Transition Matrix Elements Research Articles

Analysis of Transients in a 4-Level Flying Capacitor Converter: Time Domain Approach. Part 2: Small Normalised Voltage Command

Abstract A 4-level flying capacitor converter (FCC) operation is considered on a base of discrete state-space model. A transition matrix is obtained for a pulse width modulation (PWM) period for small normalised voltage command values [0, 1/3]. The transition matrix elements are expanded into power series by small parameters. The matrix eigenvalues are presented in the form of power series as well. Six separate transients are constructed for six possible initial FCC states on a PWM period. Inductor current and capacitors’ voltage transients are found for the voltage source power-up as the arithmetic average of the six separate transients. Finally, the discrete solutions are replaced by equivalent continuous ones. Simple and accurate formulas for inductor current and capacitors’ voltage transients demonstrate good agreement with simulation results.

Analysis of Transients in a 4-Level Flying Capacitor Converter: Time Domain Approach. Part 1: Large Normalised Voltage Command

Abstract A 4-level flying capacitor converter (FCC) operation is considered on a base of discrete state-space model. A transition matrix is obtained for a pulse width modulation (PWM) period for large normalised voltage command values [1/3, 1). The transition matrix elements are expanded into power series by small parameters. The matrix eigenvalues are presented in the form of power series as well. Six separate transients are constructed for six possible initial FCC states on a PWM period. Inductor current and capacitors’ voltage transients are found for the voltage source power-up as the arithmetic average of the six separate transients. Finally, the discrete solutions are replaced by equivalent continuous ones. Simple and accurate formulas for inductor current and capacitors’ voltage transients demonstrate good agreement with simulation results.

Relativistic configuration interaction with core polarization method for the divalent systems

SynopsisThe relativistic configuration interaction with core polarization method and program for the divalent systems have been developed. Based on this new program, the energy levels, transition matrix elements, static and dynamic dipole polarizabilities of He, Be, and Mg atoms have been calculated systematically.

Quantum vortex surfaces: a dizzying new effect in single ionization collisions

SynopsisWe study the appearance of quantum vortices in the transition matrix element of single ionization collisions. We relax all the usual geometrical restrictions on the momenta of the final-state, and demonstrate that previously observed vortex points and lines correspond to 2D and 3D intersections of a much more complex structure: a quantum vortex surface. Finally, we theoretically evaluate this complex structure for the single ionization of hydrogen by positron impact.

Optical Hall effect and gyrotropy of surface polaritons in Weyl semimetals

Weyl semimetals possess unique electrodynamic properties due to a combination of strongly anisotropic and gyrotropic bulk conductivity, surface conductivity, and surface dipole layer. We explore the potential of popular tip-enhanced optical spectroscopy techniques for studies of bulk and surface topological electron states in these materials. Anomalous dispersion, extreme anisotropy, and the optical Hall effect for surface polaritons launched by a nanotip provides information about Weyl node position and separation in the Brillouin zone, the value of the Fermi momentum, and the matrix elements of the optical transitions involving both bulk and surface electron states.

Electron Mobility in CdSexTe1-x (x = 0.25) Solid Solution: Ab Initio Calculation

In this paper an assessment of the quality of a solid solution of CdSexTe1-x is done by study of its transport properties. The description of the kinetic phenomena is carried on the base of the wave function and self-consistent potential for solid solution CdSexTe1-x (x = 0.25) which were determined from the first principles using the projector augmented waves as implemented in the ABINIT code. The scattering processes were considered in the framework of short-range scattering models where the electron interaction with polar and nonpolar optical phonons, piezoelectric and acoustic phonons, static strain centers, neutral and ionized impurities was taken into account. The transition matrix elements were obtained by integration over the unit cell using three-dimensional B-spline interpolation. For crystals with impurity concentration 5.6´1015 - 5´1018 cm-3 the temperature dependences of electron mobility and Hall factor in the range 15 - 1200 K are calculated. The theoretical curves obtained in the short-range approach differ qualitatively and quantitatively from those obtained within the long-range models in relaxation time approximation.

Tunable linear and nonlinear optical properties of chromophores containing 3,7-(di)vinylquinoxalinone core by modification of receptors moieties

To study the linear and nonlinear optical properties of chromophores with 3,7-(di)vinylquinoxalinone core, excitation energies, dipole moments, polarizabilities, the first and second hyperpolarizabilities as well as TPA cross-sections of four chromophores with different receptors in vacuum and chloroform solvent were calculated by DFT method and response theory. Two methods of the Hellmanne-Feynman theorem and the McRae equation were used to estimate the difference of the dipole moment between the excited state and the ground state. The linear polarizability and the first hyperpolarizability were calculated by the derivative method, and the second hyperpolarizability was calculated by the finite difference method. It is found that the numerical size and order of the above polarizability and hyperpolarizability were verified by using the few-state model. By studying charge-transfer excited states and the transition matrix element, the internal mechanism of TPA and transition channels were revealed. Results demonstrated that chromophore TCP with acceptor [5-dicyanomethylene-2-oxo-4-cyano-2,5-dihydropyrrol-3-yl] possesses a more obvious NLO coefficient value, and TCF with 5,5-dimethyl-2- dicyanomethylene-3-cyano-2,5-dihydrofuran-4-yl possesses the largest TPA cross-section. The current investigation is expected to provide theoretical support for the development of chromophores with 3,7-(di)vinylquinoxalinone π-electron bridge in NLO materials.

