Lifetime measurements of lowest states in the g 7 / 2 h 11 / 2 rotational band in 112

Giles, M.M.; Cullen, D.M.; Singh, B.S. Nara; Hodge, D.; Taylor, M.J.; Mallaburn, M.J.; Sosnin, N.V.; Barber, L.; Smith, J.F. ; Capponi, L.; Smolen, M.; Scholey, C.; Rahkila, P.; Grahn, T.; Badran, H.; Girka, A.; Greenlees, P.T.; Julin, R.; Konki, J.; Nefodov, O.; Ruotsalainen, P.; Sandzelius, M.; Saren, J.; Sorri, J.; Stolze, S.; Uusitalo, J.; Pakarinen, J.; Papadakis, P.; Partanen, J.; Braunroth, T.; O'Neill, G.G.


I. INTRODUCTION
The heavy mass isotopes of iodine are known to exhibit features normally associated with collective behaviour.For example, a series of strongly coupled rotational bands have been observed in the doubly-odd I isotopes [1][2][3][4].The strongly coupled nature of these bands is usually characterised by their signature splitting.Signature splitting can be quantified as the energy of the M1 transition linking the strongly coupled rotational bands minus the average energy of the M1 transitions directly above and below it [5].In 116−122 I [1,6,7], the strongly coupled rotational bands built upon the πg −1 9/2 ⊗ νh 11/2 configuration exhibit a small signature splitting, S(I π ) [1,2,5].For example, in 116 I S(9 − ) = 9 keV and in 118 I S(9 − ) = 21 keV for these πg −1 9/2 ⊗νh 11/2 bands.In contrast, in the lighter mass isotopes the collective rotational bands are interpreted to be built upon a lower-K proton g 7/2 configuration coupled to the same neutron h 11/2 orbital.As a consequence, the strong-coupled nature of the bands in the heavier mass isotopes diminishes in the lighter mass isotopes and larger signature splittings are observed.For example, in 114 I the signature splitting is S(9 − ) ∼ 400 keV [8], and becomes so large in 112 I that only one signature of the rotational band is experimentally observed [9].
112 I was previously studied by Paul et al. [9].In that work, a series of single-particle states were established at low spins, which were fed by a rotational band at higher spins.The band was interpreted as the favoured signature of πg 7/2 ⊗ νh 11/2 configuration [9].The aligned angular momentum for this band showed somewhat irregular behaviour at low rotational frequencies as the nucleus went through the simultaneous alignments of both proton and neutron h 11/2 orbitals [9].In order to shed some light on the nature of the πg 7/2 ⊗ νh 11/2 collective rotational band in 112 I, lifetime measurements have been performed in the present work using the Differential Plunger for Unbound Nuclear States (DPUNS) [10].

