Investigations of the structures of the Ru isotopes: 98Ru

As part of a systematic study of the nuclear structure of the Ru isotopes, 98Ru was investigated via the β-decay of 98Rh at iThemba LABS, and the 100Ru(p, t) reaction at the Maier-Leibnitz Laboratory. The combined data results in significant revision of the previous spin assignments and clarification of the nature of levels in 98Ru, as well as providing insights into the evolution of the structures across the Ru isotopic chain.


Introduction
The Ru isotopes lie in a region where the structure of the ground states can undergo a very rapid change as a function of neutron number.The Sr and Zr isotopes undergo the most rapid transition known across the nuclear landscape; those with N < 60 have very weakly-deformed or spherical shapes, and those with N ≥ 60 have rather well-deformed ground states [1,2].The appearance of low-lying excited 0 + states at N = 60 in Sr and Zr has been associated with shape coexistence, and consistent with this is the observation of enhanced ρ 2 (E0) values observed for the 0 + 2 → 0 + 1 transitions [3].The spectroscopic quadrupole moment, Q s , of the 2 + 1 state in 96 Sr is consistent with zero, as expected for a spherical shape, and a moderate B(E2; 2 + 1 → 0 + 1 ) value of 17.3 +4.0 −3.2 W.u. [4,5].A low-lying rotational band is also observed, but it remains unclear if it should be associated with the 0 + 2 or 0 + 3 state.In 98 Sr, matrix elements extracted from a Coulomb excitation study [4,5] were sufficient to determine the invariant Q 2 values for both the ground state and the 0 + 2 state, along with the Q s values for the 2 + 1 and 2 + 2 levels.For the ground state, the extracted β deformation parameter indicates a large deformation with β 2 = 0.5 (1).For the 2 + 2 state, the Q s value is consistent with zero, and the Q 2 (0 + 2 ) value is dramatically smaller (0.33(3) e 2 b 2 ) than that for the ground state (1.30(4) e 2 b 2 ), suggestive of a crossing of the 0 + 1 and 0 + 2 configurations between 96 Sr and 98 Sr [4,5].In the Zr isotopes, rotational bands with enhanced in-band B(E2; 2 + → 0 + ) values have been observed in 94 Zr [6] and 96 Zr [7], and a rotational band has been suggested in 98 Zr (see, e.g.Ref. [8]).The prevailing view is that the strongly deformed excited configuration for N < 60 becomes the ground state at N = 60, while the spherical or weakly-deformed ground states for N < 60 becomes excited states at N = 60.
Progressing to higher Z, the Mo isotopes also have well established shape coexistence.In 96 Mo, the 0 + 2 state has a much smaller value of Q 2 than the ground state [9].In 98 Mo, these become nearly equal [10], but the cos 3δ values indicate that the ground state is triaxial while the 0 + 2 state is prolate [10].For 100 Mo, the Q 2 values for the 0 + 1 and 0 + 2 states increase substantially, with that for the 0 + 2 exceeding the ground state value and the cos 3δ values mirror those of 98 Mo [11].Associated with this evolution, the ρ 2 (E0; 0 + 2 → 0 + 1 ) values also increase substantially with increasing neutron number [3].
