奇质量核的超越平均场玻色子费米子模型描述(英文)

对近年发展起来的一个基于核密度泛函理论和粒子核心耦合方案来计算中重质量奇A核谱性质的理论方法进行了评述。该方法首先在平均场层面通过选择合适的能量密度泛函和对力结构来自洽求解偶偶核心的势能曲面、球单粒子能级和奇粒子占有率,进一步将得到的结果作为微观输入来建立相互作用玻色子费米子模型哈密顿量,其中三个与粒子核心耦合强度相关的参数需要通过拟合一些特定奇质量核低激发谱数据来最终确定。通过对轴形变奇质量Eu同位素的低激发能谱和电磁跃迁几率的系统研究来说明该模型方法的有效性。另外,还讨论了该方法在描述轴形变奇质量核形状相变以及描述丰中子奇质量Ba同位素中八极关联方面的应用。A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.     

Infinite nuclear matter model and a new mass formula for atomic nuclei

The ground-state energy of an atomic nucleus with asymmetryβ is considered to be equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus a residual energyη called the local energy,η represents the energy due to shell, deformation, diffuseness and exchange Coulomb effect etc. Using this picture and the generalized Hugenholtz- Van Hove theorem of many-body theory a new mass formula has been developed. Based on this, a mass table containing the mass excesses of 3481 nuclei in the range 18 ⩽A ⩽ 267 has been made. This mass formula is compared with other mass models.     

Distorted wave theory of scattering of nucleons with intermediate energies on nuclei

In the context of nonrelativistic theory in the distorted wave approximation, a three-dimensional form of analytical expression for the differential cross section of scattering of nucleons with intermediate energies on atomic nuclei is derived. In the context of this theory, the main parameters of elastic scattering of protons with incident energy of 1 GeV on the ²⁰⁸Pb nucleus are determined. For inelastic scattering of protons with nuclear surface vibrations, giant multipole resonances in the excited nucleus are investigated for the collective nucleus model. The energy losses of the scattered proton are calculated together with the energies of giant dipole and quadrupole resonances and nuclear surface vibration energy. This allows the deformation parameter of the excited nucleus to be calculated.     

Self-consistent theory of finite Fermi systems and radii of nuclei

Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ _ch(r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.     

A semi-empirical correlation energy for nuclei

A semi-empirical interaction is used to calculate higher order corrections to the binding energies of even—even nuclei close to the line of stability. These corrections are taken to come from two phonon configurations and are treated as a perturbation with respect to the BCS nuclear ground state which is obtained from applying the energy density method to finite nuclei. The overall correspondence between theory and experiment for the 60 nuclei calculated between A =52 and A =234 is good, with excellent agreement for the non-deformed nuclei situated within the regions A = 72 to 144 and A = 200 to 212. The large correction enegies (several MeV per nucleus on the average) indicate that these correlations are of importance for explaining nuclear binding energies and that it is necessary to include them within energy functional itself. The fact that these correlations come almost exclusively from nucleons close to the fermi surface is also discussed.     

Complete destruction of heavy nuclei by hadrons and nuclei

The total disintegration is considered of nuclei with atomic weights ～100 and 200 by high energy hadrons and He⁴, C¹² nuclei with a momentum of 4.5 GeV/c per nucleon. It is shown that mainly nucleons are emitted, and there is no residual nucleus the mass of which is comparable to that of the primary nucleus. The probability of total disintegration is considered as a function of projectile energy and mass. The multiplicity, energy and emission angle of particles are considered as well. It is shown that the density of nuclear matter in the overlap zone of colliding nuclei exceeds the usual one by a factor of ～4. A comparison is made with interaction models. A conclusion is drawn of the collective interaction mechanism (perhaps, of the shock wave type) of particle ejection from the target nucleus at the first stage of interaction and of explosive decay of the residual nucleus at the next one.     

Nuclear energy density functionals constrained by low-energy QCD

A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional theory. Guided by two closely related features of QCD in the low-energy limit: a) in-medium changes of vacuum condensates, and b) spontaneous breaking of chiral symmetry; a relativistic energy density functional is developed and applied in studies of ground-state properties of spherical and deformed nuclei.     

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.     

A numerical study of energy transfer mechanisms in materials following irradiation by swift heavy ions

Swift heavy ions interact with electrons in materials and this may yield permanent atomic displacements; the energy transfer mechanisms that bring electronic excitations into atomic motion are not fully understood, and are generally discussed in terms of two theories, viz. Coulomb explosion and heat exchange between excited electrons and atoms, which is limited by electron-phonon coupling. We address this problem for a “generic” material using a semi-classical numerical approach where the dynamics of the evolving electron density is calculated by using molecular dynamics simulations applied to pseudo-electrons. The forces exerted on the nuclei are then used to calculated the trajectories of the nuclei. From the temporal evolution of the atomic kinetic energy, we find that the energy transfer between the electrons and the nuclei can be divided in two parts. First, a Coulomb heating starts the motion of the atoms by giving them a radial speed; this process differs from Coulomb explosion because the atoms are not displaced over interatomic distances. Second, a thermal energy transfer, as described in linear transport theory, takes place. Our study thus confirms the domination of thermal energy exchange mechanisms over Coulomb explosion models.     

Density-dependent effective interactions in finite nuclei (I)

Finite nuclei ranging from ¹⁶O to ²⁰⁸Pb are calculated using the Hartree-Fock theory and the local-density approximation. The energy of the nucleus is separated into a volume term, which can be calculated directly in terms of the nuclear matter energy density, and a residual surface term which contains a starting energy correction and to which only the long-range part of the effective interaction contributes. The results obtained are compared with experiment and with other calculations.     

Empirical proton-neutron interactions and nuclear density functional theory: global, regional, and local comparisons

Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.     

