Nuclear density functional theory

An understanding of atomic nuclei is crucial for a complete nuclear theory, for the nuclear astrophysics, for performing new experimental tasks, and for various other applications. Within a density functional theory, the total binding energy of the nucleus is given by a functional of the nuclear density matrices and their derivatives. The variation of the energy density functional with respect to particle and pairing densities leads to the Hartree-Fock-Bogoliubov equations. The “Universal Nuclear Energy Density Functional” (UNEDF) SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the-art computational infrastructure, is briefly described. The ultimate goal is to replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

Kohn–Sham density functional inspired approach to nuclear binding

A non-relativistic nuclear density functional theory is constructed, not as done most of the time, from an effective density dependent nucleon–nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin–orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces. In this pilot work, for the pairing correlations, simply a density dependent zero range force is adopted from the literature. Possible future extensions of this approach are pointed out.     

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.     

Non-linear density dependence of the Δ-self-energy in nuclear matter and its implications in pionic atoms

The $\text{Δ(}\text{3}\text{2}\text{,}\text{3}\text{2}$) self-energy in a nuclear medium is shown to be highly non-linear in density, when proper care is taken of the virtual meson propagation in the medium and retardation effects. As a consequence the p-wave absorptive potential for pionic atoms diverges appreciably from the standard ρ² form. A fit to the existing data on pionic atoms is carried out with the new functional of the density and turns out to be as good as those with the ρ² functional. The successful fits with such different density functionals are due to a very narrow range of nuclear effective densities felt by the pion in the observed pionic atoms. The influence of these effects in related problems is discussed along with the suggestion to widen the range of nuclear densities felt by the pions by looking at other nuclear phenomena.     

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 soluble model for the study of saturation in finite nuclei

The deviation of very small nuclear systems from saturation is studied. In the framework of a soluble one-dimensional model based on the energy density formalism, we establish simple expressions for the density profile, the deviation from nuclear matter density, and the Fermi energy as a function of particle number. The binding energy of the nucleus is computed and the effect of the departure from saturation is identified as a term exponentially decaying for large A. A comparison with the theory of Krappe and Nix is also presented.     

Mixed second and third energy derivatives from auxiliary density perturbation theory†

Abstract

The working equations for the calculation of mixed second- and third-order energy derivatives in the framework of auxiliary density functional theory are presented. The perturbations with respect to nuclear displacements and external homogeneous electric field components are calculated with auxiliary density perturbation theory. The presented energy derivative working equations were implemented in deMon2k and validated by vibrational spectra simulations within the double harmonic approximation. The effect of the auxiliary functions on the IR and Raman spectra simulation were analysed for the C₆₀ fullerene. As applications, vibrational spectra of icosahedral carbon fullerenes with up to 540 atoms are calculated without employing symmetry constraints.     

Toward ab initio density functional theory for nuclei

We survey approaches to non-relativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional ‘local density plus gradients’ form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wavefunction-based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

原子核物理中的协变密度泛函理论

文章介绍了原子核协变密度泛函理论的历史发展、理论框架、对原子核基态和激发态的描述以及在一些交叉学科领域的应用。首先,通过回顾原子核物理研究中的几个重要里程碑并结合二十一世纪原子核物理面临的机遇和挑战,对当前核物理的研究热点和重要课题进行了介绍。随后系统介绍了原子核协变密度泛函理论,内容包括协变密度泛函理论的历史发展、一般理论公式、介子交换模型、点耦合模型、交换项、张量相互作用、物理观测量的计算公式等。协变密度泛函理论的应用包括原子核基态性质和激发态性质的描述以及在核天体物理与标准模型检验中的应用。其中,基态性质包括原子核结合能、半径、单粒子能级、共振态、磁矩、晕现象等。激发态性质包括原子核磁转动、低激发态性质、集体转动、量子相变、集体振动等。在核天体物理与标准模型检验的应用中,主要以核纪年法测算宇宙年龄和Cabibbo-Kobayashi-Maskawa矩阵的幺正性检验等为例,介绍协变密度泛函理论在交叉学科领域的应用。     

Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem

Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Some direct formal and practical implications of the present reformulation of DFT are also discussed.     

Aluminum Hugoniot from model calculations including semicore electrons based on density functional theory

We present a method to obtain Hugoniot from model calculations based on density functional theory, and apply the method to aluminum Hugoniot. Technological advances have extended the experimental research of high energy density physics, and call for quantitative theoretical analysis. However, direct computation of Hugoniot from density functional theory is very difficult. We propose two step calculations of Hugoniot from density functional theory. The first step is molecular dynamics simulations with an ambient temperature for electrons. The second step is total energy calculations of a crystal with desired high temperatures for electrons and with the ambient temperature for electrons. We treated the semicore 2s and 2p electrons of aluminum as valence electrons only for the total energy calculations of the aluminum crystal. The aluminum Hugoniot from our model calculations is in excellent agreement with available experimental data and the previous density functional theory calculations in the literature.     

The Fourth-Order Symmetry Energy of Finite Nuclei

The fourth-order symmetry energy E_sym,4(A) of heavy nuclei is investigated based on the Skyrme energy density functional in combination with a local density approximation. Unlike some previous works, in our method, the interferences from the other energy terms are removed since it is completely isolated from the rest of energy terms. The calculated E_sym,4(A) is much less than that extracted from nuclear masses. The underlying reason for the big difference is discussed. The Brueckner theory also gives a small fourth-order symmetry energy coefficient of nuclear matter, which is also different from recent conclusions with another methods.     

Nonadiabatic ab initio molecular dynamics using linear-response time-dependent density functional theory

We review our recent work on ab initio nonadiabatic molecular dynamics, based on linear-response timedependent density functional theory for the calculation of the nuclear forces, potential energy surfaces, and nonadiabatic couplings. Furthermore, we describe how nuclear quantum dynamics beyond the Born-Oppenheimer approximation can be performed using quantum trajectories. Finally, the coupling and control of an external electromagnetic field with mixed quantum/classical trajectory surface hopping is discussed.     

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.