Decay spectroscopy at the two-proton drip line: Radioactivity of the new nuclides 160 Os and 156 W

The radioactivity of 16076 Os 84 and 15674 W 82 that lie at the two-proton drip line has been measured in an experiment performed at the Accelerator Laboratory of the University of Jyväskylä. The 160 Os nuclei were produced using fusion-evaporation reactions induced by a beam of 310 MeV 58 Ni ions bombarding a 106 Cd target. The 160 Os ions were separated in ﬂight using the recoil separator MARA and implanted into a double-sided silicon strip detector, which was used to measure their decays. The 𝛼 decays of the ground state of 160 Os ( 𝐸 𝛼 = 7092(15) keV, 𝑡 1∕2 = 97 +97−32 μs) and its isomeric state ( 𝐸 𝛼 = 8890(10) keV, 𝑡 1∕2 = 41 +15−9 μs) were measured, allowing the excitation energy of the isomer to be determined as 1844(18) keV. These 𝛼 -decay properties and the excitation energy of the isomer are compared with systematics. The 𝛼 decays were correlated with subsequent decays to investigate the 𝛽 decays of the ground state of 156 W, revealing that unlike its isotones, both low-lying isomers were populated in its daughter nuclide, 156 Ta. An improved value for the half-life of the proton-decaying high-spin isomeric state in 15673 Ta 83 of 333 +25−22 ms was obtained in a separate experiment using the same experimental systems with a

The radioactivity of 160  76 Os 84 and 156 74 W 82 that lie at the two-proton drip line has been measured in an experiment performed at the Accelerator Laboratory of the University of Jyväskylä.The 160 Os nuclei were produced using fusion-evaporation reactions induced by a beam of 310 MeV 58 Ni ions bombarding a 106 Cd target.The 160 Os ions were separated in flight using the recoil separator MARA and implanted into a double-sided silicon strip detector, which was used to measure their decays.The  decays of the ground state of 160 Os (  = 7092 (15) keV,  1∕2 = 97 +97 −32 μs) and its isomeric state (  = 8890 (10) keV,  1∕2 = 41 +15 −9 μs) were measured, allowing the excitation energy of the isomer to be determined as 1844 (18) keV.These -decay properties and the excitation energy of the isomer are compared with systematics.The  decays were correlated with subsequent decays to investigate the  decays of the ground state of 156 W, revealing that unlike its isotones, both low-lying isomers were populated in its daughter nuclide, 156 Ta.An improved value for the half-life of the proton-decaying high-spin isomeric state in 156  73 Ta 83 of 333 +25 −22 ms was obtained in a separate experiment using the same experimental systems with a

Introduction
The search for new nuclides has been an ongoing endeavour throughout the history of nuclear physics, resulting in the discovery of around 3000 species to date and providing many insights into nuclear properties [1].For odd- elements, the direct emission of a single proton generally determines the limits of observable nuclei [2] but for even- nuclei, pairing interactions reduce the  values for proton emission.Consequently,  radioactivity is the principal decay mode of the most neutron-deficient known isotopes of even- elements from plutonium ( = 94) down to osmium ( = 76).The strong dependence of the -particle tunnelling probability on the   value means that half-lives drop rapidly with increasing neutron deficiency at the limits of known nuclei.Prior to the present work the most neutron-deficient known Os isotope was 161 Os, which  decays to 157 W with a half-life of 640(60) μs [3].The next even- element below Os is tungsten ( = 74).Its lightest known isotopes are 158 W 84 , which is an  emitter with a half-life of ∼1 ms [4][5][6], and 157 W, which undergoes  decay with a half-life of 275 (40) ms [3].For even lighter elements,  decay continues as the dominant decay mode of the most neutron-deficient even- isotopes until the island of -particle emission above 100 Sn is reached.Here,  decay again dominates for the lightest known isotopes of xenon ( = 54) and tellurium ( = 52) [7][8][9][10][11].
The reason for this abrupt change in decay mode for the W isotopes is that the emission of an  particle from 157 W would involve the removal of a neutron from the  = 82 core, which impacts on the   value [12].Similar decreases in   values can be expected for its heavier isotones.Consequently, 160 Os is expected to be the lightest osmium isotope for which -particle emission is the dominant ground-state decay mode [12].Even more neutron-deficient Os isotopes are expected to undergo  decay, until the boundary of the nuclear landscape is ultimately reached with the advent of dominant two-proton emission from nuclear ground states [13,14].
