7 MeV dipole ground state transitions in 207Pb, 208Pb and 209Bi

The Doppler-broadened 7.117 MeV line from the ¹⁹F(p, αγ)¹⁶O reaction has been used to resonantly excite levels in ²⁰⁸Pb at 7071±2 and 7091±2 keV, in ²⁰⁷Pb at 7186±5 and 7206±5 keV and in ²⁰⁹Bi at 7179±5 and 7202±5 keV. On the basis of angular distribution measurements the 7071 and 7091 keV levels of ²⁰⁸Pb are assigned spins of 1 and assuming 100% ground state branching the widths are calculated to be 31±3 and 17±2 eV respectively. It is suggested that the states in ²⁰⁷Pb and ²⁰⁹Bi arise from the weak coupling of a $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron hole and an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton respectively to one or the other of the ²⁰⁸Pb levels. The widths obtained in terms of _gΓ_o²/Γ are 15±4 and 25±5 eV for the 7186 and 7206 keV levels of ²⁰⁷Pb and 24±5 and 30±5 for the levels of ²⁰⁹Bi respectively. These values are consistent with the weak-coupling suggestion.     

Molecular-orbital X-rays from 1 GeV 208Pb + 208Pb and 209Bi + 209Bi collisions

We have measured the spectra of continuum X-rays above the characteristic K lines for 4.5 to 4.8 MeV/N ²⁰⁸₈₂Pb → ²⁰⁸₈₂Pb, Pb → Bi, Bi → Pb and Bi → Bi collisions. Above ≈400 keV X-ray energy the spectral shape and intensity agree roughly with calculations of Kirsch et al. for the 1sσ molecular-orbital (MO) X-ray spectrum from Pb-Pb. Deviations from the theory below ≈400 keV suggest transitions to other MO's.     

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.     

Gamma decay of particle-core states in 209Pb

A γ-decay scheme for levels in ²⁰⁹Pb up to 4.13 MeV of excitation has been established by means of the reaction ²⁰⁸Pb(d, pγ)²⁰⁹Pb. In high efficiency p-γ coincidence measurements γ-cascades have been observed from the single-particle states and from core-excited states with very small single-particle strength. Assuming a qualitative validity of the weak-coupling model spins and main configurations of particle-core states can be deduced from their γ-decay. The $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{5}\text{2}{}^{\mathrm{?}}\text{or}\text{7}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{)}$ members of the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?3}{}^{\mathrm{?}}$ multiplet could be located. A systematic manner of doublet splitting is found for the lowest states with main configuration $\text{(}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{?3}{}^{210}\text{Pb}\text{(0}{}^{\mathrm{+}}\text{, 2}{}^{\mathrm{+}}\text{, 4}{}^{\mathrm{+}}\text{, 6}{}^{\mathrm{+}}\text{, 8}{}^{\mathrm{+}}\text{)}$. A new decay branch of the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ single-particle state is attributed to an admixture of quadrupole core vibration.     

Heavy-ion transfer reactions on 208Pb above the coulomb barrier

The selective excitation of single-particle and hole states in stripping and pick-up reactions induced by ¹¹B ions of 113.5 MeV on ²⁰⁸Pb is interpreted on the basis of a semi-classical theory. The excitations of outgoing ions and the continuum are also discussed.     

The 207Pb(d,p)208Pb reaction with high resolution

The reaction ²⁰⁷Pb(d, p)²⁰⁸Pb has been studied at E_d = 18.0 MeV using the MPI Heidelberg Emperor tandem accelerator and multiple-gap spectrograph. The average resolution of 18 keV was better than previous measurements, and this, combined with the long beam exposure, allowed many finer details of the neutron particle-hole structure of ²⁰⁸Pb to be examined. In all, 45 levels were seen up to E_x = 6.3 MeV, many of which had never been seen before. A DWBA analysis of the stripping transitions angular distributions is made, and values of (2J + 1)S_ij, energy centroids, and summed strengths are given. An interesting cluster of 1i_{$\text{11}\text{2}$} and 2g_{$\text{9}\text{2}$} levels at E_x ≈ 4.2 MeV are resolved and are compared to recent isobaric analog state data. A search for weak stripping strength to known pairing vibrations in ²⁰⁸Pb gave essentially negative results and points to the need for improved ultra-resolution measurements.     

