Identification of the J = 1 state in 218Ra populated via decay of 222Th

Citation for published version (APA): Parr, E., Smith, J. F., Greenlees, P. T., Smolen, M., Papadakis, P., Auranen, K., Chapman, R., Cullen, D., Grahn, T., Grocutt, L., Herzberg, R-D., Hodge, D., Jakobsson, U., Julin, R., Juutinen, S., Konki, J., Leino, M., McPeake, C. G., Mengoni, D., ... Uusitalo, J. (2016). Identification of the J = 1 state in 218Ra populated via decay of 222Th. Physical Review C (Nuclear Physics), 94, [014307]. https://doi.org/10.1103/PhysRevC.94.014307


I. INTRODUCTION
The phenomenon of octupole collectivity in atomic nuclei has been a topic of theoretical and experimental investigation for over half a century [1][2][3][4][5][6]. Proton and neutron orbitals with ∆l = ∆j = 3 give rise to an enhancement of the octupole part of the nucleon-nucleon interaction. This can result in collective behaviour such as octupole vibrations or, in nuclei with stronger octupole correlations, reflection-asymmetric octupole deformations, with possible evidence for the latter case recently obtained from direct measurements of B (E 3) strengths [7]. The part of the nuclear chart where the largest octupole correlations are expected is the lightactinide region around N ∼ 134 and Z ∼ 88. The ground states of nuclei in this region have been predicted to evolve from spherical at N = 130, to quadrupoleoctupole deformed around N = 134 before possessing just quadrupole-deformed shapes close to N = 140 [8]. Experimental determination of the boundaries of this possible octupole-deformed region is important to guide theoretical predictions of the strength of octupole correlations and validate those which agree.
The N = 130 nucleus 218 Ra is of interest in this regard since it lies in the transitional region between the spherical nuclei, just above the N = 126 neutron shell closure, and the region of nuclei with expected octupole components of their deformation at N ∼ 134 and Z ∼ 88. The ground state of 218 Ra is expected to be spherical [8], but it has been shown that at high spins, the yrast states form an alternating-parity sequence, with enhanced E1 transitions between the positive-and negative-parity states [9][10][11][12][13]. This high-spin structure is characteristic of strong octupole correlations, and it has been suggested that the octupole shape in this nucleus is stabilised by rotation [12,14]. The low-lying negative-parity states in 218 Ra, specifically, those with J π = 1 − and 3 − , can thus offer valuable insight into the development of octupole collectivity in this region as a function of N , and also as a function of angular momentum.
In the 1980s, Gai et al. [10] tentatively assigned the J π = 1 − state with an excitation energy of 713 keV, approximately 80 keV below the established J π = 3 − level. This observation was consistent with the interpretation that the states result from α-particle clustering, fitting well with the theoretical predictions of α-cluster models [15]. However, subsequent in-beam γ-ray spectroscopy experiments could not reproduce this observation; Wieland et al. [13] stated that no energy levels were present between the J π = 2 + and 3 − states, in contradiction to the level scheme proposed by Gai et al., and that the J π = 1 − state, therefore, presumably lies above the J π = 3 − state. This ordering of the lowenergy negative-parity levels would contradict the theory of α-particle clustering but would be consistent with an octupole-vibrational picture. Gai, however, replied [16] suggesting that the experiment performed by Wieland was not optimised to search for the J π = 1 − state and that their non observation was not enough to warrant their conclusions.
The new results presented in this paper are from the investigation of low-energy negative-parity states of 218 Ra, populated following the α decay of 222 Th. Previous studies of the α decay of 222 Th [17][18][19][20][21] have shown that it proceeds via a ground state ( 222 Th) to ground state ( 218 Ra) transition with E α = 7980(2) keV [21] and via a ground state ( 222 Th) to J π = 2 + excited state ( 218 Ra) transition with E α = 7599(2) keV [21]. In the present work, α decays from the ground state of 222 Th to the J π = 3 − and tentatively proposed 1 − states of 218 Ra have been observed for the first time.