The  = 84 isotones are also of interest because several of them have -decaying spin-gap isomers [4][5][6].In-beam spectroscopy experiments have shown that the yrast  7∕2 ℎ 9∕2 8 + states in 156 Hf and 158 W are at lower excitation energies than their respective 6 + states and as a consequence they are isomeric [15,16].This lowering in energy of the 8 + states is also evident from systematics of level excitation energies along isotopic chains [17].Similarly, the ℎ 11∕2  ⊗  7∕2 ℎ 9∕2 25/2 − state in 155 Lu is also isomeric, lying below the 23/2 − state [18,19].In all 3 isotones, the occurrence of isomerism is attributed to the lowering in energy of configurations involving neutrons in the ℎ 9∕2 orbital relative to those in the  7∕2 orbital as the occupancy of the ℎ 11∕2 orbital increases with increasing  above  = 64.The excitation energies of the 8 + isomers in 156 Hf and 158 W are 1959(1) keV [5] and 1888 (8) keV [6], respectively, and it is plausible that a similar isomer could also exist in 160 Os.As well as decay by -particle emission, there is also the possibility of a two-proton decay branch from this isomer, since the ground state of 160 Os is predicted to be unbound with  2 = 0.75 MeV [12].From the empirical formula of Ref. [20], this value is probably too low for 2 emission to be observed from the ground state and the osmium isotopes that are candidates for dominant 2 emission lie considerably further from stability [13].The feasibility of observing 2 decays from the isomer will depend on how much its excitation energy adds to the  2 value, balanced against the hindrance arising from the larger spin change involved in the decay.
Observing 160 Os  decays would also provide an opportunity to investigate for the first time the decay properties of the ground state of its daughter nuclide, 156 W.Although the ground state of 156 W is also predicted to be unbound to 2 emission,  decay is expected to dominate [12].The  decays of the lighter  = 82 isotones 148 Dy, 150 Er and 152 Yb are dominated by allowed Gamow-Teller transitions to a single 1 + state in their respective odd-odd daughter nuclei, followed by 1 -ray transitions to the 2 − ground states [21][22][23].These daughter nuclei also have a -decaying high-spin ℎ 11∕2 ⊗  7∕2 9 + isomer, but this has only been observed when populated directly in a reaction.
The 1 + states have been interpreted as being ℎ 11∕2 ⊗ ℎ 9∕2 configurations lying at excitation energies of ∼0.5 MeV above  3∕2 ⊗  7∕2 ground states.For the intermediate isotone 154 Hf, only the half-life has been determined indirectly from the time differences between  decays of 158 W and 154 Yb [24].In the case of 156 W, its daughter 156 Ta has 2 low-lying isomers with the same configurations as its isotones that are separated by only 0.1 MeV [5] and could be populated through electromagnetic decays following  decays to 1 + states.There are distinct differences in the decay properties of these states that can provide unique signatures of their population.
This letter presents measurements of the  decays of the ground state and spin-gap isomer of 160 Os, the -decay properties of 156 W and the result of a search for the competing 2-decay branches.Both nuclides lie at the proton-rich limit of the nuclear landscape, being one proton heavier than the proton emitters 159 Re [25] and 155 Ta [26], which are the lightest known isotopes of these elements.

Experimental details
The experiments were performed at the Accelerator Laboratory of the University of Jyväskylä.The 160 Os nuclei were produced in the fusion-evaporation reaction 106 Cd( 58 Ni,4) 160 Os.The 58 Ni beam provided by the K130 cyclotron bombarded the self-supporting isotopically enriched 106 Cd target foil of thickness 1 mg/cm 2 .The beam energy at the front of the target of 310 MeV was used for a period of 292 hours.The average beam intensity was 6.4 particle nA.The energy calibration for  particles was based on the  decays of 150,151 Dy, 152 Er, 155 Lu, 156 Hf and 158 Ta nuclei produced in the measurement [5,27].
In separate experiments using the same setup, the proton emitter 156 Ta was produced using the fusion-evaporation reaction 102 Pd( 58 Ni,3) 156 Ta.The self-supporting isotopically enriched 102 Pd target had a thickness of 1 mg/cm 2 and was bombarded with 294 MeV 58 Ni ions.The irradiation time and average beam intensity were 162 hours and 4.8 particle nA.These data were used to measure the halflife of the isomeric state in 156 Ta with improved precision, which in turn was used to extract the half-life of 156 W. Energy calibrations for proton emitters in all experiments were obtained from proton decays of 147 Tm and 151 Lu nuclei produced in reactions on targets of 92 Mo and 96 Ru.
