In-beam γ -ray spectroscopy of low-and medium-spin levels in 211 Po

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I. INTRODUCTION A. The nuclide 211 Po
One of the more successful models in describing the structures of nuclei is the shell model, where the structure of a nucleus is built from individual nucleons coupled together to create a greater whole.The interaction between the valence nucleons determine, for the most part, the properties of the levels in a nucleus while the other nucleons often form an inert core.And now with the advent, during the past decade, of more realistic shell-model calculations [1] and the improved roles of genuine and effective three-body forces for heavy nuclei, the prospects of future explorations seem promising.The best available testing ground for shell-model calculations in the heavy-element region is near the doubly magic 208 Pb nucleus.It is therefore important to have as a complete picture as possible of these nuclei.Even with a wide variety of experiments covering the 208 Pb region, performed over a long time span, there still remains nuclei with experimental gaps.This is mostly due to the difficulties of producing the nuclei in the 208 Pb region with stable-ion beams.
One such experimental gap is the nucleus 211 Po with mainly yrast and high-spin levels identified.With two protons and one neutron above their corresponding closed shells (Z = 82 and N = 126), the 211 Po nucleus is an interesting specimen to study not only from a shell-model perspective but also as a general test bed for other models with three-particle interactions.The shells 1g 9/2 , 0i 11/2 , and 0j 15/2 are considered to be the main actors on the neutron side, while the shells 0h 9/2 , 1f 7/2 , and 0i 13/2 play a similar part on the proton side.The isotope 211 Po is also one of the classic examples of yrast spin-gap isomers [2] of nuclei with its isomeric state of 25/2 + at 1462 keV, adding another hurdle for models to take into account.

B. Review of previous works
The first shell-model calculations on 211 Po were preformed by Auerbach and Talmi in an attempt to describe the 25/2 + * joakim.slotte@abo.fiisomeric state [3] in the same way that they were able to successfully describe the isomeric state of 93 Mo.The interaction matrices were written in the form |h 2  9/2 (J 1 )g 9/2 J with the πh 9/2 νg 9/2 interaction taken from 210 Bi and the h 2 9/2 interaction taken from 210 Po.The calculated J = 25/2 level was 1.46 MeV above the ground state compared to, at that time, known experimental value of 1.45 MeV for the isomeric state.The spin gap in 211 Po was shown to arise due to the attraction between a h 9/2 proton and a g 9/2 neutron, which is stronger in the highest spin state J = 9, than in the states J = 8-4.Accordingly, all the calculated 23/2, 21/2, and 19/2 levels were shown to be above the 25/2 state.
Faestermann et al. obtained a mean life of τ = 23 ± 2 ns and a g factor of −0.05 ± 0.02 for the 1065-keV 15/2 − state by using a pulsed α-particle beam of 22.5 MeV on 208 Pb [4].The measured lifetime and positive A 2 were consistent with an enhanced E3 transition of 18 W.u. between the 15/2 − and 9/2 + states.
By studying the protons from the one-neutron stripping reaction 210 Po(d,p) 211 Po at 17 MeV, 35 levels were observed by Bhatia et al. up to 3.9 MeV excitation [5].Extraction of spectroscopic factors and l-value assignments for many levels were made possible by comparing experimental angular distributions with distorted-wave Born approximation (DWBA) calculations.It was also shown that a simple particle-vibration coupling model was inadequate to describe the observed level structure in 211 Po.In terms of binding energy, it was seen that the low-lying states are more bound in 211 Po than in 209 Pb.It was indicated that the particle-core interaction is increased for low-lying states and less effective for states higher up in energy.
By using a basis that contains correlated particle pairs, Silvestre-Brac and Boisson preformed exact shell-model calculations for nuclei consisting of three nonidentical particles outside of the 208 Pb core [6].The Kuo-Herling (KH) and Kim-Rasmussen (KR) interactions were tested and compared to earlier experimental data.Even though some levels differed by some 300 keV, the level scheme was roughly the same with both interactions.The KR energies were slightly better while KH had better spectroscopic factors (neutrons on the 0 + ground state on 210 Po).An yrast trap of 31/2 − at around 2.4 MeV and a 37/2 + isomeric state at 3.5 MeV were predicted by both the KH and KR interactions.