II. EXPERIMENTAL DETAILS
In the present work 222 Th nuclei were produced in the fusion-evaporation reaction 208 Pb( 18 O,4n) 222 Th with a beam energy of 95 MeV, a target thickness of 0.45 mg cm −2 and a 0.1 mg cm −2 carbon degrader foil. The experiment was performed at the Accelerator Laboratory of the University of Jyväskylä, Finland. An average beam intensity of ∼18 pnA was used for a duration of ∼157 hours. The target was located at the centre of the SAGE spectrometer [22], which is used to detect prompt γ rays and internal conversion electrons; however, data from the SAGE spectrometer were not used for the results discussed here. The recoiling nuclei were separated from fission fragments and unreacted beam ions using the RITU gas-filled recoil separator [23,24] and were subsequently implanted into two double-sided silicon-strip detectors (DSSDs), which are part of the GREAT spectrometer [25] located at a focal plane of RITU. The two DSSDs each consisted of 40 horizontal and 60 vertical strips giving a total of 4800 individual detector pixels. An array of 28 silicon PIN diode detectors were located upstream of the DSSDs positioned to detect charged particles that were emitted out of the DSSDs. A multi-wire proportional counter (MWPC), which is normally placed at the entrance of GREAT to measure the energy loss and time-of-flight of recoils, was not used in this work due to the low recoil energies of the 18 O + 208 Pb reaction products. An array of three HPGe clover detectors surrounding the DSSDs was used to detect γ and X rays emitted by decaying implanted recoil nuclei.

III. DATA ANALYSIS
The DSSDs were calibrated using α particles emitted by implanted nuclei, or those in their subsequent decay chains, produced during the experiment. The α particles used were from 210 Po [E α = 5304.33 (7) (5) keV]. The absolute efficiency for the detection of γ rays in the focalplane clover detectors as a function of γ-ray energy was established by comparing the intensities of α particles in the DSSDs with intensities of γ-ray transitions in αγcoincidence data.
The α decays of 222 Th nuclei were selected by correlating either two (recoil-α) or three (recoil-α-α) signals within a single pixel of the DSSDs. Chronologically, the signals corresponded to: (i) the recoiling 222 Th nucleus entering the DSSD; (ii) the α particle emitted following the decay of 222 Th, with a time gate up to 16 ms (∼ seven half-lives); and (iii) the α particle emitted following the decay of 218 Ra, with a time gate set up to 180 µs (∼ seven half-lives). When measuring the 222 Th α-particle energies, signals in the PIN detectors of GREAT were used to veto any coincident DSSD signals, hence removing from the spectra some of the partially deposited energies from escaping α particles. However, when using the 218 Ra α decays to identify a recoil-α-α chain, no PIN detector veto or energy gate was used so as to include the escaping α particles.
Signals in the DSSDs were assumed to be due to implanting recoils, and therefore vetoed as α decays, if a γ ray or conversion electron was detected in the SAGE spectrometer at a time preceding the DSSD signal. A two-dimensional gate was set for the veto over the recoils time-of-flight through RITU (∼ 2 µs) and their energy distribution in the DSSD (∼ 2 MeV). This somewhat compensated for the absence of a MWPC at the entrance of GREAT.
The data analysis was performed using the GRAIN software [26], which was developed for use with data acquired by the Total Data Readout system.