Protons and  particles emitted at the target position during evaporation residue formation were detected using JYTube [28], which comprised 120 plastic scintillator detectors arranged in a hexagonalcylindrical geometry.Each detector was 2 mm thick and was directly coupled to a silicon photomultiplier on its back surface.The efficiency of JYTube for detecting a single proton or  particle was estimated to be ∼70%.However, JYTube is also partly sensitive to other forms of radiation (such as  rays), resulting in an extra signal occasionally being registered.Since the 160 Os nuclei would be produced via the 4 evaporation channel, JYTube was used to select only evaporation residues with no more than 1 signal detected in coincidence.The use of JYTube in this way allowed nuclei produced via neutron evaporation channels to be selected from the background of nuclei produced much more strongly through evaporation channels involving the emission of several protons and/or  particles.
The 160 Os and 156 Ta ions recoiled out of the target, passed through a carbon foil of nominal thickness 50 μg/cm 2 mounted ∼10 cm downstream of the target to reset the ionic charge-state distribution of the evaporation residues and were transported using the recoil mass separator MARA [29][30][31] to the detectors situated at its focal plane.The flight time was estimated to be ∼0.4 μs.The ions passed through a multi-wire proportional counter (MWPC) and were implanted into a double-sided silicon strip detector (DSSD).The energy signal in the DSSD and the time of flight between the MWPC and the DSSD allowed evaporation residues to be distinguished from beam-like particles.The ion optics of MARA were tuned for a charge state of 27 for the reaction with the 106 Cd target.For the 102 Pd target, charge states of 27 and 25.5 were used.In each instance this allowed for the simultaneous transmission of a total of four different charge states to the implantation detector.
The DSSD had an active area of 128 mm × 48 mm and was 300 μm thick.The strips on its front and back surfaces were orthogonal and the strip pitch of 0.67 mm on both faces provided 13824 independent pixels.The minimum time for extracting energy information from successive signals in a given strip was 8 μs.The DSSD energy thresholds were set at ∼100 keV to allow the observation of -decay signals.Two 500-μm thick silicon detectors, each with an active area of 50 mm × 70 mm, were mounted directly behind the DSSD and used to identify high-energy light ions arriving at the MARA focal plane that "punched through" the DSSD.These detectors allowed the background arising from these particles in the DSSD to be suppressed.
An array of 8 detectors was mounted to surround the DSSD in the upstream direction.These detectors formed the walls of a silicon "box" while the DSSD formed the base.Six of the box detectors had active areas of 50 mm × 50 mm segmented into 4 quadrants and were 500 μm thick.These were mounted in 2 groups of 3 around the ends of the DSSD.The other 2 box detectors were mounted centrally above and below the DSSD, between the 2 groups of square box detectors, to complete the array.These 2 detectors each measured 25 mm × 75 mm and were also 500 μm thick and segmented into 2 elements.The box detectors were assembled on a frame to complete the 4 box walls with their upstream edges aligned.These box detectors were used to suppress the background from  particles and protons emitted from within the DSSD in the upstream direction, depositing only part of their energy.
All detector signals were passed to the triggerless data acquisition system [32], where they were time stamped with a precision of 10 ns.The data were analysed using the GRAIN [33] software package.

Results
Searching for the new nuclide 160 Os presents a number of challenges.First, the most favourable compound nucleus reaction to synthesise 160 Os involves the evaporation of 4 neutrons.The cross section expected for this is likely to be only ∼1 nb, as was found for the synthesis of the exotic nuclides 166 Pt and 170 Hg by the same evaporation channel [34,35].Second, the daughter of 160 Os  decays is 156 W, which is expected to  decay with a predicted half-life of ∼130 ms [12].In principle, both of the known states in 156 Ta could be populated following the  decay of 156 W (see Fig. 1).Since  decays result in the deposition in the DSSD of a relatively small energy that unlike proton or  decays is generally not characteristic of a nuclide's decay, they are usually disregarded in correlation analyses.Therefore in order to identify 160 Os  decays, correlations must be sought with the  decays of either the ground state or the 8 + isomer of 156 Hf (populated via 156 Ta  decays), or with proton decays from 156 Ta [5,36].Correlations with the proton decays could be subject to significant background levels because the proton-energy peaks lie in the same region of the energy spectrum as  particles that escape from the DSSD without depositing their full energy.This problem is exacerbated by the relatively long time interval expected between 160 Os  decays and the proton or  decays with which they are to be correlated.  16Os.The labels  and  in the superscripts denote ground and isomeric states, respectively.The  decays of both the ground state and the isomeric state of 160 Os are expected to populate the ground state of the unknown nuclide 156 W, which is predicted to  decay [12].The red arrows denote the decays that were considered in the search for the  decay of 160 Os, namely the proton-decay branches of 156,156 Ta and the  decays of 156,156 Hf.The dashed arrows indicate the  decays of 160 Re and 160 W, which would be expected in correlated energy spectra together with 160 Os  decays.The half-life for the isomeric state in 156 Ta is from the present work.Other half-lives and branching ratios are taken from Refs.[5,36].