Warburton [8] performed shell-model calculations for 211 Po using a modified Kuo-Herling nucleon-nucleon interaction, and the results agreed fairly well with the measurements done by Bhatia [5] and Fant [7].An yrast spectrum was presented for comparison to anticipated results from fusion-evaporation reaction studies.The experimental 210 Po(d,p) 211 Po spectroscopic factors were rather accurately reproduced.
Discussions of how much of the feeding from high-lying high-spin states will bypass the 25/2 + isomer and therefore be seen in coincidence with γ -ray transitions between the lowlying states were also held.Warburton predicted the 21/2 + , 19/2 + , and 23/2 + yrast states at 1505, 1546, and 1646 keV, and the decays of these states can be expected, at least partially, to bypass the 25/2 + isomer.
Using the deep inelastic collisions, with 76 Ge at 450 MeV on 208 Pb, with the goal to populate nuclei in the vicinity of 208 Pb, Fornal et al. also studied the high-spin states above the 25/2 + α-decaying isomer in 211 Po [10].The same isomers as in Ref. [9] were detected with measured lifetime of 0.25 (7) μs for the (31/2 − ) state and 2(1) μs for the (43/2 + ) state.In their interpretation of the (37/2 − ) and the (43/2 + ) states, Fornal et al. characterized both isomers as part of a core 208 Pb excitation, in the form of (πh Single-particle states in the doubly magic 132 Sn region have corresponding single-particle states around 208 Pb with one unit larger angular momenta l and j .Fornal et al. compared the yrast level structures of the three-valence-particle nucleus 135 Te with 211 Po [11].The ordering of the corresponding states was the same and their relative energy spacings were similar, and therefore it was concluded that more complex shell-model configurations were also similar between the different regions of doubly magic nuclei.
Sun and Guo investigated the possibility of neutron halos in the excited states for N = 127 isotones using a nonlinear relativistic mean-field theory [12].The results of the calculations agreed with the experimental data of neutron halos in the excited states of 209 Pb.Furthermore, neutron halos were predicted to exist in the excited states of 2d 5/2 , 3s 1/2 , and 2d 3/2 in 207 Hg, 208 Tl, 210 Bi, and finally in 211 Po.

C. Aim of the present work
The main aim of the present work was to characterize the non-yrast low-and medium-spin states and thereby complement the structural studies by Fant et al. and McGoram et al. [7,9].The reaction mechanism was chosen to be the same as in Ref. [7] but with a slightly higher energy, and the details of the present experimental setup are briefly discussed in Sec.II.The results and level schemes are presented in Sec.III.The configurations of the different levels are discussed in Sec.IV and finally a summary is given in Sec.V.

II. EXPERIMENT AND DATA ANALYSIS
The reaction 208 Pb(α,n) was used to populate excited states in 211 Po.An enriched 208 Pb 8-10mg/cm 2 target foil was bombarded by a 23-MeV α-particle beam, with an average beam current of 13 particle nA, provided by the K130 cyclotron at the Accelerator Laboratory at the Department of Physics of the University of Jyväskylä (JYFL), Finland.Utilizing the JUROGAM I array with 43 compton-suppressed HPGe detectors, the prompt γ rays were detected.The detectors were installed in six rings around the target chamber with the angles 72.05 • , 85.84 • , 94.16 • , 107.94 • , 133.57• , and 157.60 • with respect to the beam direction.The energy resolution for HPGe detectors were 2.5 keV at 1332 keV.A total of 1.1 × 10 7 singles events were collected during 8 h of beam time.The triggerless Total Data Readout (TDR) acquisition system [13] was used to time stamp the events.Data were sorted offline with GRAIN [14] and analyzed with the RADWARE software packages [15,16].
Where feasible, γ -ray angular distributions were determined for the more intense transitions.The intensities, determined from spectra of the individual detector rings, were fitted to Legendre polynomials of the form W (θ ) = A 0 + A 2 P 2 (cosθ ) + A 4 P 4 (cosθ ) [17].In cases where the angular distribution fits yielded lower χ 2 values when A 4 was left out, they are presented as such.To complement the angular distribution analysis, a form of angular anisotropies were also used.In our case, the anisotropy is defined as A = W (72.5 • )+W (157.60 • ) 2W (94.16 • ) and was especially useful when statistics were too poor to fit the normal angular distribution.After detector efficiency corrections, some typical values for the anisotropies for pure stretched transitions were 0.76-0.98 for quadrupole transitions and 0.54-0.81for dipole transitions.Pure transitions of the type J = 0 were between 0.37 and 0.46 for quadrupole transitions and between 1.15 and 1.26 for dipole transitions, while nonstretched J = 1 quadrupole transitions have their values between 1.34 and 2.29 for downward and between 0.61 and 0.88 for upward transitions.
