Octupole states in 207 Tl studied through β decay

T. A. Berry,1 Zs. Podolyák,1, ∗ R. J. Carroll,1 R. Lică,2, 3 B. A. Brown,4 H. Grawe,5 Ch. Sotty,3, 6 N. K. Timofeyuk,1 T. Alexander,1 A. N. Andreyev,7 S. Ansari,8 M. J. G. Borge,2 M. Brunet,1 J. R. Cresswell,9 C. Fahlander,10 L. M. Fraile,11 H. O. U. Fynbo,12 E. Gamba,13 W. Gelletly,1 R.-B. Gerst,8 M. Górska,5 A. Gredley,9 P. Greenlees,14, 15 L. J. Harkness-Brennan,9 M. Huyse,6 S. M. Judge,16 D. S. Judson,9 J. Konki,14, 15, † M. Kowalska,2 J. Kurcewicz,2 I. Kuti,17 S. Lalkovski,1 I. Lazarus,18 M. Lund,12 M. Madurga,2 N. Mărginean,3 R. Mărginean,3 I. Marroquin,19 C. Mihai,3 R. E. Mihai,3 E. Nácher,19 A. Negret,3 S. Noe,3 C. Niţă,3, 13 S. Pascu,3 R. D. Page,9 Z. Patel,1 A. Perea,19 J. Phrompao,20 M. Piersa,21 V. Pucknell,18 P. Rahkila,14, 15 E. Rapisarda,2 P. H. Regan,1, 16 F. Rotaru,3 M. Rudigier,1 C. M. Shand,1 R. Shearman,1, 16 E. C. Simpson,22 S. Stegemann,8 T. Stora,2 O. Tengblad,19 A. Turturica,3 P. Van Duppen,6 V. Vedia,11 P. M. Walker,1 N. Warr,8 F. P. Wearing,9 and H. De Witte6 1Department of Physics, University of Surrey, Guildford, GU2 7XH, United Kingdom 2CERN, Physics Department, 1211 Geneva 23, Switzerland 3H. Hulubei National Institute for Physics and Nuclear Engineering, Bucharest, Romania 4Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824-1321 5GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany 6KU Leuven, Instituut voor Kernen Stralingsfysica, Celestijnenlaan 200D, 3001 Leuven, Belgium 7Department of Physics, University of York, York YO10 5DD, N Yorkshire, United Kingdom 8Institut für Kernphysik der Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany 9Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 10Department of Physics, Lund University, S-22100, Lund, Sweden 11Grupo de F́ısica Nuclear, FAMN, Universidad Complutense, CEI Moncloa, 28040 Madrid, Spain 12Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus, Denmark 13University of Brighton, Brighton BN2 4GJ, United Kingdom 14University of Jyvaskyla, Department of Physics, P.O. Box 35, FI-40014 University of Jyvaskyla, Finland 15Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland 16National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK 17Institute of Nuclear Research of the Hungarian Academy of Sciences, 4026 Debrecen, Hungary 18STFC, Daresbury Laboratory, Warrington, WA4 4AD, United Kingdom 19Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, E-28006 Madrid, Spain 20Department of Physics and Materials Science, Chiang Mai University, Chiang Mai, Thailand 21Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland 22Department of Nuclear Physics, Research School of Physics, The Australian National University, Canberra ACT 2600, Australia (Dated: March 16, 2020)

The β decay of 207 Hg into the single-proton-hole nucleus 207 Tl has been studied through γ-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the πs −1 1/2 , πd −1 3/2 and πh −1 11/2 shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states (s 1/2 -coupled) are identified and three more states (d 3/2 -coupled) are tentatively assigned using spin-parity inferences, while further h 11/2 -coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic under-estimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and non-collective t=1 states (t is the number of nucleons breaking the 208 Pb core), the effect of t=2 mixing may be reduced for octupole-coupled states. The inclusion of mixing with t=0,2,3 excitations is necessary to replicate all t=1 state energies accurately.
Introduction: One of the most prominent features of the well-studied stable doubly-magic 208 Pb nucleus is its octupole vibrational first excited state at an en- [4].
