Evidence of octupole-phonons at high spin in 207Pb

Evidence of octupole-phonons at high spin in 207 Pb D. Raleta,b , E. Clémentb , G. Georgieva , A. E. Stuchberyc , M. Rejmundb , P. Van Isackerb , G. de Franceb , A. Lemassonb , J. Ljungvalla , C. Michelagnolib , A. Navinb , D. L. Balabanskid , L. Atanasovau , A. Blazhevg , G. Bocchie , R. Carrollf , J. Dudoueth , E. Duponta , B. Fornali , S. Franchooaa , C. Franseng , C. Müller-Gatermanng , A. Goasduffk , A. Gadeaj , P. R. Johnt,k , D. Kochevav , T. Konstantinopoulosa , A. Korichia , A. Kusoglul , S. M. Lenzik , S. Leonie , R. Lozevaa,m , A. Maji , R. Perezj , N. Pietrallat , C. Shandf , O. Stezowskih , D. Wilmsenb , D. Yordanovaa , D. Barrientoso , P. Bednarczyki , B. Birkenbachg , A. J. Bostonp , H. C. Bostonp , I. Burrowsq , B. Cederwalln , M. Ciemalai , J. Collador , F. Crespie , D. Cullens , H. J. Eberthg , J. Goupilb , L. Harknessp , H. Hessg , A. Jungclausx , W. Kortenw , M. Labicheq , R. Menegazzok , D. Mengonik , B. Millione , J. Nybergy , Zs. Podolyákf , A. Pulliae , B. Quintana Arnész , F. Recchiak , P. Reiterg , F. Saillantb , M. D. Salsacw , E. Sanchisr , C. Theisenw , J. Valiente Dobono , O. Wielande a CSNSM, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, F-91405 Orsay, France CEA/DRF-CNRS/IN2P3, Bd. Henri Becquerel, BP 55027, F-14076 Caen, France c Department of Nuclear Physics, Australian National University, Canberra ACT 2601, Australia d ELI-NP, Horia Hulubei National Institute Institute for R&D in Physics and Nuclear Engineering, 077125 Magurele, Romania e Instituto Nazionale di Fisica Nucleare, Milano, I-20133 Milano, Italy f Department of Physics, University of Surrey, Guildford, GU2 7XH, UK g Institut für Kernphysik, Universität zu Köln, D-50937 Cologne, Germany h Université de Lyon, Université Lyon-1, CNRS/IN2P3, UMR5822, IPNL, F-69622 Villeurbanne Cedex, France i Institute of Nuclear Physics (IFJ), PAN, 31-342 Krakow, Poland j Instituto de Fı́sica Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain k Dipartimento di Fisica e Astronomia, Università degli Studi di Padova and INFN, Sezione di Padova, I-35131 Padova, Italy l Department of Physics, Faculty of Science, Istanbul University, Vezneciler/Fatih, 34134, Istanbul, Turkey m IPHC/CNRS-University of Strasbourg, F-67037 Strasbourg, France n KTH Royal Institute of Technology, 10691 Stockholm, Sweden o INFN, Laboratori Nazionali di Legnaro, Via Romea 4, I-35020 Legnaro, Italy p Oliver Lodge Laboratory, The University of Liverpool, Oxford Street, Liverpool L69 7ZE, United Kingdom q STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom r Department of Electronic Engineering, University of Valencia, E-46100 Burjassot (Valencia), Spain s Schuster Building, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom t Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany u Department of Medical Physics and Biophysics, Medical University-Sofia, 1431 Sofia, Bulgaria v University of Sofia, Sofia, Bulgaria w IRFU, CEA/DRF, Centre CEA de Saclay, F-91191 Gif-sur-Yvette Cedex, France x Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain y Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden z Laboratorio de Radiaciones Ionizantes, Universidad de Salamanca, E-37008 Salamanca, Spain aa Institut de Physique Nucléaire, CNRS/IN2P3-Université Paris-Sud, F-91406 Orsay, France b GANIL, Abstract A lifetime measurement of the 19/2− state in 207 Pb has been performed using the Recoil Distance Doppler-Shift (RDDS) method. The nuclei of interest were produced in multi-nucleon transfer reactions induced by a 208 Pb beam impinging on a 100 Mo enriched target. The beam-like nuclei were detected and identified in terms of their atomic mass number in the VAMOS++ spectrometer while the prompt γ rays were detected by the AGATA tracking array. The measured large reduced transition probability B(E3, 19/2− → 13/2+ ) = 40(8) W.u. is the first indication of the octupole phonon at high spin in 207 Pb. An analysis in terms of a particle-octupole-vibration