The Ru isotopes show a much smoother evolution in their structure.Indeed, crossing N = 60, there does not appear to be dramatic change in the nature of the ground state.The Ru isotopes with neutron number N ≥ 60 have a definite deformed structure.The Coulomb excitation study of 104 Ru performed by Srebrny et al. [12] provided a precise set of the invariant quantities Q 2 and Q 3 cos 3δ .For the ground-state band, the values are approximately constant up to the 8 + 1 level and correspond to β 2 ≈ 0.28 and a triaxial shape with γ ≈ 25 • [12].For the 0 + 2 level the Q 2 corresponds to β 2 ≈ 0.21, indicating substantially smaller deformation, and cos 3δ corresponding to γ = 28(6) • [12].
The structures of the Ru isotopes with N < 58 have often been discussed in terms of spherical vibrational motion.A recent survey [13] of previously claimed [14] multi-phonon spherical vibrational nuclei, that cited many examples in the Z = 40 − 50 region including some Ru isotopes, found that few viable candidates remained.In fact, it was only 98,100 Ru where a spherical vibrational nature could not be excluded.The 0 + 2 , 2 + 2 , and 4 + 1 levels lie in close proximity to each other at approximately twice the energy of the 2 + 1 state and would indeed appear to be good candidates for the two-phonon states.The structure of 98 Ru was investigated by Cakirli et al. [15], who concluded that the three-phonon (or higher) states could not be assigned in 98 Ru, and thus if 98 Ru were vibrational, the pattern appeared to terminate at the two-phonon level.The most recent experimental study by Giannatiempo et al. [16] concluded that the IBM-1 description was inadequate and that a large number of states were of mixedsymmetry character requiring an IBM-2 description [17].
Urban et al. [18] studied 102 Ru and established the higher-spin members of the 0 + 2 band.It was suggested [18] that there are two relatively unperturbed configurations for the 0 + states at N = 52 which evolve differently with N (see Fig. 5 of Ref. [18]).The first configuration forms the ground state in 96 Ru that has a nearly spherical shape.The deformation of this configuration remains approximately constant with N and always small, and at N = 60 becomes the excited 0 + 2 band.The second configuration is the 0 + 2 state in 96 Ru, and also possesses low deformation that increases with N .These two configurations cross in the vicinity of 100,102 Ru such that the deformed second configuration becomes the ground state band in 104 Ru.As a result of the mixing near the crossing, both 0 + states take on deformed characteristics.
We have initiated studies of the Ru isotopes to understand their evolving structure, and the evolution of deformation with increasing Z between the Z = 40 subshell closure and the Z = 50 shell closure.To date, this has involved: a) γ-ray spectroscopy following the β-decay of 98,100 Rh at the iThemba LABS facility, b) γ-ray spectroscopy following 99,101 Ru(n th , γ) capture reactions using the FIPPS facility of the Institute Laue-Langevin, Grenoble, c) the Coulomb excitation of 102 Ru by 12 C and 16 O beams performed using the Q3D magnetic spectrograph of the Maier-Leibnitz Laboratory at Garching, d) the Coulomb excitation of 100 Ru with a 32 S beam performed at the Heavy Ion Laboratory, Warsaw, and e) a series of measurements with direct reactions that included the 100,102 Ru(p, t) two-neutron-transfer reactions, and the 103 Rh(p, α) and 103 Rh(d, 3 He) proton transfer reactions.Herein, we report results on experiments on which we have initially focused: the β decay of 98 Rh to 98 Ru and the 100 Ru(p, t) reaction.

