Simultaneous description of wobbling and chiral properties in even-odd triaxial nuclei

A particle-triaxial rigid core Hamiltonian is semi-classically treated. The coupling term corresponds to a particle rigidly coupled to the triaxial core, along a direction that does not belong to any principal plane of the inertia ellipsoid.The equations of motion for the angular momentum components provide a sixth-order algebraic equation for one component and subsequently equations for the other two. Linearizing the equations of motion, a dispersion equation for the wobbling frequency is obtained. The equations of motion are also considered in the reduced space of generalized phase space coordinates. Choosing successively the three axes as quantization axis will lead to analytical solutions for the wobbling frequency, respectively. The same analysis is performed for the chirally transformed Hamiltonian. With an illustrative example one identified wobbling states whose frequencies are mirror image to one another. Changing the total angular momentum I, a pair of twin bands emerged. Note that the present formalism conciliates between the two signatures of triaxial nuclei, i.e., they could coexist for a single nucleus.

Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

Dirac Redux - Dirac’s Equation in Physical Spacetime without Internal Degrees of Freedom

The Dirac equation (DE) is one of the cornerstones of quantum physics. We prove in the present contribution that the notion of internal degrees of freedom of the electron represented by Dirac’s matrices is superfluous. One can write down a coordinate-free manifestly covariant vector equation by direct quantization of the 4-momentum vector with modulus m: Pψ=mψ (no slash!), the spinor ψ taking care of the different vector grades at the two sides of the equation. Electron spin and all the standard DEproperties emerge from this equation. In coordinate representation, the four orthonormal time-space frame vectors Xµ appear instead of Dirac’s Yµ-matrices, the two sets obeying to the same Clifford algebra. The present formalism expands Hestenes’ spacetime algebra (STA) by adding a reflector vector x5 that is defining for the C (particle-antiparticle) symmetry and the CPT symmetry of DE, as well as for left- and right-handed rotors and spinors. In 3D it transforms a parity-odd vector x into a parity-even vector σ=x5x and vice versa. STA augmented by the reflector will be referred to as STAR, which operates on a real vector space of same dimension as the equivalent real dimension of Dirac’s complex 4×4 matrices. There are no matrices in STAR and the complex character springs from the signature and dimension of spacetime-reflection. This appears most clearly by first showing that STAR comprises two isomorphic subspaces, one for generators of polar vectors and boosts and the other for generators of axial vectors and rotors, including Pauli spin vectors. These then help to discuss the symmetries, probability current, transformation properties and nonrelativistic approximation of STAR DE. We prove here that the information from γ-matrices is contained in spacetime-reflection, which makes the matrices redundant. Therefore, it becomes relevant to reexamine those areas of quantum physics that take the γ-matrices and their generalizations as fundamental.

Dirac Redux - Dirac’s Equation in Physical Spacetime without Internal Degrees of Freedom

The Dirac equation (DE) is one of the cornerstones of quantum physics. We prove in the present contribution that the notion of internal degrees of freedom of the electron represented by Dirac’s matrices1,2 is superfluous. One can write down a coordinate-free manifestly covariant vector equation by direct quantization of the 4-momentum vector with modulus m: Pψ=mψ (no slash!), the spinor ψ taking care of the different vector grades at the two sides of the equation. Electron spin and all the standard DE properties emerge from this equation. In coordinate representation, the four orthonormal time-space frame vectors Xµ appear instead of Dirac’s Yµ-matrices, the two sets obeying to the same Clifford algebra. The present formalism expands Hestenes’ spacetime algebra (STA) by adding a reflector vector x5 that is defining for the C (particle-antiparticle) symmetry and the CPT symmetry of DE, as well as for left- and right-handed rotors and spinors. In 3D it transforms a parity-odd vector x into a parity-even vector σ=x5x and vice versa. STA augmented by the reflector will be referred to as STAR, which operates on a real vector space of same dimension as the equivalent real dimension of Dirac’s complex 4×4 matrices. There are no matrices in STAR and the complex character springs from the signature and dimension of spacetime-reflection. This appears most clearly by first showing that STAR comprises two isomorphic subspaces, one for generators of polar vectors and boosts and the other for generators of axial vectors and rotors, including Pauli spin vectors. These then help to discuss the symmetries, probability current, transformation properties and nonrelativistic approximation of STAR DE. We prove here that the information from γ-matrices is contained in spacetime-reflection, which makes the matrices redundant. Therefore, it becomes relevant to reexamine those areas of quantum physics that take the γ-matrices and their generalizations as fundamental.