IV. RESULTS
Coincidences between α particles and γ rays were studied following the selection of a recoil-α chain and are shown in Fig. 1(a). The α particles of 222 Th were identified with the help of the diagonal lines shown on the αγ-coincidence spectrum. The lines represent a constant energy for the sum of the α-decay Q value, calculated from the α-particle energy, and the γ-ray energy. They are equal to the Q values between the 222 Th ground state and the ground state, Q[0 + ( 222 Th)→0 + ( 218 Ra)] (dashed line), and J π = 2 + state, Q[0 + ( 222 Th)→2 + ( 218 Ra)] (dotdashed line), of 218 Ra. In Fig. 1(a) the αγ coincidences assigned to three α decays of 222 Th to excited states in 218 Ra are circled and labelled, with contaminant coincidences from 213 Rn, 219 Ra and 221 Th also indicated. The α-particle energies, E α , branching ratios, b α , and hindrance factors, f , (defined in Section V A) of the four α decays identified from 222 Th along with the spins, parities and energies of states populated in 218 Ra are given in Table 1. Figure 2 shows the level scheme of 218 Ra populated by the α decay of 222 Th with the proposed J π = 1 − state included. In the present work, the halflife of the 222 Th ground state has been measured to be T 1/2 = 1.964 (2) ms. This value is lower than the previ-ous measurements of 4(1) ms [17] The α decays from the ground state of 222 Th to the ground state and the 2 + state at 389 keV of 218 Ra have previously been established, with α-particle energies of 7980(2) and 7599(2) keV, respectively [21]. In the present work, the α decay which directly populates the ground state of 218 Ra was observed with energy 7986(3) keV and branching ratio 98.16(5)%. Only random coincidences between these α particles and background γ rays were observed. The α decay to the 2 + state of 218 Ra has been observed in the present work with energy 7603(3) keV and branching ratio 1.81(1)%. These 7603-keV α particles can be seen in Fig. 1(a) in coincidence with the 389-keV 2 + →0 + γ ray. As expected, these coincidences appear on the In Fig. 1(a) coincidences between 222 Th α particles with E α = 7205(4) keV, and γ rays with energies 389 and 404 keV are indicated. The 7205-keV α particles are identified as being from 222 Th by their half-life and that of the subsequent 218 Ra decays. Figure 1(b) shows the γ rays in coincidence with the 7205-keV α-particles, contaminant coincidences are present from the escaping α decays of 219 Ra (316 keV) and 221 Th (331 keV). The intensity of the 389-keV γ ray in coincidence with the 7205-keV α particle is larger than that of the 404-keV γ-ray coincidences, when taking into account detector efficiencies and conversion coefficients. This is presumed to be due to false coincidences between 389-keV γ rays and the more abundant 7603-keV α particles which have escaped from the DSSD without depositing their full energy. From the spectrum of α-particle energies in coincidence with the 389-keV γ rays it is difficult to establish that 7205-keV α particles are present. However, γγ coincidence analysis of the spectrum in Fig. 1(b) reveals one coincidence event between the 389-and 404-keV γ rays in a virtually background free spectrum. This single count would be expected when considering the intensity of the 404-keV γ ray and the efficiency of the detector array.
C. α decay to the J π = 1 − state Coincidences between α particles with E α = 7143(4) keV, and γ rays with energy 853 keV are indicated on Fig. 1(a). Again, the 7143-keV α particles were identified as being from 222 Th by their half-life and that of the subsequent 218 Ra α decays. Figure 1(c) shows γ rays in coincidence with 7143-keV α-particles; contaminant coincidences are present from escaping α decays of 221 Th (576 keV) and 219 Ra (592 and 806 keV). The problem of contaminant αγ coincidences from 213 Rn, which has a similar γ-ray energy, was overcome by requiring a recoil-α-α tag. Figure 1(d) shows the αγ spectrum where the 213 Rn αγ coincidences are removed by the recoil-α-α requirement; six counts in the 222 Th αγ cluster remain. These coincidences appear on the Q[0 + ( 222 Th)→0 + ( 218 Ra)] line, so it is probable that the state populated by the α decay then de-excites directly to the ground state of 218 Ra. This gives a state in 218 Ra at 853 keV, which has not previously been observed. No evidence was found that this state at 853 keV decays to the 2 + state at 389 keV.
