States In 208Pb Research Articles

Suggested icosahedral states in 208Pb

The known 6+ yrast and 12+ yrare states are recognized as members of an icosa-hedral rotational band. The 18+ state at 8813 keV is newly identified as icosahedral rotor.

High spin states in the heavy nucleus 208Pb and the coupling of one-particle one-hole states to platonic shapes

Structure, spin, and parity of states in 208Pb at 9 < Ex < 17 MeV are explained by the weak coupling of the 3−, 4+, 6+ yrast, and the 12+ yrare states to one-particle one-hole yrast and yrare states. The spins of the particle and the hole are coupled in the stretched or nearly stretched mode. The ns-isomerism of three states is shown to derive from the exchange of an intruder hole and the p 1/2 hole.

Measurement of the \(\gamma \) Decay from the Energy Region of the Pygmy Dipole States Excited in the \(^{208}\)Pb\((p,p'\gamma )\) Reaction at CCB

For a few years, the medical cyclotron Proteus C-235 at the Cyclotron Centre Bronowice in Krakow, Poland has been regularly used for nuclear structure experiments. One of the ongoing studies is focused on the γ decay of collective states populated in (p, p0γ) reactions. In a recent experiment, γ decays of excited states in the energy region of the Pygmy Dipole States in 208Pb have been observed. Good efficiency and energy resolution provided by the PARIS clusters and LaBr3:Ce scintillators facilitate a comparison of the obtained energy spectra with previous measurements of pygmy states in this nucleus.

Evidence of octupole-phonons at high spin in 207Pb

A lifetime measurement of the 19/2− state in 207Pb 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 208Pb beam impinging on a 100Mo 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 207Pb. An analysis in terms of a particle-octupole-vibration coupling model indicates that the measured B(E3) value in 207Pb 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.

Discovery of collective states in 208Pb by complete spectroscopy

Most neutron and proton bound states in 208Pb are described in the shell model as one-particle onehole configurations. Besides precise data obtained with the Q3D magnetic spectrograph of the MLL (Garching, Germany) an important reaction is the inelastic proton scattering via isobaric analog resonances in 209Bi. It yields amplitudes of neutron one-particle one-hole configurations with relative signs in each stateof 208Pb. The orthogonality, normality, and sum rule relations allow to investigate the completeness of the transformation matrices of one-particle one-hole configurations describing the states in 208Pb with spins from 0− to 14− and 0+ to 12+. By this method amplitudes of unobservable one-particle one-hole configurations can be determined.The comparison of spin, parity, and dominant particle-hole components thus derived in up to 30 states of a certain spin to shell model calculations allows to identify states described as collective excitations of the entire nucleus.

Fine Structure and Collectivity of the Levels of the Pygmy Dipole Resonance in 208Pb in a Self-Consistent Model

A novel fully self-consistent microscopic approach based on the energy density functional method is employed to calculate the fine structure of the pygmy dipole resonance in 208Pb, i.e., the energies and reduced probabilities of E1 transitions for the states with energies below 10 MeV. The approach includes the random-phase approximation, quasiparticle–phonon interaction and the single-particle continuum. The theoretical results are compared to the available high-resolution data and found to agree with measured integral characteristics of the pygmy dipole resonance at energies above 5.7 MeV. Residual spin–spin forces are quantified, and their contribution is found to be significant at both low and high energies. A recently proposed criterion is employed to analyze the collectivity of the 1–states in 208Pb.

Some aspects of self-consistent higher-order interactions

After a brief review of the formalism of the self-consistent higher-order interactions, applications of a ([Q3Q3](2) · Q2) type of three-body interaction to the quadrupole moment of the 3− state in 208Pb and the energy splitting of the septuplet of states (h9/23−)I with I = 3/2, 5/2, …, 15/2 in 209Bi are discussed. It is shown that if the contribution of the three-body interaction is included, the theoretical value of the Qel(3−) moment becomes rather small compared to the experiment, but the observed small energy splitting of the septuplet can essentially be understood within the particle-vibration coupling model. Roles of non-linear field couplings provided by the self-consistent higher-order interactions are also discussed.

Electric dipole excitation of 208Pb by polarized electron impact

The cross sections and spin asymmetries for the excitation of 1- states in 208Pb by transversely polarized electrons with collision energy of 30-180MeV have been examined within the DWBA scattering formalism. As examples, we have considered a low-lying 1- state and also states belonging to the pygmy dipole and giant dipole resonances. The structure of these states and their corresponding transition charge and current densities have been taken from an RPA calculation within the quasiparticle phonon model. The complex-plane rotation method has been applied to achieve the convergence of the radial DWBA integrals for backward scattering. We have studied the behaviour of the cross sections and spin asymmetries as a function of electron energy and scattering angle. The role of the longitudinal and transversal contributions to the excitation has been thoroughly studied. We conclude that the spin asymmetry S, related to unpolarized outgoing electrons, is mostly well below 1% even at the backward scattering angles and its measurement provides a challenge for future experiments with polarized electrons.