Another way to determine the multipole of transitions is by γ -ray angular distribution from oriented nuclei (ADO) ratios [18].The main advantage with the ADO ratio is that it is independent of the gating transition.Experimentally the ADO can be seen, in our case, as I(γ 1 : 90 • ,γ 2 :all)/I (γ 1 : 133 • ,γ 2 :all).Here I (γ 1 :θ,γ 2 :all) is the intensity of the observed γ ray at the angle θ by setting gates on detectors to allow for any angle.This method requires the construction of two γ -γ matrices, corresponding to θ 1 vs all and θ 2 vs all.In the case of sorting γ -γ matrices for the ADO analysis, the detector rings at 85.84 • and 94.16 • were combined to form a new ring at 90 • .Typical ADO values in this experiment were 0.6 for stretched pure dipole transitions and 1.0 for stretched pure quadrupole transitions.Some care must be taken as the ADO ratios cannot differentiate between J = 0 dipoles or certain J = 1 mixed transitions and stretched E2s.New transitions and previously unassigned transitions were assigned E2 multipolarity for stretched quadrupole transitions and pure dipole transitions were assigned M1 or E1 multipolarity.Mixed transitions are assumed to be of the E2/M1 type.

III. RESULTS AND LEVEL SCHEME
The properties of the γ rays originating from 211 Po are summarized in Table I.New transitions have their energies marked with a n , e.g., 138.73(4) n .
Most γ -ray intensities are taken from coincidence spectra and in the cases where the intensity is determined from the single spectrum the intensity is noted with an asterisk (*) after it.Only in cases where the both the spin and parity are known of levels involved in a transition is the multipolarity explicitly written.In general, the statistical data gathered in the current work is improved compared to Ref. [7] and the differences in the intensities of earlier known transitions depend, with the higher energy of the incoming α particle in the reaction, on the feeding of levels higher in energy and spin.
The total projection spectrum of the E γ -E γ matrix is shown in Fig. 1.Two dominating peaks in Fig. 1, the 245-keV and partly the 1181-keV peaks, have their origin in 210 Po.The strong presence of 210 Po, with levels identified up to the 7 + state at 2438-keV level, compared to Ref. [7] was to be expected as the beam energy of 23 MeV is well above the (α,2n) threshold and the cross section for the (α,n) channel is rather small at this energy [19].
With higher beam energy, the higher spin states in 211 Po were more emphasized, as can be seen, for example, by the less prominent 193-keV transition and the overall increased intensity along the yrast cascade compared to Ref. [7].
Of some interest are the unidentified peaks at 709, 1264, and 1274 keV, which are also found in Ref. [7].The 709-and 1264-keV peaks are marked in Fig. 1 and the 1274-keV peak is after 1264 keV.Of these peaks, the 1274-keV one is also seen in the background spectra.No feasible background radiation correspond to these energies, and neither does gating on these energies and their coincident events help to place these γ -ray transitions in current known level schemes.

A. Construction of level schemes
The level scheme of 211 Po has been built and expanded in accordance with the findings of current work.The level scheme is presented as partial level schemes (see Figs. 2-5) and highlights cascades through different levels.A selection of gates obtained from the E γ -E γ matrix are shown in the Figs.6 and 7. A few peaks in Fig. 6 and certain areas in Fig. 7 have been rescaled.In both cases, scaling factors are placed next to the peaks in question or in the relevant parts of the spectrum.Where larger intensities of chance coincidences or contaminants make an appearance, these are marked with asterisks.
In Fig. 6(a), the gated spectrum of the 363-keV γ transition is shown while the partial level scheme in Fig. 2 mainly shows the levels above the 17/2 + level at 1427 keV.In current work, a gating time of 100 ns was used and thus transitions to the 1427 + keV level, with a lifetime of 36(2) ns [9], could be measured.Distinguishing between transitions cascading via the 1427 + keV level and other transitions coming directly to the 17/2 + level at 1427 keV is hard.Therefore, new γ transitions feeding the 17/2 + level at 1427 keV, but not in coincidence with previously known transition originating from levels above 1427 keV, are placed above this level, while technically they could decay via the (21/2 + ) isomer at 1427 + keV.
