Decay studies of the long-lived states in $^{186}$Tl

Decay spectroscopy of the long-lived states in $^{186}$Tl has been performed at the ISOLDE Decay Station at ISOLDE, CERN. The $\alpha$ decay from the low-spin $(2^-)$ state in $^{186}$Tl was observed for the first time and a half-life of $3.4^{+0.5}_{-0.4}$ s was determined. Based on the $\alpha$-decay energy, the relative positions of the long-lived states were fixed, with the $(2^-)$ state as the ground state, the $7^{(+)}$ state at 77(56)~keV and the $10^{(-)}$ state at 451(56) keV. The level scheme of the internal decay of the $^{186}$Tl($10^{(-)}$) state ($T_{1/2} = 3.40(9)$ s), which was known to decay solely through emission of 374 keV $\gamma$-ray transition, was extended and a lower-limit for the $\beta$-decay branching $b_\beta>5.9(3)\%$ was determined. The extracted retardation factors for the $\gamma$ decay of the $10^{(-)}$ state were compared to the available data in neighboring odd-odd thallium isotopes indicating the importance of the $\pi d_{3/2}$ shell in the isomeric decay and significant structure differences between $^{184}$Tl and $^{186}$Tl.

Decay spectroscopy of the long-lived states in 186 Tl has been performed at the ISOLDE Decay Station at ISOLDE, CERN. The α decay from the low-spin (2 − ) state in 186 Tl was observed for the first time and a half-life of 3.4 +0. 5 −0.4 s was determined. Based on the α-decay energy, the relative positions of the long-lived states were fixed, with the (2 − ) state as the ground state, the 7 (+) state at 77(56) keV and the 10 (−) state at 451(56) keV. The level scheme of the internal decay of the 186 Tl(10 (−) ) state (T 1/2 = 3.40(9) s), which was known to decay solely through emission of 374 keV γ-ray transition, was extended and a lower-limit for the β-decay branching b β > 5.9(3)% was determined. The extracted retardation factors for the γ decay of the 10 (−) state were compared to the available data in neighboring odd-odd thallium isotopes indicating the importance of the πd 3/2 shell in the isomeric decay and significant structure differences between 184 Tl and 186 Tl.

I. INTRODUCTION
Neutron-deficient nuclei around the neutron midshell N = 104 are interesting study cases from the nuclear structure point of view. This region of the nuclear chart is characterized by the occurrence of shape coexistence in atomic nuclei [1], a phenomenon, whereby different shapes coexist within one nucleus at low energy and which is interpreted as arising from proton excitations across the Z = 82 proton shell closure. These coexisting structures have been observed in laser spectroscopy * marek.stryjczyk@kuleuven.be [2][3][4][5], α-and β-decay [6][7][8][9][10] and Coulomb excitation [11] studies.

arXiv:2006.02161v1 [nucl-ex] 3 Jun 2020
Studying the decay pattern of the 10 − isomers in Tl isotopes can reveal information on the decay of the intruder based states in this region of the nuclear chart [8]. However, in the case of 186 Tl, the 10 (−) state is known to decay only through emission of a 374 keV γ ray [13], while, as observed in 184 Tl, the decay pattern is expected to be more complex, including multiple paths of internal decay, as well as α decay [8,9].
In this paper we present an extension of the isomeric decay scheme of the 186 Tl(10 (−) ) state, the observation of the α decay of the 186 Tl(2 − ) state and the relative positions of the three long-lived states in 186 Tl. The results of the β-decay study of all three long-lived states will be published elsewhere [14].