Dirac Redux - Dirac’s Equation in Physical Spacetime without Internal Degrees of Freedom

The Dirac equation (DE) is one of the cornerstones of quantum physics. We prove in the present contribution that the notion of internal degrees of freedom of the electron represented by Dirac’s matrices is superfluous. One can write down a coordinate-free manifestly covariant equation by direct quantization of the energy-momentum 4-vector P with modulus m: P(psi) = m(psi) (no slash!), the spinor (psi) taking care of the different vector grades at the two sides of the equation. Electron spin and all the standard DE properties emerge from this equation. In coordinate representation, the four orthonormal time-space frame vectors x0, x1, x2, x3 formally substitute Dirac’s gamma-matrices, the two sets obeying to the same Clifford algebra. The present formalism expands Hestenes’ spacetime algebra (STA) by adding a reflector vector x5, which in 3D transforms a parity-odd vector x into a parity-even vector x5x and vice versa. STA augmented by the reflector will be referred to as STAR, which operates on a real vector space of same dimension as the equivalent real dimension of Dirac’s complex 4 x 4 matrices. There are no matrices in STAR and the complex character springs from the signature and dimension of spacetime-reflection. This appears most clearly by first showing that STAR comprises two isomorphic subspaces, one for the generators of polar vectors and boosts and the other for the generators of axial vectors and rotors, comprising Pauli spin vectors. These then help to discuss the symmetries, probability current, transformation properties and nonrelativistic approximation of STAR DE. By proving that Dirac’s matrices are redundant, because all the information from them is contained in spacetime-reflection, it becomes relevant to reexamine those areas of modern physics that take Dirac matrices and their generalizations as fundamental.

Chemical Bonding by the Chemical Orthogonal Space of Reactivity

The fashionable Parr–Pearson (PP) atoms-in-molecule/bonding (AIM/AIB) approach for determining the exchanged charge necessary for acquiring an equalized electronegativity within a chemical bond is refined and generalized here by introducing the concepts of chemical power within the chemical orthogonal space (COS) in terms of electronegativity and chemical hardness. Electronegativity and chemical hardness are conceptually orthogonal, since there are opposite tendencies in bonding, i.e., reactivity vs. stability or the HOMO-LUMO middy level vs. the HOMO-LUMO interval (gap). Thus, atoms-in-molecule/bond electronegativity and chemical hardness are provided for in orthogonal space (COS), along with a generalized analytical expression of the exchanged electrons in bonding. Moreover, the present formalism surpasses the earlier Parr–Pearson limitation to the context of hetero-bonding molecules so as to also include the important case of covalent homo-bonding. The connections of the present COS analysis with PP formalism is analytically revealed, while a numerical illustration regarding the patterning and fragmentation of chemical benchmarking bondings is also presented and fundamental open questions are critically discussed.

Quantum Eigenstates of Curved and Varying Cross-Sectional Waveguides

A simple one-dimensional differential equation in the centerline coordinate of an arbitrarily curved quantum waveguide with a varying cross section is derived using a combination of differential geometry and perturbation theory. The model can tackle curved quantum waveguides with a cross-sectional shape and dimensions that vary along the axis. The present analysis generalizes previous models that are restricted to either straight waveguides with a varying cross-section or curved waveguides, where the shape and dimensions of the cross section are fixed. We carry out full 2D wave simulations on a number of complex waveguide geometries and demonstrate excellent agreement with the eigenstates and energies obtained using our present 1D model. It is shown that the computational benefit in using the present 1D model to calculate both 2D and 3D wave solutions is significant and allows for the fast optimization of complex quantum waveguide design. The derived 1D model renders direct access as to how quantum waveguide eigenstates depend on varying cross-sectional dimensions, the waveguide curvature, and rotation of the cross-sectional frame. In particular, a gauge transformation reveals that the individual effects of curvature, thickness variation, and frame rotation correspond to separate terms in a geometric potential only. Generalization of the present formalism to electromagnetics and acoustics, accounting appropriately for the relevant boundary conditions, is anticipated.

A new empirical formula for cross-sections of (n,nα) reactions

Studies on the cross-sections of (n,n[Formula: see text]) reactions which are energetically possible, about 14 MeV neutrons are quite scarce. In this paper, the cross-sections of (n,n[Formula: see text] nuclear reactions at [Formula: see text]14–15 MeV are analyzed by using a new empirical formula based on the statistical theory. We show that neutron cross-sections are closely related to the [Formula: see text]-value of nuclear reaction, in particular for (n,n[Formula: see text]) channels. Results obtained with this empirical formula show good agreement with the available measured cross-section values. We hope that the estimations on the cross-sections using the present formalism may be helpful in future studies in this field.

Vibrational molecular and nuclear spectra in terms of quantum algebras

A generalized deformed oscillator giving the same spectrum as the Morse potential is con­ structed through the use of quantum algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss, suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscilla­tors. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown. Nuclear models giving good descriptions of vibrational spectra are reviewed and the need of modifying the SUq(2) model in order to extend its region of applicability towards the vibrational limit is discussed.

Nonlinear extension of the u(3) algebra as the symmetry algebra of the three-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies and the Nilsson model

The symmetry algebra of the N-dimensional anisotropic quantum har- monic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim oscillator is studied in more detail, because of its relevance in the description of superdeformed nuclei and nuclear and atomic clusters. In this case the symmetry algebra turns out to be a nonlinear extension of the u(3) algebra. A generalized angular momentum operator useful for labeling the degenerate states is constructed, clarifying the connection of the present formalism to the Nilsson model.