The γ -ray transitions 152 and 425 keV are seen in coincidence with the 188-keV transition and have been moved from their previous placings [9], i.e., between 1616 and 1427 keV and between 1853 and 1427 keV, respectively.The new initial levels are 1768 keV for the 152-keV transition and 2041 keV for the 425-keV transition.The new γ -ray transition of 538 keV coincides with both the 188-and 425-keV transitions.Using intensity arguments, the 538-keV γ -ray transition is placed to originate from a new level at TABLE I.The first three columns give energies of the γ ray and of the initial and final states involved in the decay.Transitions marked with n are not reported earlier.The fourth column gives the γ -ray intensities normalized to the 1064-keV transition.Intensities taken from the single spectrum are marked with s , whereas the rest are taken from coincidence spectrum.Columns 5, 6, and 7 show the results of the anisotropy, angular distribution, and ADO "fits."The last columns supply the assigned multipolarities of the transition and the spins of the involved states.Mixing ratios were not deduced and transitions assigned as having a multipolarity of dipoles may include some quadrupole admixture.Quoted errors are statistical only.The gated transition used to acquire the ADO values are marked in the following way: a, 193 keV; b, 278 keV; c, 335 keV; d, 363 keV; e, 392 keV; f, 687 keV; g, 796 keV; h, 1028 keV; i, 1050 keV; j, 1121 keV; k, 1161 keV; l, 1181 keV; m, 687+363 keV.γ -ray energy Initial state Final state Intensity Anisotropy Angular distribution ADO Multi-    2578 keV, above the 2041-keV level with the de-exciting 425-keV transition; see Fig. 2.
Figure 6(b) shows the gate of 1064-keV transition decaying from the 15/2 − level at 1064 keV to the ground state.Perhaps the first notable change compared to the gate of 363 keV in Fig. 6(a) are the transitions 1189, 1250, 1288, 1342, 1384, and 1598 keV.These new transitions, among others, will be discussed more in Sec.IV and their placement in the level scheme can be seen in Fig. 3.As the 570-keV transition in 207 Pb, the decay product of 211 Po, also has a coincident 1064-keV peak [20], it is also present in Fig. 6(b).In the same gated spectrum, the 269-and 270-keV peak is a doublet consisting of both the 269-and 270-keV transitions originating from the 1679-and 1696-keV levels, respectively.
The gate of the 687-keV transition from the 11/2 + level at 687 keV can be seen in Fig. 6(c).Only the most intense γ transitions from Fig. 6(b) are seen in Fig. 6(c) as the branching at the 15/2 − level at 1064 keV heavily favors the decay path down to the ground state compare to the decay to the 11/2 + level at 687 keV.Other changes include the transitions that appear in almost two groupings, i.e., the first roughly 1030 to 1258 keV and the second one from 1355 to 1626 keV.The γ -ray transitions from these groups and their initial levels can be seen in the partial level scheme in Fig. 3.
The doublet at 474 and 475 keV in Fig. 6(c) consists of both a new transition at 474 keV, originating from the 9/2 + level at 1160 keV shown in Fig. 3, and a known transition at 475 keV between the levels 1902 + keV and 1427 + keV [9].The 475-keV transition is also seen in Figs.6(b) and 6(a).When comparing the different gates in Fig. 6, the gate of 687 keV displays mainly energetically higher γ rays while the gate of 363 keV show less energetic γ rays.The gate on 1064 keV, on the other hand, displays both low-and high-energy γ rays.Most of the peaks shown in Fig. 6(a) are also found in Fig. 6(b).
Figure 7(a) shows the gate of the 1160-keV γ -ray transition and in the right-hand side of Fig. 5 the partial level scheme of the most of the levels decaying down to the 9/2 + level at 1160 keV are shown.The 1160-keV gate in Ref. [7] was relatively empty with a few transitions at the lower end of the spectrum, while in current work, the majority of peaks in Fig. 7(a) are new.In Fig. 7(a), the 245-and 249-keV peaks are almost on top of each other.The 245-keV peak is a coincidence from 210 Po while the 249-keV peak is the transition between the levels at 1409 and 1160 keV.