coupling model indicates that the measured B(E3) value in 207 Pb is compatible with the contributions from single-phonon and single particle E3 as well as E3 strength arising from the double-octupole-phonon 6+ state, all adding coherently. A crucial aspect of the coupling model, namely the strong mixing between single-hole and the phonon-hole states, is confirmed in a realistic shell-model calculation. Keywords: AGATA spectrometer, γ–ray tracking, VAMOS++ spectrometer, Plunger device, Nuclear deformation, Octupole phonon The occurrence of collective vibrations, when a lattice of atoms or molecules oscillates uniformly at a single frequency forming a quantum-mechanical phonon, is a wellPreprint submitted to Physics Letters B known phenomenon. Such vibrations correspond, in classical mechanics, to wave-like normal modes. Quantummechanical phonons, however, exhibit particle-like propJuly 1, 2019 (a) erties, too. The excitation spectra of several different many-body systems can be described as a superposition of elementary excitation modes that are (approximately independent) fluctuations about equilibrium. There is a close relation between the internal structure of the system and the nature of these fluctuations, which may lead to density vibrations or shape oscillations. In nuclei the character of collective vibrations follows from the observation that some are spherical, like doubly-magic nuclei, while others are deformed, like most rare-earth nuclei. In an intermediate situation the shape can undergo large fluctuations about one of the equilibrium shapes. In contrast to molecules, the nuclear energy scales related to vibrational and single-particle excitations are of the same order, and thus their interweaving has profound consequences. Doubly-magic nuclei have a spherical equilibrium shape. Among them, the 208 Pb isotope, with Z = 82 protons and N = 126 neutrons, is the heaviest known doubly-magic nucleus. Its first-excited state has been established to be of natural-parity octupole type, J π = 3− c , at an excitation energy of Ex (3− ) = 2615 keV, about 800 keV lower than c the neutron shell-gap energy at N = 126, the index c stands for collective. The highly enhanced and collective + transition connecting the 3− ground c level to the 0 state has been measured to have a reduced transition + probability of B(E3, 3− c → 0 ) = 34.0(5) W.u. [1], that is, it exceeds by 34 times the Weisskopf unit or single-particle estimate. The 3− c state is interpreted as a one-phonon excitation corresponding to a nuclear surface vibration of octupole character while its microscopic structure is understood as the coherent and collective superposition of one-particle-one-hole (1p–1h) excitations across the neutron and proton shell gaps. (b) 19/2 – (c) f7/2 -1 x 3-x 3- Octupole phonon E3 transition 13/2 + f7/2 -1 x 3- 7/2 – Bexp(E3) = 34 W.u. 2.3 0+ 0.0 19/2 4.1 Bexp(E3) = 40 W.u. 3– 2.6 1.6 f7/2 -1 x 0+ 7/2 – 13/2 + coupled states 208 Pb126 82 i13/2-1 x 3- – i13/2-1 x 0+ uncoupled states 207 Pb125 82 ✌✍✎ ✦✄ ✦ ✦ ✡ ✦ ⑤✶ ✴✷✦ ✁ ❂ ✂✄☎ á ⑤✧✐✦✄ ✄✆✝✞ ✟✸ ✁ ✰ ★✄☎ á ⑤✧❢✼✝✞ ✟✭✸ ✟ ✸ ❀ ✠ ✮✁ ✸☞ ❲☛✉☛ ✸☛✠ ❲☛✉☛ ✷ ✟ ✸☞ ❲☛✉☛ ✦✄ ✦ ✡ ⑤✶✸✴✷✡ ✁ ❂ ✂✄✆ á ⑤✧✐✦✄ ✄✆✝✞ ✟✵ ✁ ✰ ★✄✆ á ⑤✧❢✼✝✞ ✟✸ ✁ Figure 1: Illustration of the particle-octupole-vibration coupling model: (a) The lowest octupole-vibrational phonon of 208 Pb, (b) selected states resulting from the particle-octupole-vibration coupling in 207 Pb, (c) uncoupled (unperturbed) states in 207 Pb, (d) wave functions of the 13/2+ and 19/2− states in the particle-octupolevibration coupling model. The energies of the known states are given in MeV. Provided that this 3− c state represents the first phonon of the octupole vibration, it is expected that the double+ + + octupole quartet (0+ c , 2c , 4c , 6c ) of two-phonon states exists at an energy of about twice Ex (3− c ) [2]. In the case of a fully harmonic vibration, all members of this quartet, and in particular the 6+ c level, decay to the one-phonon state with the characteristic reduced transition probability − − + B(E3, 6+ c → 3c ) = 2 × B(E3, 3c → 0 ). Many attempts have been undertaken to identify the members of the two-phonon octupole quartet [3, 4, 5, 6, 7, 8, 9, 10, 11]. Candidates for the lower-spin members have been proposed [10, 11] but the 6+ c member has not been identified as yet. On the basis of a large-scale shell-model calculation, including up to 2p–2h excitations, Brown [12] concluded that the 6+ c member of the double-octupole quartet is fragmented. Furthermore, he found that there are 0+ , 2+ , and 4+ states with a concentrated doubleoctupole strength but decaying via weak E1 and E2 transitions, which in themselves are not strong evidence for the special double-octupole nature of a state. strong coupling between the orbitals j1 = l1 ± 1/2 and j2 = l2 ± 1/2 if |j1 − j2 | = |l1 − l2 | = 3, preserving the relative orientation of the spin and orbital angular momenta [13, (Vol. II, p. 419)]. In addition to the particle or hole states, several excitations have been found and interpreted as a collective octupole phonon |3− c i coupled to a particle or hole. Because of the strong coupling mentioned above, such states are expected to mix (−1) (−1) (−1) × 3− i.e. |j1 i with |j2 × 3− c ; J2 i c ; J1 = j1 i and |j1 (−1) + with |j2 × 6c ; J2 i, the latter being a particle or hole coupled to a double-octupole phonon. Given this mixing, it has been suggested in Ref. [14], in analogy to the case of 147 Gd [15], that the characteristic enhancement of the − 208 B(E3, 6+ Pb, should be reflected in an c → 3c ) value in enhanced B(E3, J2 → J1 ) value in the odd-mass nucleus. The octupole excitations coupled to the low-spin ground state in 207 Pb have been investigated earlier [16, 17]. The 5/2+ state at 2624 keV and 7/2+ state at 2662 keV have − been interpreted as members of the low-spin νp−1 1/2 ×φ1 (3c ) multiplet resulting from weak coupling. The corresponding reduced transition probabilities have been measured as In the nuclei neighboring 208 Pb, with one valence particle or hole, the particle-octupole-phonon model favors 2 B(E3, 5/2+ → 1/2−) = 30(3) W.u. and B(E3, 7/2+ → 1/2−) = 28(2) W.u. [17]. The small positive energy shifts, +9 keV and +47 keV relative to Ex (3− c ), can be noticed that could be related to the blocking of the νp1/2 orbital. For 207 Pb, among the available neutron orbitals, p1/2 , p3/2 , f5/2 , f7/2 , h9/2 and i13/2 , forming a major shell 82 ≤ N ≤ 126, only the j1 = νi13/2 and j2 = νf7/2 satisfy the strong coupling rule, described above. The corresponding states, 13/2+ and 7/2− , dominantly of singlehole character, are well studied [18]. The 19/2− state and the corresponding 2485 keV transition to the 13/2+ state were assigned to 207 Pb by Schramm et al. [6], and the E3 character of the transition was recently determined by Shand et al. [19]. The 13/2+ , 7/2− , and 19/2− states were analyzed in terms of particle-octupole-vibration coupling in Ref. [14] using the experimentally known level energies and assuming the dominance of the above-mentioned orbitals. This coupling scheme is depicted in Fig. 1. In panel (a) the one-phonon state is illustrated for 208 Pb. The coupled and uncoupled states in 207 Pb are shown in panels (b) and (c), respectively. The wave functions of the 13/2+ and 19/2− states are represented as single-hole states and single-hole states coupled to a single or double octupole phonon in 208 Pb. The coefficients αi and βi , as shown in panel (d) of Fig. 1, depend crucially on the mixing matrix −1 + − element h ≡ hνi−1 13/2 |V̂ |νf7/2 × 3c ; 13/2 i, which can be calculated in a variety of ways. Its absolute value can be deduced from the excitation energies of the 13/2+ , 7/2− , and 19/2− levels in 207 Pb, leading to |h| = 0.725 MeV [14]. Alternatively, it is obtained in the context of the particlevibration coupling model [13, (Vol. II, p. 418)], where it depends on the radial overlap of the particles and the oscillating potential at the surface of the nucleus and the zero point amplitude of the nuclear vibration. Hamamoto [20] for