Damping of nuclear excitations at finite temperature

We calculate the damping of single-particle motion and of vibrational motion to lowest order in the coupling between the particles and the vibrations, using the finite temperature Matsubara formalism. The derived formulas have a complicated structure which however can be mostly understood in physical terms. We apply the theory to single-particle states in heavy nuclei, to the giant dipole vibration in ⁹⁰Zr, and to the giant quadrupole vibration in ²⁰⁸Pb. Even at temperatures of the order of 3 MeV the main peak of the giant vibrations remains essentially unaffected although it acquires a long tail at the low-energy end.     

Damping of giant dipole resonances at finite temperature

The damping width γ^↓_GDR of the giant dipole resonance, due to its coupling to doorway states, is studied within the framework of the thermal Green's functions theory. It is found that γ^↓_GDR reflects the temperature dependence of the single-particle damping width but, as a consequence of the cancellation effects between self-energy and vertex contributions, the coefficient of such a dependence is so small that it can essentially be neglected, within the temperature range of physical interest.     

Role of thermal fluctuations in the damping of the giant dipole resonance of spherical and deformed nuclei: 90Zr and 164Er

We study the damping width of the giant dipole resonance (GDR) built on the ground state and on excited states of ⁹⁰Zr, which is spherical at zero spin and temperature, and ¹⁶⁴Er which is deformed. Neither of these nuclei changes appreciably their equilibrium shape when excited. Nonetheless, fluctuations due to finite temperature produce a marked increase in the width of the GDR of ⁹⁰Zr, leaving essentially unchanged that of ¹⁶⁴Er. This is because in the case of deformed nuclei thermal fluctuations imply the sampling of both larger and smaller deformations around the equilibrium shape, while spherical nuclei can only feel larger distortions. In spite of the stability of the GDR of ¹⁶⁴Er, the angular distribution of the associated γ-rays is strongly affected by the temperature.     

Primary mass and charge distributions in the reaction of 900 MeV 132Xe ions with 197Au

A stacked foil technique and radioehemical yield measurements were combined in order to study the reaction of ¹³²Xe ions with ¹⁹⁷Au at 1.3 times the interaction barrier energy. Evidence is presented for a preferential exchange of neutrons for energy losses of up to 100 MeV. The same amount of energy damping is required for the development of a drift in the position of the centroid of the element distribution and for the evolution of full correlations in the exchange of neutrons and protons. The widths of the charge distributions at fixed mass asymmetry rise slowly as the degree of energy damping increases. This is reminiscent of classical statistical fluctuations, although the widths at large excitation energies have also been reproduced quantum-mechanically in terms of the zero-point motion of a collective isovector mode analogous to the giant dipole resonance in spherical nuclei. All results concerning the initial evolution of charge and mass distributions seem to be dominated by a hindrance of proton exchanges for large internuclear distances.     

Nuclear viscosity and widths of giant resonances

We write down a set of coupled hydrodynamic equations of the Navier-Stokes type which describe the motion of two compressible, viscous nuclear fluids. The solutions of these equations give rise to giant resonances of both isoscalar and isovector type. The viscosity terms in the equations are responsible for the damping of these resonances. Within this framework we obtain expressions for the width of the resonances as a function of the mass number A, and relations between the widths and the excitation energies for various multipolarities (J = 0⁺, 1^?, 2⁺, 3^?, 4⁺), and isospins (T = 0,1). The A dependence of the calculated widths exhibit the experimental trends of the giant dipole and isoscalar quadrupole widths. Also, as a result of the calculation we obtain estimates of the values of viscosity coefficients in nuclei.     

Damping width of double resonances

Damping width of the double giant dipole resonance of¹³⁶Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to √2 times the width of the single giant dipole resonance.     

Effect of large neutron excess on the dipole response in the region of the giant dipole resonance

The evolution of the dipole response in nuclei with strong neutron excess is studied in the Hartree-Fock plus random phase approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector giant dipole resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models. The radial separation of proton and neutron densities associated with a large neutron excess leads to non-vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator ∑_ir_i³Y₁₀, that mainly originates from uncorrelated excitations of the neutrons of the skin.     

Damping width of double resonances

Damping width of the double giant dipole resonance of ¹³⁶Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to \(\left( {3_1^ + } \right)\) times the width of the single giant dipole resonance.     

Damping of single-particle states and giant resonances in208Pb

The damping width of single-particle states and of giant resonances is estimated in ²⁰⁸Pb, based on the excitation of surface modes and T = 1 pairs. The damping is dominated by the collectivity of the surface modes, with the pairing modes playing a weaker role. For both the single-particle states and giant resonances, the predicted damping is somewhat small. This could be due to the neglect of T = 0 particle-particle correlations or to the neglect of the volume modes. The damping for the giant resonances is reduced by the coherence between particle and hole.     