The hindrance factor, f , of the α decay populating the 853-keV state is similar to that populating the J π = 3 − state. It is therefore assumed that the two states have a similar underlying structure, as described in Section V A. As no negative-parity state is known at 853 keV it is proposed as a candidate for the J π = 1 − state in 218 Ra. This proposed assignment is not in agreement with the previous tentatively assigned J π = 1 − state at 713 keV [10]. Also, population of the 1 − state by α decay would be expected from consideration of the intensity with which the J π = 3 − state is populated. It should be pointed out that no αγ coincidences with γ rays of 713 keV were observed in the present data.

A. α-decay hindrance factors
The hindrance factor of an α decay is the ratio of its experimentally observed partial half-life to the partial half-life calculated using a simple model where the preformed α particle exists in the potential of the daughter nucleus [27]. This eliminates the Q-value dependence of the decay rate and quantifies the relationship between the wavefunctions of the initial state in the mother and the final state in the daughter nuclei; a greater overlap gives a lower hindrance factor. The hindrance factor of a ground-state-to-ground-state α decay for an even-even nucleus is set to unity, meaning that hindrance factors can also be considered as a measure of the similarity of the ground state and excited state of a daughter nucleus populated by an α decay. Figure 3 shows the hindrance factors of α decays to the first J π = 1 − and 3 − states in even-even isotopes of Th, Ra and Rn around the region of expected octupole collectivity [28][29][30][31][32][33][34]. Here, the J π = 1 − and 3 − states in 218 Rn have been assigned as the 840.2-and 796.9-keV levels respectively, observed following α decay [35]. These levels were not observed using in-beam spectroscopy following a multi-nucleon transfer reaction [36], however, a negative-parity band was established down to J π = 5 − . The levels are presently assigned to have J π = 1 − and 3 − from their decay branches to the 0 + , 2 + and 4 + members of the ground-state band [35].
If the low-lying negative-parity states were the result of rotation of a reflection-asymmetric nuclear shape then they would be different projections of the reflectionasymmetric ground state. The reduction of the hindrance factors for decreasing N below 140 has therefore previously been interpreted as the onset of intrinsic reflection asymmetry [37]. In this work, a reversal of this trend is observed at N = 130 for Ra isotopes, possibly suggesting a departure from static octupole deformations in these nuclei in which the states are no longer described as rotational. This would be consistent with predictions of a near-spherical ground state at N = 130 [8] and can be interpreted as a low N boundary to the region of groundstate octupole deformations in the light actinides. An increase in hindrance also occurs at N = 132 for the Rn isotopes which has previously been noted in Ref. [38]. The possibility of α-particle clustering in the actinides has been proposed in Ref. [39]. In this model, lowlying negative-parity states arise from the mixing of the ground-state quadrupole band and a dipole phonon produced by oscillations between the α-particle cluster and the remaining core. In even-even nuclei this gives positive-and negative-parity states with the J π = 1 − state lying below the 3 − . Energies of the 1 − and 3 − states produced by this α-particle clustering mechanism in Ra and Th were calculated by Daley and Iachello [15] and were shown to agree with the available experimental data for even 218−228 Ra and 222−230 Th. The comparison included the tentative assignment for the J π = 1 − state in 218 Ra at 713 keV, 81 keV below the J π = 3 − state [10]; a result contradicted by the present work. The inverted ordering of the J π = 1 − and 3 − levels suggests that neither α-particle clustering or rotation of an asymmetric ground state are responsible for the low-lying negative parity states in 218 Ra. In this context, it should also be noted that the anomalously large reduced α-decay width of 218 Ra, cited as further evidence for α-particle clustering, has subsequently been contradicted [13,21,40,41].
