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Continuum spectrum of atomic lithium in a magnetic field of white dwarfs

ABSTRACT This paper reports on computational results of continuum spectra of atomic lithium in white-dwarf-strength magnetic fields. The adiabatic-basis-expansion method with R-matrix propagation has been used to study photoionization of magnetized alkali metal atoms. The R-matrix propagation technique and the two-dimensional matching scheme were utilized to obtain wavefunctions of the continuum states. Cross-sections of photoionization are calculated for lithium atoms in magnetic fields. Continuum spectra for its various bound-free transitions in magnetic white dwarf stars are presented as a function of field strengths ranging from 11.75 to 117.50 MG. Comparison is made between continuum spectra of diamagnetic hydrogen and lithium atoms. The comparison shows good agreement or remarkable difference for final continuum states with different symmetries in the photoionization processes concerned. A detailed analysis has been performed to understand the obtained results. The good agreement displayed manifests the reliability of the extended adiabatic-basis-expansion method. This method is suited to produce a large number of photoionization cross-section data for alkali metal atoms in a strong magnetic field, and therefore can serve as a tool to simulate continuum spectra observed in the atmospheres of magnetic white dwarfs with alkali metal atoms.

Wave functions consistent with experimental x-ray diffraction data: A hircocervus becomes reality

Since the early days of quantum physics, the possibility of obtaining wave functions consistent with experimental x-ray diffraction data has been envisioned. The idea is firmly grounded in the postulates of quantum mechanics and finds full support in the Hohenberg and Kohn theorem and Levy–Lieb search formulation of density functional theory. Within this framework, a rich history of research has unfolded over the years, introducing various strategies to obtain plausible one-electron reduced density matrices or wave functions that are compatible with x-ray structure factors. Approximately twenty-five years ago, all of this culminated with the development of the x-ray restrained wave function (XRW) approach. This method aims to determine wave functions that minimize the electronic energy of the examined systems while maximizing the statistical agreement between experimental and calculated x-ray diffraction data. Presently, the XRW technique stands as a well-established strategy, manifesting in various forms, and addressing numerous problems and challenges across chemistry, physics, and materials science. Moreover, there remains large room for improvement and extensions in the coming years. This paper will comprehensively review the current state of the x-ray restrained wave function approach, discussing its underlying foundations, historical background, theoretical details and extensions, practical applications, and forthcoming perspectives.

Role of electromagnetic interactions in the X(3872) and its analogs

We investigate the role of the electromagnetic interaction in the formation and decay of the X(3872). The binding properties of the X(3872) are studied by assuming the molecular nature and considering the S−D wave mixing, isospin breaking, and coupled channel effects, and in particular the correction from the electromagnetic interaction. The radiative decays can better reflect the difference between the charged and neutral DD¯* components, since the electromagnetic interaction explicitly breaks the isospin symmetry. We further study the radiative decay widths with the obtained wave functions for different DD¯* channels. We also explore other similar hidden-charm molecular states. The electromagnetic interaction can make the molecule tighter. Our result of the radiative decay width for X(3872)→γJ/ψ is in agreement with the experiment. The branching ratio Rγψ is less than 1 in our framework, which supports the Belle and BESIII measurements. Published by the American Physical Society 2024

Self-Consistent Study of GaAs/AlGaAs Quantum Wells with Modulated Doping

In this work, the characterization and analysis of the physics of a GaAs quantum well with AlGaAs barriers were carried out, according to an interior doped layer. An analysis of the probability density, the energy spectrum, and the electronic density was performed using the self-consistent method to solve the Schrödinger, Poisson, and charge-neutrality equations. Based on the characterizations, the system response to geometric changes in the well width and to non-geometric changes, such as the position and with of the doped layer as well as the donor density, were reviewed. All second-order differential equations were solved using the finite difference method. Finally, with the obtained wave functions and energies, the optical absorption coefficient and the electromagnetically induced transparency between the first three confined states were calculated. The results showed the possibility of tuning the optical absorption coefficient and the electromagnetically induced transparency via changes to the system geometry and the doped-layer characteristics.