Deformed Hartree-Fock calculations for semileptonic processes in nuclei

In nuclear structure calculations, the Deformed Hartree-Fock (DHF) provides generally a good description for the low-lying spectroscopic properties of odd-even, odd-odd and even-even nuclear systems of which the consideration of the deformation is motivated by many reasons. The common random phase approximations (RPA, QRPA, etc.) mostly used to accurately evaluate the transition matrix elements in many nuclear processes [1,2], are appropriate for only spherical even-even nuclear systems even though, sometimes, isotopes considered as rather deformed are studied. In the present work, we discuss the treatment within the DHF method of nuclei in the region A = 70 — 80. This region includes isotopes (like 72Ge, 76Ge, 72Se, etc) interesting for studying many nuclear processes as the ,0/3-decay, scattering of dark matter candidates off nuclei, μ~ —> e± conversions in nuclei. In our calculations the model space comprises 1P3/2, 0f5/2, 1pi/2 and 0p9/2 single particle Orbitals assuming 56Ni to be the inert core. The effective interaction employed, has been quite successfully used previously to describe many important features of the nuclei in this region. The lowest prolate Hartree-Fock single particle spectrum of some isotopes (72Ge, 76Ge) has been used to test the good angular momentum states which in this method are projected out from the intrinsic HF states. As an application, we examine the predictions of DHF for the exotic (μ~,ε~) conversion process. The contributions of all basic μ~ —> e~ operators originating from a general effective Lagrangian [2] are compared with those of normal QRPA methods obtained previously.

The exotic μ~ —» e~ conversion in Nuclei: An Interplay of Atomic, Nuclear and Particle Physics.

The partial rates of all kinematically accessible channels (for coherent and incoherent processes) of the exotic μ~ —» e~ conversion in the currently interesting nuclei 27Al, 4 8Ti, and 2 0 8Pb are investigated. The assumed muon-number violation involves exchange of various particles in conventional extentions of the standard model and in minimal supersymmetric models with R-parity conserving and R-parity violating interactions. The transition matrix elements obtained are used to extract very severe constraints for the flavor violation parameters entering the effective Lagrangians resulting in the framework of specific particle models.

Dynamic Solvent Effect in Reactions of Photoinduced Intramolecular Proton-Coupled Electron Transfer

The dynamic solvent effect (DSE) in reactions of ultrafast proton-coupled electron transfer (PCET) under nonequilibrium conditions is studied. It is found in particular that the effect depends on angle φ between the directions of the reaction coordinates that correspond to the step of photoexcitation of the system, and to the step of product formation. Several trends characteristic of such reactions are established: (i) the highest DSE value should be observed in the region of the increased exergonicity of the reaction, and the effect is weak in the region of low exergonicity; (ii) upon an increase in the transition matrix element, the maximum in the curve of the dependence of the PCET rate constant on the reaction’s exergonicity shifts toward the region of lower values; (iii) the dependence of the effective reaction time on angle φ has a pronounced minimum, the position of which depends on the energy parameters of the reactants.

Monopole moments and the $ \beta$-vibration in deformed nuclei

I revisit the theory of the $ \beta$-vibration in deformed nuclei focusing on the transition matrix elements to the ground band. The relation between monopole and quadrupole matrix elements is derived from an incompressibility assumption and is validated by self-consistent mean-field theory with several energy density functionals. With estimates of the deformation-dependent mean-field potential energy function, it is found that the excited $ 0^+$ band in 156Gd comes fairly close to meeting the criteria to be classified as a $ \beta$-vibration.

A CHARGE FORM FACTOR (CFF) OF 5He NUCLEUS

High energy electron scattering is a very powerful tool for studying geometrical details of nuclear structure. The studies provide information on static distribution of charge and magnetization in nuclei. As the interaction is relatively weak so that in the scattering process the internal structure of the target nucleus is not significantly disturbed. Using electrons as projectile, we can study how transition matrix elements vary with q2 and map out the Fourier transforms of the transition charge and current densities called Form Factors or Structure factors. In the high energy electron scattering we can know the details of the spatial distribution of transition charge and current density. In this paper we have formulated CFF for 5He nucleus

A CHARGE FORM FACTOR (CFF) OF 5He NUCLEUS

High energy electron scattering is a very powerful tool for studying geometrical details of nuclear structure. The studies provide information on static distribution of charge and magnetization in nuclei. As the interaction is relatively weak so that in the scattering process the internal structure of the target nucleus is not significantly disturbed. Using electrons as projectile, we can study how transition matrix elements vary with q2 and map out the Fourier transforms of the transition charge and current densities called Form Factors or Structure factors. In the high energy electron scattering we can know the details of the spatial distribution of transition charge and current density. In this paper we have formulated CFF for 5He nucleus

Floquet-state cooling

We demonstrate that a periodically driven quantum system can adopt a quasistationary state which is effectively much colder than a thermal reservoir it is coupled to, in the sense that certain Floquet states of the driven-dissipative system can carry much higher population than the ground state of the corresponding undriven system in thermal equilibrium. This is made possible by a rich Fourier spectrum of the system’s Floquet transition matrix elements, the components of which are addressed individually by a suitably peaked reservoir density of states. The effect is expected to be important for driven solid-state systems interacting with a phonon bath predominantly at well-defined frequencies.