The 1122-keV gate is shown in Fig. 7(b) and the corresponding level scheme shown in the middle part of Fig. 5 is constructed with most of the new transitions seen in this gate.The transitions 286 and 288 keV in Fig. 7(b) are hard to distinguish and seem to make the total peak broader.These transitions originate from the levels at 1407 and 1409 keV, respectively, and are shown, for instance, in Fig. 4.
In Fig. 7(c), the gate of 1050 keV is shown and the lefthand side of the partial level scheme in Fig. 4 shows most of the γ -ray transitions in coincidence with the 1050-keV transition.Certain peaks higher up in energy than 1227 keV in Fig. 7(c) are not placed in current level schemes, for instance, the 1274-and 1389-keV transitions, as gates on these peaks neither have enough statistics nor yield transitions to draw explicit conclusions from.
Comparing the transitions 534 keV and 564 keV, from the levels 1584 and 1614 keV, respectively, in Fig. 7(c) with the gate of 1050 in Fig. 6, in Ref. [7], one can see that the intensities have switched so that in the present study the 534-keV peak is now the larger one.This would indicate that the 1584-keV level either has a higher or the same spin value than the 1614-keV level and/or that the level feeding the 1614-keV level has a low spin value.
With a slightly lower measured energy for the 458-keV transition and slightly higher energies for the 348-and 387-keV transitions, these γ rays were placed to originate from the same level at 1508 keV as opposed to two different levels at 1508 and 1509 keV as reported in Ref. [7].There are two other instances where the two level energies are very close to one another.In the first case, the levels of interest are the levels at 1876.8(3) and 1877.0(5)keV, and in the second case, it is the levels at 2152.8(5) and 2152.9(3)keV.In the first case, the levels are assigned different spin values and are thereby clearly two different levels, see Table I, while the spin values are inconclusive in the other case and it remains unknown whether they are the same level or not.
The 1518-keV γ -ray transition is assigned to originate from the level at 1517 keV even though there is a slight discrepancy between the γ -ray energy and the energy of the level in question.The placement of the 1518-keV γ ray is based upon the coincident γ rays of the 166 and 283 keV that are also seen by the 357-keV transition from the 1517-keV level.

B. Level spin assignment
Not all levels with γ -ray transitions, with measured angular data, alone were conclusive regarding their level spin.It is possible to draw conclusions regarding the involved spins by looking at the levels connected by transitions both to and from the levels in question.In this subsection, the arguments for some of these assignments will be discussed in detail.
The spin of the levels 1443 and 1614 keV are determined at the same time, from both the decay of these levels and from the feeding decay connected to these levels; see Fig. 4. The 392-keV transition between the 1443-keV level and the 5/2 + level at 1050 keV has a measured ADO value of 0.95, and the angular distribution values are close to being isotropic in nature.Looking at the ADO value, the spin for the 1443-keV level is either 9/2 or 1/2 with a stretched quadrupole transition, 5/2 as J = 0 transition, and 3/2 or 7/2 as mixed J = 1 transition.The levels 1443 and 1614 keV are also connected through a mixed J = 1 172-keV transition and the 1614-keV level also decays to the 7/2 + level at 1122 keV with a mixed J = 1 493-keV transition and to the 5/2 + level at 1050 keV with a 564-keV transition with an ADO value of 0.95.The only possible spin values to satisfy all the end spins for the known 1050-and 1122-keV levels and the spin differences from the γ -ray transitions are 3/2 or 7/2 for the 1443-keV level and 5/2 for the 1614-keV level with the 392-keV transition being a mixed J = 1 and the 564 keV being a J = 0 transition.Out of the two possible spin values for the 1443-keV level, the 3/2 is considered to be the more likely one, as a with a spin value of 7/2 one would also expect decay to the 9/2 level at 1160 keV.
The ADO value of the 992-keV transition between the level at 1679 keV, shown in Fig. 5, and the 11/2 + level at 687 keV FIG. 4. Partial level scheme depicting mainly the decay of levels above and connected the 1050-keV level.New transitions are marked in red. is indicated as being a stretched dipole transition giving the transmitting level the possible spins of 9/2 and 13/2.The 557-keV transition between the same 1679-keV level and the 7/2 + level at 1122 keV is a mixed J = 1 transition, thereby eliminating the possibility of the 1679-keV level from having the spin value of 13/2.