Coulson–Fischer Wave Function on Self-consistent Field and Perturbation Correction

We propose a computational method to obtain Coulson–Fischer (CF) wave functions using the conventional Gaussian-type orbital function as the basis sets and the self-consistent field method. Because the obtained wave functions are similar to unrestricted Hartree–Fock functions, the electron correlation energies can be estimated by the perturbation correction using our CF wave function. Comparing the corrected total energy with the result via the full configuration interaction confirms the usability of our method.

Inclusive electron scattering in the quasielastic region with the Korea-IBS-Daegu-SKKU density functional

With the framework of KIDS (Korea-IBS-Daegu-SKKU) density functional model, the isoscalar and isovector effective masses of nucleon and the effect of symmetry energy in nuclear medium are investigated in inclusive $(e,e')$ reaction in quasielastic region. The effective masses are varied in the range $(0.7 \sim 1.0)M$ with free nucleon mass $M$, and the symmetry energy is varied within the uncertainty allowed by nuclear data and neutron star observation. The wave functions of nucleons inside target nucleus are generated by solving Hartree-Fock equation with adjusting equation of state, binding energy and radius of various stable nuclei, and effective mass of nucleon in the KIDS model. With the obtained wave functions, we calculate the differential cross section for the inclusive $(e,e')$ reaction and compare the theoretical results with Bates, Saclay, and SLAC experimental data. Our model describes experimental data better at SLAC-type high incident electron energy than those measured from Bates and Saclay. The influence of the effective mass and symmetry energy appears to be precise on the longitudinal cross section.

Time-dependent Interactions in Tunnelling Dynamics

In this paper, the tunnelling of a particle through a potential barrier is investigated in the presence of a time-dependent perturbation. The latter is attributed to the process of the energy measurement of the scattered particle. The time-dependent Schrödinger equation of the model is exactly solved. The probability density inside the barrier is calculated from the obtained wave function, proving that the tunnelling dynamics is determined not only by the transmitted and reflected waves but also by their interference. Furthermore, the interference term is time-dependent and contribute to the scattering process duration. The tunnelling time is calculated as the time needed to get the probability density inside the barrier to zero. This is the minimum duration of the measurement process before detecting the particle beyond the barrier. Based on this, a new method of estimating the tunnelling time by energy experimental measuring is proposed.

Description of isospin mixing by a generator coordinate method

Background: Isospin mixing is an interesting feature of atomic nuclei that plays a crucial role in the astrophysical nuclear reactions. However, variational nuclear structure models cannot describe it in a straightforward manner.Purpose: We propose a tractable method to describe isospin mixing within the framework of a generator coordinate method and demonstrate its usability.Method: We generate basis wave functions by applying the Fermi transition operator to the wave functions of isobars. The superposition of these basis wave functions and variationally obtained wave functions quantitatively describes isospin mixing.Results: We apply our method to $^{14}\mathrm{N}$ and show that it reasonably describes both $T=0$ and 1 states and their mixing. The energy spectrum and $E1$ transition strengths are compared with the experimental data.Conclusion: The proposed method is effective in describing isospin mixing and is particularly useful for discussing of $\ensuremath{\alpha}$-capture reactions of $N=Z$ nuclei.

Mass spectra, wave functions and mixing effects of the (bcq) baryons

Mass spectra and wave functions of the J^P=frac{1}{2}^+ (bcq) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the 1^+ and 0^+ (bc)-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the 0^+ diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the (bc)-diquark. Considering the obtained diquark form factors, the (bcq) baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the 0^+ and 1^+ diquarks. The general wave function of the frac{1}{2}^+ (bcq) baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between Xi _{bc}(Omega _{bc}) and Xi _{bc}'(Omega '_{bc}) in ground states are computed and determined to be small (sim !1%). The numerical results indicate that it is a good choice to take Xi _{bc} and Xi '_{bc} as the baryon states with the inside (bc)-diquarks occupying the definite spin.

Frequency dependent conductivity and impedance of nano material chips using Schrodinger frictional equation and treating electrons as strings

Treating electrons and particles as strings is a useful energy expression accounting for the frictional energy has been obtained this dissipated energy depends on the momentum as well as the friction coefficient. This energy relation was used to find a new modified a Schrodinger equation. The equation was solved using Greens equation. The obtained wave function amplitude is dependent on conductivity as well as the frequency. This wave function was used to find electric current density. For an insulator this current density is frequency independent. The nano chip in this case acts as a resistor that can be increased by decreasing the density of free carriers and increasing the velocity. For a good conductor the nano chip acts as a nano capacitor.

