The Interaction Energy of Well-Separated Skyrme Solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space. We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.     

Relations between the Skyrme force parameters and the nucleon-nucleon forces within the quasi-Hartree-Fock-theory

The energy-density for the Skyrme forces in the Hartree-Fock-approximation is compared with the energy-density in the quasi-Hartree-Fock-approximation for two-body nucleon-nucleon forces with hard-core repulsion. From these expressions the magnitudes of the corresponding Hartree-Fock parameters of the nucleon-nucleon force are estimated. As an example, a simple nucleon-nucleon force is constructed, which reproduces the results of the Skyrme force SII. The ambiguities of such an comparison are discussed. The Skyrme forces SII-SIV correspond to potentials with hard-core radii ≈0.5–0.7 F. Smaller hard-core radii correspond to larger exchange contributions.     

Hartree-Fock calculations of super-heavy nuclei

Hartree-Fock calculations are performed in the region of super heavy nuclei using zero range (Skyrme) forces and the finite range force G-0; the latter predict shell closure for the (α-unstable) nucleus N = 218, Z = 126 while the former do not. Calculations performed using the density matrix expansion (DME or DMEX) approximations give results similar to the Skyrme force. The problem is traced to an inadequacy of the DME, incorrectly placing the nodeless n = 1 high ? states.     

Generator coordinate calculations of giant resonances with the Skyrme interaction

The Skyrme interaction is shown to lead to significant simplifications in generator coordinate calculations. As an illustration, giant resonances are calculated using pure oscillator wave functions. We present results for monopole, dipole and quadrupole isoscalar and isovector modes using two different Skyrme forces, SIII and SIV. A good agreement with available experimental data is obtained.     

热核静态性质的一个简单模型

以扩展Skyrme力为基础,计入唯象的表面效应和Coulomb相互作用,推导了核系统的能量密度。对于有限温度情形,通过索末菲展开,得到了能量密度、自由能密度以及熵密度的解析公式。由此计算了热核物质和有限核的状态方程,每核子熵及每核子自由能。对计算结果作了比较和分析,预言了在同一框架下研究热核动力学演化的可能性。 关键词：     

CALCULATION OF MICROSCOPIC OPTICAL POTENTIAL BY USE OF THE GENERALIZED SKYRME FORCES

In this paper the calculation of the microscopic optical potential based on thegeneralized Skyrme forces which describe both the ground and excited state propertiessimultaneously has been carried out for ²⁰⁵Pb ete. The volume integral per nucleon andthe root mean square radii of the real part as well as the imaginary part of the opticalpotential have been obtained. The angular distributions of the elastic scattering andthe total cross sections by use of our computed microscopic optical potential for ^20?Pbhave also been calculated. Compared with the conventional Skyrme forces, the calculat-ed results by the generalized Skyrme forces are evidently improved The presentcalculation is also in a good agreement with experiments for the incident energy lessthan 100 MeV.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM^*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of ⁴⁸Ca+²³⁸U are nicely reproduced with the SkM^* parameter by implementing the potential into the dinuclear system model.     

Role of different Skyrme forces and surface corrections in exotic cluster decay

We present cluster-decay studies of ⁵⁶Ni^* formed in heavy-ion collisions using different Skyrme forces. Our study reveals that different Skyrme forces do not alter the transfer structure of fractional yields significantly. The cluster decay half-lives of different clusters lie within ±10% for preformed cluster models (PCM) and ±15% for unified fission models (UFM).     

Properties of deformed Λ hypernuclei

The properties of Be and B isotopes and the corresponding Λ hypernuclei are studied by using a deformed Skyrme Hartree-Fock approach with realistic nucleonic Skyrme forces, pairing correlations, and a microscopically determined lambda-nucleon interaction based on Brueckner-Hartree-Fock calculations of hypernuclear matter. The results suggest that the core nuclei and the corresponding hypernuclei have similar deformations with the same sign.     

Baryon exotics in the quark model, the skyrme model, and QCD

We derive the quantum numbers of baryon exotics in the quark model and the Skyrme model and show that they agree for arbitrary colors and flavors. We define exoticness E, which can be used to classify the states. The exotic baryons include the recently discovered qqqqq pentaquarks (E=1), as well as exotic baryons with additional qq pairs (E>/=1). The mass formula for nonexotic and exotic baryons is given as an expansion in 1/N(c) and allows one to relate the moment of inertia of the Skyrme soliton to the mass of a constituent quark.     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

Investigation of nuclear structure by using separable Skyrme interaction

Amethod of separabilization of Skyrme forces for nuclear-structure studies is briefly described. The results of relevant calculations for various nuclear-excitation modes are presented by way of example.     

Derivation of a proximity interaction between nuclei from the Hartree-Fock functional with Skyrme interactions

The potential between heavy or medium heavy spherical nuclei is derived on the basis of the proximity approximation and the assumption of undisturbed spherical density distributions. The HF-theory with Skyrme forces is used to write the energy as a functional of the density. The resulting potential consists of an isoscalar and a (much smaller) isospin-dependent part. Depending on the choice of the Skyrme parameters calculated interaction between heavy ions are close to the double folding potential or to the proximity potential. Our interaction can be factorized with a very good approximation into scaling factors and universal functions of the proximity distance in units of the surface thickness.     

Separabelized Skyrme interaction and characteristics of giant dipole resonances

The accuracy of eliminating the spurious state from the E1-transition strength distribution is studied within the random phase approximation with separabelized Skyrme forces.     

Nuclear structure calculations using momentum-dependent delta interactions (MDD)

The ground-state properties of a nucleus have been investigated using momentum- and density-dependent δ-interactions. Unlike the Skyrme type of interaction, the two-body interaction used has terms dependent on the fourth power of the relative momenta. The role of these new terms has been investigated by using the density-matrix expansion technique of Negele and Vautherin. The interaction has been used to calculate, amongst other phenomena, the ion-ion interaction potential and the nucleon-nucleus optical potential. The improvements obtained using such an interaction over the Skyrme II type of interactions (which have small odd state components) are discussed in detail. It is shown that the effective mass, $\text{m}{}^1$, is larger in magnitude than obtained by using the Skyrme II type of interaction. It has been suggested that such interactions could be more appropriate than the Skyrme type of interactions in physical situations where large momentum transfers are involved.