II. EXPERIMENTAL DETAILS AND ANALYSIS
Excited states in 112 I were populated with the 58 Ni( 58 Ni,3pn) fusion-evaporation reaction.The experiment employed a 230-MeV 4-pnA 58 Ni beam, produced with the K130 cyclotron at the Accelerator Laboratory of the University of Jyväskylä, which was used to bombard a 1.1 mg/cm 2 58 Ni target for 12 days.A 1.5 mg/cm 2  24 Mg degrader foil was placed downstream from the target.Subsequently, the degraded recoils traveled through the recoil ion transport unit (RITU) [11] triggering a multiwire proportional counter (MWPC) before they were implanted into a double-sided silicon strip detector (DSSD) [12].RITU was used to transport the recoiling evaporation products, or recoils, to the focal plane whilst suppressing any primary beam.
The target was mounted at the centre of JUROGAM-II γ-ray spectrometer, inside the DPUNS [10], along with the 24 Mg degrader foil.The JUROGAM-II array was used to measure the γ-ray intensities [13].JUROGAM-II consisted of 39 Compton-suppressed germanium detectors arranged into 4 rings, with angles θ = 76 • , 105 • , 134 • and 158 • with respect to the beam axis.Rings 1 and 2 consisted of 5 and 10 EUROGAM Phase I-type detectors at angles of 158 • and 134 • , respectively [14].The remaining two rings each contained 12 Clover detectors at θ = 76 • and θ = 105 • [15].A Total data readout (TDR) system recorded all detector events with a time stamp [16], allowing the GRAIN package to be used for offline analysis [17].
The degrader foil inside DPUNS reduced the velocity of the recoils, which split the intensity of each detected γ-ray transition into two Doppler-shifted components, I s (x) and I d (x).Here I s (x) is the component peak intensity corresponding to decays before the degrader foil (fully-shifted), and I d (x) is the component peak intensity corresponding to decays after the degrader foil (degraded).The differential decay curve method (DDCM) was used on these component peak intensities as a function of plunger distance, x = 135 µm, 210 µm, 300 µm, 590 µm and 3000 µm, to deduce the lifetimes of the states of interest [18,19].
To remove the effect of potential side-feeding from higher lying states, a gate on the fully-shifted (fs) component of the γ-ray directly above the level of interest was placed using the gf 3 software package [20,21].The lifetime was determined by using Equation 1 [18], Here, v is the average recoil velocity and {I s f eed , I d dec } denotes the intensity in the degraded component of the γ-ray from the decay of the level of interest measured in coincidence with the fully-shifted peak of the γ-ray from the decay of the direct feeding level.When a coincidence gate was set on a transition C above the level of interest, but not directly above (see Section III A), Equation 2 was used: where {I s C , I d B } is the intensity of the degraded components of transition B between the gate and the the state of interest.The term {I C ,I dec } {I C ,I B } , which is often called α [18], reflects any intensity difference between the feeding and depopulating transitions.
As 112 I was a weakly populated channel in the 58 Ni( 58 Ni,3pn) reaction, a γ-ray coincidence gate was first required to select the 112 I nuclei from other reaction products.This selection gate set a requirement that only γ-ray events in coincidence with both components of either the 203-or 210-keV γ-rays at the top of the lower-spin single-particle structure in 112 I (see Fig. 1) were used in the subsequent γ-γ lifetime matrices.These gated 2D γ-γ matrices were produced for Ring 1 versus any detector in Ring 1 or Ring 2 (All) as a function of plunger distance.Likewise, 2D gated matrices were produced for Ring 2 versus any detector in Ring 1 or Ring 2. These matrices are referred to as Ring 1-All, and Ring 2-All, respectively.In these matrices a second gate on the fully-shifted component of the γ-ray directly above the level of interest was then applied to remove potential side feeding.This gate was applied onto the All axis in order to produce the final double-gated spectra projected onto the Ring 1 or Ring 2 axis which were used for to obtain the lifetime of interest.A single gate on the fully-shifted component on the All axis was used as the Doppler shifts in Rings 1 and 2 were very similar.In this work, the double gated spectra are denoted (E below γ /E above γ ).I s (x) and I d (x) were measured and normalised to the total number of counts in the x-projection of the gated 2D matrix for a given x.A piecewise second-order polynomial was fitted to the fully-shifted component as a function of distance.The derivative of this was fitted to the degraded components and Equation 1 was used to calculate the lifetime at each of the target-to-degrader distances [19].

III. RESULTS
Figure 1 shows a partial level scheme of 112 I from this work, showing the single-particle states at low excitation energy and the collective band emerging at higher exci- 1.The level scheme observed in this work for 112 I showing the low spin single-particle levels and the higher-lying single-signature rotational band.The level scheme is in agreement with Ref. [9] apart from the ordering of the 552-and 643-keV transitions which have been reversed in the present work (See Section IV).Proposed spin assignments from Ref. [9] are shown in black, and proposed assignments from this work are shown in red.tation energies.The observed sequence is in agreement with previous studies [9] apart from the order of the first two states in the rotational band, (see Section IV).The widths of the arrows correspond to the efficiency corrected intensities measured in this experiment.The level scheme was constructed using data from clover versus clover gated γ-γ spectra, which combined the data from all distances.These detector rings are at 76 • and 105 • and hence the γ-ray Doppler shift is small.The measured γ-ray energies and intensities of the rotational structure from these gated γ-γ matrices are given in Table I.
Figure 2 shows typical spectra obtained for the band of interest, used to deduce the level scheme in Figure 1. Figure 2(a) shows a projection of the JUROGAM-II clover versus clover γ-γ fully-shifted matrix, for all distances combined for multiplicity 3 or higher events, where at least one of the events was detected in coincidence with the 203-or 210-keV transitions.The 112 I transitions are labelled with their γ-ray energies whereas γ-rays originating from other reaction channels are labelled with symbols, defined in the legend.The main contaminants, with A ≈ 80, were produced from 58 Ni reactions with the 24 Mg degrader foil.using the same gated γ-γ matrix and show decays in coincidence with the 552-and 703-keV transitions, respectively.The data were sorted using the measured recoil velocity of v/c = 0.038(2) after leaving the target (fullyshifted).The measured velocity after passing through the degrader (degraded) was v/c = 0.018(2).

