A phenomenological woods-saxon potential for p-shell nuclei

The parameters of a Woods-Saxon potential well have been determined for ten p-shell nuclei by fitting the electron scattering form factors and single-particle binding energies. The resulting radius shows, for all but very light nuclei, a regular $\text{A}\text{1}\text{3}$ dependence while the depth smoothly decreases with the increasing proton energy. The observed energy dependence may be ascribed to the non-locality of the HF potential. An energy-independent non-local potential, compatible with elastic electron and proton scattering, is proposed in the energy range ?50 to +50 MeV.     

An interaction potential for heavy-ion scattering

The long-range part of the nucleus-nucleus interaction is taken to be given by folding the density distribution of one nucleus with the real part of the single-nucleon optical potential of the other. Analytic approximations are derived for the folded potential and its derivative in the case where the density distribution and single-nucleon optical potential have Saxon-Woods form factors of equal surface thickness. The approximations are generalised to the case of different surface thicknesses and are compared with a previous parametrisation due to Broglia and Winther. The variation with mass number of the central density of the Saxon-Woods matter distribution required to obtain the correct normalisation is shown to be large and an expression for the variation is given. Some calculations are performed on various elastic scattering data using the “quarter-point recipe” of Frahn's diffraction theory. The parameters required to fit the quarter-points of the elastic cross sections are shown to be consistent with their accepted values. It is shown, however, that the quarter-point recipe leads to a larger radius for ²⁰⁸Pb than for ²³²Th. The positions and heights of the pure Coulomb barrier (L = 0) are evaluated for various nuclei. The barrier radii are found to be sufficiently large to suggest that an interaction of the folded type should be reasonable in this region.     

A dynamic polarization potential for heavy-ion scattering

The effects of target and/or projectile excitation on the elastic scattering of heavy ions are studied. The results are cast in the form of contributions to both the real and imaginary parts of the ion-ion optical potential. In particular, a trivially “equivalent” local potential (TELP) is found to simulate the effects of coupling to one or more open channels. Particular application is made to the dynamic polarization resulting from the long-range Coulomb potential. Comparison with coupled-channel calculations shows that the TELP can accurately reproduce these effects of Coulomb excitation. The correction to the absorptive potential is found to be much larger than that for the real potential. This correction is long-ranged and cannot be simulated by any reasonable adjustment of the usual Woods-Saxon form of potential. The TELP provides an alternative to performing coupled-channels calculations and may be particularly useful when reactions other than inelastic scattering are to be studied.     

Parametrization of the hybrid potential for pairs of neutral atoms

The hybrid form is a combination of the Rydberg potential and the London inverse-sixth-power energy. It is accurate at all relevant distance scales and simple enough for use in all-atom simulations of biomolecules. One may compute the parameters of the hybrid potential for the ground state of a pair of neutral atoms from their internuclear separation, the depth and curvature of their potential at its minimum, and from their van der Waals coefficient of dispersion C₆.     

Fusion oscillations for symmetric light heavy-ion systems

The low-energy fusion cross section for ²⁰Ne+²⁰Ne has been measured. The data extend the systematics on fusion oscillations for such light symmetric systems. A simple extension of the usual barrier penetration model displays the decisive role of the symmetrisation of the system. It is also capable of qualitatively explaining the trends in this effect, in particular its decreasing importance as the mass of the system increases. The structure is essentially due to the sharpness of the cut-off of transmission coefficients as a function of angular momentum. The curvature of the Coulomb barrier is important in determining these coefficients and it is shown that the required values of this quantity are consistent with reasonable values of the surface diffuseness of the nuclear potential.     

Spin-orbit potential in heavy-ion collisions

The spin-orbit potentials between heavy-ion projectiles and ¹²C target are calculated by the folding method. The projectile mass number dependence of the spin-orbit potential is presented. The contributions of the spin-orbit potential to the elastic and inelastic scatterings of the ⁶Li and ¹⁴N projectiles from the ¹²C target are calculated. The theoretical elastic polarization of the ⁶Li scattered from ¹²C is found to be appreciable.     

On the nuclear polarization potential for heavy-ion scattering

The real polarization potential ΔV due to transfer reactions is studied using a microscopic semiclassical formalism. It is found that ΔV is typically of the same order of magnitude as the corresponding absorptive potential W. Different types of possible energy dependences for ΔV and W are explored qualitatively. Specific calculations for ¹⁶O + ²⁰⁸Pb and ¹⁶O + ⁶⁰Ni scattering show features similar to those which have been deduced empirically.     

