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.     

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 giant dipole resonance photons and the shapes of hot Er and Sn nuclei

A study of the spectral and angular distributions of the high energyγ rays emitted by the giant dipole resonance (GDR) in the compound nuclei^165,167Er and¹¹⁰Sn at a variety of excitation energiesE ^*=50–90 MeV) is presented. A comparison of the data with model predictions at the equilibrium deformation and with thermal fluctuations in the adiabatic limit is discussed. In general, the adiabatic calculations give a fair account of the data exception made for Sn at very high spins.     

The width of the giant dipole resonance built on excited states of Cu compound nuclei

Continuumγ- ray spectra from the decay of⁵⁹Cu formed at an excitation energy of 100 MeV and angular momenta up to 43? by means of the reaction 190 MeV³²S +²⁷Al have been measured and analyzed. The parameters of the Giant Dipole Resonance (GDR) have been extracted using the statistical model. The derived GDR width confirms the sizeable broadening of this resonance in⁵⁹Cu already reported in our earlier investigation at 77 MeV excitation energy (J_crit=38?). Estimates of the GDR width have been performed in the adiabatic approximation. Predicted values account qualitatively for the experimental data of⁵⁹Cu as well as of the heavier isotope⁶³Cu, in which the broadening was not seen up to 77MeV excitation (J_crit=35?). The present analysis demonstrates the strong sensitivity of the GDR to spin effects in this mass region.     

GDR excitation by isoscalar probes: a means to determine the neutron-skin thickness

Inelastic scattering of α-particles can excite the isovector giant dipole resonance (GDR) via the Coulomb interaction. In spite of their isoscalar nature α-particles can also excite the GDR via the nuclear interaction due to the difference in the radii of the neutron and proton density distributions. The absolute cross section to excite the GDR in inelastic α-scattering is therefore a measure of this radial difference, the so-called neutron-skin thickness. Furthermore, since the GDR strength distribution has a centroid energy which depends on the nuclear radius, these studies, when performed in deformed nuclei, can measure the neutron-skin thickness along both the short and the long axes independently. Results of an experiment performed at KVI atE _α=120 MeV and small scattering angles, including 0°, to determine the neutron-skin thickness in²⁰⁸Pb,¹¹⁶Sn,¹²⁴Sn, and the deformed¹⁵⁰Nd are discussed and compared to earlier measurements and theoretical predictions. Future improvements in the experimental set-up are also discussed.     

Elastic and inelastic scattering of 270 MeV3He particles from58Ni,90Zr,116Sn and208Pb

Differential cross-section angular distributions for the elastic scattering of 270 MeV³He particles from⁵⁸Ni,⁹⁰Zr,¹¹⁶Sn and²⁰⁸Pb have been measured. Optical model analysis of the cross-sections has yielded the optical model parameters for³He particles at 270 MeV. Angular distributions have also been measured for the inelastic excitation of the low-lying levels in the above mentioned nuclei. A collective model analysis using the distorted wave Born approximation (DWBA) of these cross-sections with the distorted waves generated by the optical model parameters determined from the elastic scattering analysis, has yielded the reduced transition probability (B(EL)) values consistent with those reported in the literature.     

Nucleon transfer reactions to rotational states induced by206, 208Pb projectiles

In a systematic study of nucleon transfer reactions accompanied by Coulomb excitation we have bombarded¹⁵²Sm,¹⁶⁰Gd and²³²Th with^{206, 208}pb beams at incident energies close to the Coulomb barrier. Particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and in nucleon transfer reactions. One-neutron stripping and pick-up reactions on¹⁵²Sm were observed leading to known states of the rotation alignedi _13/2-bands in¹⁵³Sm and¹⁵¹Sm. In the¹⁶⁰Gd+^{206, 208}Pb systems no significant population of low lying states of product nuclei was found in the nucleon-transfer channels. Large cross sections were observed for one- and two-neutron pick-up from²³²Th at an incident energy of 6.4 MeV/u. Around the grazing angle they are of the same order of magnitude as the cross section measured for inelastic scattering. The results are analyzed in the framework of semiclassical models.     

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.     

Proton excitation of the isovector giant quadrupole resonance in 208Pb

The angular distribution of γ-rays from fast proton capture in ²⁰⁸Pb has been examined in detail by the direct-semidirect model. The interference of the dipole, quadrupole and octupole amplitudes was considered. The excitation of the isovector giant quadrupole resonance was assumed to occur at the excitation energy of 22.5 MeV, having the width of 5 MeV. The excitation of this resonance strongly influences the asymmetry of the angular distribution but the major part of the asymmetry is a consequence of the direct capture of the incident proton. Several groups of optical-model parameters were used in the calculation in order to see how they affect the results. The complex interaction coupling between the incident proton and the quadrupole giant resonance is essential to obtain good fits to the experimental asymmetry of the angular distribution of γ-rays.     

