A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition, the result is explained theoretically.

Shape Coexistence for ^179Hg in Relativistic Mean-Field Theory

The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.

Resonant Continuum in the Relativistic Mean-Field Theory

Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.

Exotic Structures of Odd-A Carbon Isotopes in the Deformed Relativistic Mean-FieldTheory

We study contributions of the pion meson and spatial component of the omega meson in the odd-A carbon isotopes. The pion and spatial omega provide small attractions in odd-A nuclei, giving rise to considerable influences on the single-particle energies rather than the bulk properties such as total binding energies, and root-mean-square (rms) radii. The ±? (spin) splittings, arising from the spatial omega, are large in 11C and 13C and drop as the isospin rises in odd-A carbon isotopes. As an isovector, the pion can shift slightly the relative potential depth of neutron and proton, contrary to the role of the rho meson. There is a general trend that both the pion and spatial omega fields reduce with the rise of isospin in the isotopic chain. From the normal nucleus to halo nucleus, an abnormal drop of the pion or spatial omega field may occur, as can be seen in 19C, 15C, and 21C.

Shape Coexistence in Neutron-Deficient At Isotopes in Relativistic Mean-Field Model

The potential energy surfaces are calculated for neutron-deficient At isotopes from A - 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.

Resonant Continuum in the Relativistic Mean－Field Theory

Energies, widths and wave functions of the single-particle resonant continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativistic mean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. The resonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 114Sn, 116Sn, 118Sn, and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determining energies and widths of resonant states.

Nuclear Fusion Research and Development Need New Relativistic Mass and Energy Corrections Given by the Information Relativity Theory

Hundred years after the conjecture of the British astronomer Eddington that the sun is powered by nuclear fusion of hydrogen, new physics theory may help make energy harvesting by nuclear fusion soon a reality. Researchers as well as investors funding fusion megaprojects are asked to deal with new relativistic corrections for mass and energy proposed by Suleiman in his Information Relativity Theory (IRT). These corrections were calculated in this contribution. It will help to decide whether a venture will be successful and to save big investments when in doubt. The assumed optimal kinetic energy for controlled nuclear fusion must be corrected to a somewhat higher level. At very high kinetic energy in the upper GeV range, it remains not enough baryonic mass to be transformed in energy. The fusion probability faded out to zero already at the golden limit of the recession speed of between target nucleon and projectile nucleon. Cold nuclear fusion, if ever possible, is recommended for protons rather than deuterons at highest experimental possible temperatures around 1000 (K) and needs fine-tuned kinetic nucleon energy. It would be also of interest whether a golden ratio based nuclear fuel confinement chamber could be beneficial. In this connection, also cold nuclear fusion setups should be discussed. Nature is governed by the golden ratio and criticality of physical systems influenced by it, and nuclear physics is not an exception. Computer simulations of the underlying controlled nuclear fusion processes should gain profit from IRT corrected starting information and may tackle anew possible low energy nuclear transmutations considering the wave-like dark components of matter and energy.

Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter

We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given value of qS. By use of this procedure, the scalar meson field in the Walecka＇s MFA and in Chin＇s RHA are quantized around the mean field, Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of Ф makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka＇s MFA, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin＇s RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka＇s MFA does not. We suggest to fix the parameter Ф at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory （QRMFT） a variational method.

Investigations on Nuclei near Z = 82 in Relativistic Mean Field Theory with FSUGold

In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field （RMF） theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.

Relativistic Brueckner-Hartree-Fock Theory for Finite Nuclei

Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus 160 is investigated as an example. The resulting groundstate properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for ab initio covariant investigations of heavy nuclei.

Relativistic Multichannel Theory:Theoretical Studies of Excited Energy Structure of Ar Atom

We here present a relativistic multichannel theory which can be regarded as an extension of traditional configuration interaction theories by including continuum configuration interactions.Our relativistic multichannel theory aims directly to calculate the compact set of physical parameters(μ_(α),U_(iα)) in multichannel quantum defect theory.Taking Ar atom as an example,we compare our calculated orbital energies with traditional configuration interaction calculations as well as experimental measurements.

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

Two-photon excitation for C_2Vmolecules based on the full relativistic theory

The present work explores a new phenomenon that not all the transition probability of two photon processes is negligible at low irradiance. The irreducible representation 2B2 of C2v is unexpected, for there is no much deviation in oscillator strength for two-photon and single-photon process A1 to 2B2. This new phenomenon is only possible to be explored by the symmetrical consideration: the necessary and sufficient condition is molecular plane coincident with yz plane or the operation σ ’v(yz) for group C2v. It is only possible to be evaluated out by use of the full relativistic quantum mechanical theory.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.