重离子碰撞中的对称势翻转

利用同位旋和动量相关的输运模型IBUU，以Sn,Sn同位素在低能与高能碰撞为例，在两种不同的对称势作用下，研究了重离子碰撞中的对称势翻转现象.我们发现从低能到高能在同位旋相分化、发射核子的中-质比、发射核子的双n/p比，中-质微分横向流观测量中均存在对称势翻转现象.对称势翻转效应的研究有利于确定对称能的密度依赖性. 关键词： 重离子碰撞 对称势翻转 对称能     

Semiclassical derivation of a local optical potential for heavy-ion elastic scattering

A semiclassical method to determine the contribution to the optical potential in the elastic channel due to the coupling to other processes taking place in heavy-ion collisions is developed. An application is made to the case of Coulomb excitation. The lowest-order term of our potential is shown to be identical to the potential derived by Baltz et al.     

The mass distribution width of heavy-ion fission for various composite systems

It is qualitatively shown that the width of the fusion-fission events increases with increasing Z²/A.     

Parametrization of the scattering wave functions of the Paris potential

The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5 at laboratory kinetic energies between 0 MeV and 400 MeV. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The smooth variation in energy of the phase shifts and of the coefficients of the polynomials permits a further parametrization of these quantities in terms of polynomials of low degree. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail.     

Comparison between heavy-ion reaction and fusion processes for hundreds of systems

A large number of heavy-ion fusion and reaction cross section data are compared in different regions of mass and energy. The totally parameter-free São Paulo potential is used as basis for comparison within the context of the barrier penetration model. The systematics indicates that, in average, the fusion process represents about 74% of the total reaction cross section. The regions of mass and energy where this result was obtained is discussed in the text.     

Pauli blocking potential applied to heavy-ion fusion reactions

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the \begin{document}$ \alpha $\end{document}-decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems \begin{document}$ ^{16} $\end{document}O + \begin{document}$ ^{208} $\end{document}Pb and \begin{document}$ ^{58} $\end{document}Ni + \begin{document}$ ^{58} $\end{document}Ni.     

Nuclear matter approach to the heavy-ion optical potential

An energy-dependent local potential for heavy-ion (HI) scattering is derived from Reid's softcore interaction using the Brueckner theory. The Bethe-Goldstone equation in momentum space is first solved with the outgoing boundary condition for two colliding systems of nuclear matter with the relative momentum K_r per nucleon. The Fermi distribution is assumed to consist of two spheres without double counting of their intersection separated by the relative momentum K_r. The angle-averaged Pauli projection function is given in the form of a one-dimensional integral. Secondly the optical potential for HI scattering is evaluated using the energy-density formalism. The energy density is calculated for two limiting cases: (i) the sudden approximation in which the spatial distribution of the two HI is described by an antisymmetrized cluster wave function, and (ii) the adiabatic limit represented by an antisymmetrized two-centre wave function. The complex HI potential is defined in terms of the energy density from nuclear matter so that both volume elements in the finite and the infinite systems have the same nucleon and kinetic energy density. This method is applied to the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O, and ⁴⁰Ca + ⁴⁰Ca potentials. The calculated results are compared with phenomenological potentials. Though in principle our approach can generate an imaginary part for the HI potential, the magnitude is too small. Reasons and possible improvements of this point are discussed.     

Equilibration of the neutron-to-proton ratio for heavy asymmetric systems in heavy-ion collisions

Some results on the charge equilibration process for the ²⁰⁵Pb (1550 MeV) + ⁷⁴Ge and ⁸⁶Kr (550 MeV) + ¹⁹⁷Au reactions obtained by on-line measurements are discussed and compared with the previous results of the ¹³²Xe (890 MeV) +¹⁹⁷Au reaction investigated using radiochemical techniques. In all cases global and isobaric charge widths were measured as a function of the excitation energy. It is shown that the corrections associated with both the evaporation process and the experimental mass or charge resolution are most important in obtaining correct primary distributions. The results confirm a preferential neutron exchange at the beginning of the reaction, as was suggested by the Brosa and Gross model. Further attempts to analyse the data with existing dynamical models have not succeeded in their present stage of development in discriminating between the assumptions of statistical versus quantal fluctuations as observed in the study of the Kr + Mo system.     

An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

A simple double-folding computation of the complex heavy-ion optical potential

We have derived a spin- and isospin-independent complex effective force to compute the ¹⁶O + ¹⁶O optical potential by the double-folding procedure. To avoid reference to a wave function, we have used superposition models to compute the values of the matter and intrinsic kinetic energy densities necessary to the local specification of the effective force. The present results compare favourably with those of a previously published, fully antisymmetrized calculation. The physcial significance and the quantitative importance of self-energy effects are discussed.