It is expected that the composition of the collective octupole excitation in terms of shell model wave functions is reflected in its behaviour when coupling to those orbitals. Knowledge of the composition of this phonon is of interest. While large-scale shell model calculations are able to describe the collective octupole and double-octupole states around 208 Pb [4,5], the energies of the octupole states are not reproduced accurately, indicating a possible gap in our knowledge. Experimental data on coupled states are therefore needed. The single-proton-hole nucleus 207 Tl is expected to feature a number of states resulting from coupling between the octupole phonon and the πs −1 1/2 , πd −1 3/2 and πh −1 11/2 states in the 2-4 MeV energy region. The capability of β decay to populate a number of excited states in the 2.5-4.0 MeV energy region [6] means that β − decay from the parent nucleus 207 Hg (J π g.s. = (9/2 + ) , Q β =4550(30) keV [7,8]) should populate a number of these coupled states in allowed and first-forbidden decays.
Experimental details: Two experiments took place at the CERN-ISOLDE facility. In both experiments, a molten lead target coupled to a VD5 FEBIAD [16] ion source was bombarded by a 1.4 GeV beam of protons and singly-charged 207 Hg was extracted. The reaction mechanism of 207 Hg production is not clear. A secondary (n,2p) reaction was assumed previously [6]. However, more recent population of N > 126 nuclei using a thin target [17] suggests an alternative production mechanism, where the role of the ∆ resonance [18] should be considered. While the reaction mechanism leading to the population of 207 Hg does not affect the results presented here, its understanding is important for planning future experiments.
In the first experiment the beam was extracted down the ISOLDE beam-line with a potential of 30 kV. Ions with mass A = 207 were selected by the General Purpose Separator (GPS) and deposited upon the tape at the ISOLDE Decay Station (IDS), at a rate of up to 5 × 10 4 pps. The four resident four-crystal HPGe clover detectors were combined with a single Miniball cluster detector [19] along the beam axis for improved total γ efficiency (22% at 100 keV, 8% at 1 MeV). Three plastic scintillator detectors were used for β gating (total β efficiency ∼ 30%). In the second experiment, aimed at γγ angular correlation measurements, the beam was extracted at 50 kV, separated with GPS and deposited at IDS at a higher rate of up to 2 × 10 5 pps. The four IDS clovers were combined with a fifth (TIGRESS [20]) clover positioned off-axis (total γ efficiency 11% at 100 keV, 4% at 1 MeV). β gating using a plastic scintillating block and photomultiplier tube surrounding the tape was switched off during the experiment as high count rates led to significant dead-time. The triggerless total data readout (TDR) system [21] at IDS was used for data acquisition.
Efficiency calibration of the array of germanium detectors was performed using 152 Eu and 60 Co sources. Extension of this calibration up to an energy of 2614 keV utilised the known ratio [1] between the intensities of the 583 keV and 2614 keV transitions in 208 Pb following β − decay of 208 Tl on the tape, measured during a separate run on the A = 208 separator setting. For angular correlations the relative efficiencies of individual detectors must be known to a high precision. Individual detectors were efficiency-calibrated as above, and were further calibrated by adjusting for relative peak intensities of ungated single transitions in 207 Tl measured during the run.
Matrices of βγ and βγγ coincidences were obtained using data from the first experiment. These were used to establish transition energies and intensities. The effect of the condition of β detection on the determined γ-ray intensities was investigated, and no systematics bias was found. Intensity balances could also be used to determine log f t values for each state.
