208Pb Core Research Articles

Large-scale shell-model study of two-neutrino double beta decay of 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd

Large-scale shell-model calculations have been performed for the study of two-neutrino double-beta (2νββ) decay in 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for 2νββ decay in 82Se. In the case of 94Zr, the glekpn effective interaction is used. For 108Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of 124Sn, 128,130Te and 136Xe, the sn100pn effective interaction is employed. For 150Nd, we have used KHHE effective interaction based on holes in a 208Pb core. We have extracted the half-lives of these nuclei for the 2νββ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative 2νββ NME with respect to the excitation energy of the intermediate 1+ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate 1+ states as much as possible in comparison to results available in the literature.

Shell-model study for 204–210Tl isotopes and core excitations across the Z = 82 and N = 126 shell gaps

In the present work, the 204–210Tl isotopes have been investigated by performing large-scale shell-model calculations, including configurations allowing both neutron and proton core excitations across the Z=82 and N=126 shell gaps. Inspired by the recent high-spin experimental data, the structure of Tl isotopes has been studied for a considerably large model space. The KHHE interaction has been used for 204–206Tl isotopes, KHH7B interaction for 204–210Tl isotopes, and additionally KHM3Y interaction has been used for 208Tl isotope. The core excitation has been performed using the KHH7B and KHM3Y interactions. The level spectra of 204–210Tl isotopes are comprehensively described and explained by multi-nucleon couplings of single-particle-hole orbitals within the valence space and by core excitations across 208Pb core. The well-known isomeric states are analyzed in terms of the shell model configurations.

Octupole states in Tl207 studied through β decay

The β decay of 207Hg into the single-proton-hole nucleus 207Tl 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−11/2, πd−13/2, and πh−111/2 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 (s1/2-coupled) are identified and three more states (d3/2-coupled) are tentatively assigned using spin-parity inferences, while further h11/2-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 underestimation 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 noncollective t=1 states (t is the number of nucleons breaking the 208Pb 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.

Two-neutron and core-excited states in Pb210 : Tracing E3 collectivity and evidence for a new β -decaying isomer in Tl210

Yrast and near-yrast levels up to an I=17ℏ spin value and a 6-MeV excitation energy have been delineated in the “two-neutron” 210Pb nucleus following deep-inelastic reactions involving 208Pb targets and a number of heavy-ion beams at energies ∼25% above the Coulomb barrier. The level scheme was established on the basis of multifold prompt and delayed coincidence relationships measured with the Gammasphere array. In addition to the previously known states, many new levels were identified. For most of the strongly populated states, spin-parity assignments are proposed on the basis of angular distributions. The reinvestigation of the ν(g9/2)2, 8+ isomeric decay results in the firm identification of the low-energy E2 transitions involved in the 8+→6+→4+ cascade, and in a revised 6+ level half-life of 92(10) ns, nearly a factor of 2 longer than previously measured. Among the newly identified states figure spin I=4–10ℏ levels associated with the νg9/2i11/2 multiplet, as well as yrast states involving νg9/2j15/2, νi11/2j15/2, and ν(j15/2)2 neutron couplings. The highest-spin excitations are understood as 1p−1h core excitations and the yrast population is found to be fragmented to the extent that levels of spin higher than I=17ℏ could not be reached. Four E3 transitions are present in the 210Pb yrast decay; three of these involve the g9/2→j15/2 octupole component, as reflected in the 21(2) and >10 Weisskopf unit enhancements of the B(E3) rates of the first two. The fourth, 16+→13−E3 transition corresponds to the 3− core octupole excitation built on the νi11/2j15/2 state, in analogy to a similar E3 coupling to the νj15/2 level in 209Pb. Shell-model calculations performed for two-neutron states and 1p−1h 208Pb core excitations are in good agreement with the data. Evidence was found for the existence of a hitherto unknown high-spin β-decaying isomer in 210Tl. Shell-model calculations of the 210Tl levels suggest the possibility of a 11+ long-lived, β-decaying state, and the delayed yields observed in various reactions fit rather well with a 210Tl assignment.

The γ-ray spectroscopy studies of low-spin structures in 210Bi and 206Tl using cold neutron capture reactions

The γ-coincidence studies of low-spin structures of 210Bi and 206Tl are presented. The 210Bi nucleus, populated in thermal neutron capture reaction, was investigated using EXILL HPGe array at Institut Laue-Langevin in Grenoble. The experimental results were compared to the shell-model calculations allowing to draw the conclusions on the nature of the low-spin excitations populated below the neutron binding energy in 210Bi (4.6 MeV). It has been found that some levels cannot be described by the valence proton and neutron couplings, but may arise from couplings of valence particles to the 3- octupole phonon of the doubly magic 208Pb core. Moreover, preliminary results of a low-spin structure measurements of 206Tl by the γ-coincidence technique, making use of the 205Tl(n,γ)206Tl reaction at the FIPPS prompt γ-ray spectroscopy facility of ILL are shown. The population of a large number of excited states of 206Tl above the ground state up to the neutron binding energy (at 6.5 MeV), within a few units of spin is expected. The analysis involving double and triple γ-coincidences and γγ-angular correlations will allow to significantly extend the experimental information on the energy and spin-parity of the levels in 206Tl. This will help shedding light on the proton-hole and neutron-hole couplings near the doubly magic core 208Pb.