Study of 98
Ru γ-ray spectroscopy following β decay is an excellent tool for the observation of weak decay branches from excited states since the backgrounds present in the spectra are much lower than typically observed for in-beam experiments.We sought to utilize the β-decay of Rh to study Ru, however Rh, being a refractory element, is not available from ISOL-style radioactive beam facilities.We thus used for this purpose the newly commissioned iThemba Tape Station which appeared ideal.Shown in Fig. 1 is a schematic of the facility.Originally designed to use the Recoil Shadow technique to capture fusion-evaporation residues on the tape, the reactions that we chose to employ, the 12 C+ 89 Y→ 101 Rh * → 98 Rh+3n and 14 N+ 89 Y→ 103 Pd * → 100 Ru+p2n reactions would not lead to sufficient recoil energies and angular dispersion to result in a significant deposit on the tape.Taking advantage of the relatively long half lives of the βdecaying states involved, which in the case of 98 Rh are 8.72 (12) min for the (2 + ) ground state, and 3.6(2) min for the (5 + ) isomer, we thus modified the infrastructure to be able to transport the Y target and its holder from the target chamber to the counting chamber.The tape, in essence, acted like a slow rabbit transport.The 89 Y target was bombarded with 47.5 MeV 12 C ions with a current up to 8 pnA for 18 minutes, and the transport to the counting station was approximately 2 minutes in duration after which the activity was counted for 18 minutes, and Figure 1.Schematic drawing of the iThemba Tape Station.The cylindrical chamber on the left is the target chamber where the irradiation takes place, the center chamber houses the spools and drive motors for the tape, and the rightmost chamber is the counting station housing the Si(Li) detector, the plastic scintillator, and is surrounded by the HPGe detectors.assigned as feeding the 2 + 1 state from, in order of their excitation energy, 2246-keV, 2277-keV, 2362-keV, and 2371-keV states.The remaining peaks in the spectrum are resulting from γ-rays feeding higher-lying states.These levels will be discussed in more detail below.
The statistics obtained in the experiment were insufficient to perform γ-γ angular correlations for the levels of interest, however, spin-parity values of states could be obtained from a complementary (p, t) reaction study.In an experiment performed using the Q3D spectrograph of the Maier-Leibnitz Laboratory, the 100 Ru(p, t) 98 Ru reaction was performed using 22 MeV proton beams with currents up to 2 µA on a 100 Ru target 110 µg/cm 2 thick.Figure 4  portion of the triton spectrum observed at an angle of 10 • corresponding to the 98 Ru excitation energy range from 2.2 -3.1 MeV.Since the two-neutron-transfer reaction strongly favours the transfer of a di-neutron in a relative S = 0 state, when performed on a J π = 0 + target, the final states populated have J π = L (−1) L , i.e., natural parity.Unnatural parity states may be populated, but extremely weakly and are usually unobservable in the spectra unless very high statistics are collected.Thus, all the peaks present in Fig. 4 are expected to correspond to natural parity states in the final nucleus, and their cross section angular distributions, examples of which are shown in Ref. [19] for the 2013-and 2427-keV levels that were consistent with an L = 4 transfer assignment, give the J π value of the populated state.The analysis of the angular distributions indicates that the 2246-keV state has a definite 2 + assignment, the 2277-keV state is a 3 − state, the 2361-keV level is a 0 + state, the 2371-keV level has spin 2 + , and the 2468-keV level is populated with angular distribution consistent with spin 2 + .There is no evidence from the (p, t) reaction data for levels at 2241, 2258, 2266, 2295, 2406, and 2435 keV.The results from Ref. [16] indicate two levels in the vicinity of 2370 keV; at 2362.5(3) keV and 2371.3(2)keV in good agreement with our observations, and no evidence for a level at 2435 keV.Furthermore, consistent with Ref. [16], we have no evidence for additional levels at 2369 keV or 2374 keV.The remaining levels listed above thus are candidates for unnatural parity.Interestingly, the 5 + level at 2547 keV, which fits well into the systematics of the γ-band members, as shown in Ref. [19], was observed in the (p, t) reaction, albeit weakly and with an angular distribution that does not match those of other levels with known J π values.The appearance of this peak in the spectra, however, indicates that the spin assignment may be incorrect.
Figure 5 gives the results of the present investigations of the levels below 2.5 MeV excitation energy.Further study is required to characterize the states not already assigned to band-like structures, especially the unnatural-parity state candidates.

Summary
The level scheme of 98 Ru has been studied by the β-decay of 98 Rh, as well as the 100 Ru(p, t) reaction.Substantial revision of the spin assignments of levels has resulted with a significant impact on the interpretation of the nuclear structure. 98Ru is no longer a candidate for spherical vibrational motion.Additional measurements will be required to further clarify the level scheme, especially above 2 MeV.The present study is the first in a series of new experiments aimed at studying the evolution of structure in the Ru isotopic chain.

Figure 4 .
Figure 4. Portion of the triton spectrum observed at θ = 10 • following the 100 Ru(p, t) reaction using a beam of 22 MeV protons.The prominent peaks are labelled with the corresponding excitation energies of 98 Ru in keV.
[16]lays a Revised level scheme for 98 Ru taking into account observations from the 100 Ru(p, t) reaction.The levels highlighted in red were not observed in the (p, t) reaction, and thus are candidates for unnatural parity states.The 2241-, 2258-, and 2295-keV levels, reported in Ref.[16]were not observed in our β-decay study.The 2369-, 2374-, and 2435-keV levels (light gray) are concluded not to exist.Spin assignments in blue are resulting from the present study.