RPA-calculations in 208Pb with a density dependent interaction

Excitation energies and excitation probabilities of the low lying states of ²⁰⁸Pb are calculated within the theory of Finite Fermi System (FFS), using a density dependent residual interaction. A strong M2-transition at 7.51 MeV is predicted.     

Properties of the quasiparticle excitations in 207Pb and 209Pb from an extrapolation of the optical-model potential

A previously developed dispersion relation approach is used to calculate the shell-model potential in the case of neutrons in ²⁰⁸Pb, in the energy domain (-50 MeV, 0). This potential contains a dispersive contribution besides a Hartree-Fock type component, and thereby includes correlation and polarization effects. The shell-model and the Hartree-Fock type potentials are assumed to have Woods-Saxon shapes with diffuseness a_v = 0.70 fm; the energy dependence of their depths and radii is calculated. The energy dependence of the shell-model potential is characterized by the effective mass, whose dependence upon radial distance and neutron energy is determined. The effective mass is a sensitive function of energy, in contrast to its Hartree-Fock type component which is nearly independent of energy. Attention is drawn to the fact that the effective mass in nuclear matter cannot be straightforwardly identified with the effective mass at the nuclear centre. The effective mass presents a sharp peak at the nuclear surface near the Fermi energy and a dip at the surface for energies 10 to 20 MeV away from the Fermi energy. The spectroscopic factors of single-particle excitations in ²⁰⁷Pb and ²⁰⁹Pb are calculated from the difference between the effective mass and its Hartree-Fock type component. The predicted values of the valence single-particle wave functions at large radial distances are in fair agreement with experimental values deduced from analyses of sub-Coulomb pickup reactions. It is shown that the dispersive contribution increases the level density parameter by about 25%, in agreement with previous microscopic or semi-phenomenological models; the calculated level density parameter is in good agreement with the empirical value.     

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.     

Properties of single-particle states in the 208Pb region

The properties of single-particle states in the ²⁰⁸Pb region are obtained by subtracting from the empirical values the dressing effects of the multipole particle-hole and pairing phonons. Use is made of the particle-vibration formalism. Single-particle energies, one-body transfer spectroscopic factors and effective quadrupole charges are examined within this framework.     

Nuclear structure calculations with a density-dependent force in 208Pb

Excitation energies and excitation probabilities in ²⁰⁸Pb of the low lying states as well as of strongly collective high lying states (generalized multipole resonances) are calculated, using a large configuration space and a density dependent interaction. Within the extended theory of finite Fermi systems moments of excited states and transition probabilities between excited states are calculated. The theoretical results are in fair agreement with the experimental values.     

Effective masses,occupation probabilities and quasiparticle strengths in 208Pb

The dispersion relation approach is applied to the calculation of the following quantities: the radial and the energy dependence of the effective masses which characterize the mean field felt by neutrons and protons in ²⁰⁸Pb; the occupation probabilities of the shell-model orbits in the correlated ground state of ²⁰⁸Pb; the state-dependent effective masses and quasiparticle strengths; the single-particle energy shifts due to correlation corrections. Parametric expressions are constructed for most of these quantities. The results are compared with those which have previously been computed or assumed by other authors.     

Dependence of the density distribution of 208Pb on the occupation probabilities of shell-model orbits

An independent-particle model for the proton density distribution of ²⁰⁸Pb is constructed; it closely approximates the Hartree-Fock calculation of Dechargé and Gogny. We investigate the modifications which arise when one introduces a depletion of the Fermi sea of the amount suggested by analyses of recent electron scattering data and by nuclear-matter calculations. The main effect of the depletion is to flatten the density distribution in the nuclear interior. The calculated density is in good agreement with the empirical one near the nuclear centre but is too small in the vicinity of 5 fm. The main consequences of the depletion are shown to be largely independent of the details of the model. It is concluded that Hartree-Fock single-particle wave functions which yield good agreement with empirical density distributions are rather different from the natural orbitals. Accordingly they should not be expected to yield a good approximation to the off-diagonal elements of the one-body density matrix, e.g. to the momentum distribution.     