the case of 207 Pb obtained the value of h = 0.710 MeV. Finally, it can also be calculated with the shell-model expression, where the particle-hole matrix elements can be obtained from particle-particle matrix elements using the Pandya transformation [21] h = r 1 2 X kk′ + −1 − − aνkk′ hνf7/2 νi−1 13/2 ; 3 |V̂νν |jνk jνk′ ; 3 i X ll′ ently, giving rise to a large mixing matrix element with the value of h = 0.655 MeV. This is the hallmark of collective behavior, which therefore is found to be present in a realistic shell-model description. The consistency of the values for the mixing matrix element derived with three totally different approaches lends support to the hole-octupolephonon interpretation of states in 207 Pb. In the following the experimental value of h = 0.725 MeV is used. The experimental value of h = 0.725 MeV was determined assuming the contribution of the collective vibrational-phonons to the 13/2+ and 19/2− states. Due to the presence of the specific orbits, the f7/2 and i13/2 for 207 Pb, a strong particle-octupole-vibration coupling is expected to attract an admixture of the double octupole state to the low-lying yrast 19/2− state, that can decay by the characteristic enhanced E3 transition. The main part of the double octupole state remains however in the higher lying 19/2− , which could be fragmented and have different decay modes. The negative energy shift of −130 keV for the 2485 keV transition between the 19/2− and 13/2+ , relative to Ex (3− c ), is therefore understood as resulting from the mixing of one-phonon state with the two-phonon state. The large B(E3, 19/2− → 13/2+ ) value, characterizing the contribution of octupole phonons, has however not been measured. A predicted B(E3, 19/2− → 13/2+ ) value is obtained (see discussion below) that is enhanced as com+ 208 pared to B(E3, 3− Pb, due to the strong mixc → 0 ) in ing and the coherent contribution of the single-phonon and single particle and the double-octupole-phonon strengths. The aim of this work was to provide the experimental evidence of the collective nature of the E3 (19/2− → 13/2+ ) transition by means of lifetime measurement. The knowledge of the strength of this transition will allow to prove the hypothesis of the strong coupling scheme and quantify the contributions of one-phonon and two-phonon states; ultimately it may prove the existence of the latter. The measurement of sub-nanosecond lifetimes of high spin states in nuclei near 208 Pb is very challenging. These high spin states can be efficiently populated in multinucleon transfer reactions of heavy ions at the energies near the Coulomb barrier [6, 14, 23]. The excited products of interest are distributed near the grazing angle, far away from the beam axis, in contrast to fusion reactions. Multi-nucleon transfer reactions produce hundreds of nuclei at the same time, therefore some selection of the reaction products is required. It can be obtained using γ − γ coincidences or using a mass analyzer or magnetic spectrometer to determine the mass number. The direct measurement of the atomic number at Z ∼ 82 for low energy ions is not possible today. Mass analyzers have typically low acceptance and are restricted to operation near 0◦ . Further, the use of the plunger technique, for measurement of sub-nanosecond lifetimes of states populated in multi-nucleon transfer reactions, requires an event-byevent measurement of the recoil velocity vector. In this work the VAMOS++ spectrometer was used to identify, for the first time, the atomic mass number of the lead- −1 − − aπll′ hνf7/2 νi−1 13/2 ; 3 |V̂νπ |jπl jπl′ ; 3 i ! , which gives the separate contributions of the neutronneutron (νν) and neutron-proton (νπ) interactions. The sums are over the neutron and proton particle-hole excitations that constitute the octupole phonon. The amplitudes aνkk′ and aπll′ are obtained microscopically in a shell-model calculation for 208 Pb with 24 single-particle energies taken from Ref. [22] and with the realistic nucleon-nucleon interaction as given in Ref. [23]. Although the off-diagonal matrix elements in the expression for h generally are small and of varying sign, multiplied with amplitudes they act coher3 54 . Pb x-rays A = 208 MQ_Q A = 206 53 5555065 4.105 50.58 0.1319 1.433 Counts [2 keV/ch] Charge Q [a.u.] MQ_Q Entries Mean x Mean y RMS x RMS y 52 51 50 49 3.9 4 4.1 4.2 4.3 Pile-up 4 10 5/2 → g.s GS_75 . 