Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

L-dependent heavy ion fusion potentials

The energyE and angular momentuml dependence of optical potential for fusion of¹⁶O+²⁰⁸Pb system, observed by Christleyet al [5], is expressed as a function of radial kinetic energy (ɛ) instead of explicitE andl dependence. It is shown that the effects of different channel couplings, which result in different effective potentials, can also be parametrized as a function ofɛ. A correlation is obtained between the energy dependent part of this effective potential and the maximum of the spin enhancement around the Coulomb barrier and both these quantities depend on the details of the channel couplings.     

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of ²⁰⁸Pb and the neutron star masses and radii with kaon condensation has been studied. We find that ²⁰⁸Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.     

S- and P-wave neutron spectroscopy Part Xd: Intermediate structure, particle-vibration states

The weak coupling particle-vibration model is extended to lowlying neutron resonances in certain even-even or odd-odd nuclei by coupling the extra particle to core excited states of the odd mass target. The odd hole or particle in the target is treated as a passive spectator. ²⁰⁸Pb and ²¹⁰Bi are studied as test cases and the calculated resonance quantities are in good general agreement with the average features of high resolution experiments. The resonances in ²⁰⁸Pb and ²¹⁰Bi are related to the same intrinsic doorway in ²⁰⁹Pb. The ²¹⁰Bi data is presented here for the first time.     

Density-dependent effective interactions in finite nuclei (I)

Finite nuclei ranging from ¹⁶O to ²⁰⁸Pb are calculated using the Hartree-Fock theory and the local-density approximation. The energy of the nucleus is separated into a volume term, which can be calculated directly in terms of the nuclear matter energy density, and a residual surface term which contains a starting energy correction and to which only the long-range part of the effective interaction contributes. The results obtained are compared with experiment and with other calculations.     

Behavior of the giant-dipole resonance in 120Sn and 208Pb at high excitation energy

The properties of the giant-dipole resonance (GDR) are calculated as a function of excitation energy, angular momentum, and the compound nucleus particle decay width in the nuclei ¹²⁰Sn and ²⁰⁸Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for ¹²⁰Sn and ²⁰⁸Pb are attributed to the fact that shell corrections in ²⁰⁸Pb are stronger than in ¹²⁰Sn, and favor the spherical shape at low temperatures. The effects shell corrections have on both the free energy and the moments of inertia are discussed in detail. At high temperature, the FWHM in ¹²⁰Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for ²⁰⁸Pb.     

The need for long range components in the effective nuclear interaction

It is shown that if one uses single particle energies from experiment and a delta residual interaction it is not possible to obtain the energy of the giant dipole and spurious states of ²⁰⁸Pb, and at the same time obtain reasonable results for the low lying two-particle spectra of ²¹⁰Pb or ²¹⁰Po. Related to the above problem, the isobaric analog state of ²⁰⁸Pb (in ²⁰⁸Bi) comes much too low in calculations using realistic interactions. It is noted here that the above difficulties can be overcome, phenomenologically at least, by adding to the effective interaction some long range repulsive components. The Bansal-French and the Schiffer interactions are examples of these. However, the dipole-dipole component of the Schiffer interaction gives much too large a splitting between the dipole state and spurious state.     

Method of induced activity for studying nuclear reactions on Pb and Sn isotopes

Nuclear reactions at the interaction of particles with heavy targets were studied using the method of induced activity. This method permits an investigation of the mechanism of residual nuclei formation in a wide range of nuclear masses beginning from light nuclei up to the nuclei with masses near to the target mass. The results of investigations of nuclear reactions on separated isotopes of lead (²⁰⁶Pb, ²⁰⁷Pb, ²⁰⁸Pb) and tin (¹¹⁸Sn) isotope performed using the method of induced activity are given.     

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 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.     

Self-consistent description of <Emphasis Type="Italic">EL</Emphasis> transitions between one-phonon states in magic nuclei

Transition probabilities between low-lying one-phonon states of magic nuclei are for the first time computed self-consistently within an approach to anharmonic effects based on the quantum theory of many-body systems. In the adopted approach, three-quasiparticle correlations in the ground state are taken into account, and the nuclear mean field is interrelated with the effective nucleon–nucleon interaction. These quantities are derived using the energy density functional method with known parameters of the Fayans functional. The E1 and E2 transitions in the ¹³²Sn and ²⁰⁸Pb nuclei are considered as an example, and a reasonably good agreement with the data on these nuclei is reached. Three-quasiparticle correlations in the ground state are shown to make a significant contribution to the probabilities of the discussed transitions.     

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.     

Non local effects induced by the particle-vibration coupling

Dynamical corrections to the single particle potential are (perturbatively) evaluated. The corrections tom ^*/m resulting from the coupling of independent (effective) fermions to collective vibrations (low energy modes) are analyzed within the NFT formalism. The results for the²⁰⁸Pb are discussed.     

Effective interactions for 208Pb + p reactions

RPA hole-particle wave functions for the lowest 2⁺ and 3^? states in ²⁰⁸Pb were used to test the validity of effective nucleon-nucleon interactions for (p, p') excitations. Excellent agreement with experiment was obtained for the long-range part of the Hamada-Johnston S-state potential. Equally good agreement was found for the elastic scattering from ²⁰⁸Pb and the (p, n) transition to the analog state. It was found to be important to include an imaginary part in the interaction. The transitions to the two excited states of ²⁰⁸Pb were found to be almost pure isoscalar, but the transitions are dominated by the neutron excitations.     

Radiative strength function and the pygmy dipole resonance in <Superscript>208</Superscript>Pb and <Superscript>70</Superscript>Ni

The pygmy-resonance parameters and the E1 strength function are derived for ²⁰⁸Pb using a fully self-consistent microscopic formalism recently developed for magic nuclei, which takes into account quasiparticle phonon interactions (or coupling to phonons) in addition to the random phase approximation. For the radiative strength function of ²⁰⁸Pb at energies above 5 MeV, the experimental data of the Oslo group are adequately described by our predictions, whereby the important role of coupling to phonons is confirmed. By comparing the measurements based on the (³He, ³He′γ) and (γ, γ′) reactions, we discuss the physical properties of the radiative strength function measured for ²⁰⁸Pb. For the neutron-rich ⁷⁰Ni nucleus, predictions for the radiative strength function and the pygmy resonance are obtained using a partially self-consistent approach, which invokes the Skyrme forces in deriving the mean field, effective nucleon–nucleon interaction, and phonon characteristics.     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

Coulomb-nuclear interference at sub-Coulomb energies

The Coulomb-nuclear interference pattern in the low-energy heavy-ion excitation of nuclei near closed-shells can be used to investigate the nuclear mass density at large distances, the nature of the effective transition operator and the presence of higher-order direct processes. Semimicroscopic single-folding calculations are compared to low-energy data for ¹⁸O excitation by ²⁰⁸Pb. A strong effect of two-step transfer reactions is predicted in the sub-Coulomb excitation of ¹⁷O by ²⁰⁸Pb.