Two-body Relativistic Equation Research Articles

Relativistic fine structure of the [formula omitted] ion [formula omitted]-levels

Motivated by the recent experimental measures of the 2p-states fine splitting of the muonic He4 ion (Krauth et al., 2021), we think it may be of interest to present an independent calculation in terms of the two-body relativistic equation for a scalar and a fermion developed in Giachetti and Sorace (2021, 2019) for mesic atoms. This work can thus be considered an addendum to these last papers in a different range for the masses of the two components. It gives theoretical results in good agreement with the recent experimental measures.

A NEW TWO-BODY RELATIVISTIC POTENTIAL MODEL FOR PIONIC HYDROGEN

The new potential model for pionic hydrogen, constructed with the employment of the two-body relativistic equation, is offered. The relativistic equation, based on the extension of the SL(2, C) group to the Sp(4, C) one, describes the effect of the proton spin and anomalous magnetic moment in accordance with the results of the quantum electrodynamics. Within this approach, using the experimental data on the strong energy level shift and width of the 1s state in pionic hydrogen as input, the pion–nucleon scattering lengths have been evaluated to be [Formula: see text] and [Formula: see text]

Numerical solution of two-body relativistic equations for the bound-state problem with confining and Coulomb potentials

Recent investigations of the meson spectroscopy often have been based on models considering mesons as quark–antiquark bound states. These models are described by three-dimensional relativistic equations with various generalizations of Coulomb and confining potentials in momentum space. Algorithms and codes are developed for numerical investigations of these equations. The modified Generalized Continuous analogue of the Newton method is used. The numerical results demonstrate the efficiency of the created software. The code allows obtaining a numerical solution with a required accuracy. The numerical results are compared with the same results obtained by other authors.

Binding energy of doubleΛhypernuclei in relativistic mean field theory

We calculate the binding energy of two $\Lambda$ hyperons bound to a nuclear core within the relativistic mean field theory. The starting point is a two-body relativistic equation of the Breit type suggested by the RMFT, and corrected for the two-particle interaction. We evaluate the 2 $\Lambda$ correlation energy and estimate the contribution of the $\sigma^*$ and $\Phi$ mesons, acting solely between hyperons, to the bond energy $\Delta{B_{\Lambda\Lambda}}$ of $^6_{\Lambda\Lambda}He$, $^{10}_{\Lambda\Lambda}Be$ and $^{13}_{\Lambda\Lambda}B$. Predictions of the $\Delta{B_{\Lambda\Lambda}}$ A dependence are made for heavier $\Lambda$-hypernuclei.

Proportionally off-mass-shell equation for unequal mass systems

A new two-body relativistic equation is presented. The major advantage of the proposed equation over existing equations in the literature is that this equation automatically adjusts itself for different mass systems. Besides unitarity and covariance, this equation gives a physically meaningful prescription of how the particles go off-mass-shell in the intermediate states. It allows the particles to go off-mass-shell proportionally to their masses so that when one of the masses becomes infinite, it automatically becomes a one-body equation for the lighter particle and for equal mass systems, it reduces to the Todorov equation. Because of the off-mass-shell prescription for the intermediate states, it will be useful for systems with a wide variety of masses such as mesons, positronium, muonium, pionium, the deuteron and light hadronic atoms.

THE RETARDATION EFFECT ON 1P1 STATES OF HEAVY QUARKONIUM

By employing the two-body relativistic equation as the starting point to calculate the spin-averaged spectrum of heavy quarkonium, we obtain a negative P-state energy difference ΔEP=E(3Pcog)−E(1P1) of charmonium, which fits the data.

A two-body relativistic equation for interacting nucleons

A relativistic equation for the study of nuclear systems is proposed. The effects due to the isovector nature of the pion field are taken into account by an additional contribution to the Green's function.

Pseudoscalar pi N coupling and relativistic proton-nucleus scattering.

Relativistic p${\mathrm{\ensuremath{-}}}^{40}$Ca elastic scattering observables are calculated using relativistic NN amplitudes obtained from the solution of a two-body relativistic equation. Results at 200 MeV are presented for three sets of NN amplitudes, two with pure pseudovector coupling for the pion and one with a 25% admixture of pseudoscalar coupling. Differences between the predictions of these three models provide a measure of the uncertainty in constructing Dirac optical potentials from NN amplitudes.

Separable approximation method for two-body relativistic scattering.

A method for defining a separable approximation to a given interaction within a two-body relativistic equation, such as the Bethe-Salpeter equation, is presented. The rank-N separable representation given here permits exact reproduction of the T matrix on the mass shell and half off the mass shell at N selected bound state and/or continuum values of the invariant mass. The method employed is a four-space generalization of the separable representation developed for Schr\odinger interactions by Ernst, Shakin, and Thaler, supplemented by procedures for dealing with the relativistic spin structure in the case of Dirac particles.

Relativistic few-body problem. I. Two-body equations

This paper begins with an explanation of the implications of the requirement that a two-body relativistic equation should approach a one-body equation when one of the masses becomes very large. It is found that the Bethe-Salpeter equation does not satisfy this requirement. An infinite family of three-dimensional equations depending on a parameter $\ensuremath{-}1\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}1$ is constructed, all of which do satisfy this limit. When $|\ensuremath{\nu}|=1$ one of the particles is on its mass shell; when $\ensuremath{\nu}=0$ both particles are equally off mass shell. The fourth order irreducible kernel for this family is studied in the expanded static limit for all $\ensuremath{\nu}$. It is found, both for scalar theories and for a realistic chiral theory of spin \textonehalf{} nucleons interacting with isovector pions, that the leading order terms in the static limit cancel for any $\ensuremath{\nu}$, and that the nonleading terms are independent of energy only for the $|\ensuremath{\nu}|=1$ equation. Other criteria for the selection of a relativistic two-body equation and implications for the form of the two-pion exchange potential are briefly discussed.

The electromagnetic interactions of composite systems

Starting from Lagrangian field theory, we derive the interaction Hamiltonian of a composite system with an external electromagnetic field. Upon this basis, we develop the theoretical foundations of the atomic Zeeman effect, with specific reference to the fine structure and Lamb shift measurements. We also explicitly verify the Drell-Hearn-Gerasimov sum rule and the low energy theorem for Compton scattering for composite systems. An essential result of our investigation is that the interaction of a loosely bound composite system with an external electromagnetic field can be well approximated by the sum of the relativistic interaction Hamiltonians appropriate to the free constituents, but that in general the nonrelativistic reduction of this Hamiltonian does not yield the sum of the corresponding free reduced (e.g. Foldy-Wouthuysen) Hamiltonians. New features of this work include an extended Salpeter equation which includes interactions with an external electromagnetic field, explicit wave packet solutions to a two-body relativistic equation, and a calculational approach to perturbation theory with composite systems in which sums over intermediate or final states preceed nonrelativistic approximations. Our explicit calculation of the DHG sum rule illustrates its super-convergent nature.