Temperature dependence of quantal and thermal dampings of the hot giant dipole resonance

A systematic study of the damping of the giant dipole resonance (GDR) in ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb as a function of temperature T is performed. The double-time Green function technique is employed to determine the single-particle and GDR dampings. The single-particle energies, obtained in the Woods-Saxon potential for these nuclei, are used in the calculations. The results show that the coupling of collective vibration to the pp and hh excitations, which causes the thermal damping width, is responsible for the enlargement of the total width with increasing temperature up to T ≈ 3MeV and its saturation at higher temperatures. The quantal width, which arises from the coupling of the collective mode to the ph excitations decreases slowly with increasing temperature. The effect of single-particle damping on the GDR width is small. The results are found in an overall agreement with the experimental data for the GDR width, obtained in the inelastic α scattering and heavy-ion fusion reactions at excitation energies E^* ⩽ 450 MeV. At high excitation energies (E^* > 400 MeV) a behavior similar to the transition from zero to ordinary sounds is observed.     

The potential energy surfaces and the giant dipole resonances of46,48,50Ti

The low energy and giant dipole resonance properties of^46,48,50Ti have been investigated within the framework of the collective model of Gneuss and Greiner. The starting potential energy surfaces were taken from Rebel and Habs from which the low energy properties were compared with both an asymmetric rotator model and a shell model calculation. The giant dipole absorption cross sections compared favourably with the experimental data. However, the scarcity of data relating to theγ-scattering from the giant dipole resonance states to the low lying levels made any detailed comparison incomplete.     

Observation of the hot GDR in neutron-deficient thorium evaporation residues

The giant dipole resonance built on excited states was observed in very fissile nuclei in coincidence with evaporation residues. The reaction ⁴⁸Ca + ¹⁷⁶Yb populated evaporation residues of mass A=213–220 with a cross section of 200 μb at 259 MeV. The extracted giant dipole resonance parameters are in agreement with theoretical predictions for this mass region.     

Pigmy and giant dipole states in stable and unstable oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ¹⁶O, ¹⁷O and ¹⁸O give reasonable agreement with experimental observations both in the low energy region below ?ω=15 MeV and in the high energy giant resonance region (15 MeV < ?ω ≤ 30 MeV). We found that the transition strength below dipole giant resonance (?ω ≤ 15 MeV) exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule and more than 40% of the cluster sum rule in heavier oxygen isotopes than ¹⁷O. The predicted Pigmy strengths in ²⁰O and ²²O are also confirmed by recent Coulomb excitation experiment at GSI.     

Symmetric and asymmetric fission in electron induced fission of 232Th

We have measured fragment kinetic energies in electron induced fission of ²³²Th for electron energies in the range 7 MeV ≦ E_e ≦ 66 MeV. The relative contribution of the distribution peak associated with high fragment kinetic energies decreases continuously with electron energy. This is interpreted as a relative increase of the symmetric fission yield as compared to the asymmetric fission yield; this fact in turn indicates a non-negligible increase in the average excitation of the fissioning nucleus, with the energy of the bombarding electrons, even above the giant dipole resonance.     

Excitation of the giant dipole resonance in the scattering of isoscalar projectiles

The excitation of the giant dipole resonance in nuclei with N > Z by isoscalar projectiles α and d is discussed within a simple collective model for isoscalar dipole excitations. Calculations have been performed for ²⁰⁸Pb; they are compared to recent data on the excitation of the new giant resonance at E_x = 13.8 MeV. For α scattering the effect of dipole excitation is quite weak but significant contributions are obtained for d scattering.     

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.     

Analog giant dipole excitation in Si(n,p) at 59.6 MeV

The parent analog of the giant dipole resonance in ²⁸Si is studied by means of the (n, p) reaction. The continuum contribution to the giant dipole region was estimated by a phenomenological parameterization. The observed cross section exhausts 31% of the SJ sum rule; 88% of the GT sum rule or 67% of the Myers-Swiatecki prediction. A comparison is made to the giant resonance region observed in the ²⁸Si(p, p') reaction which was recently used, via comparison to ²⁸Si(α, α'), to infer that the GDR in ²⁸Si is not excited or at least not seen in (p, p').     

A generalized r-matrix interpretation of the 89Y + n total cross section at low incident energies

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross-section measurements in the range of 0.9 to 1.2 MeV neutron energy is investigated using a comprehensive theory of nuclear reactions. A shell-model calculation which formed the initial stage of this study predicts satisfactorily the energies of the negative-parity states that contribute to the observed anomalies. The neutron decay widths for these resonances are evaluated using the model wave functions. The general trends in the energy dependence of the total cross section are satisfactorily reproduced by the theory. The factors that could contribute to the discrepancies between theory and experiment are discussed. The theoretical estimates of the damping widths for the two 1^? anomalies that occur in this region were within 20 to 25% of the experimental values and support the view that these are intermediate-type resonances. Their configurational structure as predicted by the model calculation suggests that they are the parent states of the T_> components of the giant dipole resonance near 21.0 MeV in ⁹⁰Zr. The distribution of E1 widths calculated for a proposed 1^? → 2⁺ (at 0.78 MeV) transition in ⁹⁰Y indicates that an anomaly corresponding to these 1^? states can also be expected in the (n, γ) reaction.