A. Lifetime Analysis
In order to extract fully-shifted and degraded component peak intensities as a function of target-to-degrader distance to perform a lifetime analysis, the fully-shifted and degraded components of the γ-ray transitions depopulating the states of interest were measured using the gated background subtracted matrices of Ring 1-All and Ring 2-All.Gaussian fits were made to the fully-shifted and degraded components.To reduce the fitting errors, the widths and centroids of the peaks were fixed.The fully-shifted widths and centroids were fixed using the 3000 µm distance and the degraded widths and centroids were fixed using the 135 µm distance.At these respective distances, only one of the fully-shifted or degraded components were present.Table II shows the fitted widths and centroids for 333-and 643-keV transitions.To examine the lifetime of the state at 1186 keV in 112 I, the 2D γ − γ Ring 1-All and Ring 2-All matrices were used to produce ((203, 210)/643 f s ) gated spectra for each plunger distance.These spectra are shown in Fig. 3.The measured centroids of the fully-shifted and degraded components are shown in dotted and dashed vertical lines, respectively.The normalised intensities of the two components of the 333-and 643-keV transitions are given at each distance in Table III.The differential decay curve method was used to find the lifetime of the state decaying by the 333-keV γ-ray transition.Figures 4(a The uncertainty shown on the lifetime fits is the weighted uncertainty of the lifetimes calculated at each distance.As the number of data points in the region of sensitivity was small, the fit to the data has relatively large uncertainties.This is partly due to not having an "anchor" point at small distances to constrain the fit.In this case, the weighted average of the lifetime from the four distance measurements results in an underestimate of the true lifetime uncertainty.A more accurate estimate of the uncertainty was made by varying the fit on the data to increase and decrease the χ 2 by 0.5, which gave an error of 20 ps.In view of this, the average lifetime of the state decaying via the 333-keV E1 γ-ray transition, using both Ring 1 and Ring 2, was deduced to be τ = 124(20) ps.cussed, to better estimate the true error on the lifetime measurement for this state, the fit on the data was varied to increase and decrease the χ 2 by 0.5.The average lifetime of the state decaying by the 643-keV γ-ray was thereby deduced to be τ = 130 (25) ps.

Lifetime of the state decaying by the 643-keV transition
It should be noted that the γ-ray intensities of the 552and 643-keV transitions from the lowest two states in the band are equal to each other within one standard deviation of their measured uncertainties in both the present and previous experiments [9].This equality of transition intensities for the lowest two transitions in the band means that their order is somewhat ambiguous.This ambiguity could potentially affect the lifetime measurement, as in order to remove potential side-feeding, the coincidence gate must be set above the transition of interest.For the lifetime analysis of the 1828-keV state shown in Fig. 1, both possible transition orderings for the 552-and 643-keV transitions were considered.
In the original level scheme proposed by Paul et al. [9] the 703-keV γ-ray directly feeds the state decaying by the 643-keV transition.For this level ordering, a lifetime analysis for the state decaying by the the 643-keV transition was performed using a gate from above on the fully-shifted component of the 703-keV transition which resulted in a lifetime of 135 (20) ps.In our revised level scheme, the 552-keV transition is the direct feeder of the 1828-keV state, and hence, for the lifetime analysis of the 1828-keV state a gate was effectively placed on the fully-shifted component of the 552-keV transition and the lifetime was found to be 130 (25) ps.In both approaches, Eq. 2 was used but the term {I s C , I d B }(x) ∼ 0. Both measured lifetime values are consistent within one standard deviation.
The agreement in the lifetime values of the 1828-keV state from the two different gates distinguishes between the ordering presented in Fig. 1 and the ordering presented in Ref. [9].If the original ordering from Ref [9] remained unchanged, our gate on the fully-shifted component of the 552 keV transition would have yielded no events in the degraded component of the 643-keV transition because the gate would have been below set the state of interest.The spectra produced using the gate on the fully-shifted component of the 552-keV transition is shown in Fig. 5 and events in both components of the 643-keV transiton are observed.Using a similar logic, if the ordering in Fig. 1 is assumed then a gate placed on the fully-shifted component of the 643-keV transition should produce no events in the degraded component of the 552-keV transition because the gate is set below the state of interest.In Fig. 7, it can be seen that no intensity in the degraded component of the 552-keV transition is observed at any target-to-degrader distance.These two points demonstrate that the 552-keV transition lies above above the 643-keV transition.This is further discussed in Section IV A.

Lifetime of the state decaying by the 552-keV transition
An attempt was made to deduce the lifetime of the state decaying via the 552-keV γ-ray transition.However, only a small component in the degraded peak of this transition was observed at the shortest 135 µm target-todegrader distance, see Figure 8.No intensity in the degraded peak was observed for larger distances.Using the ratio of degraded to fully-shifted intensities at 135 µm, an upper limit of τ ≤ 6.5 ps was deduced for the lifetime of the state decaying via the 552-keV transition.Shorter target-to-degrader distances would be required to firmly establish the lifetime of this state.