II. EXPERIMENTAL SETUP
The experiment was performed at ISOLDE, CERN as a part of a campaign dedicated to measure the decays of 182,184,186 Tl. A pure beam of 186 Tl was produced through spallation of a thick UC x target by 1.4 GeV protons, provided by the Proton Synchrotron Booster. The proton pulses (PP) were delivered every 1.2 seconds (or a multiple of this value) and grouped into the CERN proton supercycle structure (SC), whose length varied during the experiment from 20 to 40 PP. The produced thallium atoms effused from the target to a hot cavity, where they were selectively ionized in a two-step ionization process by the Resonance Ionization Laser Ion Source system [15]. The first step excitation was performed through the 6p 2 P 1/2 → 6d 2 D 3/2 transition at 276.83 nm using a dye laser system. For the second step the output from a Nd:YAG laser at 532 nm was used (details of the laser schemes are given in [15]). After the ionization, the ions were extracted from the ion source at 30 keV energy and separated with respect to their mass-to-charge ratio by the High Resolution Separator [16]. To allow for the implantation of the thallium isotopes, a beam gate was open for 90 ms after each PP. The purified beam was implanted onto an aluminized mylar tape at the center of the ISOLDE Decay Station (IDS) [17]. After every SC, the tape was moved in order to remove daughter activities.
The SPEDE spectrometer was installed in the IDS decay chamber for the detection of conversion electrons and α particles [18]. It consists of 24-fold segmented, 1-mm thick annular silicon detector, which was cooled by circulating ethanol at about −20 o C. It was situated at 15 mm distance in the backward direction of the beam, in front of the tape (see Fig. 1) and it covered about 14% of the solid angle. Behind the tape, a 0.5-mm thick 900 mm 2 PIPS silicon detector for the detection of β particles was placed. Outside the IDS chamber, there were five High-Purity Germanium Clover detectors (HPGe) used to detect the γ radiation. The γ energy and efficiency calibrations were performed by using an encapsulated 152 Eu source and a 138 Cs sample produced on-line and implanted onto the tape. At 1408 keV the energy resolution was 2.7 keV and the absolute γ efficiency was 1.95(6)%. The SPEDE spectrometer energy calibration was performed using strong transitions with known energies from the decays of 182,184,186 Tl and 138 Cs for electrons and by using known α decays of 184 Tl and 184 Hg for α particles. The electron energy resolution was 6.3 keV at 288 keV and the α energy resolution was about 190 keV at 6 MeV. All signals were collected in triggerless mode by using the Nutaq digital acquisition system [19] with 100 MHz sampling frequency.