Approaching complete low-spin spectroscopy ofBi210with a cold-neutron capture reaction

The low-spin structure of the 210Bi nucleus was investigated in the neutron capture experiment 209Bi(n,γ )210Bi performed at ILL Grenoble at the PF1B cold-neutron facility. By using the EXILL multidetector array, consisting of 46 high-purity germanium crystals, and γγ-coincidence technique, 64 primary γ rays were observed (40 new) and a total number of 70 discrete states (33 new) were located below the neutron binding energy in 210Bi. The analysis of the angular correlations of γ rays provided information about transitions multipolarities, which made it possible to confirm most of the previously known spin-parity assignments and helped establish new ones. The obtained experimental results were compared to shell-model calculations involving one-valence-proton, one-valence-neutron excitations outside the 208Pb core. It has been found that while up to the energy of ∼2 MeV each state observed in 210Bi has its calculated counterpart; at higher excitation energies some levels cannot be described by the valence particle couplings. These states may arise from couplings of valence particles to the 3− octupole phonon of the doubly magic 208Pb core and may serve as a testing ground for models which describe single particle-phonon excitations.

Do alpha particles cluster inside heavy nuclei?

New excited states have been observed in 212Po that are associated with a configuration in which an alpha particle is combined with a doubly-magic 208Pb core.

Hard-to-reach nuclei studied with deep-inelastic heavy-ion reactions

Spectroscopic studies performed with deep-inelastic heavy-ion reactions are reviewed for two regions of neutron-rich nuclei. The identification of $\nu(h_{11/2})^n$ isomers in nearly complete series of Sn isotopes and the resulting systematic of B(E2) values for isomeric transitions is presented and followed by the discussion of shell model states studied in neutron-rich Te isotopes including the new four neutron-hole isomers identified in 130 Te. Yrast spectroscopy studies of nuclei from the doubly magic 208 Pb region are described by outlining the highest spin states observed in the 208 Pb core nucleus. The E3 transitions observed abundantly in yrast decays are discussed within the framework of particle-octupole vibration coupling and the validity of a simple rule connecting energy shifts of octupole states built on one-particle states with the ones observed for two-particle states is demonstrated.

The $\pi h_{11/2}^{-1}\nu i_{13/2}^{-2}$ three-hole isomeric state and octupole core excitation in the 205 Tl nucleus

New high-spin states were identified in the 205Tl isotope produced in deep-inelastic heavy-ion reactions. The expected 29/2 + yrast state and 35/2- isomeric state with 235 ns half-life were located above the 2.6 μs isomer known from previous studies. Above this isomer a 7092 keV level was interpreted as a 41/2 + state arising from the coupling of the octupole vibration of the 208Pb core with the three-hole structure of the 35/2- isomer.

Particle octupole-vibration coupling near 208Pb

High-spin states in nuclei around 208Pb were populated in deep inelastic collisions of 136Xe and 208Pb projectiles with 208Pb targets at beam energies about 12% above the Coulomb barrier. New states in nuclei in the vicinity of 208Pb have been found that result from the coupling of one and two quasi particles to the lowest 3− excitation of the 208Pb core. They show the influence of particle octupole-vibration coupling in a pronounced and clear way and verify the validity of this concept.

γ Spectroscopy of 209Pb with deep inelastic reactions

High spin states in nuclei around 208Pb were populated in deep inelastic collisions of 76Ge, 136Xe, and 208Pb projectiles with 208Pb targets at beam energies about 12% above the Coulomb barrier. New states in 209Pb were found by measuring γ-γ-coincidences. They are interpreted as the yrast states that originate from the coupling of one neutron to the lowest excitations of the 208Pb core. The results are discussed in the frame of the shell model.

Spectroscopy of high-spin states of 206Po

The yrast and near-yrast energy levels of 206Po have been investigated to over 9 MeV excitation and up to spins of 24. The measurements consisted of γγ-coincidence data, internal-conversion-electron spectra, time spectra of γ-rays relative to a pulsed beam, excitation functions and γ-ray angular distributions. Two new isomers, with lifetimes in the 1 ns range, were found. The observed level structure is compared with the predictions of empirical shell-model calculations in which 206Po is regarded as a 208Pb core with two valence protons and four valence neutron holes. The agreement is generally satisfactory for the observed odd-parity levels and for even parity levels with J > 12; those with J = 6−12 are better accounted for by weak coupling of two valence protons to a 204Pb core in its 0 + 1 and 4 + 1 states.