The measured anisotropy of the 522-keV transition, decaying from the level at 1683 keV to the 9/2 + level at FIG. 6. Spectra obtained from the E γ -E γ matrix of prompt transitions measured by JUROGAM I gated with selected transitions in 211 Po.Prominent transitions are marked with their energies in units of keV while chance coincidences and contaminants are marked with an asterisk.The transitions 363 and 570 keV in the 1064-keV gate and the 1064-keV transition in the 363-keV gate have been downsized by the amount indicated next to the peak in question.FIG. 7. Spectra were obtained from the E γ -E γ matrix gated with selected transitions in 211 Po.Prominent transitions are marked with their energies in units of keV while chance coincidences and contaminants are marked with an asterisk.The scaled regions are marked by dashed lines and the amount of scaling done is shown by the corresponding number next to the arrows.1160 keV, shown in Fig. 5, indicates that it is a stretched pure quardupole transition.Besides the rather large A 4 /A 0 value, the angular distribution would suggest that the 522-keV transition is an upward nonstretched quadrupole transition.Leaning more toward the angular distribution and considering the above-mentioned ambiguity, the 1683-keV level is tentatively assigned the spin value of (7/2).The level at 1696 keV, to the left in Fig. 5, is given the spin value of 15/2 as two of three transitions, 269 keV to the 17/2 level at 1427 keV and 515 keV to the 13/2 level at 1181 keV, from this level have the measured values of d/q transitions.As the third 1008-keV transition does not contribute to the 1696-keV level assignment, the spin value is given based only on the two first transitions.
The level at 1726 keV, shown in the center of Fig. 3, decays both to the 7/2 + level at 1122 keV with a 605-keV transition and to the 11/2 + level at 687 keV with a 1040-keV transition.With the 1040-keV γ ray being a stretched quadrupole transition, the level at 1726 keV has the possible spin values of either 7/2 or 15/2.The spin value of 7/2, rather than 15/2, is more favorable for the conditions up by the decay to the 7/2 + level at 1122 keV to be fulfilled.
With an ADO value of 0.98, the 1128-keV transition gives the following possible spin values of 7/2 or 15/2 as a stretched quadrupole transition and 11/2 as a J = 0 transition for the level at 1815 keV.The 1815-keV level also decays to the 7/2 + and 9/2 + levels, at 1122 and 1160 keV respectively, which rules out the spin value of 15/2, and while 7/2 is possible, one would in that case also expect a transition to the 5/2 + level at 1050 keV.Therefore, the level at 1815 keV is assigned the spin value of 11/2.
The transitions originating from the 1917-keV level, i.e., the 737-keV transition to the 13/2 + level at 1180 keV and the 796-keV transition to the 7/2 + level at 1122 keV, see middle of Fig. 5, are somewhat problematic with the current data at hand.Working with mostly dipole and quadrupole transitions, the spin values for the 1917-keV level should be either 9/2 or 11/2.Ignoring the very low ADO value for the 737-keV transition, the other distribution values show properties of an upward dipole transition, indicating that the 1917-keV level should have a spin value of 11/2.On the other hand, the analysis of the properties of the 796-keV transition shows that it is a J = 1 mixed transition and out of the two possible spin values, for the 1917-keV level, the 9/2 works best in this case.With conflicting evidence, the 1917-keV level is marked as either 11/2 or 9/2.
The ADO value for the 973-keV γ -ray transition between the 2023-and 1050-keV levels proposes a stretched quardupole transition, i.e., initial level as either 9/2 or 1/2.The spin value for the 2023-keV level is then set as 1/2 as it also decays to the 1/2 − level at 1578 keV; see Fig. 4.
A spin value of 1/2 was assigned to the level at 2033 keV shown in the right-hand side of Fig. 4 as the transition from this level to the 1050-keV level and is a stretched quadrupole, while the new transition at 455 keV, also from the 2033-keV level, decays to the 1/2 − level at 1578 keV, ruling out the 9/2 assignment.
The fits for the angular distribution and the anisotropy for both the 755-and the 758-keV transition are far from optimal, and the ADO values alone are used for tentatively suggested spin values of 11/2 or 3/2 for the 1877-keV level and the 2186 + keV level is either 25/2 or 17/2.Of the two possible spin values for the 2186 + keV level, the 25/2 is the more likely one, as the level decays to the 1427 + keV level and not to the 17/2 + level at 1427 keV.These transitions and involved levels are shown in Fig. 2.