The identification of  decays of the 8 + isomeric state in 160 Os should be more straightforward than those from its ground state owing to the expected high -decay energy and consequently its short halflife.Fig. 2(a) shows part of the energy spectrum of  decays measured in the DSSD within 250 μs of an evaporation residue being implanted into the same pixel, with the additional condition that no more than 1 signal was observed in JYTube.The 158 Ta peak is noticeably broadened because its short half-life of 6.1 μs means that its decays occur on the rapidly falling tail of the pulse of the implanted ion event [37,38].In addition to these peaks, a new activity comprising 23 counts is visible at an energy of 8890 (10) keV, which is in the energy region where  decays of the 160 Os high-spin isomer would be expected.Fig. 2(b) shows the -decay energies plotted against the natural logarithm of the time difference between the  decay and the preceding evaporation residue implanted into the same DSSD pixel.Short-lived decays appear as groups towards the bottom of this plot.These include the decays of the isomers in 158 Ta and the  = 84 isotones 155 Lu, 156 Hf and 158 W. The group of events highlighted in the ellipse are short-lived, high-energy decays that are candidates for  decays of the spin-gap isomer in 160 Os.A half-life of 41 +15 −9 μs was extracted for this distribution, which passes the 90% confidence test outlined in ref. [39], confirming that the origin of these events is consistent with the decay of a single activity.As with other half-life values presented below, the 8 μs dead-time period was subtracted from the individual decay times when deducing this value.
In order to assign these candidate  decays to 160 Os it is necessary to correlate them with subsequent decays as discussed above.Fig. 2(c) shows that these decays are correlated with the proton decays of 156 Ta or the  decays of either the ground state or isomeric state of 156 Hf as expected from Fig. 1, confirming their assignment as  decays of 160 Os.Removing the constraint on the number of hits observed in JYTube does not increase the number of events in this region of the spectrum, as would be expected for a reaction channel involving only the evaporation of neutrons.The event slightly to the right of the ellipse in Fig. 2(b) is not assigned as a decay of 160 Os because no subsequent decay event  158 Ta and the events in the ellipse that are assigned as  decays of the isomer in 160 Os.(c) Correlation matrix of "mother" -decay events occurring within 400 μs of an evaporation residue being implanted into the same DSSD pixel with "daughter" decays occurring within a further 1.75 s in the same pixel.Note that the minimum energy threshold was set in software to exclude -decay events from these correlations.The candidate 160 Os  decays can be seen to fall within the 3 groups inside the red squares corresponding to daughter proton decays of 156 Ta and the  decays of the ground state and isomeric state of 156 Hf.The corresponding correlations of the  decays of the ground state of 160 Os are indicated by the purple squares.The green square highlights  decays of 160 Re correlated with proton decays of the ground state of 156 Ta, while the magenta squares highlight  decays of 156 Hf that are preceded by the  decays of 160 Re and 160 W. Note that the energy scales are valid for  decays and therefore give apparent proton energies that are ∼40 keV too low.
was observed in the same DSSD pixel within 5 s of this event.Details of the measured decay energies, time differences and number of observed JYTube coincidences for the decay chains assigned to 160 Os are presented in Table 1.
