Properties Of Bound States Research Articles

On highly accurate, bound state calculations of the molecular diatomic ions

Results of highly accurate calculations obtained recently for a number of Coulomb two-centre ions with the unit electrical charges and are presented. In particular, we have determined (to very high accuracy) the total energies and other bound state properties of the ground (bound) states in the two-centre adiabatic (or molecular) H, D, HD, HT, T and DT ions. In these computations we used the new masses of hydrogen isotopes, which have been measured in recent high-energy experiments. Theory of soft adiabatic three-body systems with the unit electrical charges is also discussed. An accurate mass-interpolation formula is derived and tested for the total energies of model two-centre ions with very heavy masses of the point particles ( 100,000 ). This formula allows one to evaluate (to high accuracy) the total energies and other bound state properties of arbitrary two-centre ions, including very heavy systems. We also determine the upper mass limit for applicability of our universal expansion in the relative and/or perimetric coordinates. Highlights An effective procedure is developed for highly accurate numerical computations of bound states in the two-center molecular ions. Properties of many actual two-center ions, including the both and ions, have been determined to very high accuracy. Theory of the soft adiabatic (two-center) three-body systems is developed. Properties of these ions are now known to high accuracy. Accurate numerical method which allows one to predict the total energies and other properties of truly adiabatic systems with very large (or infinite) nuclear masses has been proposed, applied and studied in detail.

Ultrasensitive light confinement: Driven by multiple bound states in the continuum

We propose a unique framework to study the topological properties of an optical bound state in the continuum(BIC). We employ the interactions between proximity resonances undergoing avoided resonance crossing in a specialty optical microcavity. We utilize a continuous system parameter tuning to induce destructive interference between the resonances with cancelling leakage losses. Similar to the physical insight of Friedrich-Wingten type-BIC, we demonstrate the evolution of an ultra-high quality mode. We report the formation of a special-BIC line in the system parameter space connecting locations of multiple quasi-BICs. Aiming to develop a novel scheme to enhance the performance of optical sensing in microcavity, we study the sensitivity of transmission coefficients and quality factor to sense even ultra-small perturbations in the system configuration.

Yu-Shiba-Rusinov states of a single magnetic molecule in ans-wave superconductor

We use the numerical renormalization group theory to investigate the Yu-Shiba-Rusinov (YSR) bound state properties of single magnetic molecules placed in an s-wave superconducting substrate. The molecule consist of a large core spin and a single orbital, coupled via an exchange interaction. The critical Coulomb interaction for the singlet/doublet transition decreases in the presence of this exchange interaction for both ferro and anti-ferromagnetic couplings. The number of YSR states also increase to two pairs, however, in the singlet phase, one of the pairs have zero spectral weight. We explore the evolution of the in-gap states using the Anderson model. Away from the particle-hole symmetry point, the results suggest a doublet-singlet-doublet transition as the on-site energy is lowered while keeping the Coulomb interaction fixed. To understand these results, we write down an effective model for the molecule in the limit of large superconducting order parameter. Qualitatively, it explains the various phase transitions and spectral nature of the in-gap states. Finally, we analyze the effects of magnetic anisotropic fields of the core spin on in-gap states. Due to internal degrees of freedom of the spin excited states, a multitude of new states emerges within the gap. Depending on the sign and strength of the uniaxial anisotropic field, the results indicate up to three pairs of YSR states.

Theory of exciton-electron scattering in atomically thin semiconductors

The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with Quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for Quantum Monte-Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

Mass-dependencies of the bound state properties for three-body positronium-like exitonic complexes

Mass-dependencies of a number of bound state properties are investigated in some light two-electron exitonic complexes (or clusters) $Z^{+} e^{-} e^{-}$, where $m_e \le m_Z \le 2 m_e$. These exitonic complexes (or model ions) play a great role in modern solid state physics, since such complexes describe optical absorption in a number of semiconductors. We also derived and tested a number of accurate mass-interpolation formulas for these properties. In general, our mass-interpolation formulas allow one to predict (fast and accurately) numerical values of these bound state properties in the `new' exitonic complexes, i.e., in three-body exitonic complexes with new mass ratios.