Dielectronic recombination along high Rydberg states of Mg+ and Si11+ ions

In solving the multi-channel equation, I got the analytical expression of the multi-channel wave functions in terms of the solutions of the corresponding homogeneous equations. The homogeneous solutions are described in WKB Wenzel (1926 Z. Phys. 38 518) representation for both open and closed channels, and are calculated numerically using analogous means. By treating the open and closed channels equivalently in the calculation of the multi-channel wave functions, the generalized interaction matrix and generalized scattering matrix can be obtained for all the channels. With the obtained wave functions and generalized scattering matrix, the dielectronic recombination (DR) process can be calculated within the close-coupling framework by employing Bell and Seaton’s analytical deductions. In the method, high Rydberg states can easily be involved in numerical calculations. The method was applied to the calculations of DR of Mg+ and Si11+ ions along their high Rydberg states. The results are compared with those of the published experiments. Excellent agreements have been achieved, except at the extreme high Rydberg states for Si11+ ions, which is discussed in this paper.

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

We propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (St\"uckelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in $(1+1)$ dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schr\"odinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude ${E}_{0}$ and frequency $\mathrm{\ensuremath{\Omega}}$, with a period determined by the St\"uckelberg phase, (2) the cutoff order of HHG is determined by $2e{E}_{0}/\ensuremath{\hbar}{\mathrm{\ensuremath{\Omega}}}^{2}$, with $e$ being the electron charge, and that (3) noninteger harmonics, controlled by the St\"uckelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter $\ensuremath{\gamma}=(\mathrm{\ensuremath{\Delta}}/2)\mathrm{\ensuremath{\Omega}}/e{E}_{0}$, with $\mathrm{\ensuremath{\Delta}}$ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

Drastic change of inelastic scattering dependent on the development of dineutron correlations in Be10

We investigated the development and breaking of the dineutron correlation in $^{10}$Be by analyzing the elastic and inelastic scatterings with a framework combing the microscopic structure and reaction models. For studying the structure, the $^{10}$Be nucleus was constructed under the assumption of a four-body ($\alpha + \alpha + n + n$) cluster model. In this work, we focused on the change in the inner structure for the 0$_1^+$, 2$_1^+$, and 2$_2^+$ states when the strength of the spin-orbit interaction is varied. The inner structure, including various physical quantities such as energy, radius, and transition strength, is drastically influenced by the strength of the spin-orbit interaction. In particular, the development and breaking of the dineutron correlation is governed by the spin-orbit strength. The differences in the inner structure can be manifested by applying the obtained wave functions to elastic and inelastic scatterings with a proton target at $E/A =$ 59.4 and 200 MeV. Although the 0$_1^+$ and 2$_1^+$ states are significantly influenced by the spin-orbit strength of the nuclear structure calculation, the elastic and inelastic cross sections are not much affected. On the other hand, the inelastic cross section of the 2$_2^+$ state depends greatly on the spin-orbit strength of the structure calculation. Thus, we discovered a way to measure the degree of the development of dineutron cluster structure based on its sensitivity to the inelastic cross section of the 2$_2^+$ state of $^{10}$Be.

Generalized WKB theory for electron tunneling in gapped α−T3 lattices

We generalize Wentzel-Kramers-Brillouin (WKB) semi-classical equations for pseudospin-1 $\alpha-\mathcal{T}_3$ materials with arbitrary hopping parameter $0 < \alpha < 1$, which includes the dice lattice and graphene as two limiting cases. In conjunction with a series-expansion method in powers of Planck constant $\hbar$, we acquired and solved a system of recurrent differential equations for semi-classical electron wave functions in $\alpha-\mathcal{T}_3$. Making use of these obtained wave functions, we analyzed the physics-related mechanism and quantified the transmission of pseudospin-1 Dirac electrons across non-rectangular potential barriers in $\alpha-\mathcal{T}_3$ materials with both zero and finite band gaps. Our studies reveal several unique features, including the way in which the electron transmission depends on the energy gap, the slope of the potential barrier profile and the transverse momentum of incoming electrons. Specifically, we have found a strong dependence of the obtained transmission amplitude on the geometry-phase $\phi = \tan^{-1} \alpha$ of $\alpha-\mathcal{T}_3$ lattices. We believe our current findings can be applied to Dirac cone-based tunneling transistors in ultrafast analog RF devices, as well as to tunneling-current control by a potential barrier through a one-dimensional array of scatters.

