + ) value is much smaller in 128 Pd than in 130 Cd, as expected in the exact seniority classification, namely, B(E2; υ = 2, n = 4) = 1 9 B(E2; υ = 2, n = 2).This observation indicates that both the J π = 8 + and 6 + states in the N = 82 isotones have good seniority υ = 2 in the well isolated πg 9/2 subshell, in consequence of the robust shell closure.
The level scheme of 126 Pd constructed in the current work is also shown in Fig. 2. The 693-keV γ ray, which is the most intense peak of those observed in delayed coincidence with 126 Pd ions [Fig.1(b)], is assigned as the 2 + → 0 + transition.The coincidence spectrum with a gate on the 542-keV γ ray clearly exhibited γ rays at energies of 693, 788, and 86 keV, but not at 1330 keV, indicating that two parallel cascades stem from a common level at 2023 keV.The 86-keV transition is placed just above the 2023-  keV level, because this γ ray was observed to precede all the four transitions.
The γ rays below these isomers, except for the 86-keV line, have been also observed in coincidence with electrons that were associated with the prior implantation of 126 Pd, as demonstrated in Fig. 1(c).This observation implies the existence of a long-lived, higher-spin isomer which decays via the cascades that include electromagnetic transitions with relatively large total conversion coefficients.With gates on these γ rays, a prominent peak can be found in an electron spectrum [marked with "I" in the inset of Fig. 1(d)]; this corresponds to the conversion electrons for the 86-keV, E2 transition (α T = 2.374).In Fig. 1(d), a γray at 297 keV is clearly visible in addition to the γ rays below the (5 − ) isomer by gating on the 86-keV IC peak.
The appearance of the 297-keV peak is emphasized by taking a γ-ray time condition earlier than electron events, as is evident from the inset of Fig. 1(c), suggesting that this new γ ray precedes the highly converted 86-keV transition.Thus, the long-lived isomer can be identified at an excitation energy of 2406 keV.A peak marked with "II" in the inset of Fig. 1(d) is expected to arise from the conversion electrons for the 297-keV transition, being most likely of an E3 character (α T = 0.1197).In addition to the internaldecay branch, β decay from the long-lived isomer was observed to populate excited states at high spins in 126 Ag.The isomeric half-life was determined to be 23.0(8)ms by taking a weighted average of those derived from the time distributions of the internal-and external-decay branches.
The main surprise in the present work is the small energy difference between the (10 + ) and (7 − ) isomers, ΔE 10 + 7 − , in 126 Pd, compared to the analogous levels in the heavier N = 80 isotones, as demonstrated in Fig. 3. Since these two levels consist predominantly of maximally aligned two neutron-hole configurations, (ν1h −2 11/2 ) 10 + and (ν1h −1 11/2 2d −1 3/2 ) 7 − , their level energies depend on the singleparticle energies (SPEs) of the ν1h 11/2 and ν2d 3/2 neutron orbits, as well as the strength of interactions between them.It can be seen in Fig. 3 that the energy of the 11/2 − level relative to the 3/2 + ground state in the neighboring N = 81 isotones decreases when approaching Z = 50.Note that these states are of one neutron-hole nature, and that the smooth reduction in energy can be essentially interpreted in terms of a short-range proton-neutron interaction as follows: The π1g 7/2 proton orbit lies just above the Z = 50 shell closure.The monopole interaction between π1g 7/2 and ν1h 11/2 , a spin-flip pair with Δ = 1 and Δn = 0, is stronger than the π1g 7/2 -ν2d 3/2 pair, due to the larger overlap between the radial wave functions of the two orbits.Therefore, when emptying the π1g 7/2 subshell, the ν1h 11/2 orbit is relatively less bound than the ν2d 3/2 one.The moderation in the slope at higher Z may be ascribed 7 − , in N = 80 (filled circles) and between the 11/2 − and 3/2 + states in N = 81 (filled squares).For Z ≤ 50, the differences in energy between the 1h 11/2 and 2d 3/2 neutron orbits calculated by V MU interaction [8] and ΔE 10 + 7 − by shell-model (SM) calculations with monopole corrections (MC) are also depicted.
to the partial occupation of the π2d 5/2 orbit, which exerts a weaker (stronger) monopole interaction on the ν1h 11/2 (ν2d 3/2 ) neutrons than π1g 7/2 .As is evident from the comparison in Fig. 3, a similar trend is observed for ΔE 10 + 7 − .This finding supports that these isomers can serve as sensitive probes for the evolution of the constituent neutron shell orbits.
Below Z = 50, protons in the π1g 9/2 subshell play a major role in changing the neutron SPEs, because this orbit is near the Fermi surface.The neutron SPEs are estimated by the monopole-based universal interaction, V MU , which consists of the Gaussian central force and the tensor force based on the π+ρ meson exchanges, using the parameters fixed in Ref. [8].The V MU interaction has been applied to other regions of exotic nuclei and successfully reproduced various types of the shell evolution [8]. Figure 3 shows the evolutions of the relative 11/2 − energy starting from the experimental value in 131 Sn, predicted by the V MU calculation with A = 130.In the calculation, the π1g 9/2 subshell is considered to be well isolated between Z = 50 and 40.In Fig. 3, only with the central force the 11/2 − energy rapidly decreases to negative values as the proton number decreases, indicating that the ν1h 11/2 orbit moves away from the ν2d 3/2 one towards the N = 82 gap.If there is the tensor force effect, however, the slope becomes less steep.The observed reduction in ΔE 10 + 7 − from 130 Sn to 126 Pd is consistent with the expectation of V MU including both the central and tensor forces, given the same trend as the 11/2 − relative energies.Based on these findings, it can be concluded that the tensor force slows down the upward drift of the ν1h 11/2 SPE when protons are removed from the π1g 9/2 orbit below 132 Sn.

