Characterizing the atomic mass surface beyond the proton drip line via a-decay measurements of the s1/2 ground state of 165Re and the h11/2 isomer in 161Ta

The a-decay chains originating from the s1/2 and h11/2 states in 173Au have been investigated following fusion-evaporation reactions. Four generations of a radioactivities have been correlated with 173Aum leading to a measurement of the a decay of 161Tam. It has been found that the known a decay of 161Ta, which was previously associated with the decay of the ground state, is in fact the decay of an isomeric state. This work also reports on the first observation of prompt g rays feeding the ground state of 173Au. This prompt radiation was used to aid the study of the a-decay chain originating from the s1/2 state in 173Au. Three generations of a decays have been correlated with this state leading to the observation of a previously unreported activity which is assigned as the decay of 165Reg. This work also reports the excitation energy of an a-decaying isomer in 161Ta and the Q-value of the decay of 161Tag.


I. INTRODUCTION
Proton and α-decay Q-value measurements provide important information on the nuclear mass surface far from the valley of β stability. There are many examples of long chains of α decays between nuclear ground states which, if connected to a nuclide of known mass excess, would allow the mass excesses of nuclei beyond the proton drip line to be determined. Often these nuclei are too shortlived or too weakly produced to be measured directly by precision methods such as Schottky mass spectrometry or Penning trap mass spectrometry.
A representative example of direct relevance to the present study is the work of Poli et al. [1], who measured proton and α-particle emission from the πs 1/2 ground state and πh 11/2 isomeric state in 177 Tl. As illustrated in Fig. 1, the daughter of 177 Tl proton decays is 176 Hg. The α-decay Q-values of the decay chain of 176 Hg are known down to 152 Er, which decays to 148 Dy the mass of which is known from Penning trap measurements [2]. The experimental data therefore allowed the mass excesses of the πs 1/2 ground states and πh 11/2 isomeric states of 177 Tl, 173 Au, 169 Ir and 165 Re to be deduced. The mass excesses of 152 Er, 156 Yb and 160 Hf were subsequently measured directly using Schottky mass spectrometry [3] and the values obtained were consistent with those deduced from the mass excess of 148 Dy and the relevant α-decay Q-values.
In the present work, the known α decay of 161 Ta is shown to be correlated with the α decays of the πh 11/2 states in 173 Au, 169 Ir and 165 Re, indicating that it also originates from a πh 11/2 -based state, rather than a πs 1/2based state as had been previously assumed [4]. This establishes the complete α-decay chain from the πh 11/2 isomeric state in the proton-unbound 177 Tl down to the corresponding state in 149 Ho, which constitutes the ground state of this nuclide [5]. In addition, a previously unobserved radioactivity has been correlated with the α decay of the ground states of 173 Au and 169 Ir indicating that this new decay originates from the πs 1/2 -based ground state of 165 Re. As the masses of both 148 Dy [2] and 149 Ho [3] have been measured, this study not only provides a cross check of the mass excesses deduced in Ref. [1] but, perhaps more importantly, allows the Qvalue of the α decay of the πs 1/2 -based state in 161 Ta and the energy difference between this state and the πh 11 based state to be deduced.

II. EXPERIMENTAL DETAILS
The 173 Au nuclei were produced via fusion-evaporation reactions induced by the bombardment of a 0.5 mg/cm 2 92 Mo target of 97 % isotopic enrichment with a beam of 84 Sr 16+ ions. The Sr beam was provided by the K130 cyclotron of the Accelerator Laboratory of the University of Jyväskylä with an energy of 392 MeV for approximately 140 hours and 400 MeV for approximately 145 hours with an average beam current of 150 enA. The change in beam energy was performed with an aim to increase the production of 173 Hg [6] nuclei which was the primary aim of the experiment.
At the target position, 34 high-purity Ge detectors, ten of EUROGAM Phase 1 type [7] and 24 clover detectors [8], were positioned to facilitate the detection of prompt γ radiation. The recoiling fusion-evaporation residues (recoils) were separated from the unreacted beam using the RITU He-filled magnetic separator [9] and were transported to the RITU focal plane where the GREAT spectrometer [10] was located. Here the recoils traversed an isobutane-filled multi-wire proportional chamber (MWPC) before implanting into one of two 300 µm-thick double-sided Si strip detectors (DSSD). The average rate of recoil implantations was found to be ≈ 150 Hz across both of the DSSDs. In addition to the MWPC and the DSSDs, the GREAT spectrometer comprised a box of 28 Si PIN diode detectors, a planar Ge detector and four clover-type Ge detectors. The MWPC provided energy loss and (in conjunction with the DSSDs) time-of-flight information, which was used to separate the recoils from any residual scattered beam. The signals from all detectors were passed to the Total Data Readout aquisition system [11] where they were time stamped with a precision of 10 ns to facilitate temporal correlations between the implantation of recoils in the DSSDs and their subsequent radioactive decays. The data were analysed using the Grain software package [12].