There are 3 160 Os -decay events in Fig. 2(c) correlated with 156 Ta proton decays.Two of these have daughter decay energies that are consistent with proton emission from the ground state of 156 Ta that is also observed following  decays of 160 Re that are highlighted by the green

Table 1
Data recorded for all of the decay chains assigned to 160 Os from the present work. 1 and  1 are the energies and times after the implantation of the preceding evaporation residue into the same DSSD pixel of the 160 Os  decays.  are the corresponding energies of the  ℎ member of the decay chain and   are their time after the preceding decay event in the DSSD pixel.The times   have not been corrected for the 8 μs minimum observation time.However, the half-lives presented in the text have had a correction for this applied.The JYTube fold is the number of coincident signals observed in JYTube in association with the evaporation residue for each chain.Energies of decays below 2 MeV have been calibrated using the proton decays of 147 Tm and 151 Lu.The superscript letters denote the assignments to decays following 160 Os  decays where they could be identified.square.The energy of the third daughter event is more than 100 keV higher, which would be consistent with proton emission from the highspin isomeric state in 156 Ta [5].The next decay observed in the same DSSD pixel is consistent with it being an  decay of 155 Lu, produced via an unobserved  decay of 155 Hf, confirming that this daughter event is a proton decay of 156 Ta.The observation of proton decays of the ground state of 156 Ta following 160 Os  decays shows that the  decays of 156 W can lead to population of this state.This feeding pattern is the one observed in lighter  = 84 isotones [21][22][23].The decays of the ground state of 156 Ta were studied by Darby et al., who found that the competing decay branch led to feeding of only the ground state of 156 Hf, with a branching ratio of 29(3) % [36].The observation of correlations of 160 Os  decays with those of the isomeric state in 156 Hf therefore confirms that the  decays of 156 W also lead to population of the isomeric state in 156 Ta, as suggested by the highest-energy 156 Ta proton decay.The -decay branches of both states in 156 Ta populate the ground state of 156 Hf, so the 5 observed correlations of 160 Os  decays with  decays of the ground state of 156 Hf could have passed through either state in 156 Ta.As expected from Fig. 1, correlations of  decays of 160 W and 160 Re with those of the ground state of 156 Hf were observed and are highlighted by the magenta squares in Fig. 2(c).

Chain
The knowledge gained from the  decays of the isomeric state in 160 Os can be used to search for the  decays of its ground state.A group of 3 events, highlighted by a purple square, can be seen in Fig. 2(c) with a daughter energy consistent with  decays of the 156 Hf isomeric state.These events are assigned as  decays of the ground state of 160 Os and the half-life deduced from these 3 decays is 107 +147 −40 μs.As can be seen from Table 1, the number of observed JYTube coincidences for each of these events is compatible with an evaporation channel involving only neutrons.The other 2 purple squares indicate where the other daughter decays might be expected to appear.No events are visible where 156 Ta proton decays would be expected, but 1 event is seen where 156 Hf ground-state  decays should occur and the evaporation residue was observed with no coincident signals in JYTube.This  decay occurred 105 μs after the implantation of an ion into the same DSSD pixel, a time difference which is consistent with the half-life deduced for the other 3  decays assigned to the ground state of 160 Os.Combining the data for all 4 decays gives a half-life of 97 +97 −32 μs and an -decay energy of 7092 (15) keV for the ground state of 160 Os.
The position sensitive MWPC allowed for an analysis of the distribution of events across the MARA focal plane.It was found that the events assigned as  decays of the ground state and isomeric state in 160 Os were consistent with a nuclide with  = 160, further supporting the assignments.In addition, despite the low correlation efficiency owing to the long half-lives and high implantation rate, 2 of the chains in Table 1 also include an  decay of 152 Er that is populated following  decays of 152 Yb and 152 Tm.
It is possible to determine the half-life of 156 W without observing its  decays directly, as has been done for other nuclei [24,40], provided that the decay path following the 160 Os  decays is unambiguous.That means that the chains involving the  decays of the 156 Hf ground state cannot be used for this purpose because it is populated through the  decays of both states in 156 Ta.Although the half-life of the ground state of 156 Ta has been precisely measured as  1∕2 = 106(4) ms [36], the uncertainty on the half-life of the 156 Ta isomer is rather large ( 1∕2 = 375(54) ms) [5].Since the majority of 156 W decays appear to feed the isomeric state of 156 Ta, a measurement of the half-life of this state with Fig. 3. Energy spectra of decays measured in the DSSD.Peaks are labelled with their assignments.(a) Decays that were followed by an  decay of 155 Lu in the same pixel in the measurements with the 102 Pd target.See text for details of the timing conditions.The broad distribution extending to higher energies is from the decays of 159 W nuclei in which the  particles escape from the DSSD without depositing their full energy.The inset shows the distribution of the time differences between ions being implanted and events in the 156 Ta protondecay peak in the same DSSD pixel.The red curve shows the fit to this time distribution.(b) Decays occurring within 370 μs of an ion being implanted into the same DSSD pixel that were followed within a further 12.5 ms by an  decay of 158 W in the measurement with the 106 Cd target.The only clear peak below 3.5 MeV is from proton decays of 159 Re.The inset shows a higher-energy region of the spectrum, in which a few  decays of 162 Os can be seen.improved precision is desirable in order to obtain a more precise halflife for 156 W. Fig. 3(a) shows the energy spectrum from the experiment using the 102 Pd target of events observed between 30 ms and 1875 ms of an evaporation residue being implanted into the same DSSD pixel that were then followed by a 155 Lu  decay occurring between 100 ms and 5 s later.A MWPC position corresponding to a mass number of 156 was required in order to optimise the purity of the spectrum.The proton-decay peaks from the ground state and isomeric state of 156 Ta are clearly visible.The inset shows the time differences between the ion implantation and 156 Ta isomer proton-decay events, plotted on a logarithmic time axis.The fitted curve is for the half-life of 333 +25 −22 ms deduced from these data using the method of Ref. [41].
