J. Bartel

Evaporation of light particles from a hot, deformed and rotating nucleus☆

Abstract The dependence of the transimission coefficient on the deformation, the collective rotation and excitation energy of the compound nucleus emitting light particles is introduced in the framework of Weisskopfs evaporation theory. The competition between fission and particle evaporation is treated by a Langevin equation for the fission variable coupled to the emission process. Detailed calculations are presented on the decay of different Gd and Yb isotopes at an excitation energy of about 250 MeV. These calculations demonstrate the importance of the effects of nuclear deformation and of the initial spin distribution on the evaporation.

Rotations in nuclei — a semiclassical description

Abstract An explicit formulation of extended Thomas-Fermi density functionals relevant to a microscopic description of rotating nuclei within the Skyrme Hartree-Fock formalism, is presented up to order h 2 . Simple analytical expressions have been obtained for the dynamical moments of inertia within this semiclassical framework. Phenomena identical to Landau orbital diamagnetism and Pauli spin paramagnetism have been exhibited upon using standard Skyrme force parametrizations. Both effects almost cancel. As a result, the Thomas-Fermi moments of inertia, which assume explicitly the rigid-body expression, turn out to represent a rather good approximation of the semiclassical results. Finally the validity of the Inglis formula is discussed in this context.

Mean field description of fusion barriers with Skyrme's interaction

Abstract Fusion barriers are determined in the framework of the Skyrme energy-density functional together with the semi-classical approach known as the Extended Thomas–Fermi method. The barriers obtained in this way with the Skyrme interaction SkM ∗ turn out to be close to those generated by phenomenological models like those using the proximity potentials. It is also shown that the location and the structure of the fusion barrier in the vicinity of its maximum and beyond can be accurately described by a simple analytical form depending only on the masses and the relative isospin of target and projectile nucleus.

FISSION DYNAMICS IN THE FOUR-DIMENSIONAL DEFORMATION SPACE

A four-dimensional deformation space adapted to describe the fission dynamics of hot, rotating nuclei is proposed. The deformation coordinates consisting of the elongation, neck formation, left-right asymmetry and nonaxiality result in fission barriers much lower and thiner than those obtained in the spherical-harmonics expansion using the same number of deformation parameters.

Equilibrium deformations of rotating nuclei in a self-consistent semiclassical approach

Abstract We study here equilibrium deformations of rotating nuclei within a self-consistent semiclassical cranking approach using the SkM ∗ Skyrme effective interaction. The different axial rotational configurations, i.e. where the rotation axis is parallel or perpendicular to the symmetry axis, are studied as well as the Jacobi bifurcation into triaxial rotational equilibrium shapes. Finally the validity of the concept of a rotating liquid drop which has been widely used for the determination of average shapes of rotating nuclei is assessed by comparison with our microscopic results.

SADDLE-POINT MASSES OF EVEN-EVEN ACTINIDE NUCLEI

In the framework of the macroscopic-microscopic approach the Yukawa folding procedure is used together with the Lublin-Strasbourg Drop liquid-drop type energy to describe atomic nuclei in the actinide region. The nuclear deformation is described by a 4-dimensional shape parametrisation similar to the well-known Funny-Hills expression. It is demonstrated that left-right asymmetry and non-axiality are present at the first and second saddle and should be included in the theoretical description. The importance of a different deformation of the proton and the neutron distribution also appears in the present analysis.

Generalized routhian calculations within the Skyrme-Hartree-Fock approximation

Abstract We consider here variational solutions in the Hartree-Fock approximation upon breaking time reversal and axial symmetries. When decomposed on axial harmonic oscillator functions, the corresponding single particle triaxial eigenstates as functions of the usual cylindrical coordinates (r, θ, z) are evaluated on a mesh in r and z to be integrated within Gauss-Hermite and Gauss-Laguerre approaches and as Fourier decompositions in the angular variable θ. Using an effective interaction of the Skyrme type, the Hartree-Fock Hamiltonian is also obtained as a Fourier series allowing a two-dimensional calculation of its matrix elements. This particular choice is shown to lead in most cases to shorter computation times compared to the usual decomposition on triaxial harmonic oscillator states. We apply this method to the case of the semi-quantal approach of large amplitude collective motion corresponding to a generalized routhian formalism and present results in the A = 150 superdeformed region for the coupling of global rotation and intrinsic vortical modes in what is known after Chandrasekhar as the S-ellipsoid coupling case.

The potential energy surface of

The potential energy surface of 240Pu is analyzed in the scission region within an elaborate macroscopic–microscopic approach, using the Lublin–Strasbourg-drop model, an improved Strutinsky shell-correction method and the BCS (Bardeen–Cooper–Schrieffer) treatment of pairing. The modified funny-hills nuclear shape parameterization, used in the present study, is further improved by introducing new collective coordinates κ and ψ for the elongation and neck-constriction. These variables are shown to be very well suited for the scission region. Within a limited number of dimensions, the model is able to explain fission modes in the actinide region. More specifically, the present work indicates that the peak of the mass distribution at in the low-energy fission of 240Pu is mainly caused by strong neutron shell corrections.

^{240}

Selfconsistent mean-field calculations have been performed with the SkM* Skyrme force for 140 spherical even-even nuclei at temperatures 0≤T≤4 MeV. Single-particle level densities for this sample of nuclei are determined for various temperatures. The average dependence of the single-particle level density on mass number A and isospin is given and compared with previous estimates obtained using the relativistic mean-field and different semiclassical approaches.

Pu around scission

Abstract Out of self-consistent semi-classical calculations performed within the so-called Extended Thomas-Fermi approach for 212 nuclei at all even angular momentum values I ranging between 0 and 80 ħ and using the Skyrme SkM ∗ effective force, the I -dependence of associated liquid drop model parameters has been studied. The latter have been obtained trough separate fits of the calculated values of the strong interaction as well as direct and exchange Coulomb energies. The theoretical data basis so obtained, has allowed to make a rough quantative assessment of the variation with I of the usual volume and surface energy parameters up to spin of ∼ 30–40ħ. As a result of the combined variation of the surface and Coulomb energies, it has been shown that this I -dependence results in a significant enhancement of the fission stability of very heavy nuclei, balancing thus partially the well-known instability due to centrifugal forces.