Mechanisms for the appearance of prescission γ-rays and their related T-odd asymmetries

Conditions for the appearance and observation of prescission γ-rays emitted by a fissioning nucleus before its separation into fission fragments were investigated within the quantum theory of fission. It was demonstrated that these conditions can be fulfilled in the γ-decay of giant electric isovector dipole resonances in a fissioning nucleus that become excited due to the nonadiabaticity of the collective deformation motion of the nucleus at the final stages of its prefission evolution. Angular and energy distributions of prescission γ-rays emitted by unpolarized fissioning nuclei were analyzed. Characteristics of T-odd asymmetries in angular distributions of prescission γ-rays were investigated for fission of unpolarized target nuclei induced by polarized cold neutrons, and these correlations were shown to be similar in nature to the T-odd ROT correlations earlier found for α-particles emitted in ternary nuclear fission.     

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.     

Nuclear Energy Density Functional and the Nuclear α Decay

We study the nuclear α decay of heavy nuclei using nuclear energy density functionals. This allows us to write the structure of the nuclear α potential inside the parent nucleus in terms of the proton and neutron density profile of the daughter nucleus with ad hoc parameters which control the strength of the potential. We adopt the Skyrme force model, Gogny force model, and relativistic mean field model to get the nucleon density profiles inside heavy nuclei. This approach is then applied to get predictions for unknown decay halflives of heavy nuclei and our results are compared with other model predictions.     

Resonance internal conversion as a way of accelerating nuclear processes

A theory of resonance conversion (RC) is presented. It is shown that by resonance conversion being a natural extension of traditional internal conversion, into the subthreshold domain, in a number of cases, it strongly affects nuclear de-excitation. Moreover, as it concentrates transition strength in narrow bands corresponding to atomic spectral lines, it is a unique tool for accelerating nuclear processes. Along with the wellknown process of non-radiative nuclear excitation through electron NEET transition and the inverse RC process, resonance conversion provides convenient mathematics for a number of crossing-invariant processes involving a nucleus and electrons, excitation and de-excitation of nuclei, by a hyperfine magnetic field, spin mixing of nuclear states via an electron shell, a hyperfine interaction and magnetic anomalies in an atomic spectra, and the excitation of nuclei in collisions accompanied by the ionization of an electron shell, in muon decay in the orbit, etc. Mechanisms of isomer pumping via a laser-radiation-induced RC and of isomer energy triggering in a resonance laser radiation field are considered. An especially strong effect can be obtained in hydrogen-like ions, with practically no RC damping. The theory is also generalized to the case of discrete Auger transitions.     

Resonances-Excitation Calculation Studies Investigation of Δ（3, 3） in Ground State of 90Zr Cold Finite Heavy Nucleus at Equilibrium and Under Large Compression

A non-relativistic microscopic mean field theory of finite nuclei is investigated where the nucleus is described as a collection of nucleons and delta resonances. The ground state properties of ⁹⁰Zr nucleus have beeninvestigated at equilibrium and large amplitude compression using arealistic effective baryon-baryon Hamiltonian based on Reid Soft Core (RSC)potential. The sensitivity of the ground state properties is studied, suchas binding energy, nuclear radius, radial density distribution, and singleparticle energies to the degree of compression. It is found that the mostof increasing in the nuclear energy generated under compression is used tocreate the massive δ particles. For ⁹⁰Zr nucleus under compression at 2.5 times density of the normal nuclear density, the excited nucleons to δ's are increased sharply up to 14% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels are calculated and their behaviors under compression are examined too. A good agreement between results with effective Hamiltonian and thephenomenological shell model for the low lying single-particle spectra isobtained. A considerable reduction in compressibility for the nucleus, andsoftening of the equation of state with the inclusion of the $\Delta $'s inthe nuclear dynamics are suggested by the results.     

Relation between total energy,electronic potential at the nucleus and chemical potential. Application to the helium isoelectronic series in Hartree-Fock theory

A formal relation between the total energy, the electronic potential at the nucleus and the chemical potential is derived within the context of density functional theory of atomic ions, using the homogeneity properties of the energy functional. An explicit application is then performed for two-electron ions in the context of the Hartree-Fock approximation.     

On the Liguid-Gas Phase Transition and the Instability of Hot Nuclei

Based on a simple semi-empirical energy density, the free energy density for a hot nucleon system is derived, from which the equations of state P(T, p) and chemical potentials μ_q(T, p) for both finite nucleus and infinite nuclear matter are acquired. The liquid-gas phase transition and the instability of hot nuclei are analysed with these ingredients within the framework of thermodynamic's. Both critical temperature T_c for infinite nuclear matter and limiting temperature T_lim, for finite nuclei are predicted and compared with previous calculations.     

Configurational transitions in processes involving metal clusters

We define the configurational state of an atomic system, e.g. a cluster of metal atoms, in terms of the nuclear coordinates of a specific local minimum of the potential energy surface (PES). Three types of configurational transitions are reviewed: chemical reactions, phase transitions in clusters and catalytic chemical processes involving clusters as catalysts. The analysis of the first two cases shows that although vibrational degrees of freedom of nuclei and configurational degrees of freedom are separable in lowest order, thermal motion of nuclei nevertheless influences the rate of a configurational transition. Therefore the height of the barrier that separates configurational states of the transition for the PES differs from the effective activation energy for this transition. For example, ignoring the thermal motion of atoms in Lennard-Jones clusters leads to a predicted value of their melting points twice which accounts for the thermal motion of atoms. Hence, in determining parameters governing configurational transitions, evaluation of the PES parameters, say, within the framework of DFT (density functional theory) must be augmented by information from molecular dynamics or some other method that accounts for nuclear motion.