The half-life of 156 W was determined to be 153 +64 −39 ms from the time differences between 160 Os  decays and subsequent 156 Ta proton decays or 156 Hf isomer  decays, taking into account the half-lives of the intermediate -decaying states.This half-life is in good agreement with the value of 130 ms predicted in Ref. [12].
It is interesting to examine the -decay signals presented in Table 1 with this knowledge of the 156 W half-life.The assignments as  decays of 156 W or the ground state or isomeric state of 156 Ta are based on the energies observed in the decay chains and/or the time differences between the signals.For example, in chains 7 and 15 the time differences between the  decays and the following  decays of the isomer in 156 Hf are too long to be consistent with them being decays of the 156 Ta isomer, so they must be decays of 156 W. The energy spectrum of the -decay events presented in Table 1 is shown in Fig. 4(a), with assignments for the  decays they represent indicated by their colour.This can be compared with the corresponding spectrum measured for  decays of the ground state of 156 Ta populated by  decays of 160 Re nuclei produced in this experiment that is shown in Fig. 4(b).The higher energies measured for chains 7 and 15 can be understood as pile-up of the energy signals of 156 W  particles with conversion electrons emitted in low-energy electromagnetic decays of excited states in 156 Ta.Known transitions in 156 Hf are not strongly converted, so  decays of 156 Ta tend to produce signals of lower energy.The fraction of -decay signals that were registered for 156 Ta  decays following 160 Re  decays was 6(2) %, which is lower than appears to be the case for 156 W  decays.This observation is also consistent with conversion-electron emission following  decays of 156 W.
The assignments of the -particle signals to the decays of specific states allowed chains 2 and 5 also to be used for determining the halflife of 156 W, thereby reducing the uncertainty compared with the value deduced above using the information only from proton-and -decay signals.Furthermore, the time differences for 156 W  decays themselves were used where they had been measured.Chains 1, 9, 13 and 16 that terminate with an  decay of the ground state of 156 Hf without the measurement of any  decays could not be used because these decay paths remained ambiguous.After applying corrections for unobserved intervening  decays where appropriate, a more precise value of 157 +57 −34 ms was determined for the half-life of 156 W.
The data were searched for evidence of 2-decay branches from 160 Os and 156 W. Two-proton emission from 160 Os would be followed by  decays of 158 W [6]. Fig. 3(b) shows the energy spectrum of decay events observed in the same DSSD pixel within 370 μs of an evaporation residue being implanted that were followed within 12.5 ms by an  decay of 158 W. Peaks assigned as proton decays of 159 Re [25] and  decays of 162 Os [6] are visible, but there is no other statistically significant peak that could be attributed to 2 decays from 160 Os.
If it were to occur, evidence for 2 radioactivity from 156 W would appear in Fig. 2(c), where there is a single event with a daughter energy of around 4 MeV that has a mother energy consistent with an  decay of the isomeric state in 160 Os.This energy is much higher than the predicted  2 value of 0.43 MeV for 156 W [12], so it is more likely to be an  particle emitted from 156 Hf that escaped from the DSSD without depositing its full energy.There is also no clear sign of a peak in Fig. 2(c) in the energy region where 156 W 2 decays might be expected following  decays of the ground state of 160 Os, although there are some events that are assumed to be escaping  particles.

Discussion
The -decay  value of 7274 (15) keV measured in the present work for the ground state of 160 Os fits in well with the systematic variation of   values with neutron number for neutron-deficient even-even nuclides from Yb to Os.The   value for 160 Os is slightly higher than would be expected from a linear extrapolation of   values from heavier isotopes.Such increases are also evident for the other  = 84 isotones and become larger with increasing .Larger values are also found for  = 128 isotones compared with extrapolations from their heavier isotopes [42].In contrast, ref. [12] predicts a lower   value for 160 Os than 162 Os, although its predicted   values appear to be consistently overestimated for  = 86 isotones.The excitation energy of the -decaying isomer in 160 Os determined from the difference in measured   values is 1844 (18) keV.This value would be consistent with a continuing smooth trend in  = 84 isotones of decreasing excitation energies of the yrast  7∕2 ℎ 9∕2 8 + states with increasing  that leads to the formation of the spin-gap isomers.Extrapolating the trends of gradually increasing excitation energy with  of the lower-spin states suggests that not only is the 8 + state in 160 Os below the 6 + state but it could possibly even lie below the 4 + state too.