1 2 1→ - 3/ g.s GS_d75 Entries 2284773 Mean - 556.9 RMS 497.1 - - + 5/2 5/2 1 /2 1 → + 1→ 3 1 1 → 7/2 7/2 /2 9 208 1 Pb 103 1 102 500 A/Q - 1000 1500 2000 2500 Energy [keV] Figure 2: Two-dimensional identification matrix obtained with the VAMOS++ spectrometer. Nuclei with atomic mass number A = 206 and A = 208 are highlighted for several charge states measured in the spectrometer. Due to the low velocity of the recoils, an element identification (Z) is not possible. Figure 3: γ-ray spectrum gated on mass A = 207 at the target-todegrader distance of 75 µm. The transitions marked with a circle correspond to the Coulomb excitation of the 100 Mo target, Doppler corrected using the velocity vector of the heavy partner. like ejectiles at energies ranging from 1 to 2 MeV/u. The required mass resolution was reached only for a part of the focal plane setup (∼ 15%), which resulted in reduced statistics. In this letter we present the results of the first lifetime measurement of the J π = 19/2− level in 207 Pb, proving the one-octupole phonon nature of this state and suggesting the existence of a double-octupole 6+ c state in 208 Pb. The experiment was performed at the Grand Accélérateur National d’Ions Lourds, Caen, France using the RDDS method [24], in combination with a multi-nucleon transfer reaction in inverse kinematics. A 208 Pb beam at 6.25A MeV impinged on an enriched 1.9 mg/cm2 -thick 100 Mo target followed by a 2 mg/cm2 thick Ni degrader. Beam-like reaction products were detected and identified on an event-by-event basis in the large-acceptance VAMOS++ spectrometer [25, 26]. The optical axis of the spectrometer was positioned at 26o with respect to the beam axis, at the grazing angle of the beam-like products. The VAMOS++ spectrometer allowed the identification of the reaction products in mass-over-charge (A/Q) and atomic charge (Q), and ~ ) necessary for the Doppler provided the velocity vector (V correction. Figure 2 shows a typical two-dimensional identification matrix obtained in the present experiment. The Xaxis represents the mass-over-charge ratio as a function of the atomic-charge state. Mass resolution of ∼ 0.9/208 (FWHM) was obtained. The analysis procedure is further detailed in Ref. [27]. Excited-state half-lifes (T1/2 ) were measured using the RDDS technique with the plunger device of the University of Cologne [28]. Doppler-corrected prompt γ rays, emitted before and after the Ni degrader foil, were measured by the HPGe AGATA tracking array [29, 30] placed at backward angles in a compact geometry (target-to-detector distance of 148.5 mm). The γ-ray energy Doppler correction was performed using the recoil ~ ), obtained from the VAMOS++ spectrometer, velocity (V after the Ni degrader, and the position of the first γ-ray interaction obtained from the Orsay Forward Tracking algorithms using standard parameters [31]. Figure 3 shows the Doppler-corrected γ-ray spectrum measured in the AGATA spectrometer, selected with mass A = 207 in the VAMOS++ spectrometer for the 75 µm target-to-degrader distance. Transitions at 570 keV, 898 keV, 1770 keV, and 2485 keV belong to 207 Pb. The 2067 keV line corresponds to the shifted component of the 207 Pb short-lived (T1/2 = 660 fs [32]) 7/2+ 1 state decay in − to the 5/21 state. The transition at 2615 keV corresponds 208 Pb; it is a contaminant from to the 3− c state decay in the random coincidence resulting from the inelastic scattering of the beam. The transitions marked with a circle correspond to the 100 Mo decay following Coulomb excitation, Doppler corrected using the velocity vector of the beam-like ion, measured after the degrader. Figure 4 