Mass spectrum and strong decays of strangeonium in a constituent quark model * *Supported by the National Natural Science Foundation of China (U1832173, 11775078, 11705056, 11405053)

In this work we calculate the mass spectrum of strangeonium up to the multiplet within a nonrelativistic linear potential quark model. Furthermore, using the obtained wave functions, we also evaluate the strong decays of the strangeonium states with the model. Based on our successful explanations of the well established states , , , , and , we further discuss the possible assignments of strangeonium-like states from experiments by combining our theoretical results with observations. It is found that some resonances, such as and , listed by the Particle Data Group, and and , newly observed by BESIII, may be interpreted as strangeonium states. The possibility of as a candidate for or cannot be excluded. We expect our results to provide useful references for looking for the missing states in future experiments.

The time independent fractional Schrödinger equation with position-dependent mass

In this paper, we present a fractional form of Schrödinger equation using the Kallil’s derivative method. Then we investigate the capability of this equation to obtain the wave functions and its energy levels for a particle trapped in infinite potential well (IPW) for the range1<α≤2. We also, present the fractional form of the Schrödinger equation for a particle with position-dependent mass (PDM) and by using it, we obtain wave functions and its energy levels in range 0 <α≤1 and in different amounts of η and μ in which μ + η = 1/2. It seems that our method is very useful to solve the problems in PDM case.

Redundant poles of the S-matrix for the one-dimensional Morse potential

We analyze the structure of the scattering matrix, S(k), for the one-dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of antibound poles, there exist infinite redundant poles, on the positive imaginary axis, which do not correspond to either of the other types. We explain in detail the role of these redundant poles, in particular when they coincide with the bound poles. This can be solved analytically and exactly. In addition, we obtain wave functions for all these poles and ladder operators connecting them.

Ground state wave functions for single-band Hubbard models from the Gutzwiller conjugate gradient minimisation theory

The Gutzwiller conjugate gradient minimisation (GCGM) theory is an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. Previous applications of GCGM provides satisfying accuracy of ground-state energy of Hubbard models. In the current work, we address the problem of whether the obtained wave function is a good approximation for the true ground state by comparing the correlation functions with the benchmark data. Our results confirms the accuracy of the reproduced ground state of the regular Hubbard model, but with some exception for the frustrated Hubbard model.

Quantum information-entropic measures for exponential-type potential

The approximate solutions of the Schrödinger equation with the central generalized Hulthén and Yukawa potential are investigated within the framework of the functional method. The obtained wave function and the energy levels are used to study the Shannon entropy, Renyi entropy, Fisher information, Shannon Fisher complexity, Shannon power and Fisher-Shannon product in both position and momentum spaces for the ground and first excited states. The theoretic information theories such as Shannon entropies Sr,Sp, Fisher information Ip,Ip and Renyi entropies Rβ as well as the information entropy probability densities ρ(r),ϕ(p) are illustrated graphically. The Bialynicki-Birula – Mycielski (BBM) inequality for the Shannon entropies and the Cramer-Rao inequality for the Fisher information are satisfied for the potential model.

Selected strong decays of pentaquark State P_c(4312) in a chiral constituent quark model

The newly confirmed pentaquark state P_c(4312) has been treated as a weakly bound (Sigma _cbar{D}) state by a well-established chiral constituent quark model and by a dynamical calculation on quark degrees of freedom where the quark exchange effect is accounted for. The obtained mass 4308 MeV agrees with data. In this work, the selected strong decays of the P_c(4312) state are studied with the obtained wave function. It is shown that the width of the Lambda _cbar{D}^* decay is overwhelmed and the branching ratios of the p,eta _c and p,J/psi decays are both less than 1 percentage.