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.     

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.     

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.     

Binding energies of even-even superheavy nuclei in a semi-microscopic approach

The structure of some even-even superheavy nuclei with the proton number Z = 98?120 is studied using a semi-microscopic but not self-consistent model. The macroscopic energy part is obtained from the Skyrme nucleon-nucleon interaction in the semi-classical extended Thomas-Fermi approach. A simple but accurate method is derived for calculating the direct part of the Coulomb energy. The microscopic shell plus pairing energy corrections are calculated from the traditional Strutinsky method. Within this semi-microscopic approach, the total energy curves with the quadrupole deformation of the studied superheavy nuclei were calculated. The same approach features the well known ²⁰⁸Pb or ²³⁸U nuclei. For each nucleus the model predictions for the binding energy, the deformation parameters, the half-density radii and comparison with other theoretical models are made. The calculated binding energies are in good agreement with the available experimental data.     

同位旋对断前粒子发射的壳结构依赖性

用扩散模型研究了壳对幻数附近的核,即²⁰⁴Pb,²⁰⁸Pb,²¹²Pb和¹²⁸Sn,¹³²Sn,¹³⁶Sn,在裂变过程中蒸发轻粒子多重性的影响.发现壳能够影响粒子发射的同位旋依赖性,并且该影响的大小与复合系统的自旋和激发能有关.计算表明角动量在壳影响同位旋相关的粒子发射中起到了显著的作用,而高激发能弱化了壳的影响.     

Direct and compound contributions to (n, γ) cross sections

We have investigated the direct and compound nucleus contributions to the²⁰⁸Pb (n, γ)²⁰⁹Pb reaction in the region 2.25–7.25 MeV. We have used for the compound nucleus cross sections a modified Hauser-Feshbach theory in the presence of direct reactions. The corrections to the traditional Hauser-Feshbach theory are found to be small in this case.     

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.     

Impact of nuclear structure on production and identification of new superheavy nuclei

Using the microscopic-macroscopic approach based on the modified two-center shell model, the low-lying quasiparticle spectra, ground-state shell corrections, mass excesses and Q _α -values for even Z superheavy nuclei with 108 ≤ Z ≤ 126 are calculated and compared with available experimental data. The predicted properties of superheavy nuclei show that the next doubly magic nucleus beyond ²⁰⁸Pb is at Z ≥ 120. The perspective of using the actinide-based complete fusion reactions for production of nuclei with Z = 120 is studied for supporting future experiments.     

Energy deposition and GDR emission in the reaction 209Bi(α,α′) at 240 MeV

Neutron fold distributions measured for the reaction ²⁰⁹Bi(α,α′) at 240 MeV have been analyzed with the help of Statistical Model calculations to determine the distribution of excitation energy, E_x, in the primary target fragments as a function of the projectile energy loss, EL. The reconstructed distributions in excitation energy feature a plateau which extends from the kinematical limit E_x = EL to very small excitations, indicating a variety of interactions of the beam particles with the target nucleus. The requirement of an additional coincidence with a light charged particle leads to the selection of a significant higher average excitation energy. Those results are extrapolated to explore the effects of including the excitation energy distributions in the analysis of previous GDR measurements in ²⁰⁸Pb. Corrections of the derived GDR parameters due to the partial transfer of excitation energy are suggested.     

Self-Consistent Calculations of the Quadrupole Moments of the Lowest 3<Superscript>–</Superscript> States in Sn and Pb Isotopes

self-consistent approach to anharmonic effects based on the quantum many-body theory is for the first time used to calculate the quadrupole moments of the lowest 3^– states in Sn and Pb isotopes, including the ¹⁰⁰Sn, ¹³²Sn, and ²⁰⁸Pb doubly magic ones. The consistency between the mean nuclear field and the effective interaction is maintained using the energy-density-functional method with known parameters of the Fayans functional. Thereby, the quadrupole moments of the lowest 3^– states of isotopes with nucleon pairing are reliably predicted, and the existing data for the ²⁰⁸Pb isotope are reproduced. It has been shown that the new three-quasiparticle correlations are responsible for slightly more than half of the observed effect and the remaining part is due to the quadrupole polarizability of the nucleus.     