shows Doppler corrected γ-ray spectra measured in the AGATA spectrometer, selected on mass A = 207 in the VAMOS++ spectrometer, for five target-todegrader distances (75 µm, 200 µm, 625 µm, 1000 µm, and 2000 µm) for the relevant transitions used for the lifetime measurement. Since the Doppler correction used the velocity measured after the degrader, the unshifted (U) component corresponds to the events where the γray was emitted after the degrader and shifted (S) to the events where gamma-ray was emitted before the degrader. The velocity of ions detected in VAMOS++ ranged from 14 to 22 µm/ps, and the decrease of the velocity in the degrader was typically about 13%. Events with a relative angle greater than 138◦ , between the γ-ray and the outgoing-particle velocity vector, were selected to enhance the clear separation between the shifted (S) and unshifted (U) components of the γ-ray transitions. The parameters required for the Doppler correction using the AGATA and VAMOS++ spectrometers were obtained using the inelastic scattering of the 208 Pb in a data set without the thick Ni degrader. On the left panel of Fig. 4, the two 4 75 µm S19/2- 300 600 400 100 200 200 µm 800 300 600 200 400 100 200 400 625 µm 600 200 400 100 200 1000 µm 600 200 400 100 200 200 2000 µm 300 100 200 100 50 2400 2450 2500 Energy [keV] 1700 300 400 Distance [ µm] 500 600 These states, having a very long effective lifetime, are taken into account in the analysis, following the method described in Ref. [24]. The lifetime was extracted from the first three distances where the RDDS analysis showed maximum sensitivity. The lifetime analysis procedure was verified using the known decay of the the 2+ 1 state in 206 Pb (T1/2 = 8.30(24) ps [33]). The deduced value from this experiment is T1/2 = 12(3) ps, taking into account the feedings from the 3+ and 4+ states, in reasonable agreement with the published value. 400 150 200 Figure 5: Mean lifetime (τ ) determination of the 19/2− state of 207 Pb. The continuous red line corresponds to the fitted mean value of τ as the dashed lines correspond to its 1σ error bar. 800 300 50 40 30 20 10 100 800 300 400 S7/2- 800 200 400 Counts / 2 keV U19/2- τ[ps] 400 1720 1740 1760 1780 Energy [keV] The result of the lifetime analysis for the 19/2− state decaying by the 2485 keV transition in 207 Pb is presented in Fig. 5. The deduced value of T1/2 = 20(4) ps, corresponds to B(E3, 19/2− → 13/2+ ) = 40(8) W.u., assuming a branching ratio of 100%. When compared with the + 208 B(E3, 3− Pb, it is a clear c → 0 ) = 34.0(5) W.u. in first indication that the octupole-vibrations play an important role in the nature of the 19/2− state. Further, the different contributions to the octupole strength can be evaluated. With the wave functions of the 19/2− and 13/2+ states as given in Fig. 1(d) and with the two-to-one− − + phonon strength B(E3, 6+ c → 3c ) = 2 × B(E3, 3c → 0 ), the reduced transition matrix element can be written as follows: Figure 4: Doppler corrected γ-ray spectra for mass A = 207 as a function of the target-to-degrader distance. Left: the 19/2− → − 13/2+ transition in 207 Pb. Right: the 7/2− 1 → 5/21 transition in 207 Pb used for normalization. components, shifted (S) at 2454 keV and unshifted (U) at 2485 keV, of the 19/2− → 13/2+ transition in 207 Pb are observed. Within the RDDS technique, a decay curve was constructed from the intensities of the unshifted (U19/2− ) component of the 19/2− → 13/2+ transition normalized − 207 Pb as a function to the 7/2− 1 → 5/21 transition in of the target-to-degrader distance. The 7/2− 1 state, at an excitation energy of 2339.9 keV, decays by a γ-ray transition of 1770.2 keV to the first-excited 5/2− 1 state. Only the shifted component (S7/2− ) was observed due to the very short lifetime of the 7/2− 1 state (see right panel of Fig. 4). The γ-ray transition intensities were determined assuming for all distances the same width and centroid for the peaks. The normalization using the sum of the shifted (S19/2− ) and unshifted (U19/2− ) components of the 2485 keV transition is in agreement, within the statistical uncertainties, with the normal− ization using the 7/2− 1 → 5/21 transition. The former has a higher statistical error due to the weak intensity of the shifted (S19/2− ) component. In the following, all quoted errors are statistical. In agreement with the level scheme of 207 Pb [19], γ-γ-coincidence analysis showed two transitions above the 13/2+ state populating the 19/2− state: the 21/2− → 19/2− and 23/2− → 19/2− transitions with the respective energies of 592 keV and 749 keV and feeding of 20(6)% and 37(5)%, respectively. h13/2+ ||E3||19/2− i r 20 · h0+ ||E3||3− c i 7 = · + √ (α19 · α13 + 2 · β19 · β13 ) r 10 −1 ||E3||νi−1 · hνf7/2 13/2 i · α19 · β13 7 The coefficients α and β can be taken from the analysis in [14]. With Woods-Saxon radial wave functions and an effective charge eeff = 1.35(45)e, one obtains the −1 single-hole reduced matrix element hνf7/2 kE3kνi−1 13/2 i = 3 −359(119) e fm [14]. The errors associated with the effective charge and the reduced transition matrix element follow from the experimental precision of the B(E3, 15/2− → 9/2+ ) in 209 Pb [34]. The first term in the equation, proportional to α19 α13 multiplied with the collective E3 matrix element, provides the dominant contribution, with cor− rections stemming from the two-to-one-phonon 6+ c → 3c 5 transition (second term, proportional to β19 β13 ) and the −1 −1 transition (third term, propor→ νf7/2 single-hole νi13/2 tional to α19 β13 ). NP) Phase II, a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund - the Competitiveness Operational Programme (1/07.07.2016, COP, ID 1334). This work was supported by the BMBF under grant No. 05P18RDFN9. A.G and R.P were partially supported by Ministry of Science, Spain, under the Grants FPA201784756-C4 and SEV-2014-0398, and by the EU FEDER funds. A.E.S was partially supported by the Australian Research Council grant No. DP0773273. Three different scenarios can be considered along with the calculated reduced transition probability (in parenthesis): (i) Neglecting the strong coupling and the twophonon contribution using α19 = α13 = 1 and β19 = β13 = 0 (34.0(5) W.u.) (ii) Neglecting the two-phonon contribution using α19 = 1, α13 = 0.98, β19 = 0 and β13 = −0.19 (37(2) W.u.) (iii) Considering all the contributions using α19 = 0.97, α13 = 0.98, β19 = −0.25 and β13 = −0.19 (40(2) W.u.). The errors associated with the calculated + 208 values result from those of B(E3, 3− Pb and c → 0 ) in eeff . The observed strength and a comparison with the above calculated values suggest an enhancement with re+ 208 spect to the known B(E3, 3− Pb. All contric → 0 ) in butions, including the two-phonon state, add coherently to reach maximum collectivity. The measured value is compatible, within the error bar, with the predicted value. However the experimental uncertainty remains too large to disentangle the presence of the strong particle-octupole coupling and the two-phonon state. To achieve this goal, the experimental uncertainty for the case of 207 Pb has to reach at least the level of 2%. Further, a more precise determination of the effective charge, which is a main source of uncertainties in the calculations, would be required. References [1] R. H. Spear, et al., Phys. Lett. B 128 (1) (1983) 29–32. doi:10.1016/0370-2693(83)90067-9. [2] J. Blomqvist, Phys. Lett. B 33 (8) (1970) 541–544. doi:10.1016/0370-2693(70)90342-4. [3] M. A. J. Mariscotti, et al., Nucl. Phys. A 407 (1) (1983) 98–126. doi:10.1016/0375-9474(83)90310-X. [4] R. Julin, et al., Phys. Rev. C 36 (1987) 1129–1131. doi:10.1103/PhysRevC.36.1129. [5] H. J. Wollersheim, et al., Z. Phys. A 341 (2) (1992) 137–144. doi:10.1007/BF01298473. [6] M. Schramm, et al., Z. Phys. A 344 (1) (1992) 121–122. doi:10.1007/BF01291029. [7] B. D. Valnion, et al., Z. Phys. A 350 (1) (1994) 11–12. doi:10.1007/BF01285046. [8] C. Fahlander, et al., Phys. Scr. 1995 (T56) (1995) 243. [9] E. F. Moore, et al., Nucl. Instr. Meth. Phys. Res. B 99 (1) (1995) 