Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of ²⁰⁸Pb and ⁴⁰Ca by a ²⁰⁸Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for ²⁰⁸Pb and 20% for ⁴⁰Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.     

Response functions of 58Ni, 116Sn AND 208Pb to the excitation of intermediate-energy α-particles

Inelastic scattering of 340 MeV and 480 MeV α-particles has been measured on ⁵⁸Ni, ¹¹⁶Sn and ²⁰⁸Pb up to 60 MeV excitation energy. Consistent background subtraction and multipole analysis has provided the repartition of multipole strength for all three nuclei. The so-obtained response functions show the already known low-energy giant resonances in a detailed way, as well as new giant resonances at high energy.     

Elastic and inelastic scattering of 120 MeV 18O from 208Pb and the spin alignment of the 2+ state of 18O

The elastic and inelastic scattering of ¹⁸O ions at 120 MeV from a target of ²⁰⁸Pb have been studied. Cross sections for excitation of the 2⁺ state at 1.982 MeV in ¹⁸O and of the 3^? state at 2.61 MeV in ²⁰⁸Pb were measured. In addition, the populations of the m-substates for the ¹⁸O excitation were deduced from the Doppler-broadened line shapes. The data were subjected to a coupled-channels analysis using either Woods-Saxon or folding-model potentials. In addition, the ¹⁸O excitation was found to be described very well by use of a semi-microscopic model. The analyses consistently indicated the presence of a positive static hexadecapole moment of several e · fm⁴ for the 2⁺ state of ¹⁸O. The m-substate population distributions were found to be better fitted if a vector spin-orbit coupling was introduced for the 2⁺ state of ¹⁸O with a sign opposite to that for the nucleon-nucleus case.     

Effects of non-orthogonality and virtual excitations in direct reactions (III)

Formulae are presented concerning the effects of virtual Coulomb excitation on the transfer of nucleons between heavy ions at energies below the Coulomb barrier. These formulae are applied towards calculation for the ²⁰⁸Pb(¹⁶O, ¹⁷O)²⁰⁷Pb reaction at 69.1 MeV. Generally, the effect is found to be of the order of 10% but it is not discernable owing to the small reaction cross sections. Suggestions are presented for extending the analysis to higher energies where the situation is more favourable.     

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.     

Pion bound states in nuclei

Bound π-nuclear states can appear under certain realistic conditions in finite nuclei. The best prospects are certain medium-weight nuclei with dense central regions and large neutron excess. Numerical illustrations are given for ¹⁶O, ²⁸Si, ³²Na and ²⁰⁸Pb with realistic parameters for the interaction. Further, we show that the usual low-energy π nuclear potential develops pathological features like an infinity of bound states beyond a certain critical strength. The natural remedies are indicated.     

Evidence of projectile polarisation effects on the reaction 208Pb(17O, 16O)209Pb

Coupled reaction channels calculations (CRC) of the reactions ²⁰⁸Pb(¹⁷O, ¹⁶O)²⁰⁹Pb leading to different states of ²⁰⁹Pb are compared with DWBA predictions at projectile energies of 78, 86 and 102 MeV. The calculations exhibit strong effects of multistep processes on Q-value and angular-momentum-mismatched transfer reactions. It is shown that the contribution to the transfer through the inelastic excitation of ¹⁷O contains a major part of the multistep effect. A simple three-channel model comprising the elastic, inelastic and transfer channels is constructed which simulates the CRC effects on the transfer cross sections. The polarization effects of the eliminated channels give rise to effective potentials which are mainly imaginary.     

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.     

Fission and emission of H and He in the reactions of 215 MeV16O with181Ta,208Pb and238U

The reactions of 215 MeV¹⁶O with¹²C,¹⁸¹Ta,²⁰⁸Pb and²³⁸U have been studied. Inclusive measurements for⁴He emission are given from each target, and for fission and^1,2,3H from Ta, Pb and U. For H/He a high-energy, forward-peaked component is observed with characteristics similar to those reported by others. At backward angles a low-energy, nearly-isotropic component is also observed for⁴He that cannot be accounted for by emission from fully accelerated fission products. The spectral shapes for this evaporative component are compared with statistical model calculations, and information is obtained concerning the effective barriers to emission. For the reactions of¹⁶O with¹²C, complete fusion seems to be overwhelmed by incomplete fusion. Fission angular distributions and cross sections are also presented and discussed.     

Barriers for pion-induced fission near A = 208

Measured fission cross sections for π⁺ and π^? beams of 150 MeV on isotopically separated targets near A=208 show a smooth dependence of the fission probability on the target mass, without any indication of the increased fission barriers expected for fission at low excitation near doubly magic ²⁰⁸Pb. Extraction of fission barriers from these data is attempted for a range of possible excitation energies, finding that these barriers are near 8 MeV near A=208, without much sensitivity to the assumed excitation energy.     

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in ¹²⁰Sn and ²⁰⁸Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for ¹²⁰Sn and 40 MeV/nucleon for ²⁰⁸Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in ²⁰⁸Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.     

Energy dependence of the 16O208Pb effective interaction

The Coulomb-nuclear interference in the excitation probability of the 2.615 MeV (3⁻) state of ²⁰⁸Pb by ¹⁶O at θ_CM=172° for bombarding energies 57 MeV ⩽E_lab⩽79 MeV has been studied. The data are described by an effective interaction which has a behaviour similar to that expected from the dispersion relation connecting the real and imaginary parts of the generalized optical potential.     

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.     

DWBA approach to inelastic scattering at medium energies

Medium energy proton elastic and inelastic scattering to states of ⁵⁸Ni and ²⁰⁸Pb, and ⁴He elastic and inelastic scattering to states of ⁴⁰Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb.     

Axially symmetric time-dependent Hartree-Fock study of the 208Pb + 208Pb reaction

A time-dependent Hartree-Fock calculation assuming axial and reflection symmetry constraints is performed for the head-on collision of ²⁰⁸Pb + ²⁰⁸Pb systems at E_lab≈1600 MeV. The calculation suggests the excitation of surface modes in the reaction and the energy loss characteristic of a deep inelastic process. An estimate of neck-radius and neck-formation time is given.     

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.     

Excitation of giant resonances in intermediate energy heavy-ion reactions

Quasielastic and deep inelastic processes in the reaction ¹⁶O + ²⁰⁸Pb have been studied at bombarding energies of 10–80 MeV per nucleon. The excitation probability of the giant modes becomes larger with increasing energies. At a given bombarding energy the multiple excitation of low-lying modes becomes predominant as the angle of observation moves away from the grazing angle. Near grazing, no appreciable background of this character is found for bombarding energies above 30 MeV per nucleon. At these energies the electromagnetic interaction becomes the most effective way to excite the giant modes in the excitation energy interval of 10–20 MeV. The importance of Coulomb excitation for the highest bombarding energies makes the excitation of isovector modes no longer negligible.     

The low-energy isoscalar dipole resonance in spherical nuclei

It is shown that localization of the low-energy isoscalar 1^? strength observed in a recent Groningen experiment may be caused by incompressible flow vibrations with considerable contribution of a solenoidal component. Calculations performed here without free parameters predict the energy of the isoscalar low-energy dipole resonance of the order of 40A ^?1/3,Me V. This estimate agrees well with data obtained on ⁹⁰Zrand ²⁰⁸Pb.