Model three-body problem in the molecular mass limit

The bound states of a three-body molecule composed of two identical heavy nuclei and a light “electron” interacting through short-range s-wave potentials are studied. The spectrum of three-body bound states grows as the mass ratio m between the heavy and light particles increases, and presents a remarkable vibration rotation structure that can be fitted with the usual empirical energy formulas of molecular spectroscopy. The results of the exact three-body calculation for the binding energy and bound-state wavefunction are compared with the predictions of the Born-Oppenheimer method for the same system. We find that for m > 30, the Born-Oppenheimer approximation yields very good results for both the binding energies and wavefunctions. For smaller m (1 <m < 30) the Born-Oppenheimer results are still surprisingly good and this is shown to be related to the range of the two-body interactions.     

A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior

Three-body systems with two-body point interactions are studied. These systems are the universal low energy limits of three-body problems with short-range two-body forces. Hence if there are infinitely many spherically symmetric three-body bound states with energies E_n then lim_n→∞E_n/E_n+1 = e^2λσ, where σ is explicitly computed.     

Approximate Treatment of 3-Body Coulomb Systems: Discrete Spectrum

We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite-rank approximation is used for Coulomb potential in the Lippman?CSchwinger equation, that results in a system of one-dimensional coupled integral equations. Preliminary numerical results for three-body atomic and molecular systems like H ^?, He, pp?? and other are presented.     

Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems

A new method for discretizing a three-body continuum with the aid of the L ₂ basis of stationary wave packets is considered within the problem of three-body scattering. Substantial advantages of employing this basis in solving problems of few-body scattering are demonstrated. Specific applications of this approach are exemplified by exploring the problem of scattering of a composite particle on a heavy nucleus with allowance for the excitation of this particle to continuum states. This is done within two alternative approaches: a direct wave-packet discretization of a three-body continuum and a method that is based on the Feshbach projection formalism. It is shown explicitly that the resulting scattering amplitudes are convergent as the number of wave-packet states that are taken into account is increased. The results obtained here are compared with the results of other authors whose treatment was based on alternative methods for discretizing a continuum.     

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ ₁ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m ₂ ~ t ^α , α< 1, on length scales beyond ξ ₁. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.     

Alternative treatment of the three-body problem

For solving the three-body problem with local potentials a model HamiltonianH ₀ containing an interaction between one particle and the centre-of-mass of the other two interacting particles is introduced. The total HamiltonianH is obtained byH=H _o +W whereW is a “residual interaction” in close analogy to the nuclear shell model. At a certain stage of the calculationsH ₀ has to be replaced by a new model Hamiltonian \(\tilde H_0 \) containing plane waves. The resolvent (and thereby theT-matrix) of the three-body problem is calculated by operator techniques. It is possible to draw some conclusions concerning three-body properties from these general expressions. Therefore this attempt may be considered as a supplementary treatment, in addition to the Faddeev-equations, of the three-body problem: it exhibits the discrete spectrum, the simple and the twofold continuum ofH arising from the corresponding states ofH ₀, and provides some approximation methods.     

The first order of the hyperspherical harmonic expansion method

The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the L_m-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the L_m-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the L_m-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus.     

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.     

Measurement of the kaon mass difference mL-mS by the two regenerator method

The K⁰ mass difference has been measured by the two regenerator method. The result is: Δm = m_KL ? m_KS = (0. 534 ± 0.003) × 10¹⁰ sec^?1.     

Mixing angles,mass matrix and CP violation in the Kobayashi-Maskawa model

We analyze the K_L ? K_S mass difference Δm and CP-violating parameters η_+? and η₀₀ in terms of the mixing angles of the six-quark Kobayashi-Maskawa model. In contrast to previous analyses, we include a parameter to allow for uncalculable contributions of low-mass intermediate states to the mass matrix. As a result, Δm provides only weak constraints on the mixing angles but stronger constraints may possibly be obtained using data on η₀₀.     

Zur formelmäßigen Darstellung des Ionisierungsquerschnitts für den Atom-Atomstoß und über die Ionen-Elektronen-Rekombination im dichten Neutralgas

Thomson's classical theory for the calculation of ionisation cross sections in electron-atom encounters is applied for calculating the ionisation cross section for atom-atom collisions. A very simple formula is obtained permitting a rapid calculation of the total ionisation cross sections as a function of the kinetic energyE _a and the massm _A of the ionizing atom, and of the binding energyE _i and the number ξ_i of equivalent electrons in the electronic shell to be ionized. The formula is in good agreement with quantum mechanical calculations and with experimental results. It can be applied to ionization from ground and from excited states. From this formula one obtains an expression for the rate coefficient for ionization in the center-of-mass system of the colliding particles. Then, the method of detailed balancing is applied to calculate the rate coefficient for ion-electron three-body collisional recombination with a neutral atom acting as the third body. This latter formula is applicable to recombination into the ground and into excited states.     

QED based two-body Dirac equation

A two-body Dirac equation is derived from quantum electrodynamics by consideration of crossed and uncrossed photon exchange. The equation is symmetric in the particle labels, and it reduces to the one-body Dirac equation when either particle's mass becomes infinite. The condition that negative-energy states must propagate backward in time is incorporated. Virtual pair contributions are taken into account to leading order in m⁻¹ in a consistent and nonperturbative manner such that continuum dissolution cannot occur. A straightforward extension provides three-body and N-body equations.     

Structure and dynamics of few-helium clusters using soft-core potentials

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r ₀ of the He-He potential (r ₀/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.     

Effect of interband scattering on kinetic coefficients and estimates of the parameters of the band spectrum of Sb2Te3

It has been shown that uncertainties in the interpretation of experimental data on transport phenomena in Sb₂Te₃ are resolved in the two-band model with the consistent inclusion of the interband hole scattering. The performed calculation is in quantitative agreement with the experimental data in the temperature range from 77 to 400 K for the following parameters of the band spectrum: the effective mass of the density of states of light holes m _d1 ≈ 0.6m ₀ (where m ₀ is the free electron mass), the effective mass of the density of states of heavy holes m _d2 ≈ 1.8m ₀, and the energy gap between nonequivalent extrema of the valence band ΔE _v(T) ≈ 0.15–2.5 × 10^?4 T eV.