Analytic continuation of scattering data to the region of negative energies for systems that have one and two bound states

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The α+d and α+¹²C systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles—one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Padéapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.     

Temperature dependence of bound state spectra in field theory

We analyze the behaviour of kinks and semiclassical bound states at finite temperatures by applying quantum statistics to the fluctuations which determine the quantum dynamics of these states. We consider two theories in one space dimension — the ?⁴ theory with a dynamical symmetry breaking and the Gross-Neveu model. For the ?⁴ theory, the one-loop temperature corrections are obtained by using temperature-dependent Green function techniques. We show that the same result can be obtained by applying quantum statistics to the fluctuations around the kink. For the Gross-Neveu model, the temperature dependence of the bound states, which correspond to time-independent field configurations, is obtained. We show that for every bound state there exists a critical temperature at which this state breaks up into its constituents. This critical temperature increases with the number of constituents of the bound state.     

Microscopic multi-channel calculations for the10Li system

A microscopic multichannel calculation for the¹⁰Li system has been performed in the framework of the Refined Resonating Group Method. Elastic neutron scattering off the⁹Li ground state and transitions into four excited states were considered. The energy spectrum of¹⁰Li is deduced from a phase shift analysis. Besides theJ ^π = 1⁺ ground state, five excited states are identified.     

Coexistence of confinement and propagating waves: a quantum paradox

The example of a multi-channel system which possesses both bound (not quasi-bound!) and scattering states at the same energy value E is demonstrated. As another multi-channel peculiarity having no one-channel analogues we found a class of absolutely transparent interaction matrices without bound states.     

NN̄ bound states and resonances near threshold from ππ, πN,NN interactions

The long and medium range NN? potential is deduced by G parity transformation from a new NN theoretical potential which was in turn derived from πN and ππ interactions. Assuming very simple forms for the short range part, we examine the ability of this potential to explain the NN? bound states and resonance at energies near threshold.     

Branch-point singularities of multichannel eigenamplitudes and protonium spectrum

The relation between the branch-point singularities of multichannel eigenamplitudes and the stability of the bound-state spectrum is examined. The important conclusion is that the spectrum is unstable in the neighborhood of the cross-over points. The formalism is applied to the S-wave $\text{p}$p-atom bound states.     

General solution of relativistic one-channel inverse scattering problem

We find explicitly in the p-representation the kernels of the logarithms of unitary operators transforming the free Hamiltonian into the general solution of the one-channel inverse scattering problem, when bound states are absent. Then we construct the transformation of the Hamiltonian adding to its spectrum the given set of bound states without changing the scattering operator. Other generators of the Poincaré group are constructed in a similar way. The proof of some relevant limits is given.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.     

On the existence of bound states of N-particle systems in one and two dimensions

We give sufficient conditions for the existence, in one and two dimensions, of bound states of a system of N-particles interacting via two-body potentials.     

Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45^○ to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg–Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.     

Stability of the 2 + 2 Fermionic System with Point Interactions

We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m₂ ≈? 0.58 such that the system is stable, i.e., the energy is bounded from below, for \(m \in [m_{2}, m_{2}^{-1}]\). So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.     

Transport through a quantum dot coupled to two Majorana bound states

We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays 4π periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD–Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.     

Valence band contributions to photoluminescence excitation spectra of tightly bound holes in zincblende semiconductors

Photoluminescence excitation (PLE) spectra of deep acceptor states in ZnSe, for example the Cu-related luminescence band at ≈1.95 eV, contain a prominent excitation band at ≈3.25 eV. This band lies above the structure marking the lowest direct E_O band gap E_g by the spin-orbit splitting energy Δ of the valence bands at Γ. The higher energy feature is either absent or greatly de-emphasised in the PLE spectra of shallow acceptor states in ZnSe and of the oxygen iso-electronic trap in ZnTe, where the electron rather than the hole is tightly bound. However, a significant PLE component at E_g + Δ is observed for deep acceptor-like states in ZnTe, where Δ is ≈0.95 eV. Efficient PLE at E + Δ for luminescence from deep acceptor-like states is shown to be consistent with the extended wave-vector contributions to the bound state wave-functions of holes of binding energies ≈Δ.     

Étude des états excités du noyau 34Cl: (I). Courbe d'excitation de la réaction 33S(p, γ)34Cl, énergies,rapports d'embranchement et vies moyennes des niveaux du 34Cl

Resonance energies and strengths are reported for forty-five ³³S(p, γ)³⁴Cl resonances in the range E_p = 1.0–2.0 MeV. Analysis of the γ-ray spectra by means of two Ge(Li) detectors leads to precise excitation energies of bound states and branching ratios of resonant levels and bound states. New bound levels are found. The reaction Q-value is 5140.3 ± 1.5 keV. Mean lives (or limits) of twelve bound states of ³⁴Cl have been obtained from DSA measurements at seven of the studied ³³S(p, γ)³⁴Cl resonances.     

Optimization studies of the CERN-ISOLDE neutron converter and fission target system

Pion- and photo-induced inelastic reactions off protons are studied in a multichannel partial-wave analysis. Properties of nucleon and ?? resonances are derived and compared to previous analyses. Amplitudes are shown for transitions to N??, ??K, and ??K final states.     

Distinguishing Quantum States with Holevo Bound and Its Application to Spatially Separated Bell States

Consider a system prepared in one of the quantum states of the ensemble {ρ _i } with a priori probability p _i . We prove that the quantum state can be deterministically distinguished if and only if the information gain from the measurement reaches the Holevo bound. We find it can be applied to distinguish spatially separated Bell states. A single copy of spatially separated Bell state cannot be distinguished under local operation and classical communication (LOCC), but it can be identified with an ancillary qubit. When two ancillary qubits are used, a spatially separated Bell state can be identified without demolition.     

Binding in velocity dependent potentials and pion-nuclear systems

Properties of bound states in velocity-dependent potentials are discussed and the WKB approximation is established and used to derive quantization conditions for such states. The most updated zero-range optical potential for pionic atoms is reviewed and employed for the calculation of strongly bound π^? nuclear states. Some of the several physical mechanisms, in particular the πN finite interaction range, which affect the whole issue of binding and critically determine the number of bound states expected, are qualitatively discussed. Unless dynamical suppression of π^? nuclear absorption occurs below threshold, the calculated states are too wide to be considered as well-defined physical states.     

Atomic band structure effects on resonant scattering of atoms from solid surfaces

Bound state resonances related to the band structure of adsorbed atoms and their usefulness for determining the periodic components of atom-solid interaction potential are theoretically investigated. A variety of specular intensity patterns associated with bound state resonances near the Brillouin zone boundaries are exhibited. The (10) and (11̄) bound state resonances give rise to two split specular minima with the splitting depending essentially on v₁₀ for a fixed beam energy; however, the detailed features are dependent on other periodic components. For incidence along a crystal symmetry direction, symmetrization of basis states not only makes numerical computation very efficient, but also implies that there is only one specular minimum for a pair of bound states which are equivalent by symmetry. The (01) and (10) resonances along and near the x = y direction are presented to illustrate the symmetrization principle. The depth of one of the specular minima decreases and finally vanishes as the symmetry direction is approached. The single specular minimum corresponds to a resonance with the bound state which is a symmetric linear combination of (01) and (10) states in a potential well of v₀ + V₁₁. As expected, the shift in positions of specular minima caused by the periodic surface potential increases with decreasing beam energy.     

Sufficient conditions for the existence of bound states in a potential without spherical symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.