The production cross section for the isomeric state in 160 Os in this experiment was estimated from the yield of  decays in Fig. 2(a) to be ∼0.5 nb, assuming a MARA transport efficiency of 40% and allowing for 41% of the  particles escaping from the DSSD without depositing their full energy.The number of correlated decay chains for the ground state of 160 Os was 3.5 times lower, so the combined cross section was ∼0.6 nb.This value is comparable to the value estimated for 170 Hg [35], but is slightly lower than the cross section estimated for the production of 166 Pt via the 4 evaporation channel [34].Substantially stronger population of the 8 + isomers than the ground states in fusion-evaporation reactions was also found for the isotones 156 Hf [15] and 158 W [16].
Reduced  widths were calculated for the decays of the two states in 160 Os using the measured energies and half-lives [43].A value of 60 (30) keV was deduced for the ground state assuming Δ = 0, which is compatible with an unhindered  decay, while assuming Δ = 8 yielded a reduced alpha-decay width of 2.3(6) keV for the isomeric state.The latter value is consistent with a hindrance factor of ∼20, as observed for the  decays of the other  = 84 spin-gap isomers [5].
Calculations were also performed with the Superfluid Tunnelling Model (STM) as described in Ref. [44], which has been successfully applied previously to the description of  decay including that of other N = 84 isotones [45,46].The model involves the evolution of the parent nucleus, under the action of the residual nuclear interaction dominated by pairing, to a cluster-like configuration of the daughter nucleus and  particle.The calculations of the ground-state  decay require an estimate of the pairing gap, Δ, and here we used the same parametrisation as discussed in Ref. [46].The calculated value of the half-life of the ground-state decay is 55 μs, which is to be compared to our experimental value of 97 +97 −32 μs.For the isomeric state the pair gap must be reduced and the angular momentum change between initial and final states taken into account.These factors reflect the nature of the spingap isomers in this region.Reducing the pairing gap to 60% of the value for the ground state, and assuming Δ = 8, the calculated half-life is 13 μs, which is to be compared with our experimental value of 41 +15 −9 μs.The pairing gap for the isomer would need to be reduced to 55% of the ground-state value to reproduce the half-life.This is consistent with the systematics in Ref. [46] and reflects the observed hindrance factors of the spin-gap isomers in the N = 84 isotones [5].
The decay chains of 160 Os observed in the present work allow insights to be gleaned on the -decay of 156 W, see Fig. 1.Of the 18 chains presented in Table 1, 2 involved proton decays of  3∕2 ground state of 156 Ta.Since the  decay of this state only leads to significant population of the ground state of 156 Hf [36], the 9 chains that involved  decays of the 8 + isomer in 156 Hf must have proceeded through the ℎ 11∕2 isomer in 156 Ta [5].In addition, there was 1 chain with proton decay from the isomer in 156 Ta.The remaining 6 chains involved  decays of the 156 Hf ground state, which is fed in the  decays of both states in 156 Ta [5].The measured time intervals in the decay chains indicate that 2 of these proceed through the isomeric state in 156 Ta, but the paths of the other 4 chains remain uncertain.
The present results for the  decay of 156 W indicate strong feeding of the ℎ 11∕2 isomer in 156 Ta.This behaviour is different to 152 Yb and its lighter isotones, for which  decays lead predominantly to population of the  3∕2 ground state [21][22][23].Multiplets of states formed by coupling the odd proton and neutron are likely to exist at low excitation energies in 156 Ta and may open up favourable -decay paths from the 1 + state to the ℎ 11∕2 isomer.Something akin to this has been observed in 160 Re, where a -decay path from the ℎ 11∕2 isomer to the  3∕2 ground state exists [47].It would be interesting to investigate the  decays of the intermediate isotone 154 Hf to see which decay pattern it follows and the insights this offers into the evolving structure of nuclei at the  = 82 shell closure as  increases.The statistics that could be obtained in such a study should be much higher than was possible for 156 W in the present work and may allow the identification of  rays emitted from states in 154 Lu populated in 154 Hf  decays.