308–311. doi:10.1016/0168-583X(94)00687-3. [10] M. Yeh, et al., Phys. Rev. Lett. 76 (8) (1996) 1208–1211. doi:10.1103/PhysRevLett.76.1208. [11] M. Yeh, et al., Phys. Rev. C 57 (5) (1998) R2085–R2089. doi:10.1103/PhysRevC.57.R2085. [12] B. A. Brown, Phys. Rev. Lett. 85 (25) (2000) 5300–3. doi:10.1103/PhysRevLett.85.5300. [13] A. Bohr, B. R. Mottelson, Nuclear Structure, World Scientific, 1998. [14] Rejmund, M., et al., Eur. Phys. J. A 8 (2) (2000) 161–164. doi:10.1007/s100500070102. [15] P. Kleinheinz, et al., Phys. Rev. Lett. 48 (1982) 1457–1461. doi:10.1103/PhysRevLett.48.1457. [16] E. Grosse, et al., Nucl. Phys. A 174 (3) (1971) 525–538. doi:https://doi.org/10.1016/0375-9474(71)90400-3. [17] O. Häusser, et al., Nucl. Phys. A 194 (1) (1972) 113–139. doi:10.1016/0375-9474(72)91055-X. [18] F. G. Kondev, S. Lalkovski, Nucl. Data Sheets 112 (3) (2011) 707–853. doi:10.1016/j.nds.2011.02.002. [19] C. Shand, et al., Acta Phys. Pol. B 46 (3) (2015) 619. doi:10.5506/APhysPolB.46.619. [20] I. Hamamoto, Phys. Rep. 10 (2) (1974) 63 – 105. doi:10.1016/0370-1573(74)90019-2. [21] S. P. Pandya, Phys. Rev. 103 (4) (1956) 956–957. doi:10.1103/PhysRev.103.956. [22] M. Rejmund, et al., Phys. Rev. C 59 (5) (1999) 2520–2536. doi:10.1103/PhysRevC.59.2520. [23] J. Wrzesiński, et al., Eur. Phys. J. A 10 (3) (2001) 259–265. doi:10.1007/s100500170111. [24] A. Dewald, et al., Z. Phys. A 334 (2) (1989) 163–175. doi:10.1007/BF01294217. [25] M. Rejmund, et al., Nucl. Inst. Meth. Phys. Res. A 646 (1) (2011) 184 – 191. doi:10.1016/j.nima.2011.05.007. [26] M. Vandebrouck, et al., Nucl. Inst. Meth. Phys. Res. A 812 (2016) 112 – 117. doi:10.1016/j.nima.2015.12.040. [27] D. Ralet, et al., Phys. Scr. 92 (5) (2017) 054004. [28] A. Dewald, et al., Prog. Part. Nuc. Phys. 67 (3) (2012) 786 – 839. doi:10.1016/j.ppnp.2012.03.003. In summary, a large B(E3, 19/2− → 13/2+ ) = 40(8) W.u. reduced transition probability has been measured in 207 Pb based on the lifetime measurement of the 19/2− state using the RDDS technique. Such collective character indicates that the dominant component of this state is a single-hole excitation coupled to the octupole phonon of the 208 Pb core. The energy lowering of the 2485 keV transition in 207 Pb, as compared to the 2615 keV transition in 208 Pb, is consistent with a mixing with a state containing the double-octupole-phonon excitation. The measured reduced transition probability is compatible with a contribution from the two-to-one-octupolephonon E3 transition. Further information on the doubleoctupole-phonon state can be obtained by a more precise lifetime measurement of the 19/2− state in 207 Pb or of the corresponding 21/2+ state in 209 Pb, where the B(E3) was predicted to be 50 W.u. [14]. In addition, a more accurate measurement of the lifetime of the 15/2− state in 209 Pb is mandatory to improve the precision of the E3 effective charge. The authors are grateful for the help of the GANIL staff and of the AGATA collaboration. D. R. Chakrabarty is gratefully acknowledged for the careful reading of the manuscript. This work was supported by the European Union Seventh Framework through ENSAR (Contract No. 262010) and partly funded by the P2IO LabEx (ANR-10-LABX- 0038) in the framework Investissements dávenir (ANR-11-IDEX-0003-01) managed by the French National Research Agency (ANR). DLB is supported by the Extreme Light Infrastructure Nuclear Physics (ELI6 [29] S. Akkoyun, et al., Nucl. Inst. Meth. Phys. Res. A 668 (2012) 26 – 58. doi:10.1016/j.nima.2011.11.081. [30] E. Clément, et al., Nucl. Inst. Meth. Phys. Res. A 855 (2017) 1 – 12. doi:10.1016/j.nima.2017.02.063. [31] A. Lopez-Martens, et al., Nucl. Inst.s Meth. Phys. Res. A 533 (3) (2004) 454 – 466. doi:10.1016/j.nima.2004.06.154. [32] O. Husser, et al., Nucl. Phys. A 194 (1) (1972) 113 – 139. doi:10.1016/0375-9474(72)91055-X. [33] F. Kondev, Nucl. Data Sheets 109 (6) (2008) 1527 – 1654. doi:10.1016/j.nds.2008.05.002. [34] C. Ellegaard, et al., Phys. Lett. B 25 (8) (1967) 512–514. doi:10.1016/0370-2693(67)90224-9. 7