III. RESULTS
A. α decay of the (2 − ) state Figure 2 shows the α-decay energy spectrum registered by the SPEDE spectrometer during the experiment. Due to a limited energy resolution, it was not possible to resolve the fine structure α decays. Based on the: (i) systematic trend of the α-particle energies (see Figs. 1 and 9 in Ref. [9]), (ii) the previous experimental measurements of the α decay of 186 Tl and 186 Hg [20,21], and (iii) the behavior of the peak intensity as a function of time, the peak around 5.7 MeV was associated with the α decay of 186 Tl, while the peak at around 5.1 MeV stems from a weak ground-state to ground-state α-decay of 186 Hg to 182 Pt (branching ratio b α = 0.016(5)%, E α = 5094 (15) keV [21]).
In total, six γ-ray transitions have been observed in coincidence with the α particles associated with the decay of 186 Tl (see Table I and Fig. 3). Four of them, 104 keV, 129 keV, 144 keV and 273 keV transitions, were previously observed and placed in the level scheme in the 182 Hg to 182 Au β-decay study [22]. Based on the α- γ-γ coincidences (see Fig. 4), the newly identified 141 keV transition was placed on top of the 129 keV level, while the 202 keV transition remains unplaced. The decay scheme is presented in Fig. 5.
Two levels at 129 keV and 273 keV known from the β-decay study of 182 Hg(0 + ) are both suggested to have spin 1 or 2 and a negative parity [22]. The feeding of these low-spin levels in the α decay of 186 Tl suggests a low spin for the α-decaying state, despite the fact that this state has a similar half-life to the 10 (−) state (see Sec. III C). The existence of such level, with spin-parity (2 − ), has been proposed from the α-decay studies of 190 Bi [12]. Therefore, we suggest that the observed γ-ray transitions  To check the possible α decays of the other long-lived states in 186 Tl, the number of counts in the α-decay spectra gated on the 129 keV and 273 keV γ-ray transitions were compared to the number of counts in the single-α energy spectrum. To remove the influence of the 5094 keV α particles from the 186 Hg decay, the comparison range was set between 5.4 and 6.5 MeV. Both γ-gated spectra were corrected by the detection efficiency and by the total conversion coefficient calculated using BrIcc [24]. The 202 keV transition was not included because it is unplaced in the decay scheme while the 141 keV and 144 keV transitions were not included to avoid double counting of the α particles since they feed the 129 keV level. Furthermore, the 104 keV transition was not used for gating, because it may also originate from the decay of the (7 + ) state in 182 Au [25]. To account for this feeding, the α energy spectrum gated on the 129 keV transition was corrected by the total intensity of the 104 keV transition, 32(3)%, from the 182 Hg β-decay studies [22]. From this comparison, the γ-gated-α counts can reproduce 105(7)% of the total number of α counts in the The 25 keV transition has not been observed, however, it is known from the β-decay studies [22]. The spin-parity of the 182 Au ground state is taken from Ref. [23] while the spin assignments of the excited states and the placement of the γray transitions are taken from Ref. [22], with an exception of the newly observed 141 keV transition (plotted in red). The spin-parity of 186 Tl is taken from Ref. [12] and the half-life comes from our analysis.
single-α energy spectrum suggesting that the vast majority of the registered α decays originates from the (2 − ) state (see Sec. IV A).
Based on the measured α-particle energies with a gate on the 129 keV γ-ray transition, the energy of the α decay feeding the 129 keV level was determined to be E α = 5670(51) keV (see Fig. 6) and it corresponds to the Q α,tot = Q α + E γ = 5924(52) keV. Due to limited statistics, it was not possible to fit the α energies feeding other states. The extracted Q α,tot and the atomic masses of 4 He and 182 Au [26,27] allowed us to calculate the atomic mass of the 186 Tl(2 − ) state 185978582(60) µu and to compare it with the atomic mass of the 186 Tl(7 (+) ) state (185978664.2(67) µu [27,28]). Our analysis indicates that the (2 − ) state is the ground state and the 7 (+) level has an excitation energy of 77(56) keV. Based on our result and the α-particle energies [6,12], it was also The single γ-ray energy spectrum (Fig. 7) shows the 374 keV transition previously assigned to the 10 (−) → 7 (+) decay [13]. By using γ-γ coincidences, another decay cascade deexciting through an 18 keV transition was established. Furthermore, a β-decay channel of the 10 (−) state was identified.
The 267 keV γ-ray transition has been observed in coincidence with thallium K α X-rays (Fig. 8), as well as in coincidence with a γ-ray energy gate set between 89 and 90 keV (Fig. 9). These results are consistent with the α-decay study of 190 Bi, where the 267 keV γ-ray transition was proposed to deexcite the x + 356 keV level to the x + 89.5(4) keV state [6,12]. These observations also imply that the x + 374 keV level deexcites through an 18 keV transition to the x + 356 keV state. In the present work, the other γ-rays deexciting the x+356 keV level [6] were not observed; the 75 keV transition overlaps with the background lead K α X-rays, while the 281 keV and the 356 keV transitions overlap with strong γ rays in 186 Hg. The proposed decay scheme is presented in Fig.  10.
The γ-ray intensities of the 267 keV and 374 keV transitions were extracted from the single γ-ray energy spectrum (see Fig. 7 and Table II). To estimate the total intensity of the 18 keV transition, the spectrum shown in Fig. 6c of Ref. [6] was analyzed. The peaks at 267 keV, 281 keV and 356 keV contained ≈60 counts, ≈20 counts and ≈54 counts, respectively. The detection efficiencies a Estimated based on the data presented in [6], see text for details. b Calculated using BrIcc [24] assuming given multipolarity. c Average value of conversion coefficient for pure M 1 and pure E2 transition, calculated using BrIcc [24].
for the 281 keV and the 356 keV transitions were 98% and 86% relative to the efficiency for the 267 keV transition, respectively, following the calibration provided in Ref. [30]. To estimate the contribution from the internal conversion, all three transitions were considered to be pure M 1 or pure E2 which resulted in the total feeding of the x + 356 keV state being equal to 1.8(2)% and 1.4(2)%, respectively. Since the true transition multipolarities are not known, 1.6(4)% was adopted as the total intensity of the 18 keV transition.
To determine the possible β-decay branch from the 10 (−) state in 186 Tl, the feeding to the known high-spin states (≥ 9) in 186 Hg was analyzed. It was assumed that both, direct and indirect, feeding of these states origi-nates only from the decay of the 186 Tl 10 (−) state. In total, six high-spin states in 186 Hg have been observed in our study: the 10 + state at 2078.1 keV, the (9 − ) at 2427.6 keV, the (9) at 2573.8 keV, the 12 + at 2620.1 keV, the (10 + ) at 2636.4 keV and the 10 + at 2833.6 keV. By comparing the feeding to these states with the isomeric decay, a β branching equal to 5.9(3)% was extracted. It should be noted that the presented method allows us to estimate only the lower limit for the β branching since we observed decays of several states with the unknown spins [14], which can be also fed through the decay of the 10 (−) state.