Decay spectroscopy of neutron-rich rare-earth isotopes
It is well known that rare-earth isotopes beyond N = 90 have well-deformed prolate shapes.According to the fundamental phenomenon of the nuclear collectivity being enhanced as the number of valence nucleons increases, it is conjectured that the maximum ground-state deformation occurs in dysprosium-170 ( 170 Dy: Z = 66, N = 104), which lies at the middle of the major shells for both proton and neutron between the well-established doubly closedshell isotopes 132 Sn (Z = 50, N = 82) and 208 Pb (Z = 82, N = 126).In the actual nuclei, however, the stability of shape should be influenced by the presence of sub-shell closures, residual interactions, and possibly, the neutron excess.Therefore, well-deformed nuclei in this neutronrich region can serve as a benchmark for testing nuclear mean-field model calculations.
Concerning astrophysical interest, it has been suggested that the decay properties of deformed nuclei in this neutron-rich region, such as neutron emission probabilities and β-decay rates, play a significant role in forming a pygmy peak around A = 160 in the r-process solar abundance distribution [9].This is the so-called the rare-earth element (REE) peak, which appears between the prominent r-process peaks at A ≈ 130 and 195.While it is understood that the main r-process peaks are due predominantly to the "waiting point" nuclei arising from the competition between slow neutron-capture rates and long βdecay lifetimes at the neutron closed shells, the REE peak appears far away both from the proton and neutron shell closures, suggesting the presence of a different mechanism for its formation.In this context, the nuclear deformation in this neutron-rich region is considered to significantly affect the REE peak formation.However, it is still unclear how the nuclear shape evolves and where the deformation maximum takes place in the double midshell region because spectroscopic information on the excited states remains scarce due to the difficulties in access to this neutron-rich region.Theoretical models that are often used as input for r-process calculations can not reproduce the experimentally measured deformations very well.Thus, the REE peak can serve as a unique probe of the rprocess nucleosynthesis, despite its less abundance than the other major peaks at A ≈ 130 and 195, and better knowledge on the evolution of collectivity in this region is required.
The major aim of the present work is to scrutinize the structural evolution of Dy isotopes in the double midshell region by means of γ-ray spectroscopy following isomer and β decays, with particular attention to the physics cases and observables characteristic of deformed nuclei as outlined below:

