Discovery of 157 W and 161 Os

The nuclides 157 W and 161 Os have been discovered in reactions of 58 Ni ion beams with a 106 Cd target. The 161 Os α -decay energy and half-life were 6890 ± 12 keV and 640 ± 60 μs. The daughter 157 W nuclei β -decayed with a half-life of 275 ± 40 ms, populating both low-lying α -decaying states in 157 Ta, which is consistent with a 7 / 2 − ground state in 157 W. Fine structure observed in the α decay of 161 Os places the lowest excited state in 157 W with I π = 9 / 2 − at 318 ± 30 keV. The branching ratio of 5 . 5 + 3 . 1 − 2 . 2 % indicates that 161 Os also has a 7 / 2 − ground state. Shell-model calculations analysing the effects of monopole shifts and a tensor force on the relative energies of 2f 7 / 2 and 1h 9 / 2 neutron states in N = 83 isotones are presented.

The study of nuclei far from the line of β stability has revealed significant modifications of single-particle energies.It has been shown that the presence of a tensor component in the nucleonnucleon effective interaction is important for understanding the shell structure of neutron-rich nuclei.This gives rise to particular shifts in the relative energies of specific orbitals, depending on their occupancy [1,2].This tensor term most probably plays a significant role in determining the structure of much heavier nuclei [3,4], as revealed through the evolution of the relative energies of single-particle levels in isotopic or isotonic chains of nuclei at closed shells [5].In this work, focusing on the region at the proton drip line above N = 82, the structure of nuclei is governed at low spin and excitation energy by valence neutrons in the 2f 7/2 and 1h 9/2 orbitals and protons in the 3s  orbitals [6].In particular, one expects the proton-neutron tensor force component acting between protons filling the 1h 11/2 orbital and a single neutron in the 1h 9/2 or 2f 7/2 orbitals to modify their relative single-particle energies in a specific way that differs from the changes arising only from a central force.
The excitation energies and spectroscopic factors of 9/2 − states in the stable N = 83 isotones 139 56 Ba, 141 58 Ce, 143 60 Nd and 145 62 Sm were recently measured using transfer reactions [7].This allowed the centroid energy of the ν1h 9/2 orbital relative to the ν2f 7/2 orbital to be deduced in these nuclei, see Fig. 1.Above Z = 64, the occupation probability of the π1h 11/2 orbital increases with increasing Z and the energy difference between the ν2f 7/2 and ν1h 9/2 orbitals is expected to drop rapidly.Unfortunately, the heavier isotones required to extend these systematics above Z = 64 are all unstable, rendering the measurement of spectrosopic factors and thus of the single-particle content for these states impossible at present.However, the measured energy differences between the lowest-lying 9/2 − and 7/2 − states for the N = 83 and N = 85 isotones plotted in Fig. 1 do indeed show a rapid drop above Z = 64.Although caution should be exercised in case there is significant fragmentation of single-particle strength in nuclei when moving away from stability, the measured spectroscopic factors for both 7/2 − and 9/2 − levels for Z 64 [7,8] suggest this drop is reflecting the gradual approach in energy of the 1h 9/2 and 2f 7/2 neutron single-particle orbitals.The steep slope for these heavy N = 83 isotones suggests that the energies of the neutron single-particle orbitals may even become inverted for high Z.New experimental data for nuclei above Z = 70 are necessary to provide a definitive answer on this possibility.
In this Letter we present the discoveries of 161 76 Os 85 and 157 74 W 83 , which have 23 fewer neutrons than their lightest stable isotopes.The experiment was performed at the Accelerator Laboratory of the University of Jyväskylä.The 161 Os nuclei were populated in the 106 Cd( 58 Ni, 3n) reaction.The target was a 1.1 mg/cm 2 thick, self-supporting 106 Cd foil of 96.5% isotopic enrichment.Average beam currents were 2.3 particle nA for 104 hours at 290 MeV, 4.7 particle nA for 75 hours at 300 MeV and 3.0 particle nA for 96 hours at 310 MeV.The gas-filled separator ritu [10] transported the reaction products to the great spectrometer [11].α-decay spectroscopy was facilitated by two adjacent double-sided silicon strip detectors (DSSDs) into which the reaction products were implanted.The DSSDs had an active area of 60 mm × 40 mm and a thickness of 300 μm.The strip pitch of 1 mm gave a total of 4800 independent pixels, which made it possible to correlate decays occurring within a few seconds of each other.All detector signals were passed to the triggerless data acquisition system [12], which time stamped them with a precision of 10 ns, allowing temporal correlations to be analysed using the grain software package [13].