C. Half-lives of the (2 − ) and 10 (−) states
The half-life of the 10 (−) state was obtained by simultaneously fitting an exponential function to the number of the γ rays and the K conversion electrons stemming from the 374 keV transition (Fig. 7) plotted as a function of time (Fig. 11). The fitting range was set from 400 to 7000 ms after the PP and the likelihood function was built assuming that all the points are following a Poisson distribution. The results of the fit are presented in Fig. 11 (red and blue curves). The obtained value of T 1/2 (10 (−) ) = 3.40(9) s is in agreement with 4.5(13) s reported in Ref. [31] and 3(1) s reported in Ref. [32], however, it is more than 2σ away from the 2.9(2) s reported in Ref. [13].
FIG. 8. The background-subtracted γ-γ spectrum gated on the thallium X-rays. A negative background is related to much higher intensity of the Hg Kα X-rays. Two dips at 251 keV and 356 keV are related to the subtraction of the strong γ-rays from the decay of 186 Hg to 186 Au and 186 Tl to 186 Hg, respectively. In the inset, a portion of the singleγ energy spectrum with the gate region (dark gray) and the background region (light gray) used to create the γ-ray energy spectrum shown, is plotted. FIG. 9. The background-subtracted γ-γ spectrum gated on the γ rays between 89 and 90 keV. In the inset, a portion of the single-γ energy spectrum with the gate region (dark gray) and the background region (light gray) used to create the γ-ray energy spectrum shown, is plotted.  are presented in Fig. 11 (green curve). The extracted half-life is equal to 3.4 +0. 5 −0.4 s. This value was compared to the results obtained from the fitting of the exponential function to the time distribution of the α particles with energies between 5.4 and 6.5 MeV (Fig. 11, purple curve). The extracted half-life of 4.16(10) s is larger, but in agreement within 2σ. The discrepancy might be explained by a small admixture of the α particles from the long-lived 186 Tl(7 (+) ) state (T 1/2 = 27.5(10) s [29]), thus we adopted T 1/2 = 3.4 +0. 5 −0.4 s as the half-life of the (2 − ) state. However, we note that the expected admixture should be small, which was presented by comparing the number of single-α and α-γ events (see Sec. IV A).

IV. DISCUSSION
A. α-decay of the (2 − ) state Because of the limited α-energy resolution and the inability to extract the b α value from the current data set, it was not possible to determine the reduced α-decay widths. Nevertheless, some conclusions can be drawn from the presented results.
The population of the low-spin states in 182 Au is consistent with the pattern observed in the α-decay studies of the neighboring isotope 184 Tl, where the low-spin state has a higher α-decay branching than the high-spin state. In 184 Tl, b α (2 − ) = 1.22 (30)%, compared to 0.47(6)% for the 7 (+) state and 0.089(19)% for the 10 (−) state [9].
In-beam studies [25] revealed the existence of two bands in 182 Au built on top of isomeric states with proposed spins and parities of (6 + ) and (10 − ). Thus, it cannot be excluded that the 10 (−) state in 186 Tl is α decaying directly to the (10 − ) isomer in 182 Au, without emission of a γ ray.
In the case of the possible α decay of the 186 Tl(7 (+) ), it could decay to the 182 Au(7 + ) state and then deexcite by emission of a 104 keV γ ray to the (6 + ) isomeric state. However, a γ ray with the same energy is emitted from the decay of the 129 keV state in 182 Au, known from the β-decay study of 182 Hg [22]. The γ-intensity ratio of the 104 keV to 129 keV obtained from this work (0.24 +0.05 −0.04 ) is in agreement with the ratio extracted from the β-decay study (0.23(2) [22]) and suggests that the majority of the 104 keV transition originates from the α-decay of the 186 Tl(2 − ) state. However, it should be noted that the 104 keV transition (from the 129 keV level to the 25 keV level) is known to be E1 [22] with a total theoretical conversion coefficient α tot (E1) = 0.376(11) [24], while the 104 keV (7 + ) → (6 + ) transition would be a mixed M 1/E2 transition with α tot (E2) = 4.42(19) and α tot (M 1) = 6.49(21) [24]. Thus, it cannot be excluded that the 186 Tl(7 (+) ) state has an α-decay branch. This would be consistent with the observed difference between half-lives obtained from the α particles and α-γ events, however, the 5(7)% excess intensity of α-γ events compared to the single-α events indicates that this branching  [8,34]. The retardation factors for 186 Tl should be treated as a lower limit since the β-decay branching ratio is given only as a lower limit.