Low-lying levels in even-even isotopes
Spectroscopic study of low-lying levels in even-even nuclei provides significant information on nuclear shapes and the resulting collective motions.According to the global systematics, it is empirically known that the deformation parameter β is inversely proportional to the square root of the first 2 + level energy E(2 + 1 ) [10], while the R 4/2 = E(4 + 1 )/E(2 + 1 ) ratio represents the rigidity limits of quadrupole collectivity being either rotational (∼ 3.33) or vibrational (∼ 2.0). Figure 4 shows the evolution of the low-spin states in the Dy isotopic chain.Inspection of the 2 + 1 and 4 + 1 states indicates that the vibrational → rotational phase transition takes place around A = 88, and the R 4/2 values approach the rigid-rotor limit towards the middle of the neutron shell.
Low-lying non-yrast states are sensitive probes for microscopic structure of deformed nuclei.In general, the second 2 + states ( 2 + 2 ) are associated predominantly with the bandhead of the γ-vibrational band.A qualitative explanation for the occurrence of the γ-vibrational K π = 2 + state at relatively low excitation energy can be given in terms of the single-particle orbits in the deformed potentials; the operator r 2 Y 22 acts on the single-particle states occupying a specific Nilsson orbit Ω[Nn z Λ] which satisfies the selection rule, ΔN = Δn z = 0 and ΔΛ = ΔΩ = ±2, giving rise to the γ-vibrational motions in the collective dynamics.In the region of interest, there are several pairs of orbits that meet the r 2 Y 22 selection rule near the proton and neutron Fermi surfaces.The wave function of the 2 + 2 state consists of a number of such two-quasiparticle excitations, which coherently contribute to the γ-vibrational amplitudes.Meanwhile, the interpretation of the excited 0 + states (0 + 2 ) is rather complicated because there are several origins of the K π = 0 + excitations like the β vibration, pairing excitations, two-γ-phonon vibration, and intruder states.The K π = 2 − states observed in the even Dy isotopes are interpreted as the band head of the octupole vibrational band with the predominant component π

K-forbidden decays from multi-quasiparticle states (K isomers)
The region of well-deformed nuclei around A = 170 − 180 (Z ∼ 70, N ∼ 110) is known for the existence of lots of K isomers [11,12], including those with half-lives longer than one hour.K quantum number is defined as the projection of the total nuclear spin on the symmetry axis of the deformed nucleus.In addition to the spin selection rule, electromagnetic transitions connecting the states with different K values (ΔK) are required to fulfill a selection rule that the multipole order of the transition λ is equal to or greater than ΔK, namely, λ ≥ ΔK.However, this K-conservation law is often violated due to various sources of symmetry breaking, such as Coriolis effects and softness in terms of the γ (axially-asymmetric) degree of freedom, and hence strongly hindered transitions can take place.Such K-forbidden transitions are evaluated practically in terms of a reduced hindrance f ν = F 1/ν , where F = T 1/2 (γ)/T W 1/2 represents a hindrance relative to the Weisskopf single-particle estimate of the decay half-life, with the degree of K-forbiddenness defined by ν = ΔK −λ.It is known empirically that the value of f ν ranges from 30 to 200 when K is well sustained for both the initial and final states.
High-Ω orbits near the Fermi surface can contribute to the emergence of high-K isomers at relatively low excitation energy.In general, a large (and robust) axial deformation yields good conditions for the formation of high-K isomeric states.Thus, the discovery and characterization of such high-K multi-quasiparticle states will shed light on various aspects of nuclear structure, such as intrinsic orbits near the Fermi surface, paring and other residual interactions, and the degree of axial symmetry in deformed nuclei.Furthermore, it is likely that high-K isomers decays through low-lying excited levels not only in the groundstate band, but also in deformed-vibrational bands which represent crucial information for understanding the evolution of deformed structure.
This work focuses particularly on isomeric states that are expected to appear in 170 Dy (N = 104) with K π = 6 + and in 172 Dy (N = 106) with K π = 8 − .The near-stability N = 104 isotones are well known to have K π = 6 + isomers [13], which are interpreted as being based on the two-quasineutron configuration ν 2 7/2 − [514] ⊗ 5/2 − [512].Configuration-constrained potential-energy-surface calculations for the K π = 6 + configuration predict the analogous isomer at about 1.2 MeV in 170 Dy [14].The large deformation and high degree of axial symmetry, predicted for both the two-quasineutron K π = 6 + state and groundband members to which the isomer decays, suggest that this nucleus may represent an extremely good example of a "pure" K isomer [14].Considering the N = 106 isotones, K π = 8 − isomers which decay via an E1 transition to the yrast 8 + state have been identified over a broad range of proton number [13].The K π = 8 − configuration is interpreted as the two-quasineutron configuration ν 2 7/2 − [514] ⊗ 9/2 + [624].Based on the systematic behavior of the hindered E1 decays [15], it is expected that the E1 transition which de-excites the K π = 8 − isomer in 172 Dy will have a reduced hindrance of f ν ≈ 100, resulting in a half-life of a few seconds.This is expected to be comparable to that of the ground state in this neutron-rich region, presumably leading to competition from β decay in the isomer decay.
Neutron-rich rare-earth nuclei around A = 170 were produced by in-flight fission of a 238 U 86+ beam at 345 MeV/u with the intensity of 12 pnA on average, impinging on a beryllium target with a thickness of 5 mm.The nuclei of interest were separated through the BigRIPS separator based on their physical and magnetic properties [16].For purification of the secondary beams, wedge-shaped aluminum degraders with thicknesses of 4.5 and 1.0 mm were installed at the first (F1) and second (F5) dispersive focal planes, respectively.Identification of particles with the atomic number (Z) and the mass-to-charge ratio (A/Q) was achieved on the basis of the ΔE-TOF-Bρ method, in which the energy loss (ΔE), time of flight (TOF), and magnetic rigidity (Bρ) were measured using the focal-plane detectors on the beam line.The secondary beams were transported with two different settings of the slits on the beam line; one is optimized for 170 Dy 66+ , and the other for 172 Dy 66+ .The obtained particle-identification spectra are shown in Fig. 5.About 8.3×10 3 172 Dy ions were identified through the BigRIPS spectrometer.
The identified particles were implanted into a highly segmented active stopper system, named WAS3ABi [5], which consisted of two double-sided silicon-strip detectors (DSSSD) stacked compactly.Each DSSSD had a thickness of 1 mm with an active area segmented into sixty and forty strips (1-mm pitch) on each side in the horizontal and vertical dimensions, respectively.The DSSSDs also served as detectors for electrons following β-decay and internal conversion (IC) processes.Gamma rays were detected by the EURICA spectrometer [5], which consisted of twelve Cluster-type detectors, each of which contained seven HPGe crystals packed closely, which were developed for the former EUROBALL array.The γ-ray measurements were carried out with a time condition up to 100 μs relative to the trigger signal generated either from a plastic scintillation counter placed at the end of the beam line or from WAS3ABi.The beam, electron, and γ-ray events were timestamped and recorded by independent data-acquisition systems.For the analysis of beam-γ delayed coincidence, the γ-ray data sets were combined with those of the beam particles on an event-by-event basis using information on the time stamp.Isomeric states with (sub)microsecond were identified with appropriate time gates.Meanwhile, all data sets containing beam, electron, and γ-ray events were used for β-γ and IC-γ coincidence analyses, in which the implantation of an identified particle was associated with the subsequent electron events that were detected in a given correlation area in the DSSSDs where the beam particle was implanted.Decay half-lives (T 1/2 ) in the millisecond range were extracted from the time distributions of γ-ray gated electron events with respect to the fragment implantation.
Figure 6 exhibits a γ-ray spectrum measured in coincidence with electrons within 4 seconds after implantation of fully-stripped 172 Dy ions.It is expected that the observed γ-ray spectrum consists of the transitions not only following the β decay from the ground state, but also deexciting the long-lived K π = 8 − isomer that is predicted for the N = 106 isotone as mentioned above.It will be possible to distinguish the internal and external decays by gating on time and energy spectra of electrons detected in the DSSSDs.The detailed analysis is still ongoing.

