Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

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. Received: 22 November 1997     

On the β-γ directional correlations in the β-decay of 208Tl

The relevance of the quenching effects induced by charge-exchange collective fields and Δ-isobar-hole excitations is discussed in the case of the β-γ angular correlations in the decay of ²⁰⁸Tl to the 5^?₁, 4^?₁ and 5^?₂ levels in ²⁰⁸Pb. It is found that, although these effects give rise to a large hindrance of the β-moments, they influence the anisotropy factor only very weakly. Satisfactory agreement between theoretical predictions and experimental data is obtained for all the transitions.     

High multipolarity electroexcitations in 207Pb and 206Pb

We report the identification of new high multipolarity transitions in ²⁰⁷Pb and ²⁰⁶Pb by the measurement of their form factor. A comparison to the corresponding excitations in ²⁰⁸Pb is presented.     

The soft Giant Monopole Resonance as a probe of the spin-orbit splitting

The isoscalar monopole response is studied in doubly magic ²⁰⁸Pb , ^{100, 132}Sn nuclei using the Skyrme HF+RPA model. A low-energy strength is predicted and corresponds to almost pure single-particle excitations. These pure single-particle excitations allow to analyse the splitting of the corresponding spin-orbit partners. A good agreement with the spin-orbit splitting data is found in the case of ²⁰⁸Pb . The experimental width of the giant monopole resonance may hinder the measurement of the soft monopole mode.     

Gamow-Teller and dipole strength in the 208Pb(n,p) reaction

Earlier data on the ²⁰⁸Pb(n,p)²⁰⁸Ti reaction at 198 MeV has been analysed using the multipole decomposition technique, and the contributions to the spectra from L = 0 and 1 transitions determined. The L = 0 cross section has been found to be smaller than values given by the calculations of MacFarlane [3] for Gamow-Teller transitions, using three different forms for the population of single particle states about the Fermi energy. Comparison is made with GT-strength values obtained from a more recent mean field calculation of these populations, and with an older nuclear structure calculation of properties of the lead nuclei. The L = 1 strength distribution is also reported.     

Sub-Coulomb transfer reactions on 208Pb with carbon and oxygen projectiles

Single-neutron transfers induced by ^{12, 13}C and ^{16, 17, 18}O projectiles on ²⁰⁸Pb and the ¹²C(¹⁷O, ¹⁶O)¹³C reaction have been studied at energies close to the Coulomb barrier. These processes are well described by the distorted-wave Born approximation. Coupled-channels effects are found to be small. Normalization factors have been determined for all projectile and target transitions, and also for the triton-deuteron overlap by comparison with previous measurements of the ²⁰⁸Pb(d, t)²⁰⁷Pb reaction. The root-mean-square (rms) radii of single-particle neutron wave functions in ²⁰⁸Pb and ²⁰⁹Pb were calculated using known spectroscopic factors. The distribution of the point neutron excess density in the surface region of ²⁰⁸Pb has been derived and its rms radius determined to be 5.93 ± 0.13 fm with a local potential model. This is in good agreement with theoretical predictions, but is considerably larger than estimates based on Coulomb energy differences. The phenomena of core polarisation by the odd particle or hole outside ²⁰⁸Pb is discussed using the single-particle orbitals determined in this work.     

A study of particle-vibration multiplets in 203Tl using the 205Tl(p,t)203Tl, 208Pb(p,t)206Pb and 206Pb(p,t)204Pb reactions

The ²⁰⁵Tl(p, t)²⁰³Tl reaction has been used at 26.2 MeV to obtain additional information on the particle-vibration multiplets in ²⁰³Tl. Enhancement factors for the L = 0 and L = 2 transitions to the lower excited states of ²⁰³Tl were well accounted for by using enhancement factors from the ²⁰⁶Pb(p, t)²⁰⁴Pb reaction and the wave functions from the intermediate coupling calculations of Covello and Sartoris. Additional data on the ²⁰⁸Pb(p, t)²⁰⁶Pb reaction at 26.2 MeV were used along with data at other energies to examine the energy dependence of the zero-range enhancement factors.     

Excitation of high-spin unnatural parity states in 208Pb from the (p,p′) reaction at 135 MeV

Differential cross sections for the excitation of states at 6.42, 6.73 and 7.04 MeV in ²⁰⁸Pb by 135 MeV protons are reported. Both the excitation energies and the backward peaked angular distributions observed in this experiment and in a recent (e, e′) experiment strongly suggest that these states are predominantly one-particle-one-hole excitations with J^π = 12^?, 14^? and 12^?, respectively. The present (p, p′) data are interpreted using a distorted wave impluse approximation and the effect of configuration mixing between the two 12^? states is investigated.     