Isotope
Eγ ( The isomeric character of the 374 keV state suggests that M 2 or E3 are possible multipolarities for the 18 keV transition. For any higher multipolarity, the intensity of the 18 keV transition would be negligible compared to the 374 keV E3 transition. Retardation factors F w , which are defined as a ratio of the Weisskopf estimate and the experimental transition strength, favor E3 multipolarity for the 18 keV compared to M 2. The latter would lead to F w = 3.5(10) × 10 7 which is at least two orders of magnitude higher compared to the similar transitions in the neighboring isotopes (see Table III). Thus, the 18 keV transition is proposed to have multipolarity E3 and, consequently, the spin (7 + ) has been tentatively assigned to the state at x + 356 keV. This spin assignment is also supported by the α-decay study of 188,190 Bi to 184,186 Tl [6]. A reduced α-decay width to the x + 356 keV level in 186 Tl (δ 2 α = 0.11(3) keV) obtained in Ref. [6] is similar to the reduced α-decay width feeding the 320 keV level in 184 Tl (δ 2 α = 0.16(6) keV), which has been proposed to be the (7 + 2 ) state, see Fig. 12. The measurements of the magnetic moments indicated that 186 Tl(7 + 1 ) is dominated by the [πs 1/2 ⊗νi 13/2 ] 7 + configuration, while 184 Tl(7 + 1 ) should have a ≈20% admixture from a [πd 3/2 ⊗ νi 13/2 ] 7 + configuration [3,35]. This admixture can explain the difference in the retardation factors of the 506 keV and 374 keV E3 transitions (Table  III). In both 184 Tl and 186 Tl the dominant configuration of the 10 − intruder state was determined from the magnetic moment measurements to be [πh 9/2 ⊗ νi 13/2 ] 10 − [2, 3] and from a single-particle approach, the transition between the πh 9/2 and πd 3/2 requires a smaller angular momentum change (∆ = 3) compared to the transition between the πh 9/2 and πs 1/2 (∆ = 5). This change was proposed in Ref. [8] to be the reason for the 374 keV transition in 186 Tl being retarded by an order of magnitude more, relative to the 506 keV transition in 184 Tl. In contrast, the retardation of the 10 − → 7 + 2 transitions  12. (Color online) Systematic information from the α-and isomeric decay studies in 184,186 Tl. Next to each α transition, the energies and the reduced decay widths calculated using the Rasmussen formalism [33] are presented. The color code represents the main underlying proton single particle configuration as interpreted from magnetic moment measurements and systematics configurations [2,3,8] with the states involving the πs 1/2 orbital plotted in blue, the πd 3/2 orbital plotted in green, and the πh 9/2 orbital plotted in red. The energies of the excited states in thallium isotopes are shifted to set the 7 + 1 states at 0. Experimental data are taken from our analysis and Refs. [2,3,6,8] in 184 Tl and 186 Tl are within the factor of two similar (note the large experimental uncertainties). This can be explained as due to a substantial contribution of the proton d 3/2 component in these 7 + 2 states.

V. CONCLUSIONS
The decay of the long-lived states in 186 Tl was studied at ISOLDE, CERN. The existence of the (2 − ) state was confirmed and its half-life of 3.4 +0. 5 −0.4 s was determined for the first time through the observation of its α decay. Six γ-ray transitions were measured in coincidence with the α decay of 186 Tl, which allowed the construction of an α-decay scheme feeding the levels in 182 Au.
Based on the α-decay energy, the 7 (+) state in 186 Tl was positioned 77(56) keV above the (2 − ) ground state and the (10 − ) level in 190 Bi was placed 182(57) keV above the (3 + ) ground state. The decay scheme of the 186 Tl(10 (−) ) state was extended, the half-life of 3.40(9) s was measured and a limit for the β-decay branching ratio has been deduced. The more detailed internal decay pattern observed for the 10 (−) state is consistent with the 'intruder' origin of the isomer and follows a clear trend throughout the thallium isotopic chain. Based on the E3 retardation factors for the 10 (−) → 7 (+) transitions, as well as additional information from bismuth α-decay studies, the x + 356 keV state was tentatively assigned with (7 + ) spin. A comparison with a neighboring isotope of 184 Tl indicated significant differences in the structure of the 7 + states.

ACKNOWLEDGMENTS
We acknowledge the support of the ISOLDE Collaboration and technical teams. This project has received funding from the European Unions Horizon