The evolution of low-lying negative-parity octupolevibrational states moving from spherical to quadrupoledeformed systems is well understood [42]. In spherical nuclei, negative-parity states can be produced by the 2 + ⊗ 3 − multiplet of the coupled quadrupole and octupole vibrational phonons [43,44]. The J π = 1 − state of the multiplet has E(1 − ) ≃ E(2 + ) + E(3 − ) and therefore appears above the 3 − phonon state. In nuclei with static quadrupole deformation the 3 − octupolevibrational phonon couples with this deformation [45]. This produces four states with K π = 0 − , 1 − , 2 − and 3 − where K is the projection of the phonon angular momentum onto the nuclear symmetry axis. These states are the band heads of four octupole-vibrational bands, of which those with K π = 0 − and 1 − have a lowest energy state with J π = 1 − . Therefore in moving from a spherical to a well-quadrupole-deformed nucleus the relative ordering of the 1 − and 3 − states will reverse.
A study of the systematics of the low-lying negativeparity states observed in both the even-even lanthanides (Z ≃ 56, N ≃ 90) and light actinides (Z ≃ 88, N ≃ 136) was carried out by Cottle and Bromley [46]. By plotting E(3 − )−E(1 − ) against E(4 + )/E(2 + ) for the nuclei in the lanthanide region, it was shown that the behaviour is consistent with that expected for the octupole-vibrational description of the low-lying states, as shown in Fig. 3(a) of Ref. [46]. However, the interpretation of the results for the Rn, Ra and Th nuclei was less conclusive due to the 218 Ra data point not matching the expected trend for the octupole-vibrational description. Figure 4 shows the variation of E(3 − ) − E(1 − ) with E(4 + )/E(2 + ) for the nuclei 224−232 Th, 218−228 Ra and 218−222 Rn [28][29][30][31][32][33][34] with the present result for 218 Ra replacing that tentatively assigned by Gai et al. [10]. The new data point is consistent with that expected for an octupole vibrational description of the states in 218 Ra, and also across the light actinides.
Predictions by Nazarewicz and Olanders [8] give a picture of octupole vibrations about a spherical nuclear shape for 218 Ra and rotation of an asymmetric ground state when increasing the neutron number to N ≃ 134. The evolution of the relative positions of the 1 − and 3 − states, as shown in Fig. 4, is not only consistent with the evolution of octupole-vibrational states in an increasingly quadrupole deformed system, but could also be said to be consistent with the predicted onset of rotational states of an octupole-deformed ground state. Evidence for this second scenario is also provided by the evolution of the hindrance factors presented earlier.

VI. SUMMARY
In summary, a state with an excitation energy of 853 keV has been identified in 218 Ra and proposed as a candidate for the J π = 1 − state. This observation was made following the identification of α decay of 222 Th to both the proposed 1 − state and 3 − state in 218 Ra by means of αγ coincidence analysis. The hindrance factors of these α decays are larger than those populating analogous states in nuclei with larger N . This then reverses the trend in the Ra isotopes, of decreasing hindrance fac-tor as the neutron number is reduced. These observations are presented as possible evidence for a boundary to the region of static octupole deformations in the radium isotopes. The excitation energy of the 1 − state above that of the 3 − state is presented as an indication that octupole vibrations produce these low-energy levels, as opposed to α-particle clustering or rotations of a reflection-asymmetric ground state. The data for the Th, Ra and Rn isotopes are also consistent with a picture of octupole vibrations of a near-spherical ground state at N = 130, moving to rotations of a reflection-asymmetric ground state at N = 134.   (4) FIG. 1. Energies of coincident α particles and γ rays following the decay of 222 Th. Panel (a) shows the coincidences when requiring a recoil-α correlation. The diagonal lines represent a constant energy for the sum of the α-decay Q value, calculated from the α-particle energy, and the γ-ray energy; The energies are those between the 222 Th ground state and the ground state (dashed) and 2 + state (dot dashed) of 218 Ra. Panels (b) and (c) show the γ rays in coincidence with α-particle energies of 7205 keV and 7143 keV, respectively. Panel (d) shows the αγ coincidences when requiring a recoil-α-α correlation, as discussed in the text.