The 1108-keV transition in 210 Po, between 2 + levels at 2290 and 1181 keV, affects the anisotropy and angular distribution analysis of the 1110-keV transition in 211 Po between the 1797-keV and the 11/2 + , at 687 keV, levels.The ADO value for the 1110-keV γ -ray transition points to a stretched dipole transition and since the 1797-keV level also decays to the 1427-keV level with a spin value of 17/2 + , the level in question, shown in Fig. 3, is assigned the spin value of 13/2.

IV. DISCUSSION
This section aims to clarify the configurations of certain levels in terms of the shell Even though many levels do not have spin and parity assigned to them, it is still possible to deduce configurations from the apparent decay paths and by comparing the levels in 211 Po with its close neighboring nuclei.The main configurations assigned to levels in 211 Po are summarized in Table II.Quantitative comparison between the configuration assignments made in this work will be compared with model calculations in a future publication.
Looking at the 211 Bi nucleus, one finds a similar story of only four out of five contenders for the corresponding configuration [22,23].The elusiveness of the 11/2 + state in 211 Po is mentioned in Ref. [8] by Warburton by remarking that the k = 2 and 3, i.e., second and third, 11/2 levels were predicted to have the spectroscopic factor values, S + n , below that of perception for the 210 Po(d,p) reaction.As the k = 3 11/2 state was identified in current work with the 208 Pb(α,γ n) reaction as the 1409-keV level, one is left to wonder why the k = 2 11/2 + is not apparent.
The π (h 9/2 ) The 17/2 + level at 1427 keV will also be brought up to discussion, in the mixed level configurations, Subsec.IV H, due to its decay to the 15/2 − level at 1064 keV.The decay between these two levels could be seen as the transition between π (h 9/2 ) 2  4 + ⊗ νg 9/2 and π (h 9/2 ) 2 0 + ⊗ νj 15/2 .As will be discussed, this unlikely transition is made possible due to octopole mixing of the latter state.
Assigning levels to the π (h 9/2 ) 2 6 + ⊗ νg 9/2 configuration is harder compared to previous configurations with current data and the lack of theoretical coverage of said configuration.In this configuration, 10 states are expected with spin values ranging from 21/2 down to 3/2, and with the 21/2 level locked as the 1427+ keV level, the remaining 9 have to depend on future endeavors.
The π (h 9/2 ) 2 8 + ⊗ νg 9/2 configuration was not part of this study as these levels are hard to reach with currently used reactions and energy.Still, a few words can be said about it.The 25/2 + isomer at 1462 keV is from the π (h 9/2 ) 2  8 + ⊗ νg 9/2 configuration, which yields 13 states with spin values ranging from 25/2 to 7/2.The 27/2 + at 1820 keV is the only other level previously assigned to this configuration [9].With current data, another level belonging to this multiplet is most likely the 21/2 level at 1541 keV.Besides the levels mentioned in Fant et al. [7], a further three levels are added to the list of possible candidates of the π (h 9/2 ) 2  2 + ⊗ νi 11/2 configuration.The list would then be as follows: 1678, 1715, 1726, 1797, 1809, 1815, 1877, and 1944 keV.With some degree of confidence, the levels 1679 and 1797 keV can ruled out by examining other decay routes these levels take.Both mentioned levels, for example, also have transitions to π (h 9/2 ) 2 4+ ⊗ νg 9/2 configuration levels, therefore making their inclusion in the π (h 9/2 ) 2  2 + ⊗ νi 11/2 configuration unlikely.Some of the candidate levels have only the dipole or quadrupole nature of their decay transitions known.Considering that spin values of the 2 + ⊗ νg 9/2 levels start with the 5/2 + to the 13/2 + in ascending order, one would expect the situation to be the same in the 2 + ⊗ νi 11/2 case.With this in mind, the following levels, with corresponding spins 1726 (7/2), 1809 (9/2) 1815 11/2, 1877 (13/2), and 1944 (15/2), are suggested as the 2 + ⊗ νi 11/2 multiplet and are shown in Fig. 3.