Alpha-nucleus elastic scattering at intermediate energies

Elastic scattering of 288,340,480 and 699 MeV Alpha-particles was measured on ²⁰⁸Pb, ¹¹⁶Sn and ⁵⁸Ni. The data were analysed in terms of a phenomenological optical model. The optical potentials obtained were found to vary consistently with the target nucleus and the incident energy. The radial zone where the potentials are well determined was studied in detail. The data for ²⁰⁸Pb were also analysed with a folding model. The energy dependence of the strong-absorption radius and of the reaction cross section shows that the nuclear surface becomes slightly transparent for incident energies above 150 MeV per nucleon.     

Temperature dependent shell corrections: Numerical estimates for the lead region

Temperature dependent shell corrections are evaluated. The permanence of the shell structure and changes in the level density parameter are discussed for finite temperatures. Numerical estimates for²⁰⁸Pb are given.     

Effect of complex coupling in inelastic cross sections,asymmetries and spin flip in the DWA

The effects of adding an effective imaginary part to real inelastic microscopic form factors in DWA are investigated. Calculations are compared to data for the proton differential cross sections and asymmetries of the lowest-lying states of ¹²⁰Sn, ⁵⁸Ni, and ²⁰⁸Pb. Proton spin flip is calculated for ¹²⁰Sn. Both collective imaginary and effective microscopic imaginary contributions were considered. The most substantial improvements were in fits to asymmetry data. Collective-model calculations indicate the effects of complex coupling are comparable to those of the deformed spin-orbit well.     

Many-body effects in resonant pion-nucleus scattering

The many-body approach of Barshay et al. for resonant pion-nucleus scattering is extended to non-uniform density distribution s and compared with recent total cross section data for ¹²C, ³²S, ¹²⁰Sn and ²⁰⁸Pb. For light nuclei the shapes and magnitudes are very well reproduced and represents an improvement over fits not using many-body corrections. A recent modification suggested by linearing the Low equation is seen to be not very significant for these calculations.     

The beta-decay of95Rb and97Rb

In this paper the spectra ofα particles emitted in (p, α) reactions induced by ～24 MeV protons on adjacent target nuclei, onemagic, with a magic neutron or proton shell and the othernear magic, with one more nucleon outside the shell, are measured and compared. The nuclei investigated are^{90, 91}Zr,¹²²Sn,¹²³Sb,^{142, 143, 144}Nd,²⁰⁸Pb and²⁰⁹Bi. The weak population of low energy levels of the residual nucleus from thenear magic target nucleus and the excitation of homologous states in the residual nuclei from neighbouringmagic andnear magic target nuclei convincingly prove that in most of the cases the unpaired nucleon outside the magic shell acts as a spectator in the process. The implications of these experimental findings are discussed.     

Isotope Dependence of Superheavy Nucleus Formation Cross Section

The dynamical process in the superheavy nucleus synthesis is studied on the basis of the two-dimensional Smoluchowski equation. Special attention is paid to the isotope dependence of the cross section for the superheavy nucleus formation by means of making a comparison among the reaction systems of ^54Re＋204pb, ^56Re ＋206Pb, and ^58Fe＋^208Pb. It is found by this comparison that the formation cross section is very sensitive to the conditional saddle-point height and the neutron separation energy of the compound nucleus. Reaction systems with lower height of conditional saddle-point and smaller neutron separation energy are more favourable for the synthesis of the superheavy nucleus.     

Shell effects on state densities with given numbers of excited protons and neutrons

A new method is introduced to calculate particle-hole state densities taking into account the complete structure in both the proton and neutron shells. The results are given for three nuclei: ²⁰⁸Pb, ¹⁷²Yb and ¹¹⁷Sn. They are compared with previous formulae and with two other expressions derived in the present paper. Strong shell effects are displayed and discussed.