Liquid-drop effects in sub-barrier fusion reactions

We introduce an operational measure for the enhancement of the fusion cross section at sub-barrier energies in terms of an asymptotic energy shift ΔE. It is shown that ΔE has a continuously growing trend with the size of the system. This trend is explained in terms of neck formation using the liquid-drop model. Deviations from this trend are attributed to strong coupling to specific channels.     

Effect of positive Q-value neutron transfers on sub-barrier fusion reactions

The role of positive Q-value neutron transfers in sub-barrier fusion reactions has been studied with a modified quantum coupled channels model with all order couplings(CCFULL model). Neutron rearrangement related only to the dynamical matching condition with no free parameters is implemented in the model, which provides a way to understand especially the Q-value dependence of sub-barrier fusion reactions. The fusion cross sections of the collision systems ~(40)Ca+~(94,96)Zr have been calculated and analyzed. The general trend of experimental data can be reproduced well with additional channels for neutron rearrangement. We find that enhancement of sub-barrier fusion cross sections is closely related to the Q-value of the transferred neutrons, in particular for channels with sequential even number transferred neutrons.     

Spin distributions in heavy-ion fusion reactions

Spin distributions are calculated for the ¹⁶O + ²³²Th fusion reaction, taking into account both inelastic and transfer channels. The static deformations of the target play an important role. The calculated cross sections for complete fusion are in good agreement with the measured fission yields, whereas the anisotropies are underpredicted. This indicates that there is a serious inconsistency in the interpretation of the data.     

Transfer reactions and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems ⁴⁰Ca + ^90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target ⁹⁶Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data. Received: 2 May 2002 / Accepted: 4 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: montagnoli@pd.infn.it, Fax +39049 8277102, Tel. +39049 8277117. RID="b" ID="b"On leave from the China Institute for Atomic Energy, 102413 Beijing, China. Communicated by C. Signorini     

Probing sub-barrier fusion and extra-push by measuring fermium evaporation residues in different heavy ion reactions

The production of fermium isotopes was attempted by complete fusion of different targets and projectiles spanning a wide range of effective entrance channel fissilities below and above the predicted threshold valuex _eff ^thr ?0.7. For the most asymmetric systems where fusion is expected to occur without dynamical hindrance we investigate to what extent the expected amount of sub-barrier fusion contributes to the production of fermium evaporation residues. For increasingly symmetric systems the experimental fusion barriers are found to exceed the fusion barriers predicted by the proximity formalism. The barrier heights are discussed in the framework of both the extra-push model and the surface friction model.     

Residual velocity distributions in complete and incomplete fusion reactions

Theoretical simulation of residual velocity distributions at various mass windows for complete and incomplete fusion reactions have been done for the system⁴⁰Ar+²⁴Mg at the incident energies of 1100, 800 and 600 MeV. The comparison of the residual velocity distributions enables us to have a qualitative understanding about the relative contributions of the complete and incomplete fusion processes in intermediate energy heavy ion reaction.     

Study of fusion Q-value rule in sub-barrier fusion of heavy ions

A vast body of fusion data has been analyzed for different projectiles and target nuclei. It is indicated that the sub-barrier fusion depends on the fusion Q-value. In terms of a recently introduced fusion Q-value rule and an energy scaling reduction procedure, the experimental fusion excitation functions are reduced and compared with each other. It is found that the reduced fusion excitations of selected fusion systems show a similar trend. The fusion data for massive nuclei are in agreement with the Q-value rule. In the fusion process, the Q contribution should be considered. Within this approach, the sub-barrier fusion cross sections of most fusion systems can be predicted without involving any structure effects of colliding nuclei. Instances of disagreement are presented in a few fusion systems. The use of the energy scaling as a criterion of possible experimental data inconsistency is discussed. More precise experimental fusion data need to be measured.     

Nuclear structure effects in sub-barrier fusion cross sections

The total fusion cross sections around and down to ≈ 12 MeV below the Coulomb barrier in the c.m. system have been measured with the Munich heavy-ion recoil spectrometer for 30 projectile-target combinations: ^{32, 36}S + ^{92, 94, 96, 98, 100}Mo, ^{100, 101, 102, 104}Ru, ¹⁰³Rh, ^{104, 105, 106, 108, 110}Pd, The excitation functions can be reproduced with a one-dimensional barrier penetration model by increasing the nuclear radii by $\text{ΔR ? 0.255 ± 0.035}\text{fm}$ and introducing a gaussian distribution of the nuclear radius R with a standard deviation σ_fit(R). The σ_fit(R) can be explained as being due to quadrupole vibrational fluctuations of the surface-to-surface distance at the barrier and to two-neutron-transfer reactions with positive Q-values.     