The lightest known osmium isotopes are short-lived nuclei and decay predominantly by α-particle emission [14].In order to isolate α decays of 161 Os from the large number of counts in the α-decay energy spectrum of Fig. 2(a), correlations were sought with the α decays of 157 Ta, populated via the β decay of 157 W, see Fig. 2(d).Two low-lying α-decaying states are known in 157 Ta: the π1h 11/2 state decays by emitting 6213 keV α particles with a halflife of 4.3 ms [14], while the π3s 1/2 ground state has a half-life of 10.1 ms and emits 927 keV protons, with a branching ratio of 3.4%, and 6117 keV α particles [15].Fig. 2(b) shows the energy spectrum of the decays in Fig. 2(a) that are followed within 4 s by either 157 Ta α decay.The strongest peak in this spectrum is the 6.27 MeV α decay of the π1h 11/2 state in 161 Re, which populates the corresponding state in 157 Ta [14,15].The peak at 6.5 MeV is from 163 Os α decays correlated with those of 159 W [14,16], the low-energy tail of whose 6.3 MeV α-decay line extends into the 157 Ta energy gate, while the peak at 6.1 MeV arises from 162 Re α decays correlated with the 6.05 MeV α decays of 158 Ta [17], which also falls within the 157 Ta energy gate.The 155m Lu and 156m Hf peaks [14] arise from random correlations.The clear peak comprising ∼200 counts at 6890 ± 12 keV is a new activity that we assign as the α decay of 161 Os.The energy fits in well with the systematic variation of α-decay Q-values with neutron number, while the yield corresponds to a cross section of ∼10 nb, or one 161 Os nucleus in every 5 million evaporation residues.
The half-life of this activity was determined as 640 ± 60 μs using the method of maximum likelihood [18].A reduced α-decay width of 37 ± 5 keV for 161 Os was calculated from the measured α-decay energy and half-life, assuming s-wave emission [19].This is compatible with the value of 45 ± 4 keV for its odd-A isotone 159 W.
If the ground state of 157 W were a ν1h 9/2 state, its β decay would proceed mainly to the π1h 11/2 state in 157 Ta through a favoured Gamow-Teller transition [20], but if the ground state were a ν2f 7/2 state, then neither 157 Ta state could be fed directly by an allowed decay.Instead, the β decays would feed intermediate states that γ decay and one could expect both 157 Ta states to be populated.Fig. 2(c) shows the energy spectrum of 157 Ta α decays that follow the 161 Os α decays within 4 s.From this spectrum it is evident that both α-decaying states in 157 Ta are fed by the β decay of 157 W, confirming that a ν2f 7/2 state represents its ground state.The half-life of 157 W was deduced to be 275 ± 40 ms from the time differences between the 161 Os and 157 Ta α decays.
Observing fine structure in the α decay of 161 Os could reveal its ground-state configuration, see Fig. 3.One difficulty is that in the excitation energy region of ∼300 keV expected from the systematics, there is potentially interference from α decays of 163 Os to 159 W, see Fig. 2(b).To eliminate this source of background, only decays appearing in Fig. 2(b) that were followed more than 70 ms later by a 157 Ta α decay were considered.In addition, when decays occur shortly after the implantation of an ion, the measured peak widths are broader owing to variations in the shaping amplifier baseline.Decays occurring less than 250 μs after ion implantation were therefore also excluded.The resulting spectrum is shown in Fig. 2(e), in which a group of counts at 6580 ± 30 keV can be seen.
The time distribution of these counts is compatible with the halflife measured for the main 161 Os α-decay line.The possibilities that these counts arise from decays of 163 Os or from a fluctuation in background levels can both can be excluded with 99% confidence, while the possibility that the counts could be part of the low-energy tail of the main 161 Os α-decay line can be excluded with a confidence of 90% [21].These counts are therefore tentatively assigned as α-decay fine structure of 161 Os.
The branching ratio for this activity is 5.5 +3.1 −2.2 % and the excitation energy in 157 W is 318 ± 30 keV.These values are consistent with a 7/2 − ground state in 161 Os that decays to an excited 9/2 − state in 157 W as well as its ground state (see Fig. 3).Note that if the ground state of 161 Os were 9/2 − rather than 7/2 − , the branching ratio should be much larger than is observed, as indicated by Fig. 3. Branching ratios for 161 Os α decay to the first excited 9/2 − state in 157 W as a function of its excitation energy calculated using the method of Rasmussen, in which the penetration of an α particle through the real part of an optical model potential barrier is computed using the WKB approximation [19].The dashed curve is the branching ratio to the excited state in 157 W that would be expected for a 9/2 − ground state in 161 Os, while the solid line is for a 7/2 − ground state.The same reduced width has been assumed in all calculations.The data point indicates the measured values from the present work.
the dashed line in Fig. 3.This is because with a 9/2 − groundstate spin assignment for 161 Os the α decay to the excited state in 157 W could then proceed by s-wave emission, while the decay to the ground state would proceed by d-wave emission, which is relatively hindered by the additional centrifugal component to the potential barrier.The measured excitation energy of the 9/2 − state above the 7/2 − ground state in 157 W is plotted in Fig. 1.