Extremely imbalanced two-dimensional electron-hole-photon systems

We investigate the phases of two-dimensional electron-hole systems strongly coupled to a microcavity photon field in the limit of extreme charge imbalance. Using variational wave functions, we examine the competition between different electron-hole paired states for the specific cases of semiconducting III-V single quantum wells, electron-hole bilayers, and transition metal dichalcogenide monolayers embedded in a planar microcavity. We show how the Fermi sea of excess charges modifies both the electron-hole bound state (exciton) properties and the dielectric constant of the cavity active medium, which in turn affects the photon component of the many-body polariton ground state. On the one hand, long-range Coulomb interactions and Pauli blocking of the Fermi sea promote electron-hole pairing with finite center-of-mass momentum, corresponding to an excitonic roton minimum. On the other hand, the strong coupling to the ultra-low-mass cavity photon mode favors zero-momentum pairs. We discuss the prospect of observing different types of electron-hole pairing in the photon spectrum.

Elastic and vibrationally-resolved excitation cross sections for electron impact with MgF radical using R-matrix

We report the calculations of elastic and vibrationally- resolved electronic excitation cross sections by an electron impact on MgF radical by using the R-matrix approach in the 0.1–10 eV energy range. A systematic study considering various basis sets, polarisation and the Born closure technique is performed. For bench mark study, we have used the basis sets like 6-31G*, 6-311G*, DZP and cc-pVTZ to understand the bound state properties of MgF. The final target and hence the scattering calculations are reported using the cc-pVTZ basis set as it yielded the best ground state energy, dipole moment and the energy thresholds of the excited states. Various scattering models like Static Exchange (SE), Static-Exchange-Polarisation (SEP) and Close-Coupling (CC) models are invoked to investigate the role of correlation and polarisation effects on the cross sections. The trial wave function of the entire scattering system (MgF + electron) consists of the ground and many excited states. These target states are constructed by including correlation effects via configuration interaction (CI) approach. Other types of cross sections like differential, momentum transfer, ionisation and elastic rate constants are also reported.

Theoretical calculation of the [formula omitted] radiative capture reaction

We present a new calculation of the Li6(p,γ)7Be radiative capture astrophysical S-factor in a cluster model framework. We consider several intercluster potentials, adjusted to reproduce the Be7 bound state properties and the p−6Li elastic scattering phase shifts. Using these potentials, we calculate the astrophysical S-factor, obtaining a good agreement with available data, and the photon angular distribution. Finally, we discuss the consequences of a hypothetical resonance-like structure on the S-factor.

Bound state properties from the functional renormalization group

We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two atoms confined by a wave guide in the presence of spin-orbit coupling terms within a K-matrix scattering framework. The tunability of resonances, induced by the interplay of the external wave guide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the K-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective low- energy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Scientific Reports 4, 1 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energy- dependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.

Calculating hadron properties from dynamical hadronization in the Functional Renormalisation Group

We report on a functional renormalisation group approach to bound state properties similar to the Dyson-Schwinger–Bethe-Salpether approach. The current approach is set-up for the two-flavour quark-meson model for an illustration of the basic properties. This allows us to access the pion and sigma poles and decay properties. First numerical results are presented and evaluated. We also discuss the next steps.

Extrapolation of scattering data to the negative-energy region

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

Bound state properties of ABC-stacked trilayer graphene quantum dots

The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts (Song et al 2016 Nano Lett. 16 6245), we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a potential exhibits a transition from one group of Landau levels to another group, which can be understood analytically through perturbation theory. Our results provide insight into the transport property of TLG QDs, with possible applications to study of spin qubits and valleytronics in TLG QDs.

Observation of interspecies Feshbach resonances in an ultracold K39−Cs133 mixture and refinement of interaction potentials

We observe interspecies Feshbach resonances due to s-wave bound states in ultracold $^{39}$K-$^{133}$Cs scattering for three different spin mixtures. The resonances are observed as joint atom loss and heating of the K sample. We perform least-squares fits to obtain improved K-Cs interaction potentials that reproduce the observed resonances, and carry out coupled-channel calculations to characterize the scattering and bound-state properties for $^{39}$K-Cs, $^{40}$K-Cs and $^{41}$K-Cs. Our results open up the possibilities of tuning interactions in K-Cs atomic mixtures and of producing ultracold KCs molecules.