Evolution of giant dipole resonance width at low temperatures – New perspectives

High energy photons from the decay of giant dipole resonances (GDR) built on excited states provide an excellent probe in the study of nuclear structure properties, damping mechanisms etc., at finite temperatures. The dependence of GDR width on temperature (T) and angular momentum (J) has been the prime focus of many experimental and theoretical studies for the last few decades. The measured GDR widths for a wide range of nuclei at temperatures (1.5 < T < 2.5 MeV) and spins (upto fission limit) were well described by the thermal shape fluctuation model (TSFM). But, at low temperatures (T < 1.5 MeV) there are large discrepancies between the existing theoretical models. The problem is compounded as there are very few experimental data in this region. At Variable Energy Cyclotron Centre, Kolkata, a programme for the systematic measurement of GDR width at very low temperatures has been initiated with precise experimental techniques. Several experiments have been performed by bombarding 7–12 MeV/nucleon alpha beam on various targets (⁶³Cu, ¹¹⁵In and ¹⁹⁷Au) and new datasets have been obtained at low temperatures (T < 1.5 MeV) and at very low spins ( $J < 20 \hbar $ ). The TSFM completely fails to represent the experimental data at these low temperatures in the entire mass range. In fact, the GDR width appears to be constant at its ground state value until a critical temperature is reached and subsequently increases thereafter, whereas the TSFM predicts a gradual increase of GDR width from its ground state value for T > 0 MeV. In order to explain this discrepancy at low T, a new formalism has been put forward by including GDR induced quadrupole moment in the TSFM.     

201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

Elastic and inelastic scattering of 1.03 GeV 12C projectiles

Elastic scattering cross sections of 86 MeV/N ¹²C ions on ¹²C, ^NATCa, ⁸⁹Y and ²⁰⁸Pb targets has been measured together with inelastic scattering to the 4.4 MeV state of ¹²C. There is some indication for giant (quadrupole) resonance excitation in ⁴⁰Ca. Optical model and DWBA analyses are reported. Nuclear transparency effect is discussed.     

The 208Pb(n,p)208Tl reaction at En = 97 MeV

Double-differential cross sections of the ²⁰⁸Pb(n,p) reaction have been measured at 97 MeV in the angular range 0°–30° for excitation energies up to 40 MeV. The experimental proton spectra have been compared with calculated spectra obtained with a statistical multistep direct reaction theory, in which charge exchange and inelastic response functions are described microscopically in the quasiparticle random phase approximation. The direct parts of the spectra have also been distributed on different multipole components by using a decomposition technique, based on sample angular distributions calculated within the distorted-wave Born approximation.     

Relativistic DWBA calculations for polarization transfer in proton inelastic scattering

The matrix element for inelastic scattering of protons leading to the excitation of collective states in even-even nuclei is calculated in the framework of Dirac phenomenology using a DWBA approach. The deformed parts of the Lorentz scalar and four-vector optical potentials serve as the transition operators. The results are compared with the recently measured polarization transfer coefficients on ⁴⁰Ca and ²⁰⁸Pb at 500 MeV. The agreement with experiment is good.     

用高能核子非弹性散射研究核力有效势

本文用扭曲波玻恩近似法及多体高能近似法,处理了原子核对高能核子的非弹性散射现象。在具有可靠的靶核激发态波函数的情况下,可利用这些理论处理方法研究核内两核子间的有效势,本文具体就碳核对185MeV入射核子的非弹性散射进行了计算。在计算中利用了粒子-空穴模型核波函数。在采用了具有各种交换性质并包含自旋轨道耦合项的有效势后,用一组合理的位阱参数,由多体高能近似法计算的理论值可与几个微分截面及极化实验曲线同时符合。     

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.     

Giant M1 resonance in the direct-semidirect model for nucleon radiative capture

The direct-semidirect model for nucleon radiative capture proceeding via giant E1 and E2 resonance states is extended to account for capture through collective M1 excitation. The ²⁰⁸Pb(N, γ₀) and ¹⁴⁰Ce(N, γ₀) reactions are investigated in the 2–10 MeV energy interval. For the M1 and isoscalar E2 neutron capture processes, calculations provide cross section values of the same order of magnitude, as well as comparable effects on γ-ray angular distributions. The model proves to be an appropriate framework for discussing the E1-M1 and E1-E2 interference processes, giving useful suggestions as to effects arising from the presence of the M1 and E2 collectivities.