The monopole shifts for single-particle states in the N = 82-126 shell-model space were calculated using a spin-isospin exchange part of the central Yukawa-type force with a strength of 10 MeV (see Ref. [22] for more details).The results agree reasonably well with the measured centroid energies [7]: the behaviour up to Z = 64-66 is to a large extent due to the radial overlap of the proton orbitals, when filling the 1g 7/2 and 2d 5/2 orbitals, with the neutron 1h 9/2 and 2f 7/2 orbitals, respectively.This causes an initial small drop and subsequent upsloping behaviour of the latter two neutron orbitals, as observed experimentally in the energy centroids.Once the proton 1h 11/2 orbital starts to fill, the neutron 1h 9/2 state decreases quickly in energy, relative to the 2f 7/2 orbital.Therefore with solely a central force one expects approaching ν1h 9/2 and ν2f 7/2 orbitals beyond Z = 64, see Fig. 1.This effect is primarily due to the greater spatial overlap of the ν1h 9/2 orbital with the π1h 11/2 orbital, mainly filling beyond Z = 64, as compared with the ν2f 7/2 orbital.
Adding a tensor force with a strength of 20 MeV [23,24] to the Yukawa force describes well the observed systematics of the ν1h 9/2 and ν1i 13/2 [7] single-particle energy difference in the region 56 Z 62 and also slightly improves the relative energy shift of the ν1h 9/2 versus the ν2f 7/2 orbital, already starting at Z = 52.However, doubling the strength of the tensor term does not lead to any significant further improvement, but rather worsens the agreement with measurements for the ν1i 13/2 orbital in N = 83 isotones.This gives an indication of the constraints on the strength of the tensor force component.When filling the proton 1h 11/2 orbital (orbital angular momentum parallel to the spin orientation), the typical signature of the presence of a tensor force in relative single-particle energy changes with generalized spin-orbit partners is a strong decrease in energy of the antiparallel oriented orbital (here the neutron 1h 9/2 orbital) relative to the energy of the parallel oriented orbital (here the neutron 2f 7/2 orbital).This effect is much less pronounced in the present N = 83 nuclei because of the difference in the radial quantum number n and the subsequent strongly reduced radial overlap between the 2f and 1h orbitals.A similar effect has been observed for the N = 28 nuclei and the changing neutron 1f 7/2 to 2p 3/2 energy gap with decreasing proton number, starting at 48 Ca, down to 44 S, 42 Si (removing protons from the 2d 3/2 orbital) and further down to 36 O (removing protons from the 2d 5/2 orbital) [25].It is important to stress the fact that for the N = 20 and N = 28 mass region, these conclusions follow from an effective interaction describing the full sd-pf shell-model space [26] and carrying out a decomposition in its central, vector and tensor components.In the paper by Smirnova et al. [25], and, independently by Otsuka et al. [27], it was shown that one needs the cooperative effect of both a central and a tensor force in order to describe the observed changing shell structure in light and medium-heavy nuclei.It would be instructive in the future to construct a realistic effective interaction in the model space spanning the Z = 50-82 proton orbitals as well as neutrons filling the N = 82-126 neutron orbitals to overcome the limitation of using a more phenomenological approach of considering the combined effect of a central and tensor force.
The discoveries of 161 Os and 157 W mark them among the most distant known nuclides from the line of maximum β stability.Our measurements show that a 7/2 − state forms their ground states and that the excitation energy of the 9/2 − state in 157 W continues the trend of decreasing values with increasing occupation of the π1h 11/2 orbital.The presence of a tensor component in the nucleon-nucleon effective interaction, in addition to the central component, appears to be important in order to improve agreement with the measured data for N = 83 isotones, although interactions with tensor terms fitted globally to a range of data need to be developed before definitive conclusions can be drawn [5].

Fig. 1 .
Fig. 1. (Colour online.)The triangles show energy differences measured from transfer reactions on stable nuclei of the centroid energies determined for the 2f 7/2 and 1h 9/2 neutron single-particle orbitals for N = 83 isotones, while energy differences between the lowest-lying 7/2 − and 9/2 − states for N = 83 and N = 85 isotones are shown by the squares and circles, respectively.The open square shows the value for 157 W from this work.Data are taken from [7,9].Comparison of data for N = 83 isotones with shell model calculations of the ν1h 9/2 -ν2f 7/2 energy difference with (thick line) and without (dashed line) the added tensor force.The calculations are normalized to the value for 133 50 Sn 83 .

Fig. 2 .
Fig. 2. (a) Spectrum of α decays occurring within 4 ms of an ion implantation into the same DSSD pixel.(b) As (a), but with the additional requirement that the α decay is followed within 4 s by either of the α-decay branches of 157 Ta [15].(c) Spectrum of 157 Ta α decays following α decays in the 161 Os peak.(d) Decay scheme of 161 Os and related nuclei.The spin and parity assignments for the states in 161 Os and 157 W are from the present work.(e) Spectrum of α decays occurring between 250 μs and 1.5 ms after an ion implantation into the same DSSD pixel that are followed between 70 ms and 1.5 s later by either of the α-decay branches of 157 Ta.