In order to characterise observed states, spin-parity assignments must be made. Angular correlation measurements are one method and have not previously been performed at the IDS. The probability distribution for emission of a γ ray at an angle θ relative to a coincident γ ray directly preceding or following it is given by the equation where, for I 1 L is the angular momentum of the photon): k is an even integer for which k max = min(2I 2 , 2L 1 , 2L 2 ) ; P k (cos θ) are Legendre polynomials; Q k are solid angle correction coefficients; and A k are the angular correlation coefficients which can be related to the spins, multipolarities and mixing ratios through angular momentum considerations (see ref. [22]). Here k > 4 is safely ignored. Fits of W (θ) normalised to A 0 may be compared with theoretical A 2 , A 4 values to support or rule out certain combinations of level spins. The added degrees of freedom caused by mixing mean that the method is most effective when applied to stretched electric transitions, which can generally be assumed to be unmixed. Angular correlation measurements were performed using data from the second experiment (five clover detectors) in order to support spin-parity assignments. Correlations were calculated between individual HPGe crystals in order to reduce solid angle spreading and increase the number of detector-detector angles. Placing the fifth detector off-axis reduced the symmetry of the system and as a result gave an increase in the number of angles. The angles available in the data set of 320 crystal-crystal pairs are summarised in Table I. Add-back was performed by assuming the crystal of greatest energy deposition to be the initial point of interaction of the γ ray. The solid angle correction coefficients Q k were calculated using the integration method [23], and the approach was verified using coincidences in the decay of 152 Eu. More details are given in ref. [24].   (3) 0.07 3104.9 (9/2 − ) 254.1(2) (M1) 0.24 (2) 0.2 3013.8 (7/2 − ) 345.2(3) (M1) 0.08 (2) 0.03 2985.8 (9/2 − ) 373.0(2) (M1) 0.063 (5) 0.02 2912.6 (9/2 − ) 446.3 (2) (3) 0.04 2985.8 (9/2 − ) 595.6(2) (M1) 0.061 (5) 0.02 2912.6 (9/2 − ) 669.0(2) (M1) 0.037 (4) 8 1 × 10 −3 3800.0 † (9/2, 11/2) 3143.2 (9/2 − ) 656.2(2) (E1) 0.025 (2) 5 × 10 −3 3104.9 (9/2 − ) 695.8(4) (E1) 0.0014 (6) 2 × 10 −4 1348. 3 1 × 10 −4 † Positive parity is assumed for branching ratio calculations.
Results: A level scheme for 207 Tl below Q β = 4550(30) keV has been built using β-gated γ and γγ coincidence spectra. The full level scheme is shown in Fig. 1, and the full list of observed transitions and intensities is recorded in Table II. Data from the 2014 experiment were used due to the comparatively lower level of background in the spectra and the ability to gate on β signals, further improving the quality of the spectra. Examples of γ-ray spectra in coincidenceswith the 351 keV and 1683 keV transitions are shown in Fig. 2. Transitions were verified by cross-comparison with the 2016 data. All possible transitions between states were analysed in coincidence spectra. As well as observing fifteen previously-known states [7], eleven new states and 78 new transitions have been placed in this analysis. These states lie at energies of 3013. 8 3644.2, 3800.0, 3850.0 and 3940.3 keV. The states at 3634 and 3644 keV were tentatively suggested in the previous β-decay work [6].
Electron conversion coefficients are dependent on transition multipolarities and multipolarity mixing ratios. It is possible to infer conversion ratios indirectly by gating on the initial gamma ray in a γ-γ-γ cascade and attributing any intensity imbalance after correcting for efficiency between the second and third transitions to electron conversion. From the 1591-1332-351 keV and 1910-1332-351 keV coincidences we obtain the total internal conversion coefficient α(351.2 keV) = 0.23 (5). The result is in agreement with a previous result α K (351.2 keV) = 0.2041(37) measured by Gorodetzky et al. [25], and corresponds to the mixing ratio |δ M1+E2 (351.2 keV)| ≤ 0.8.
Values of log f t have been calculated for each observed state, taking into account ingoing and outgoing internal transition intensiies (conversion-corrected [26] assuming zero mixing, except in the case of the 351.2 keV transition where the measured value is used) and assuming that the remainder populating intensity comes from direct βdecay population. A spin and parity of J π = (9/2 + ) is assumed for the decaying ground state of 207 Hg [7]. The results are shown in Table III. These are used to support spin-parity assignments given their close empirical relation to the degree of forbiddenness of a decay [27].
Transition strengths in terms of the single-particle Weisskopf estimates may be calculated exactly but this requires a knowledge of level lifetimes. However, if the single-particle strength of one transition de-populating a state can be assumed, the relative strengths of other transitions de-populating the same state may be deduced using the relative intensities. These assumed strengths take into account the systematics of this region in the nuclear chart. The magnetic transitions do not exhibit any useful trends, but the electric transitions do, as described in the following paragraph.