Polarization in nuclear excitation by electron impact

Electron–electron polarization correlations from nuclear excitation by spin-polarized electrons are studied within the distorted-wave Born approximation. Restriction is made to spin-0 and to unpolarized spin-12 nuclei. When Coulomb scattering is dominant the resulting spin asymmetries may exceed those from elastic scattering. However, at the backmost scattering angles or for large transition current densities where magnetic scattering prevails, there is a strong suppression of the transverse polarization correlations. Predictions are made for the excitation of the lowest 3− and 5− states of 208Pb and the lowest 52− state of 89Y by 60–220 MeV electrons.

Observation of bound and unbound 1− states in 208Pb by particle spectroscopy

Using the Q3D magnetic spectrograph of the Maier-Leibnitz-Labaratorium at Garching (Germany), experiments on the 208Pb(d,d'), the 207Pb(d,p), the resonant and the non-resonant 208Pb(p,p') reactions were performed. The 208Pb(p,p') reaction was investigated near all seven known isobaric analog resonances in 209Bi. The excitation energies of about 300 states in 208Pb at Ex < 8MeV were determined with an accuracy of about 100 eV. The mean distance between states in 208Pb is about 10keV up to the neutron threshold (S(n) = 7368 keV). The number of 1− states observed by particle spectroscopy up to the proton threshold (S(p) = 8.00 MeV) is close to the number predicted by the schematic shell model without residual interaction. The structure of several 1− states is deduced from particle spectroscopy. Four out of the seven lowest 1− states contain about 80% strength of a single configuration.

Octupole transitions in the 208Pb region

The 208Pb region is characterised by the existence of collective octupole states. Here we populated such states in 208Pb + 208Pb deep-inelastic reactions. γ-ray angular distribution measurements were used to infer the octupole character of several E3 transitions. The octupole character of the 2318 keV 17− → 14+ in 208Pb, 2485 keV 19/2− → 13/2+ in 207Pb, 2419 keV 15/2− → 9/2+ in 209Pb and 2465 keV 17/2+ → 11/2− in 207Tl transitions was demonstrated for the first time. In addition, shell model calculations were performed using two different sets of two-body matrix elements. Their predictions were compared with emphasis on collective octupole states.

Isospin character of low-lying pygmy dipole states in 208Pb via inelastic scattering of 17O ions.

The properties of pygmy dipole states in 208Pb were investigated using the 208Pb(17O, 17O'γ) reaction at 340 MeV and measuring the γ decay with high resolution with the AGATA demonstrator array. Cross sections and angular distributions of the emitted γ rays and of the scattered particles were measured. The results are compared with (γ, γ') and (p, p') data. The data analysis with the distorted wave Born approximation approach gives a good description of the elastic scattering and of the inelastic excitation of the 2+ and 3- states. For the dipole transitions a form factor obtained by folding a microscopically calculated transition density was used for the first time. This has allowed us to extract the isoscalar component of the 1- excited states from 4 to 8 MeV.

Single-particle widths in 208Bi and 209Bi determined from the inelastic proton scattering by 207Pb and 208Pb

Single-particle widths in 209Bi for all particle orbits s1/2, d3/2, d5/2, g7/2, g9/2, i11/2, j15/2 and for the hole orbits p1/2, p3/2, f5/2, f7/2 are deduced from the study of about fifty states in 208Pb with rather pure particle-hole configurations. Relative single-particle widths of the 0+ isobaric analog resonance (IAR) in 208Bi for the orbits p3/2, f5/2, f7/2 are deduced from the 207Pb(p, p′) reaction. The 207Pb(p, p′) and 208Pb(p, p′) reactions via IAR were studied in a scattering chamber experiment of the Max-Planck institute for nuclear physics (Heidelberg, Germany) at scattering angles 40° ≤ Θ ≤ 170°. The semiconductor detectors yielded a resolution of 11–15 keV. Proton energies E p = 14.99, 16.30, 16.45, 16.60, 17.40, 17.47, 17.75 MeV covered the g9/2, j15/2, d5/2, g7/2, and d3/2 IARs in 209Bi, and 11.0 < E p < 11.8 MeV the 0 + IAR in 208Bi. The differential cross sections for nearly 70 levels in 208Pb were determined with an uncertainty of the solid angle of about 2%. Similar measurements of 208Pb(p, p′) with the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium (Garching, Germany) 35–45 years later yielded a resolution of about 3 keV. The uncertainty of the differential cross section was 10–30%. Scattering angles covered 20° ≤ Θ ≤ 115° and Θ = 139°. The nonresonant (p, p′) reaction often dominates at scattering angles Θ ≲ 100°. Therefore, only the combination of the two data sets, i) backward angles, precise solid angles but modest resolution, ii) medium scattering angles and high resolution, allows to determine in an iterative manner both the structure of particle-hole states in 208Pb and the relevant single-particle widths in 209Bi .