III. EXPERIMENTAL RESULTS
A. Alpha decay of 173 Au m There are considerable experimental challenges in establishing decay correlations with low-Z members of αdecay chains. Firstly, the relatively long half-lives mean that correlations can become obscured by interfering radioactivities produced as a result of competing reaction channels. Secondly, low α-decay branching ratios mean that large samples of parent nuclei are typically needed to facilitate such studies. However, these are generally produced with rather lower cross sections than their descendents thus further compounding the difficulties of studying long α-decay chains.
In the present study, approximately 190,000 recoilα( 173 Au m ) events were produced in order to provide a sufficient sample of correlated 169 Ir m , 165 Re m and 161 Ta m α decays. The decay chain was analysed by selecting 173 Au m α decays occurring within 100 ms of a recoil being implanted into the same DSSD pixel. All decays fulfilling this criterion are shown in Fig. 2(a). The only other conditions imposed on the search for subsequent decays were that they all had to have been observed in the same pixel and within 15 s of the implantation. The energy of the α particles corresponding to the decay of 173 Au m was found to be 6739 (15) keV which is in good agreement with the error-weighted mean of previous measurements of this activity [13]. It is worth noting at this point that the DSSDs were calibrated using α lines at 5407, 6038 and 6315 keV corresponding to the known activities of 170 Os [14] (not visible in Fig. 2(a)), 174 Pt [15] and 172 Pt [16], respectively. In addition to the energy measurement the difference in time between each recoil implantation and the detection of 173 Au m α decays was recorded and the distribution was fitted using the leastsquares method. The half-life of this radioactivity was measured to be 12.2(1) ms which is consistent with previous measurements [13].
The first decays observed following the 173 Au m α decays are shown in Fig. 2(b). The dominant peak in this spectrum has an energy of 6120 (14) keV which is consistent with previous measurements of the α decay of an isomeric state in 169 Ir. The half-life of this decay was measured using a similar method to the 173 Au m activity except in this case the difference in time between the 173 Au m and 169 Ir m α decays were recorded. A least-squares fit to this distribution yielded a half-life of 280(1) ms which is in good agreement with previous studies [1]. A branching ratio of 78(6) % was measured for the α decay of this state which agrees well with the value of 84(8) % reported by Poli et al. [1]. In addition to the main peak, a further two, relatively weak, peaks can be seen in Fig. 2(b) which have been identified as resulting from the α decay of the ground states of 173 Pt and 172 Pt. These nuclei represent the most prominent α decays observed in this study and their presence in the spectra of Fig. 2(b) can be understood as a consequence of the incorrect correlation of 173 Au m α decays with implanted 173 Pt and 172 Pt nuclei. This also explains the appearance of a peak associated with the α decay of 173 Pt in Fig.s 2(c) and (d).
Shown in Fig. 2(c) are those decays observed following the detection of a 173 Au m α decay occurring within 100 ms of an implanted recoil and the subsequent detection of an 169 Ir m α decay, all in the same pixel. The dominant peak in this spectrum has a measured energy of 5520(6) keV which is in good agreement with the previous observations of the decay of 165 Re m [17]. A halflife of 1740(60) ms was measured for this activity which is in good agreement with earlier work [17]. In addition, a branching ratio of 13(1) % was measured which agrees well with the value of 13(3) % established in earlier work [18]. Fig. 2(d) shows all decays which were preceded by an α decay within 100 ms of the implantation of a recoil followed by the sequential observation of the α decays of 169 Ir m and 165 Re m . The dominant peak in this spectrum has an energy of 5142(6) keV. The energy of this activity is in good agreement with the previously reported value for the α decay of 161 Ta (5148(5) keV [4]). The maximum-likelihood method [19] was used to fit the time distribution between the detection of 165 Re m and 161 Ta α decays and has yielded a half-life of 4.5 (11) s. This value is consistent with previous measurements [17]. The branching ratio for the α decay of this state was found to be 7(3) %. This represents the first occasion that this ratio has been reported as a result of an experimental measurement. The measured value is in good agreement with the estimated branching ratio of 5 % [4].