originating from this configuration and are most likely in the middle of the possible multiplet spin range.The higher and lower end spin levels from this multiplet are expected to decay along other paths as the spin difference to the 11/2 + level at 687 keV will be too large.The levels at 2253, 2314 (17/2), 2352 (11/2), 2406 (13/2), and 2448 keV, shown in Fig. 3, are considered to be candidates for the π (h 9/2 ) 2  2 + ⊗ νj 15/2 configuration levels.The 2448-keV is somewhat problematic as the spin for this level is measured to be either 13/2 or 17/2, and these spin values are already tentatively assigned to the 2406 and 2314-keV levels This means that one of the above mentioned levels does not belong the 2 + ⊗ νj 15/2 multiplet.In the search other candidate levels, it is prudent to remember 48% of the 15/2 − level at 1064 keV is 3 − ⊗ νg 9/2 [4].With this mixing in mind, the levels from the 2 + ⊗ νj 15/2 multiplet could also include admixture of the form 2 + ⊗ (3 − ⊗ νg 9/2 ) and decay to the 4 + ⊗ νg 9/2 levels would be possible.There are other levels in the relevant energy region; e.g., the mean value of the 2 + in 210 Po at 1181 keV added to the energy of j 15/2 in 211 Po at 1064 keV yields an energy of 2245 keV, but without explicit measured spin and parity it is hard to determine which final level should be included.
With higher energy, the 2622-and 2701-keV levels are then considered to belong from the π (h 9/2 ) 2  4 + ⊗ νj 15/2 configuration.The 2448-keV level mentioned earlier in the discussion might actually originate in this multiplet.As in the case of the π (h 9/2 ) 2  4 + ⊗ νi 11/2 configuration levels, these levels are probably from the middle of the configuration spin range.

D. Single-neutron particle states of νd 5/2 and νs 1/2
The single-neutron states νd 5/2 and νs 1/2 in 209 Pb reside at 1567 and 2032 keV, respectively [24][25][26].In the current work, the assigned levels for the corresponding single-particle states in 211 Po are the (5/2) level at 1584 keV and the 1/2 level at 2033 keV, shown in the level scheme presented in Fig. 4. Also, a comparison between the single-particle states in 209 Pb and the currently assigned single-particle states 211 Po are shown in Fig. 9.The single-neutron states of νg 7/2 and νd 3/2 are found at the energies of 2449 and 2547 keV respectively in 209 Pb [24].With current data, there are no levels with the right energy and spin for a corresponding νg 7/2 state in 211 Po.The level at 2547 keV in 211 Po would be the perfect candidate for the νd 3/2 state energywise, but without a measured spin value for this level it is difficult to asses which configuration it belongs to.So, out of the three states with predicted neutron halos in 211 Po [12], two, i.e., the νd 5/2 and νs 1/2 states, are now identified.
The π (h 9/2 ) 2 2 + ⊗ νd 5/2 configuration, with spins from 9/2 + to 5/2 + , would probably end being around an energy of 2765 keV, i.e., the 2 + in 210 Po at 1181 keV added to the energy of the d 5/2 in 211 Po at 1584 keV.The 1578-keV level was proposed in Ref. [7] to be the first neutron hole νp −1 1/2 level.The spin and parity for the 1578-keV level was evaluated to be 1/2 − in Ref. [7] and its measured half-life of 3.5 ns correlates well with the half-life of 3.96 ns [27] of the corresponding neutron hole, νp −1 1/2 , at 2149 keV in 209 Pb [24].The γ -ray transition of 645 keV, between 2224and 1578-keV levels in 211 Po, shows quadrupole properties supporting the idea that it is the next neutron hole νf −1 5/2 .The neutron hole levels in 211 Po, i.e., 1578 and 2224 keV, are shown in the level scheme in Fig. 4. In Fig. 9, these two states are compared to the neutron holes in 207 Pb and 209 Pb.
As can be seen, the neutron holes in 211 Po are similarly spaced as their corresponding neutron holes in 207 Pb [20] and 209 Pb [24].Although when comparing 211 Po with 209 Pb, there

FIG. 1 .
FIG.1.The total projection spectrum of the E γ -E γ matrix.Only the most prominent peaks are marked with their energies.The presence of the 210 Po nucleus is seen by the 245-keV peak and partly the 1181-keV peak while the 207 Pb nucleus is noted by the 570-keV peak.

TABLE I .
(Continued.)γ -ray energy Initial state Final state Intensity Anisotropy Angular distribution ADO Multi- FIG. 5. Partial level scheme displaying transitions cascading through the 1181, 1122-, and 1160-keV levels.New transitions are marked in red.

TABLE II .
Main configurations assigned to levels.Levels marked with an asterisk have not yet been identified or the spin value has not been determined.
A. The π (h