Study of theγdecay of high-lying states in208Pb via inelastic scattering of 17O ions

A measurement of the high-lying states in 208Pb has been made using 17O beams at 20 MeV/u. The gamma decay following inelastic excitation was measured with the detector system AGATA Demonstrator based on segmented HPGe detectors, coupled to an array of large volume LaBr3:Ce scintillators and to an array of Si detectors. Preliminary results in comparison with (γ,γ’) data, for states in the 5-8 MeV energy interval, are presented.

Effect of the non-locality factor for bound states in 208Pb

We describe the bound nucleons for 208Pb with non-local nuclear potentials by solving the integral equation generated from the Schrodinger equation in momentum space. The binding energies, the potential depth, the diffuseness, the radii, and the non-local parameter are obtained by fiiting the experimental data. The wave functions of the bound nucleons due to non-locality are shown to be repulsive compared with the wave functions generated by the local potential.

Excitation energies of particle-hole states in 208Pb and the surface delta interaction

The schematic shell model without residual interaction (SSM) assumes the same excitation energy for all spins in each particle-hole configuration multiplet. In 208Pb, more than forty states are known to contain almost the full strength of a single particle-hole configuration. The experimental excitation energy for a state with a certain spin differs from the energy predicted by the SSM by −0.2 to +0.6 MeV. The multiplet splitting is calculated with the surface delta interaction; it corresponds to the diagonal matrix element of the residual interaction in the SSM. For states containing more than 90% strength of a certain configuration and for the centroid of several completely observed configurations, the calculated multiplet splitting often approximates the experimental excitation energy within 30 keV. The strong mixing within some pairs of states containing the full strengths of two configurations is explained.

High resolution particle spectroscopy in 208Pb

By using the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at München, particle-hole states in 208Pb are investigated. With the reaction 208Pb(p, p') at energies 14 < Ep < 18MeV an instrumental resolution of δEp′Ep′ = 3 · 10−4 is achieved for protons without energy loss in the target. For lower energies Ep′ an exponential tail with a width proportional to the effective target thickness appears. Below Ex = 8.2 MeV more than 250 states in 208Pb are observed. Excitation energies are derived with uncertainties of 0.1 keV for strongly excited states by calibration with known data from Nuclear Data Sheets. 208Pb(p, p') via isobaric analog resonances (IAR) in 209Bi allows to determine the neutron particle-hole components of each state in 208Pb. The selective excitation in an IAR yields the parity for each state. Spin and dominant neutron particle-hole configurations of a state are determined from the mean cross section and the shape of the angular distribution for 208Pb(p, p'). From about 120 particle-hole states predicted by the shell model in 208Pb below Ex = 6.1 MeV, about 50 states with negative parity and 30 states with positive parity are identified.

Neutron particle-hole structure of states in 208Pb determined from the proton decay of the d5/2 isobaric analog resonance in 209Bi

Neutron particle-hole structure of states in 208Pb determined from the proton decay of the d5/2 isobaric analog resonance in 209Bi

Erratum to: Neutron particle-hole structure of states in 208Pb determined from the proton decay of the d5/2 isobaric analog resonance in 209Bi

Proton scattering on 208Pb via isobaric analog resonances (IARs) in 209Bi generates neutron particle-hole configurations in excited states of 208Pb . The spin and parity of the neutron particle correspond to the spin and parity of the resonance. We performed experiments on the 208Pb (p, p’) reaction via all known isobaric analog resonances in 209Bi with the Q3D magnetic spectrograph in Munchen. We observed more than 130 levels in the range of excitation energies E x < 6.4 MeV. In the proton decay of the d 5/2 resonance, 29 levels have cross-sections larger than 5% of the maximum cross-section of any level. Six levels in the range 4.6 < E x < 5.2 MeV correspond to states with known spins and major $\ensuremath \nu(d_{5/2}^{+1} p_{1/2}^{-1})$ strength. Six levels in the range 5.7 < E x < 6.4 MeV contain most of the $\ensuremath \nu(d_{5/2}^{+1} p_{3/2}^{-1})$ strength. At least one level originates from an unresolved doublet. Among the states with a major $\ensuremath \nu(d_{5/2}^{+1} p_{3/2}^{-1})$ component, only states with spins 1- and 3- are firmly identified. The comparison to previous data taken with semiconductor detectors reveals details of the structure of at least 18 states in the range 4.6 < E x < 6.4 MeV.

High resolution particle spectroscopy in 208Pb with the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at München

By using the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at München, particle-hole states in 208Pb are investigated. The reaction 208Pb(p, p') via seven known isobaric analog resonances in 209Bi and the reaction 207Pb(d,p) were studied. An instrumental resolution of about 3keV for protons without energy loss in the target is achieved; depending on the effective target thickness the peak shape becomes asymmetric with a tail of 3-8 keV width. A dozen doublets of states at less than 2 keV or even vanishing distance are resolved by the selective excitation in different analog resonances. For excitation energies 3.9 < Ex⪅6.1 MeV in 208Pb, 80 states with negative parity and 30 states with positive parity are predicted by the shell model. Most states are identified and work is going on to determine their structure.