Three-Nucleon Bound States and the Wigner-SU(4) Limit

We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory (EFT) that is an expansion in powers of $R/a$, with $R$ the range of the nuclear force and $a$ the nucleon-nucleon ($N\!N$) scattering lengths. In the Wigner-SU(4) limit, the triton and Helium-3 point charge radii are equal. At NLO in the range expansion both are $1.66$ fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the $N\!N$ scattering lengths gives a ${}^3\mathrm{H}$ point charge radius of $1.58$ fm, which is remarkably close to the experimental number, $1.5978\pm0.040$ fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ${}^3\mathrm{He}$ point charge radius we find $1.70$ fm, about 4% away from the experimental value of $1.77527\pm0.0054$ fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties.

Accurate computations of bound state properties in three- and four-electron atomic systems in the basis of multi-dimensional gaussoids

Results of accurate computations of bound states in three- and four-electron atomic systems are discussed. Bound state properties of the four-electron lithium ion Li $$^{-}$$ in its ground $$2^{2}S$$ -state are determined from the results of accurate, variational computations. We also consider a closely related problem of accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.

A model study on a pair of trapped particles interacting with an arbitrary effective range

We study the effects of the effective range of interaction on the eigenvalues and eigenstates of two particles confined in a three-dimensional (3D) isotropic as well as one- or quasi-one dimensional harmonic (1D) traps. For this we employ model potentials which mimic finite-range s-wave interactions over a wide range of s-wave scattering length as including the unitarity limits . Our results show that when the range is larger than the 3D or 1D harmonic oscillator length scale, the eigenvalues and eigenstates are nearly similar to those of noninteracting two particles in the 3D or 1D trap, respectively. In case of 3D, we find that when the range goes to zero, the results of contact potential as derived by Busch et al (1998 Foundations of Physics 28 549) are reproduced. However, in the case of 1D, such reproducibility does not occur as the range goes to zero. We have calculated the eigenvalues and eigenstates in a 1D harmonic trap taking one dimensional finite-range model potential. We have also calculated the bound state properties of two particles confined in a highly anisotropic quasi-1D trap taking three-dimensional finite-range model potential, and examined whether these quasi-1D results approach towards 1D ones as the aspect ratio η of the radial to axial frequency of the trap increases. We find that if the range is very small compared to the axial size of the trap, then one can reach 1D regime for . However, for a large range, one can almost get 1D results for smaller values of η. This study will be important for the exploration of two-body or many body physics of trapped ultracold atoms interacting with narrow Feshbach resonance for which the effective range can be large.

Nonrelativistic lattice study of stoponium

We calculate the bound state properties of stoponium using lattice formulation of nonrelativistic effective field theory for stop which is moving nonrelativistically in the rest frame of stoponium. Our calculation method is similar to that employed in lattice nonrelativistic quantum chromodynamics (NRQCD) studies for charmonium and bottominum. Using $16^3 \times 256$ quenched lattice gauge field configurations at $a^{-1} = 50(1) {\rm GeV}$, we obtain the stopoinium mass and the lattice matrix element which is related to the wavefunction at the origin for the $1S$ state and find that the lattice $|R_{1S} (0)|^2/M_{1S}^3$ is $3.5 \sim 4$ larger than that from a potential model calculation for $200 {\rm GeV} \le M_{1S} \le 800 {\rm GeV}$.

CalculableR-matrix method for the Dirac equation

An efficient version of the calculable R-matrix method, a technique for determination of scattering and bound-state properties, is extended to the Dirac equation. The configuration space is divided into internal and external regions at the channel radius. In both regions, the introduction of a Bloch operator allows restoration of the Hermiticity. The most general Bloch operator contains three free parameters. With a basis without constraint at the channel radius in the internal region, the phase shifts converge to the same value for any choice of these parameters. Nevertheless, some choices provide a faster convergence than others. Determination of the bound-state energies is performed with an extension of the method using a second set of basis functions in the external region. Neither the knowledge of asymptotic expressions nor a large channel radius is required. These R-matrix methods are particularly simple and very accurate when combined with the Lagrange-mesh method. No analytical or numerical evaluation of matrix elements is then necessary. Very accurate phase shifts are obtained with a Legendre mesh for various short-range potentials. A combination of Legendre and Laguerre meshes provides accurate energies for the bound states even for potentials with a Coulomb-like asymptotic behavior.

On the Q-dependence of the lowest-order QED corrections and other properties of the ground 11S-states in the two-electron ions

Formulas and expectation values which are need to determine the lowest-order QED corrections (∼α3) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the quasi-singular Vinti operator and 〈reN−2〉 and 〈ree−2〉 expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived for the bound state properties of the two-electron ions as the function of the nuclear electric charge Q.