Figure 1 (
Figure1(a) shows a γ-ray energy spectrum measured in delayed coincidence with128 Pd ions.Four γ rays at ener-

Figure 1 .
Figure 1.Gamma-ray spectra measured (a) in coincidence with 128 Pd ions within a time range of 0.15−25 μs, (b) in coincidence with 126 Pd ions within 0.15−5 μs, and (c) within 50 ms after the 126 Pd implantation with a gate on an electron-γ time difference of −0.5 ≤ Δt eγ ≤ 0.5 μs.Contaminants from the granddaughter 126 Cd are marked with filled circles.The inset magnifies the energy region from 230 to 310 keV measured with −4.0 ≤ Δt eγ ≤ 0.5 μs (red) and −0.5 ≤ Δt eγ ≤ 50 μs (blue).(d):γ rays measured with −4.0 ≤ Δt eγ ≤ 0.5 μs, and additionally, with a gate on the electron peak marked with "I" in the inset, where the spectrum depicted with the red line (multiplied by a factor of ten) is obtained with a sum of gates on the γ rays below the (5 − ) isomer in 126 Pd, while the blue line represents an electron spectrum without γ-ray gates.

Figure 4 .
Figure 4. Systematic of the low-lying levels in even-even Dy isotopes.

Figure 6 .
Figure 6.Gamma-ray spectrum measured in coincidence with electrons within 4 s after implantation of fully-stripped 172 Dy ions.