Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?

The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin-$\frac12$ Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like

A Self-Consistent Model for Positronium Formation from Helium Atoms

The differential and total cross sections for electron capture by positrons from helium atoms are calculated using a first-order distorted wave theory satisfying the Coulomb boundary conditions. In this formalism a parametric potential is used to describe the electron screening in a consistent and realistic manner. The present procedure is self consistent because (i) it satisfies the correct boundary conditions and post-prior symmetry, and (ii) the potential and the electron binding energies appearing in the transition amplitude are consistent with the wave functions describing the collision system. The results are compared with the other theories and with the available experimental measurements. At the considered range of collision energies, the results agree reasonably well with recent experiments and theories. [Note: This paper will be published on volume 42 of the Brazilian Journal of Physics

Theoretical study of the recoil-ion momentum distribution for single-electron capture in fast

The first-order Coulomb–Born  approximation with the correct boundary conditions is used to investigate the recoil-ion momentum distribution of single-electron capture in fast collision of the fully stripped ions with the ground-state helium-like atoms. To this end, both the frozen core three-body (3B) and the active electron four-body (4B) versions of the theory are developed to calculate the post and prior transition amplitudes. The calculations are performed for the energetic collision of fully stripped boron ions with helium atoms as an example, and the obtained results are compared to the experimental data as well as the results of the other theories. The comparison shows that the 3B theory provides a reasonable description of the recoil-ion momentum distribution in shape but not in magnitude. However, there is a considerable difference between the results obtained from the prior and post forms of this formulation. Also, although the 4B model is closer to the reality of the problem, its results deviate significantly from the measurements, both in magnitude and shape

Molecular three-body Brauner-Briggs-Klar theory for ion-impact ionization of molecules

Molecular three-body Brauner-Briggs-Klar (M3BBK) theory is developed to study the single ionization of diatomic molecules by ion impact. The orientation-averaged molecular orbital (OAMO) approximation is used to reduce the required computer time without sacrificing the performance of the method. The post-collision interaction (PCI) between the scattered projectile and the ejected electron is included. The theory is applied to collision of protons with hydrogen molecules. Results are obtained for two different kinematical regimes: i) fast collisions and low emission energies, and ii) not so fast collisions and higher emission energies. For both considered regimes, experimental fully differential cross-sections as well as different theoretical calculations are available for comparison. These comparisons are carried out and discussed

A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials

A method is presented to reduce the singular Lippmann-Schwinger integral equation to a simple matrix equation. This method is applied to calculate the matrix elements of the reaction and transition operators, respectively, on the real axis and on the complex plane. The phase shifts and the differential scattering amplitudes are computable as well as the differential cross sections if the R- and/or T-matrix elements on the energy-shell are known. The method is applicable by using the Gaussian quadratures based on the Legenre, Laguer Chebyshev and shifted Chebyshev polynomials. Choosing the nodal points and weight functions depends on the aspects of the problem

Three-body dynamical interference in electron and positron collision with positronium atom

In this project, the Faddeev-Watson-Lovelace (FWL) formalism is generalized to large scattering angles. The angular range includes 0-180 degrees. Using this method, the charge transfer differential cross-sections are calculated, in a second-order approximation, for collision of energetic positrons and electrons with neutral positronium atoms. In this approximation, the rearrangement amplitude contains two first-order and three second-order partial amplitudes. The first first-order term is the Born amplitude in a first-order approximation. The second one corresponds to capturing the transferred particle without perturbing the state of this particle. This term, in fact, describes a knock-on process. Since the masses of the particles and the absolute values of their charges are equal, one expects that the second-order terms be similar in magnitude. This aspect causes the instructive interference of the partial amplitudes in some angles and destructive interference in some others. However, it is predicted that these amplitudes have local maxima in direction of the recoiling of the projectile. In order to investigate this situation, the second-order partial amplitudes are calculated and their relations with the parity of the initial and final states of the scattering system are analyzed. In particular, the role of dynamical interference of these partial amplitudes in creation of the kinematical peak and the peak corresponding to the knock-on scattering in angular distribution of the differential cross sections is investigated