Neutron quadrupole transition strength in C10 deduced from the C10(α,α′) measurement with the MAIKo active target

Elastic and inelastic alpha scatterings on $^{10}$C were measured using a 68-MeV/u radioactive $^{10}$C beam incident on the recently developed MAIKo active target system. The phenomenological effective $\alpha$-$N$ interaction and the point-nucleon density distribution in the ground state were determined from the elastic scattering data. The cross sections of the inelastic alpha scattering were calculated using this interaction and density distribution and were compared with the experiment to determine the neutron quadrupole transition matrix element $M_{n}$ between the ground state and the $2_{1}^{+}$ state at $E_{x} = 3.35$ MeV in $^{10}$C. The deduced neutron transition matrix element is $M_{n} = 6.9\, \pm0.7\, \mathrm{(fit)}\, \pm1.2\, \mathrm{(sys)}$ fm$^{2}$. The ratio of the neutron transition strength to proton transition strength was determined as $M_{n}/M_{p} = 1.05\, \pm0.11\, \mathrm{(fit)}\, \pm0.17\, \mathrm{(sys)}$, which indicates that the quadrupole transition between the ground state and the $2_{1}^{+}$ state in $^{10}$C is less neutron dominant compared to that in $^{16}$C.

Spherical topological insulator nanoparticles: Quantum size effects and optical transitions

We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers $j$ and $m=-j, -j+1, \dots, j$ for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires $j$ to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues $(-1)^{j\mp 1/2}$. The existence of energy eigenstates having the same $j$ but opposite parity enables optical transitions where $j$ is conserved, in addition to those adhering to the familiar selection rule where $j$ changes by $\pm 1$. All optical transitions satisfy the usual selection rule $\Delta m = 0, \pm 1$. We treat intra- and inter-band optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependences of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multi-band models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

Effect of Size on the Electronic Structure and Optical Properties of Cubic CsPbBr3 Quantum Dots

The size effect on the electronic structure and optical properties of cubic CsPbBr3 perovskite quantum dots is investigated by using an 8-band ${k}\cdot{p} $ model based on effective-mass envelope function theory with exciton binding energy consideration. Quantum dots with smaller size have larger bandgaps due to quantum confinement. The transition matrix element (TME) is also influenced by the size. The optical gain of such material is calculated by considering TME, Fermi factor, injected carrier density, quantum dot size, and dephasing rate. Higher density of injected carrier is needed for smaller quantum dot to get a positive optical gain. The peak of optical gain has a blue shift as the size of quantum dot decreases. When the carrier density increases for a quantum dot with certain size, a blue shift in emission peak position can be observed due to band filling effect. Smaller quantum dots have higher differential optical gain at carrier densities within certain range.

Nuclear transition matrix elements for neutrinoless double-β decay of 76Ge isotope within PHFB approach

Employing projected–Hartree–Fock–Bogoliubov (PHFB) model, nuclear transition matrix elements (NTMEs) [Formula: see text] for the neutrinoless double-[Formula: see text] decay of [Formula: see text]Ge isotope are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons. By considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interactions, it is noticed that the effect due to SRC on NTMEs [Formula: see text] and [Formula: see text] involving the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. Presently, the model-dependent uncertainties in the average NTMEs [Formula: see text] and [Formula: see text] turn out to be about 10% and 37%, respectively.

Photon-Drag Effect in p-Type Tellurium

The paper suggests spectral and temperature dependences of the light absorption coefficient and photon-drag effect in p-type tellurium exposed to linear polarized light. The photon momentum is considered both in the law of conservation of energy and the matrix element of optical transition between subbands of tellurium valence band. Photoelectric current is measured as time approximation of the hole momentum relaxation.

Deep minima and vortices for positronium formation in low-energy positron-hydrogen collisions

Using the two-channel Kohn and inverse Kohn variational methods, we investigate ground-state positronium (Ps) formation in positron-hydrogen collisions in the Ore gap. We find two zeros in the Ps-formation scattering amplitude fPs and corresponding deep minima in the Ps-formation differential cross section (DCS), and we determine their positions accurately. Due to azimuthal symmetry, each zero in fPs is part of separate circular rings of zeros for an azimuthal angle range of zero to 2π. We study the velocity field associated with fPs in which we treat the magnitude of the momentum of the incident positron and the angle of the outgoing positronium as variables, and we refer to this velocity field as the extended velocity field. We show that it has two vortices that are connected with the zeros in fPs, and that it rotates in opposite directions around the two zeros in fPs. Previously, vortices in the velocity field associated with the transition matrix element have provided an explanation for deep minima in DCSs for direct ionization. With the introduction of the extended velocity field, our work shows that vortices can occur also for charge exchange.