The 2676 keV state is assigned 7/2 − . It populates both the 11/2 − and 1/2 + states, fixing the spin-parity to 7/2 − . The angular correlation of the 993 keV transition with the 1683 keV E2 transition (Fig. 3(i)) supports stretched dipole character for the former transition.
The 2709 keV state is assigned 5/2 − . It populates the 3/2 + and 1/2 + states only and is populated weakly by higher-lying states, implying low spin. Population by (9/2 − ) states from above allows (5/2, 7/2) − . The log f t result is consistent with unique first-forbidden decay and would be unusually high for first-forbidden decay when compared to the surrounding states. The 5/2 − assignment is motivated by the predicted energy of the The 2913 keV (9/2 − ) state populates the 11/2 − state and the 3/2 + state. This allows a 7/2 − or 9/2 − assignment. Due to the strong branching to the 11/2 − state and the lack of branching to the 5/2 + and 1/2 + states, a 9/2 − assignment is preferred. The log f t result is consistent with allowed or first-forbidden decay. Angular correlation of the 2561 keV transition with the 351 keV M1+E2 transition (Fig. 3(ii)) supports the assignment. Angular correlations of the 1564 keV transition with the 423 keV (Fig. 3(iii)) and 446 keV (ref. [32]) (M1+E2) transitions feeding from (9/2 − ) states are slightly inconsistent with the alternative 7/2 − spin-parity assignment.
The 2986 keV (9/2 − ) state populates the 11/2 − state and the 3/2 + state. This allows a 7/2 − or 9/2 − assignment. Due to the strong branching to the 11/2 − state and the lack of branching to the 5/2 + and 1/2 + states, a 9/2 − assignment is preferred. The log f t result is consistent with allowed or first-forbidden decay. Angular correlation of the 2635 keV (E3) transition with the 351 keV M1+E2 transition (Fig. 3(iv)) is consistent with either assignment.
The 3014 keV (7/2 − ) state populates both the 11/2 − and 1/2 + states. This suggests a 7/2 − spin-parity assignment. It also populates the 5/2 + state strongly as would be expected for a J < 9/2 state. The similarity of these decays to those of the 2676 keV state supports a 7/2 − assignment. The angular correlation of the 1331 keV (E1) transition with the 1683 keV E2 transition (ref. [32]) supports stretched dipole character for the former transition.
The 3494 keV (5/2 − , 7/2) state populates only the 3/2 + state and so J > 7/2 is ruled out. The log f t result is too low for second-forbidden decay, restricting the assignment to J = (5/2 − , 7/2). The possibility of this state being identical to the 3474(6) keV 7/2 + state observed previously [7] has been considered [32] but is thought to be unlikely due to the energy difference.
Our spin-parity assignment is at odds with the most recent Nuclear Data Sheets compilation [7] in some cases. For the 2676 keV state our 7/2 − assignment is in agreement with the suggestion of [6]. The (5/2 + ) assignment of the compilation is based on the (pol d, 3 He) transfer reaction of [13], which reports a small d 5/2 contribution, however the fit with the experimental data is clearly not good. Similarly, (9/2) + is suggested by the compilation for the 2986 and 3105 keV states, with the parity assignment based on the (d, 3 He) measurement of [12] reporting a g+10%d component for a group of unresolved states around this energy. In contrast, reference [13] cannot confirm this character. In all three excited states discussed, the misinterpretation was probably due to the (partially) octupole character of these states, with the collective octupole phonon having components from a large number of orbital pairs.

Shell-model calculations:
The experimental findings are compared to shell-model calculations using the KHM3Y interaction. The latter has previously been successful in describing the octupole phonon (and double octupole excitation) in 208 Pb [5] and in describing nuclei consisting of the 208 Pb core plus several particles/holes [33]. The calculation has previously been applied to 207 Tl and compared to the findings of an experiment studying high-energy yrast states [4].
Discussion: The relation of the experimental level scheme to calculated levels is shown in Fig. 4. The differences between experimental and theoretical state energies are plotted in Fig. 5. We discuss octupole state assignments here.