IV. DISCUSSION
In the previous work [9], Cranked Shell Model (CSM) and Total Routhian Surface calculations (TRS) [22,23] were performed in order to interpret the underlying con- figuration of the single rotational band in 112 I.These calculations predicted that the rotational structure in 112 I had a πg 7/2 ⊗ νh 11/2 configuration at low rotational frequencies.Additionally, in the previous work, DCO ratios for several γ-ray transitions were measured.For example, the 643-keV transition was reasoned to be an E2 transition from the DCO ratio of 1.04 (8) and the 333-keV transition was reasoned to be a dipole transition with some possible E2 mixing from the measured DCO ratio of 0.64(7) [9].Based on these DCO ratios along with the TRS calculations, the state at 1186 keV was assigned to be the (7 − ) band-head of the πg 7/2 ⊗ νh 11/2 configuration [9].From Ref. [9], the lower lying levels are due to single-particle structure.
A. Ordering of the states in the πg 7/2 ⊗ νh 11/2 band The aligned angular momentum or alignment, i x , for the πg 7/2 ⊗νh 11/2 band is plotted (black solid line) in Figure 9, from Ref. [9].The large (∼20 ) gain in aligned an- gular momentum around rotational frequencies ω ∼ 0.4 MeV was interpreted to be due to simultaneous alignment of both proton and neutron in the h 11/2 orbitals [9].Hence, the configuration of the structure at high rotational frequencies was deduced to be based upon a π g . This configuration was the basis of the spin assignment for the band.
In the previous work [9], the γ-ray transitions in the rotational structure were ordered based on their intensities and coincidence relationships alone.In the present work, lifetimes of several of the states in this πg 7/2 ⊗νh 11/2 rotational band have been measured for the first time.These lifetimes, and measured γ-ray coincidence relations between fully-shifted and degraded components of consecutive transitions, suggested a reordering of two transitions in the band was required compared to Ref [9].Fig. 5 shows the γ-rays from the 643-keV transition in coincidence with the fully-shifted component of the 552-keV transition.Events in both the fully-shifted and degraded components of the 643-keV transition are observed.The degraded component of the 643-keV transition can only be in coincidence with the fully-shifted component of the 552-keV transition if the 643-keV transition occurs after the 552-keV transition in time, supporting the ordering in Fig. 1.In a similar way, Fig. 7 shows the γrays from the 552-kev transition in coincidence with the fully shifted component of the 643-keV transition.No events in the degraded component of the 552-keV transition are observed at any distance.This suggests the 552-keV transition occurs before the 643-keV transition, again supporting the ordering presented in Fig. 1.This lifetime evidence supports a reordering of the 552-and the 643-keV transitions compared to the level scheme in Ref. [9].However, it must be noted that the short lifetime of the state at 2381-keV would also produce spectra with no events in the degraded component of the 552-keV transition.Figure 1 shows the revised level scheme for the πg 7/2 ⊗ νh 11/2 rotational band based on the evidence presented in Section III A.
The long lifetime of the state at 1828-keV indicates that the state at 1186-keV has non-collective or hindered single-particle behaviour (See Section IV B).This suggests that the 1186-keV state may not belong to the band.Thus, based on our lifetime measurements, we propose that the (7 − ) band-head may in fact be higher at 1828 keV.The rotational band is then built upon this (7 − ) band-head state at 1828-keV as suggested in Ref. [9].Hence, Fig. 1 also shows revised tentative spin assignments for the rotational band.
Figure 9 shows the aligned angular momentum for the reordered structure in 112 I (red squares) where the first two states in the rotational band have been reversed in accordance with our lifetime measurements and the state at 1186-keV is no longer part of the band.The new tentative spin assignments from Fig. 1 are used The revised alignment plot affects the alignment pattern of the lowest two states and does not change any of the proposed configurations and band crossings concluded in Ref. [9].
The deformation deduced from the lifetime measurement of the 643-keV transition in the present work was β 2 = 0.021 (8) [25].This is 10 times smaller than the value predicted by the TRS calculations.Hence it was concluded that the state at 1186 keV does not form a part of the band.The deformation obtained from the limit on the lifetime of the 552-keV transition was β 2 ≥ 0.13 [25].This deformation is more comparable to that predicted from the TRS calculations for the πg 7/2 ⊗ νh 11/2 configuration, although the experimental value is only a lower limit.A more thorough lifetime experiment focused on 112 I would be required in order to make a full comparison with TRS.