Single-particle potential and quasiparticle properties of protons in 208Pb

The real part V( r; E) of the proton- 208Pb mean field is approximated by a Woods-Saxon potential with diffuseness equal to 0.70 fm. Its depth U v ( E) and radius R v ( E) are extrapolated from positive to negative energy by using a previously developed iteration procedure based on the dispersion relation which connects the real and imaginary parts of the mean field. It is shown that these extrapolated values are quite stable with respect to changes of the main input of the calculation, namely a set of empirical optical-model potentials. Near the Fermi energy the potential radius R v ( E) has a characteristic energy dependence which is qualitatively similar to that recently found in the case of neutrons in 208Pb. However, interesting differences exist. For nucleon energies larger than 10 MeV, the mean field felt by protons has approximately the same root mean square radius as that felt by neutrons. In contradistinction, the root mean square radius of the proton potential at the Fermi energy is sizeably smaller than that of the neutron potential. Furthermore, the potential depth U v ( E) approximately has a linear energy dependence from −20 MeV to +50 MeV in the case of protons, while in the case of neutrons it displays a plateau at small energy. The calculated potential V( r; E) is the sum of a Hartree-Fock type contribution V HF( r; E) and of a dispersive contribution ΔV( r; E) which is due to excitations of the 208Pb core. If V HF( r; E) is assumed to have a Woods-Saxon shape, ΔV( r; E) is found to be surface peaked, even at energies as large as 30 MeV at which in the case of neutrons ΔV( r; E) has a Woods-Saxon shape. The proton single-particle energies calculated from the full potential V( r; E) are in good agreement with the empirical values, while those obtained from the Hartree-Fock type component V FH( r; E) alone are too widely spaced. The energy dependence of V( r; E) is characterized by the effective mass m ∗(r; E) , whose dependence upon r and E is calculated. At the nuclear centre, the effective mass is almost independent of energy in contrast to the neutron case; this difference is ascribed to the Coulomb barrier. At the nuclear surface, m ∗ displays a sharp enhancement peak for E close to the Fermi energy, as in the neutron case. The spectroscopic factors of single-particle excitations in 207Tl and 209Bi are calculated from the ratio between m ∗ and its Hartree-Fock type approximation; they are in fair agreement with empirical values deduced from recent electron inelastic scattering data.

Extrapolation from positive to negative energy of the Woods-Saxon parametrization of the n- 208Pb mean field

The real part V( r); E) of the nucleon-nucleus mean field is assumed to have a Woods-Saxon shape, and accordingly to be fully specified by three quantities: the potential depth U v ( E), radius R V ( E) and diffuseness a v ( E). At a given nucleon energy E these parameters can be determined from three different radial moments [ r q ] v = (4 π/ A) ∝ V( r; E) r q d r. This is useful because a dispersion relation approach has recently been developed for extrapolating [ r q ] V ( E) from positive to negative energy, using as inputs the radial moments of the real and imaginary parts of empirical optical-model potentials V( r; E) + iW( r; E). In the present work, the values of U v ( E), R v ( E) and a v ( E) are calculated in the case of neutrons in 208Pb in the energy domain −20 < E < 40 MeV from the values of [ r q ] V ( E) for q = 0.8, 2 and 4. It is found that both U V ( E) and R v ( E) have a characteristic energy dependence. The energy dependence of the diffuseness a a ( E) is less reliably predicted by the method. The radius R V ( E) increases when E decreases from 40 to 5 MeV. This behaviour is in agreement with empirical evidence. In the energy domain −10 MeV < E < 0, R V ( E) is predicted to decrease with decreasing energy. The energy dependence of the root mean square radius is similar to that of R V ( E). The potential depth U v slightly increases when E decreases from 40 to 15 MeV and slightly decreases between 10 and 5 MeV; it is consequently approximately constant in the energy domain 5 < E < 20 MeV, in keeping with empirical evidence. The depth U v increases linearly with decreasing E in the domain −10 MeV < E < 0. These features are shown to persist when one modifies the detailed input of the calculation, namely the empirical values of [ r q ] v ( E) for E > 0 and the parametrization [ r q ] w ( E) of the energy dependence of the radial moments of the imaginary part of the empirical optical-model potentials. In the energy domain −10 MeV < E < 0, the calculated V( r; E) yields good agreement with the experimental single-particle energies; the model thus accurately predicts the shell-model potential ( E < 0) from the extrapolation of the optical-model potential ( E > 0). In the dispersion relation approach, the real part V( r; E) is the sum of a Hartree-Fock type contribution V HF( r; E) and of a dispersive contribution ΔV( r; E). The latter is due to the excitation of the 208Pb core. The dispersion relation approach enables the calculation of the radial moment [ r q ] ΔV ( E) from the parametrization [ r q ] w ( E): several schematic models are considered which yield algebraic expressions for [ r q ] Δ V ( E). The radial moments [ r q ] HF( E) are approximated by linear functions of E. When in addition, it is assumed that V HF( r; E) has a Woods-Saxon radial shape, the energy dependence of its potential parameters ( U HF, R HF, a HF) can be calculated. Furthermore, the values of ΔV( r; E) can then be derived. It turns out that ΔV( r; E) is peaked at the nuclear surface near the Fermi energy and acquires a Woods-Saxon type shape when the energy increases, in keeping with previous qualitative estimates. It is responsible for the peculiar energy dependence of R V ( E) in the vicinity of the Fermi energy.