B. Alpha decay of 173 Au g Previous measurements of the energy of the α decay of the ground state of 173 Au have yielded an error-weighted mean value of 6683(9) keV [13]. The proximity of this line to that corresponding to the decay of the 173 Au isomeric state means that isolating the α-decay chain associated with the 173 Au ground state is problematic. To aid the analysis, prompt γ rays feeding the 173 Au ground state were investigated. Fig. 3(a) shows a backgroundsubtracted spectrum of prompt γ rays observed at the target position in delayed coincidence with α particles having an energy consistent with the decay of the ground state of 173 Au. The γ-recoil-α( 173 Au g ) events were only considered if the α particle was detected within 150 ms and in the same pixel as the implanted recoil. Three γ rays, of energies 207, 327 and 726 keV, have been identified for the first time as feeding the ground state of 173 Au. A 173 Au g α-tagged γγ matrix was also constructed and Fig. 3(b) shows those γ rays observed in coincidence with the 327 keV transition. Although this spectrum demonstrates that the 327 and 726 keV transitions are mutually coincident, it has not been possible on the basis of the present data to construct a level scheme. Fig. 4(a) shows decays occurring within 100 ms of the implantation of a recoil with the added condition that they were also in delayed coincidence with either a 327 or 726 keV γ ray detected at the target position. The relatively low γ-ray detection efficiency (∼ 5 %) at the target position, combined with the background introduced by Compton scattering, ensures that this gating technique is not sufficiently selective to isolate the 173 Au g α decays but has the effect of enhancing them (compare Figs. 2(a) and 4(a)). The 173 Au g α decays have been measured to have an energy of 6688 (14) keV and using the least-squares method the half-life of the activity was found to be 26.3 (12) ms. Both the energy and half-life values measured here agree well with previous measurements [1]. Fig. 4(b) shows those decays observed to follow 173 Au g α decays which occurred in the same pixel and within 100 ms of the implantation of a recoil. The two peaks in this spectrum correspond to α decays with energies of 6019 (14) and 6120 (14) keV. These values are consistent with the previously reported energies for the decay of the ground state and an isomeric state of 169 Ir, respectively. A low-energy tail on the 173 Au m peak, arising from a combination of escaping α particles and the effects of radiation damage on the Si detectors, results in a spectrum which contains both 169 Ir g and 169 Ir m α decays. The number of 169 Ir m α decays present in Fig. 4(b) is consistent with the number of 173 Au m α decays included in the gate used to identify the α decay of the ground state of 173 Au. (b) all second-generation decays following the detection of a 173 Au g α decay occurring within 100 ms of a recoil implantation in the same pixel and with the same γ-ray conditions as (a); (c) third-generation decays, subject to the same conditions as (b) but which were also preceded by an α decay having an energy < 6030 keV.
The half-life of the radioactivity associated with the decay of the 173 Au ground state was measured to be 570 (30) ms is in good agreement with previous studies [1]. The branching ratio for the α decay of this state was found to be 57(9) %, which is in good agreement with the value of 45(15) % obtained in previous studies [20].
Third-generation α decays which follow the decay of both 173 Au g and 169 Ir g and are in delayed coincidence with 327 or 726 keV prompt γ rays, are shown in Fig. 4(c). The two peaks visible in this spectrum correspond to α decays of energies 5520(6) and 5556(6) keV. The former is in good agreement with the previously reported energies of the decay of 165 Re m . Similarly to the situation discussed above, the number of 165 Re m α decays observed in Fig. 4(c) is consistent with the number of 169 Ir m included in the gate used to identify the ground state decays of 169 Ir. The second peak is a previously unreported acitivity. The clear correlation of this new activity with the decays of both 173 Au g and 169 Ir g leads to its assignment as the α decay of the ground state of 165 Re. To determine the half-life of this new activity, the α( 169 Ir g )-α( 165 Re g ) time spectrum was fitted using the maximum-likelihood method [19] and this yielded a value of 1.6(6) s. A branching ratio of 14(8) % has been measured for the α decay of this state.  [4,29,30,33,[40][41][42][43][44][45][46][47].

IV. DISCUSSION
Prior to the undertaking of this work, the known α decay of 161 Ta was assumed to be the result of the decay of the ground state [4]. However, from the results presented above it is apparent that the 5142(6) keV α decay is in fact the decay of the high-spin isomeric state in 161 Ta. The deduced Q α value of 5273(6) keV is plotted in Fig. 5(a) and can be seen to continue the near-linear trend of the decreasing Q α values with increasing neutron number.
The Q α -value for the previously unreported decay of the ground state of 165 Re is plotted in Fig. 5(b). This value appears to fit very well with the linear trend already established by the neighboring Re isotopes. In combining this new measurement with the α-decay Q values of Fig. 1 and the mass excess of 156 Yb reported by Litvinov et al. (-53283(28) keV [3]), it is possible to determine the mass excess for the ground state of 161 Ta: -38816(40) keV.