The empirical formula for 2-decay half-lives proposed in ref. [20] was used in that work to estimate values for superheavy nuclei.Using it for the states of interest in the present work with the  2 values from ref. [12] yields values of ∼10 66 s and ∼10 46 s for the ground states of 156 W and 160 Os, respectively.The corresponding values for the isomeric state in 160 Os decaying to the ground state and isomeric state in 158 W are ∼10 22 s and ∼10 48 s, respectively.Although one should be cautious regarding the accuracy of the predicted values, in all cases they are many orders of magnitude longer than the measured half-lives.This is consistent with the expectation that 2 radioactivity from ground states will only compete with other decay modes in much lighter isotopes of these elements [13,14].However, it is interesting to note that the predicted 2-decay half-life for the isomer in 160 Os to the ground state of 158 W is by far the shortest of these values, suggesting that isomers may yet provide candidates for this decay mode in heavy nuclei that could be more easily accessed experimentally.
The calculations of ref. [12] predict a drop of ∼2 MeV in the   value moving to 159 Os and that  decay will dominate.It might be possible to measure -decay properties of 158,159 Os using a similar approach to that in the present work to measure 156 W decays, populating the Os isotopes via the expected  decays of 162,163 Pt.This appears to be very challenging, given that the lightest currently known Pt isotope is 165 Pt [35].Nevertheless, a measurement of 162 Pt would be very interesting as it is the next even-even  = 84 isotone above 160 Os.The  value for 2 emission from 162 Pt is likely to be higher than those of 156 W and 160 Os, but 2 emission from both its ground and isomeric states will still have to compete with  decay.

Summary
The radioactive decays of 160 Os and 156 W have been observed for the first time.When compared with their respective lighter isotones, the decay properties of the ground state and isomeric state in 160 Os exhibit similar behaviour, whereas the  decay of 156 W follows a different pattern of populating isomeric states in its daughter.The measurements for 160 Os extend the knowledge of excited states in even-even isotopes across a wide range of neutron numbers, extending from  = 84 to  = 122 [48].The reduced excitation energy of the isomeric 8 + state in 160 Os compared with its isotones points to the continuing importance of the interaction of ℎ 9∕2 neutrons with ℎ 11∕2 protons approaching the  = 82 shell closure.With the expected limit of -decaying osmium isotopes having been reached and the low production cross sections, it will be very challenging to extend decay spectroscopy measurements to even lighter osmium and tungsten isotopes.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Schematic diagram showing the expected -decay chain of160 Os.The labels  and  in the superscripts denote ground and isomeric states, respectively.The  decays of both the ground state and the isomeric state of 160 Os are expected to populate the ground state of the unknown nuclide 156 W, which is predicted to  decay[12].The red arrows denote the decays that were considered in the search for the  decay of 160 Os, namely the proton-decay branches of 156,156 Ta and the  decays of 156,156 Hf.The dashed arrows indicate the  decays of 160 Re and 160 W, which would be expected in correlated energy spectra together with 160 Os  decays.The half-life for the isomeric state in 156 Ta is from the present work.Other half-lives and branching ratios are taken from Refs.[5,36].

Fig. 2 .
Fig. 2. (a) Energy spectrum of  decays measured in the DSSD within 250 μs of an ion being implanted into the same pixel.Peaks are labelled with their assignments.Note the expanded vertical scale to the right of the dot-dash line.(b)The energies of  decay plotted against the natural logarithm of the time difference between the  decay and the preceding evaporation residue implanted into the same DSSD pixel.The dashed lines are drawn to guide the eye to the  decays of the spin-gap isomers of 155 Lu, 156 Hf, 158 W, 158 Ta and the events in the ellipse that are assigned as  decays of the isomer in 160 Os.(c) Correlation matrix of "mother" -decay events occurring within 400 μs of an evaporation residue being implanted into the same DSSD pixel with "daughter" decays occurring within a further 1.75 s in the same pixel.Note that the minimum energy threshold was set in software to exclude -decay events from these correlations.The candidate 160 Os  decays can be seen to fall within the 3 groups inside the red squares corresponding to daughter proton decays of 156 Ta and the  decays of the ground state and isomeric state of 156 Hf.The corresponding correlations of the  decays of the ground state of 160 Os are indicated by the purple squares.The green square highlights  decays of 160 Re correlated with proton decays of the ground state of 156 Ta, while the magenta squares highlight  decays of 156 Hf that are preceded by the  decays of 160 Re and 160 W. Note that the energy scales are valid for  decays and therefore give apparent proton energies that are ∼40 keV too low.

Fig. 4 .
Fig. 4. (a) Energy spectrum of the -decay events presented in Table 1.The colours indicate the assignments to specific -decaying states.(b) Energy spectrum of  particles observed within 530 ms of an  decay of 160 Re and followed within 115 ms by an  decay of the ground state of 156 Hf.