The energy dependence of the spectroscopic factors for the 208Pb(p,d)207Pb reaction

The ²⁰⁸Pb(p,d)²⁰⁷Pb reaction has been studied at 26.3 MeV and data at 121 MeV reanalyzed. These data, along with the data of others at 22, 35, 41 and 55 MeV, have been compared with zero- and exact-finite-range DWBA calculations carried out in a consistent fashion to determine the energy dependence of the spectroscopic factors for the six strong single-neutron-hole states in ²⁰⁷Pb. Strong energy dependencies were noted for the spectroscopic factors, particularly for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{,}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$and$\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ states. Variations in the calculations provided no satisfactory understanding of the problem.     

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.     

Decay of 48K, 49K and 50K

The ⁴⁸K, ⁴⁹K and ⁵⁰K nuclides have been produced in high energy fragmentation and analyzed by mass spectroscopy techniques. Their half-lives have been measured as 6 ± 1 s, 1.1 ± 0.3 s and and 0.7 ± 0.3 s, respectively. The γ-rays from their radioactive decay have been observed and the corresponding γ-intensities measured. The nuclide ⁵⁰K is shown to be a delayed neutron emitter. The antianalog states in the daughter Ca nuclei with a $\text{(1d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?}}$ neutron configuration, preferentially populated in the β-decay, have been located. The corresponding $\text{1d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ neutron single-particle energy is found to remain approximately constant for these neutron-rich Ca isotopes.     

Low-energy transitions in the 197Pb and 198Pb isotopes

The ¹⁹⁸Pb and ¹⁹⁷Pb isotopes are produced through the ¹⁸⁶W(¹⁶O, 4n, 5n) reactions. Conversion-electron, γ- and X-ray spectra are measured using the compound-nucleus recoil method. Conversion coefficients and multipolarities are deduced for a large number of transitions. Together with angular distribution measurements and the results of γγt multidimensional coincidences they lead to decay schemes for the two isotopes. Microscopic calculations, performed in the two- or three-quasiparticle approximation with a surface delta interaction, fail to reproduce completely the observed properties, showing similar defects for the odd and even isotope.     

Analyzing powers of the continuum spectra: 65 MeV polarized protons on 12C, 28Si, 45Sc, 58Ni, 93Nb, 165Ho, 166Er and 209Bi

Analyzing powers of the continuum spectra were measured for 65 MeV protons from ¹²C, ²⁸Si, ⁴⁵Sc, ⁵⁸Ni, ⁹³Nb, ¹⁶⁵Ho, ¹⁶⁶Er, ${}^{209}\text{Bi}\text{(}\text{p}\text{,}\text{p\#}\text{prime;}\text{X}\text{)}$ and ($\text{p}$, dX) reactions and from ⁹³Nb, ²⁰⁹Bi($\text{p}$, αX) reactions. The analyzing powers of the continuum spectra were found to be small at forward angles where the pre-equilibrium process is important. However they do not show a systematic tendency. This feature indicates the importance of the spin-dependent interaction as well as nuclear structure effects. On the other hand, the analyzing powers were very large and positive at backward angles where the shape of the energy spectra resembles that of an evaporation spectrum. The maximum values of the analyzing power in the backward hemisphere depend on the target mass for the A < 45 mass region and they are as large as 15%, 20% and 35% for ${}^{93}\text{Nb}\text{(}\text{p}\text{,}\text{p}\text{′}\text{X}\text{)}$, ($\text{p}$, dX), ($\text{p}$, αX) reactions at E_X = 20 MeV, respectively. These large values are mainly due to the entrance channel effect. There is no appreciable even-odd mass effect on the analyzing power for medium-mass nuclei. These features were unexpected from the conventional pre-equilibrium reaction models.