Self-consistent calculations within the Green’s function method including particle-phonon coupling and the single-particle continuum

The Green’s function method in the Quasiparticle Time Blocking Approximation is applied to nuclear excitations in ¹³²Sn and ²⁰⁸Pb. The calculations are performed self-consistently using a Skyrme interaction. The method combines the conventional RPA with an exact single-particle continuum treatment and considers in a consistent way the particle-phonon coupling. We reproduce not only the experimental values of low-and high-lying collective states but we also obtain fair agreement with the data of non-collective low-lying states that are strongly influenced by the particle-phonon coupling.     

A study of the reactions208Pb(d,d)208Pb and208Pb(d,p)209Pb at energies above and below the Coulomb barrier

The reactions²⁰⁸Pb(d, d)²⁰⁸Pb and²⁰⁸Pb(d, p)²⁰⁹Pb have been studied in the energy region from below to above the Coulomb barrier. An optical-model analysis of the elastic scattering results has been performed to obtain parameters for a DWBA analysis. Distorted wave calculations for the direct transitions leading to single-particle states in²⁰⁹Pb have been used to extract spectroscopic factors. Only two deuteron potential sets give a good account of the stripping data throughout the energy region studied.     

Neutron particle-hole electric dipole states in 206, 207, 208Pb

Inelastic proton scattering on ²⁰⁶Pb, ²⁰⁷Pb and ²⁰⁸Pb through isobaric analog resonances has been used to study neutron particle-hole excitations with large ground-state γ-branches in these Pb isotopes. Relative (p, p′) cross sections at 90° are extracted for structures selectively excited on the $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{,}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ resonances. Interpretation of excitations is ²⁰⁶Pb and ²⁰⁷ Pb in terms of coupling to states in ²⁰⁸Pb is discussed. Branching ratios for 1^?states in ²⁰⁸Pb at 4.84, 5.29, 5.94 and 6.31 MeV and the $\text{1}\text{2}{}^{\mathrm{+}}$ state in ²⁰⁷Pb at 4.63 MeV are deduced.     

Fine Structure and Collectivity of the Levels of the Pygmy Dipole Resonance in <Superscript>208</Superscript>Pb 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.     

Reaction spectroscopy with even tin isotopes

The two-particle transfer reactions ^{116, 118}Sn(t, p) and the inelastic scattering of 55 MeV protons from ¹¹⁶Sn and 16 MeV protons from ^{116, 118, 120}Sn are analysed for various transitions to collective and non-collective states in the final nucleus using DWBA. Form factors have been calculated with wave functions containing two-quasiparticle excitations of neutrons in open and closed shells as well as 1p-1h transitions from closed proton shells. In the inelastic scattering, generally a Serber-type Gaussian effective interaction was inserted. The results are compared with those obtained on the assumption of two-quasiparticle excitations in a restricted configuration space only. For both types of reaction, reasonable agreement with experimental data is obtained for the angular distribution. In the (t, p) reaction the measured and calculated relative cross sections agree within a factor of two. For the inelastic scattering, apart from relative cross sections the mass dependence of the collective excitations and the influence of four-quasiparticle excitations have been examined. The transition to the collective 2⁺ level in ¹¹⁶Sn was calculated with the proton component of the wave function corrected according to electromagnetic measurements. From inelastic scattering it follows that the transitions to negative-parity states especially are not described satisfactorily by the wave functions used. Cross sections for unobserved higher excited levels have been estimated.     

Theoretical response to the discovery of deeply bound pionic states in208Pb(d,3He) reactions

Recently, deeply bound pionic states were found experimentally in (d,³He) reactions on²⁰⁸Pb. They found an isolated peak structure in the bound region below the pion production threshold. We study theoretically these excitation functions in (d,³He) reactions on²⁰⁸Pb at T _d =600 MeV. We found very good agreement with the (d,³He) excitation functions and could identify the underlying structures of the pionic states. We study the energy dependence of the (d,³He) reactions and the change of the excitation functions with the incident energy.     

208Pb(p, α)205Tl reaction at 16.475 MeV

The (p, α) reaction was studied on a²⁰⁸Pb target at 16.475 MeV. Nineteen states were observed in²⁰⁵Tl, up to 3.6 MeV in excitation. Angular distributions were obtained for five strong proton-hole transitions, and DWBA fits made to determinelj values. Results are compared with previous²⁰⁶Pb(t, α)²⁰⁵Tl,²⁰⁶Pb(d,³He)²⁰⁵Tl,²⁰⁵Tl(p, p′), and²⁰⁵Tl(n, n′) work.     

M1 resonances in unstable magic nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p 1 h?phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei^56,78Ni and^100,132Sn are calculated. For comparison, the experimentally known Ml excitations in⁴⁰Ca and²⁰⁸Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus⁷⁸Ni and the neutron deficient nucleus¹⁰⁰Sn.