On the Foundations of the Classical Relativistic Theory of the Field of an Accelerated Extended Charge

The effect of nonzero extent of an electric charge is considered within the assumption that the structure of the charge at rest is spherically-symmetric and the current vector is linear in the acceleration. An exact expression for the electromagnetic field of the charge is obtained, which depends on the specific form of the charge distribution. We have developed the approximations which deal with the charge distribution through its low-order moments, for the case in which the particle velocity does not considerably change over the time it covers a distance of the order of its own size. We have also rigorously justified the Lorentz-Abraham-Dirac expression for the radiation friction (we have identified a more general context for this expression as well as its applicability domain). We have also studied the radiation field and demonstrated that in some cases, the radiation virtually vanishes even for large accelerations. Ways of further development of the theory have been pointed out, in order to include more general forms of the current vector (dependence of the deformation of the charge structure on the acceleration, rotation of the structure around the centre of the charge, ultrarelativistic regimes).

Reformulation of Relativistic Quantum Field Theory Using Region-Like Idealization of the Elementary Particle

The existence of any elementary particle in universe requires the existence of some region of universe occupied by it. By taking the volume of this occupied region, the author will reformulate the relativistic quantum field theory using new 3-dimensional region-like idealization of elementary particles and hereinafter will call the total volume of all regions occupied by the elementary constituent particles of the quantum system the occupied volume. Also the author will call the set of all regions of universe filled by elementary constituent particles of the quantum system the occupied path. Always any quantum system is existed at a head of its occupied path. This path is growing by mutual filling and leaving regions of universe by its elementary constituent particles. The conservation of this elementary constituent particle requires the conservation of its occupied volume during this process. This requirement could be summarized by the following conditions: 1) the total volume of all regions of universe filled by the elementary constituent particles of the quantum system minus the total volume of all regions of universe left by these elementary constituent particles must be equal to the occupied volume of the quantum system;2) the total increase in the occupied volume of the quantum system due to the absorption of another elementary particles from outside its occupied regions minus the total decreasing in its occupied volume due to the emission of another elementary particles outside its occupied regions must be equal to the occupied volume of it. The wave-particle duality of the elementary constituent particles implied accumulation of them as the finite set of interfered waves. This accumulation of elementary constituent particles causes the absolute probabilistic nature of event of finding the elementary consistent particle in specified interfered wave, and hence the mathematical representation of this interfered wave should take into account the value of probability amplitude of finding an elementary particle inside the region occupied specified interfered wave. In quantum theory this probability amplitude corresponds to complex amplitude of the wave function of interfered wave. Also in Hilbert’s representation of the quantum theory these wave functions are representing the components of the quantum state vector. In this paper the author will develop the transformation theory of the region-like quantum state of the quantum system.

Benchmark Calculations on the Atomization Enthalpy,Geometry and Vibrational Frequencies of UF_6 with Relativistic DFT Methods

Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.

Relativistic Correction of the Rydberg Formula

The relationship E = −K holds between the energy E and kinetic energy K of the electron constituting a hydrogen atom. If the kinetic energy of the electron is determined based on that relationship, then the energy levels of the hydrogen atom are also determined. In classical quantum theory, there is a formula called the Rydberg formula for calculating the wavelength of a photon emitted by an electron. In this paper, in contrast, the formula for the wavelength of a photon is derived from the relativistic energy levels of a hydrogen atom derived by the author. The results show that, although the Rydberg constant is classically a physical constant, it cannot be regarded as a fundamental physical constant if the theory of relativity is taken into account.

Relativistic multichannel treatment of autoionization Rydberg series of 4s^2nf(n=4-23)J~π=(7/2)° for scandium

Based on relativistic multichannel theory, this paper calculates the energy levels of autoionization Rydberg series 4s^2nf（n=4- 23）J^π -（7/2）° of scandium at different levels of approximation within the framework of multichannel quantum defect theory. The present results show that the dipole polarizations play an important role. Considering the dynamical dipole polarization effects, this paper finds that the difference between calculated and experimental quantum defects for the 4s^2nf（n=4- 23）J^π -（7/2）° series is generally about 0.01- 0.03. Furthermore, the reason that 4s^216f is obscured in experimental spectra is suggested to be the interaction with the neighbouring resonance state converged to 3d^2（^1G4） of Sc^＋.

Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure

Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks （BTNs） evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.