The pair of states at 2676 keV and 2709 keV has previously been assumed [6,9] to correspond to the doublet of πs −1 1/2 × 3 − octupole-coupled states owing to their energies and tentative spin-parities. This analysis supports the tentative assignments and asserts the octupole character. As further evidence supporting the respective 7/2 − and 5/2 − spin-parity assignments, the relative strengths of the E1 and E3 transitions de-populating these states agree with those calculated by Hamamoto [36]. Experimentally and theoretically the states are separated in energy from the states lying above by around 200 keV. These states are predicted by the KHM3Y cal-culation to lie at 2453 keV and 2489 keV respectively. This gives respective observed energy shifts ∆E M3Y = E exp. − E KHM3Y = +0.223 MeV and +0.256 MeV.
Placing the πd −1 3/2 × 3 − octupole-coupled states is less clear and so remains tentative. These have spin-parities 3/2 − , 5/2 − , 7/2 − and 9/2 − , and would be expected to lie close to 3 MeV in energy if coupling is weak as for the πs 1/2 × 3 − states. The strength of the transition directly de-exciting the coupled phonon state (populating the 3/2 + state at 351 keV) is expected to be stronger than the corresponding transition for a non-collective state. KHM3Y shell model calculations predict state energies, transition strengths and wave functions. The wave functions clearly differentiate between calculated octupole and non-octupole states, with octupole state wave functions dominated by contributions from ∆l = ∆j = 3 excitations across the shell gaps.
The search for the 3/2 − and 5/2 − d 3/2 octupolecoupled states is hindered by a lack of statistics due to both lower spin and greater β-decay forbiddenness. Apart from the 5/2 − state at 2709 keV, these two are the only J < 7/2 states expected to exist between 2.5 and 3.5 MeV in energy. A single candidate state is observed: the 3197 keV state is assigned (5/2 − ) here. It is thought that the 3/2 − state remains unobserved, populated negligibly in β decay and with very little internal population from higher-spin states lying above. The 5/2 − state is predicted by the KHM3Y calculation to lie at an energy of 2911 keV, giving an observed energy shift ∆E M3Y = +0.286 MeV. Four (7/2 − ) states are observed above the 7/2 − 1 state, lying at 3014 keV, 3274 keV, 3431 keV and 3592 keV. The 7/2 − 2 state is predicted by the KHM3Y calculations to have octupole character and to lie at an energy of 2784 keV. Experimentally this would correspond to the 3014 keV state, but the 3274 keV state is also considered based on its energy. Each of the (7/2 − ) states populates the 5/2 + state at 1683 keV with an (E1) transition and the πd −1 3/2 state at 351 keV with an (M2+E3) transition. The latter would be expected to be enhanced for the octupole state. The relative transition strength of the (M2+E3) transition from the 3014 keV state, when using the (E1) transition as a benchmark, is around 60% greater than that of the corresponding transition from the 3274 keV state. This supports tentative assignment of collective octupole character to the 3014 keV state, and given the relative energies of the states, this appears likely. However, it is also possible that the octupole strength might instead be split, most likely between the 3014 keV and 3274 keV states, rather than concentrated in one state as predicted by the KHM3Y calculation. This could be attributed to the underestimation of the octupole energy by several hundred keV: the energy difference E(7/2 − 3 ) − E(7/2 − 2 ) is calculated to be 0.61 MeV whereas it is observed to be 0.26 MeV. As the octupole states are higher in energy than predicted by the calculations they are closer to the multitude of states with equal J π , increasing the degree of mixing.
The density of observed 9/2 − states (eight placed in the energy range 2.9-3.5 MeV) makes exact assignment difficult, with increased uncertainty over predicted configuration mixing. The KHM3Y calculations predict the 9/2 − 1 state to have octupole character, which here would correspond to the 2913 keV state. The 2986 keV and 3105 keV states are considered to be the next-most likely candidates owing to energy ordering and strong octupole-deexciting transitions. Each of these three states populates both the 11/2 − isomer with an M1+E2 transition and the 3/2 + πd −1 3/2 state with an E3 transition. Calculation of octupole relative transition strengths, using the isomerpopulating M1+E2 transition as a benchmark, suggests that the 2635 keV transition (depopulating the 2986 keV state) is the strongest. This supports tentative assignment of d 3/2 -coupled octupole character to the 2986 keV state. However, as for the 7/2 − states, this is not robust evidence. The phonon strength could also be split between the three states at 2913, 2986 and 3105 keV. E(9/2 − 2 )−E(9/2 − 1 ) is calculated to be 0.27 MeV whereas it is observed to be 0.07 MeV.