Elastic electron-nucleus scattering in a relativistic theory of nuclear structure

The transverse elastic form factor of 209Bi is calculated using a Dirac wave function for the valence proton orbiting a relativistic Hartree 208Pb core. Comparison is made with a corresponding nonrelativistic calculation, and relativistic interaction effects in the nuclear current operator are discussed.

High spin yrast states in N = 126 isotones

A comprehensive spectroscopic investigation of yrast levels in three N = 126 isotones, 212Rn, 213Fr and 214Ra, is presented. We report measurements of prompt and delayed excitation functions, γ-γ and X-γ coincidences, g-factors, linear polarizations and angular distributions of γ-rays. Yrast spectra in these nuclei extend to high spin and are rich in isomers. The isomerism and the spin dependence of yrast energies for N = 126 isotones are discussed in terms of excitations of valence protons with and without contributions from the 208Pb core.

Shell model calculations of two to four identical-“particle” systems near 208Pb

The structure of the nuclei 204–206Pb, 210–212Pb, 210Po, 211At, and 212Rn is studied in terms of conventional nuclear shell models. An inert 208Pb core is assumed, and active particles (holes) are distuibuted in the low-lying single-particle (hole) orbits. Experimental single-particle energies are used for the one-body part of the effective residual interaction. Realistic interaction matrix elements developed for this mass region by Kuo and Herling are used for the matrix elements of the two-body part of the residual interactions. As much as possible, other effective one-body operators for electromagnetic observables are derived from experimental data on the single-particle (hole) nuclei 207Pb, 209Pb, and 209Bi. Observables treated are ground state binding energies, excitation energies, strengths for one- and two-particle transfers, and E2 and M1 observables. Generally, excellent agreement is found. The configuration mixing calculations do not remove anomalies in the magnetic moments of excited states in 206Pb and 212Rn. Many states in these nuclei are predicted by the models which have not been observed as yet. It is found that a truncation scheme for doubly even nuclei treated here in which only seniority-0 and seniority-2 states are allowed is potentially very useful.

Quadrupole core vibrations in the A = 211 isobars

States of the A = 211 isobars are described as three particles coupled to each other and to a vibrating 208Pb core. Model parameters are extracted from available data on A = 209, 210 isobars, but it is necessary to postulate a form for the two-body interaction to obtain all necessary matrix elements. Energy spectra and reduced transition probabilities are calculated and compared with experiment.

The structure of 209Bi

Abstract A high resolution study of the 209Bi(p, p′) reaction has been conducted at incident proton energies of 14.95 and 16.10 MeV to compare the resonant and direct excitations, respectively, of levels in 209Bi. The energies for transitions to over eighty levels in 209Bi up to an excitation energy of 4.4 MeV were measured, many of which have not been reported previously. Angular distributions from the 16.10 MeV direct scattering measurement are compared with angular distributions from proton scattering on 208Pb performed at the same incident energy, and those groups of levels in 209Bi corresponding to the 3−(2.615 MeV), 5−(3.198 MeV), and 2+(4.086 MeV) excitations of the 208Pb core are identified. The macroscopic weak-coupling model is employed in a discussion of these results and, while the description of these levels in terms of excitations of 208Pb is shown to be qualitatively correct, several significant differences between this simple model and the data are observed. In particular, for levels corresponding to the [ h 9 2 π ⊗ 208 Pb (5 − )] configuration, it is emphasized that the microscopic 2p-1h structure of the excitations must be considered in order to account for the direct transition strengths.

Semi-realistic shell model studies in the lead region. II. 211Bi

The semi-realistic approach described earlier is applied to a calculation of the 208 Pb ± 3 nucleus 211Bi. It is shown that the anomalously low lying 7 2 − first excited state arises from the particularly strong coupling between the f 7 2 single-proton state and the 7 2 − member of the i 13 2 ⊗ 208Pb(3 −) core multiplet.