Quantum calculations of Coulomb reorientation for sub-barrier fusion

Classical mechanics and time dependent Hartree-Fock (TDHF) calculations of heavy ions collisions are performed to study the rotation of a deformed nucleus in the Coulomb field of its partner. This reorientation is shown to be independent of the charges and relative energy of the partners. It only depends upon the deformations and inertias. TDHF calculations predict an increase by 30% of the induced rotation due to quantum effects while the nuclear contribution seems negligible. This reorientation modifies strongly the fusion cross section around the barrier for light deformed nuclei on heavy collision partners. For such nuclei a hindrance of the sub-barrier fusion is predicted.     

On the interpretation of heavy-ion sub-barrier fusion data

We study the well-known deviation of measured fusion cross-sections below the barrier from predictions of one-dimensional tunnelling models. A simple parametrisation of measured excitation functions is discussed which allows to identify a smooth general trend depending only on gross nuclear properties. The parametrisation is substantiated by quantum mechanically exact calculations in a two-dimensional tunnelling model. Various possibilities for the geometrical interpretation of the second degree of freedom are discussed. Neck formation is identified as the most probable degree of freedom effecting the overall behavior of sub-barrier fusion.     

The sub-barrier fusion of40Ar with144,148,154Sm

The cross sections for production of evaporation residues (σ _er) and for fusion-fission (σ _ff) have been measured for⁴⁰Ar+^{144, 148, 154}Sm at sub-barrier energies by observation of x-ray emission from radioactive products and by direct,ΔE?E identification of fission fragments, respectively. These isotopes span the transition region from spherical (¹⁴⁴Sm) to strongly deformed (¹⁵⁴Sm) equilibrium shapes. The cross section for fusion,σ _fus=σ _er+σ _ff, is found to vary markedly at low energies with the isotope number and, hence, with the quadrupole collectivity of the target. The thresholds for fusion of¹⁴⁸Sm and¹⁴⁴Sm are, respectively, ～3.5 MeV and ～7 MeV (c.m.) higher than for fusion with¹⁵⁴Sm. These differences and the energy dependence of the fusion cross sections are discussed in terms of the effect of nuclear deformation on heavy-ion fusion. A comparative analysis of results for¹⁶O+Sm and⁴⁰Ar+Sm in terms of static deformation indicates thatσ _fus for the Ar+Sm system at very low energies is enhanced relative to the prediction for a one-dimensional barrier based on a fit toσ _fus for¹⁶O+Sm. This may be an indication that additional degrees of freedom (such as formation of a neck or fragment elongation) may be important for fusion with the larger projectile. At energies above the fusion barrier, values ofσ _fus for^{144, 148}Sm are nearly equal, but are significantly smaller than for¹⁵⁴Sm. This is in contrast to the results of previous experiments with¹⁶O projectiles in whichσ _fus (¹⁶O+¹⁴⁸Sm) andσ _fus (¹⁶O+¹⁵⁴Sm) were nearly equal above the barrier. These differences, observed for^{144, 148}Sm and¹⁵⁴Sm at energies above the barrier may reflect a new mechanism which is not encompassed by a static theory.     

Liquid-drop model description of heavy ion fusion at sub-barrier energies

The enhancement of the heavy ion fusion cross section at sub-barrier energies is studied in the liquid-drop model approach. The shape of the system is described by two spheres smoothly connected by a neck, and the kinetic and potential energies are calculated within this parametrization. Underbarrier fusion cross sections for symmetric projectile-target combinations are calculated in the WKB approximation and a comparison with the available data is made. The agreement is quite satisfactory, except for those systems in which the reaction is strongly affected by the details of the nuclear structure of the collision partners.     

Microscopic calculation of 58,64Ni + 124,132Sn sub-barrier fusion

The fusion cross-sections of ^58,64Ni + ^124,132Sn are investigated through a coupled-channel approach using a density- and energy-dependent effective Brueckner G-matrix interaction. Microscopic Skyrme-Hartree-Fock proton and neutron density distributions are used in the calculations. A good agreement with the experimental data of the fusion cross-sections of these neutron-rich systems has been obtained, which favors the present microscopic approach for calculating the interaction potentials and fusion cross-sections.     

Peculiarities of the sub-barrier fusion with the quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of the fusion cross-section, angular momentum, and astrophysical S -factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at the turning point the decrease rate of the cross-section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.     

Anomalously broad Raman scattering spectrum due to two-magnon excitation in hexagonal YMnO3

A strong and broad Raman scattering (RS) spectrum is observed from two-magnon processes in YMnO3. The spectrum is analyzed by taking account (i) the magnon-exciton interaction and (ii) the magnon-phonon coupling in the intermediate state. Anomalous broadening of the RS is attributed to the large superexchange interaction between manganite ions and subsequent modification of magnons under the presence of the exciton and phonons in the intermediate state.