The final octupole-coupled states considered are the πh −1 11/2 × 3 − states. Of those expected to be populated, the 7/2 + state is calculated to lie the lowest in energy, at 3679 keV, with the 9/2 + and 11/2 + states lying around 100-200 keV higher. The 17/2 + state has been observed at 3813 keV [4], giving ∆E M3Y = +0.132 MeV. This is in line with results for πs −1 1/2 , πd −1 3/2 coupled states in this analysis. The observed 3800, 3850 and 3940 keV states are not assigned parity and lie in this energy region, and so are candidates for octupole character. Previously a state at 3987 keV, not observed in this work, was assigned L = 4 and some πg −1 7/2 strength [13], making this more likely to correspond to the 7/2 + octupole-coupled state.
Characterisation of states not resulting from octupole coupling here is difficult as they are less easy to identify through any particular multipole enhancement. The experimentally observed states with tentative spinparities not assigned octupole character are assigned to calculated states in order of energy. The 3634 keV and 3644 keV (11/2 − ) states are assigned to the calculated 11/2 − 4 and 11/2 − 5 states due to the similarities in energy separation. The states at 3494, 3570, 3800, 3850 and 3940 keV are not assigned exact spin-parities. Comparison of experimentally observed level energies in 207 Tl with those predicted by calculations using the KHM3Y interaction, described in text. Single-particle states are not shown as these were fixed in calculations. Character assignments for collective octupole and non-collective states are shown. lations. As a start, mixing between t=0 and t=1 should be taken into account. This was not done since it requires the determination of a new Hamiltonian in which all of the single-particle energies are readjusted to reproduce the experimental separation energies for A=207 and A=209 relative to 208 Pb. This, of course, requires calculations for all of these nuclei. Mixing between t=0 and t=1 lowers the energies of the states dominated by t=0, i.e. they get pushed down due to mixing with the higher energy 1p-2h states. This will increase the relative energies of the t=1 states. Mixing with t=2 states is expected to reduce the energies of the t=1 states, but would also reduce the energy of the ground state as 0 + nucleon pairs are easier to excite across the shell gap. Finally, mixing with t=3 states would be expected to reduce the energies of t=1 states. It is likely that t=2 (2p-3h) and t=3 (3p-4h) would be needed to achieve energy convergence at the level of about 100 keV. A previous investigation in the smaller model space around 98 Cd [37] found that the inclusion of mixing up to t=3 is necessary to ameliorate the difference between measurement and theory. Including this amount of configuration mixing for the region around 208 Pb is not computationally feasible at this time.
To address the discrepancy between octupole and non-octupole predictions in this analysis, the t=2 mixing would need to have a relatively smaller effect on the collective octupole-coupled states. The mechanism for this difference is not clear, although it could relate to weak coupling of the collective phonon with t=0 states. Spin is not thought to have a significant effect, since these states are all of similar, relatively low, spin. Wilson et al. discussed the rectifying effect of t=2 mixing on high-spin states [4].

Conclusions:
The γ-decay scheme of 207 Tl has been investigated following population through β decay from the J π = (9/2 + ) ground state in 207 Hg. An extended level scheme has been established containing several newly observed states and transitions and through a combination of approaches, including angular-correlation measurements, spin-parities have been suggested for most states. States resulting from coupling between t=0 single-proton-hole states and the collective octupole phonon have been identified where possible. Comparison with the results of state-of-the-art shell model calculations, using an extensive model space, indicate a discrepancy between the energy predictions of octupole-coupled states and other non-collective coupled states. This is also the case for collective states observed in other nuclei neighbouring 208 Pb [1,7,29]. We speculate that a reduction in the degree to which the collective states couple to t=2 excitations could resolve this difference.