As a result of the observation of the α decay of 165 Re g in the present work, it is possible to determine the excitation energy of the high-spin state in 161 Ta which is given by: Using the α-decay energies reported here and the excitation energy of the α-decaying isomeric state in 173 Au, 214(23) keV as reported by Poli et al. [1], it has been determined that the high-spin state in 161 Ta has an excitation energy of 95 (38) keV. Taking this analysis one step further, the knowledge of the energy difference of the two α-decaying states in 157 Lu, 26(7) keV [4], allows the Q α -value of the unobserved decay of the ground state of 161 Ta to be determined: Q α ( 161 Ta g ) = 5204 (39) keV. This new value is plotted in Fig. 5(b) where once more it fits well with the trend established by the neighboring Ta isotopes.
Using the measured mass excess for 156 Yb and the α-decay Q values of Fig. 1, the mass excesses of the ground and isomeric states in 149 Ho can be deduced. The deduced mass excess of the high-spin state in 149 Ho is -61648(40) keV which agrees remarkably well with the directly measured value of Litvinov et al. [3] of -61646(31) keV. The mass excess deduced for the low-spin state of 149 Ho was found to be -61582(58) keV which is in-line with expectations based on the previously known 49 keV excitation energy of the πs 1/2 -based isomer in 149 Ho [21].
The mass excesses deduced in the present work are compared with the values reported in the most recent Atomic Mass Evaluation (AME2012) [22,23] in Fig. 6. Overall, there is very good agreement between the values obtained in this study and those in the evaluation with the deduced mass of 161 Ta being the notable exception. This discrepancy is possibly the result of the inclusion of the incorrectly assigned α-decay of 161 Ta. Indeed, if the 69 keV energy difference between the Q α values of 161 Ta m and 161 Ta g is taken into account then the difference between the mass reported here and the AME2012 value is similar to those found for the other five nuclides plotted in Fig. 6.
The consistency in the mass measurements indicated by the agreement between the deduced masses of the ground and isomeric states of 149 Ho and the masses measured in Ref. [3] suggests that all of the α decays proceed between ground states with no electromagnetic decays occurring at any points in the decay chain between 177 Tl and 149 Ho. This is indicative that the single-particle configurations, established as πh 11/2 and πs 1/2 in the heavier members of the decay chain, are also consistent down the entire decay chain. This conclusion is supported by the reduced width measurements, calculated using the Rasmussen formalism [24] and assuming s-wave emisssion, which are listed in Table I. The reduced widths measured in the present work have been compared to the value corresponding to the α decay of the ground state of 212 Po. These hindrance factors, also listed in Table I are consistent with unhindered α decays. In Ref. [25] an extensive level scheme of excited states in 161 Ta built upon a proposed J π = 11/2 − state was reported. However, in that work it was not possible to establish whether this level or a 9/2 − level was the lowest-lying πh 11/2 state. The separation energy of the J π = 9/2 − and the 11/2 − states in the neutron-deficient Ta isotopes is observed to decrease from 99 keV in 167 Ta [26], 71 keV in 165 Ta [27] to 45 keV in 163 Ta [28].
Extrapolating to 161 Ta suggests the separation could be as low as ≈ 20 keV in this nuclide. This would be accommodated within the 40 keV uncertainty on the deduced mass excess for the high-spin state in 149 Ho meaning that the question regarding the spin and parity of the πh 11/2based state in 161 Ta cannot be resolved by the present study. Indeed, it remains unclear whether the α-decaying isomer in 161 Ta has J π = 9/2 − or 11/2 − .
In summary, fusion-evaporation reactions have been used to populate states in 173 Au. Gamma-ray transitions populating the ground state of 173 Au have been identified. In addition, the α-decay chains originating from the isomeric πh 11/2 state and the πs 1/2 ground state have been studied, culminating in the observation of the α decay of 161 Ta m and 165 Re g , respectively. As well as reporting a new activity in the decay of 165 Re g and confirming that the known α decay of 161 Ta is associated with the high-spin isomer, this work has enabled the relative energies of the α-decaying states in 161 Ta to be established. In combining these new measurements with the information already available on 157 Lu it has also been possible to deduce the Q α -value for the decay of the ground state of 161 Ta. As a result of the present work Q p -values of -129(24) keV and -37(21) keV have been determined for the ground and isomeric states of 161 Ta, respectively, indicating that these states are only just bound with respect to proton emission.

ACKNOWLEDGMENTS
Financial support for this work has been provided by the UK Science and Technology Facilities Council (STFC) and by the EU 7th framework programme "Integrating Activities -Transnational Access", project number: 262010(ENSAR) and by the Academy of Finland under the Finnish Centre of Excellence Programme 2012-2017(Nuclear and Accelerator Based Physics Research at JYFL). TG acknowledges the support of the Academy of Finland, contract number 131665. The authors would like to express their gratitude to the technical staff of the Accelerator Laboratory at the University of Jyväskylä for their support. The authors would also like to thank Charles Reich for stimulating discussions.