V. CONCLUSIONS
In summary, the new lifetime measurements made in the present work reveal that the structure of the proposed rotational band in 112 I is more complicated than intensity and coincidence measurements alone reveal.Although the majority of the level scheme in this work is consistent with that established in Ref. [9], the lifetime measurements suggest a reordering of the lowest two transitions in the band.The relatively long lifetime of the state at 1828-keV suggest that it is the (7 − ) band-head.Hence, new tentative spin assignments have been given on the assumption that the state at 1828 keV is the true bandhead of the πg 7/2 ⊗ νh 11/2 band.Higher statistics data from a gamma-ray spectroscopy or additional lifetime experiment, optimised for 112 I would be required to help fully confirm the revised level ordering presented here.
FIG.1.The level scheme observed in this work for 112 I showing the low spin single-particle levels and the higher-lying single-signature rotational band.The level scheme is in agreement with Ref.[9] apart from the ordering of the 552-and 643-keV transitions which have been reversed in the present work (See Section IV).Proposed spin assignments from Ref.[9] are shown in black, and proposed assignments from this work are shown in red.

FIG. 2 .
FIG.2. 112I spectra obtained from JUROGAM-II clover versus clover γ-γ matrices.(a) Single-gated projection using gates on both the 210 and the 203-keV transitions. 112I transitions are labelled with their energies and contaminants are labelled with symbols given in the legend.Panel (b) shows a double-gated spectrum, using the same gate as panel (a) in coincidence with an additional 552-keV gate.Panel (c) is also a double-gated spectrum using the gate from (a) and an additional gate on the 703-keV transition.

FIG. 3 .
FIG.3. 112I double gated spectra from the Ring 1-All (left) and Ring 2-All (right) matrices, using gates on both components of the 203-or 210-keV γ-ray transitions with the fullyshifted component of the 643-keV γ-ray transition.The fullyshifted (blue-dashed) and degraded (red-solid) components of the 333-keV peak for Ring 1 and Ring 2 are shown for targetto-degrader distances 135 µm to 3000 µm, for (a) to (e) and (f) to (j).The presented spectra are Doppler corrected with respect to the recoil velocity after the target (v/c = 0.038(2)%).

FIG. 4 .
FIG. 4. (a) Lifetime analysis of the state in 112 I decaying via the 333-keV transition, based on DDCM using the Ring 1 (left) and Ring 2 (right) detectors.The intensities of the fully-shifted components of the 333-keV γ-ray as a function of distance are shown in (b) and (e), with the degraded components in (c) and (f).

Figure 5
Figure 5 shows the ((203, 210)/552 f s ) double-gated spectra used to obtain the intensities of the two components of the 643-keV transition.The intensities of each

FIG. 6 .
FIG.5. 112I double gated spectra projected from the Ring 1-All and Ring 2-All matrices, using gates on both components of the 203-or 210-keV γ-ray transitions with the fully-shifted component of the 552-keV γ-ray transition.The fully-shifted (blue-dashed) and degraded (red-solid) components of the 643-keV peak for Ring 1 and Ring 2 (left and right) are shown for target-to-degrader distances 135 µm to 3000 µm, for (a) to (e) and (f) to (j).The presented spectra are Doppler corrected with respect to the recoil velocity after the target (v/c = 0.038(2)%).

FIG. 7 .
FIG. 7. 112 I double gated spectra from the Ring 1-All (left) and Ring 2-All (right) matrices, using gates on both components of the 203-or 210-keV γ-ray transitions with the fully-shifted component of the 643-keV γ-ray transition.The fully-shifted (blue-dashed) component of the 552-keV peak for Ring 1 and Ring 2 is shown.No intensity in the degraded component of the 552-keV peak is observed at any distance.The presented spectra are Doppler corrected with respect to the recoil velocity after the target (v/c = 0.038(2)%).

FIG. 9 .
FIG.9.Aligned angular momentum or alignment, ix, for the band structure in 112 I from Ref.[9] in black solid, and from this work (red-dashed) with the first two states in the band reordered (see text for details).Harris parameters [24] J0 = 152 MeV −1 and J1 = 254 MeV −3 6 have been subtracted from each band plotted in the figure.

TABLE II .
The centroids (C) and widths (W) of the fullyshifted and degraded components of the 333-and 643-keV transitions in 112 I from the Ring 1-All and Ring 2-All doublegated matrices.The double gates ((210, 203)/643 f s ) and ((210, 203)/552 f s ) are used, respectively.