Non-relativistic approximations to the pion production operator in 4He(p,nπ+)4He

Various non-relativistic pion production operators are applied in the study of the ⁴He(p, nπ⁺)⁴He process. We compare their predictions with fully covariant calculations of the external emission graphs both for pseudovector and pseudoscalar coupling. It is found that the non-relativistic pion production operators cannot reproduce the relativistic results quantitatively, in particular for the pseudoscalar case. The simple static pion production operator gives agreement with the relativistic pseudovector results to within a factor three or four. Adding recoil terms to this static operator has a significant effect on the cross section but does not improve the agreement with the relativistic results. The implications of PCAC and the soft-pion theorem for the relativistic calculation are studied. The uncertainty in the cross section in the soft-pion approach is found to be considerably smaller than the difference between pseudovector and pseudoscalar results or between the relativistic pseudovector result and its non-relativistic approximations.     

Isobar giant resonance formation in self-conjugate nuclei

The production of isobars with concomitant giant resonance excitations due to peripheral collisions of relativistic heavy ions is investigated. The interaction is described by a modified form of the central term in the one-pion-exchange potential (OPEP) where the projectile ordinary spin operator is replaced by a transition spin operator which describes the creation of an isobar from a nucleon. The scattering is analyzed using time-dependent harmonic perturbation theory to determine the reaction total cross sections. The results obtained, which are valid for reactions involving self-conjugate nuclei, are applied to the specific collison of 2.1 $\text{GeV}\text{nucleon}$¹⁶O projectiles with ¹²C targets at rest. Cross sections are investigated using two different models for the nuclear spin states. In the first model, the many-body nuclear spin state is reduced, in the spirit of a particle-hole state, to an equivalent two-body state called a particle-core state. In the second model, the many-body spin states are described by unsymmetrized products of individual particle spins. Properties of the spin giant resonance and isobar giant resonance states are investigated. Finally, isobar decay and isobar/pion absorption effects are discussed.     

The influence of ambiguities in the pion production operator on (p, π+) cross sections

Various aspects of the pionic stripping mechanism for (p, π⁺) reactions are studied in a momentum-space DWBA framework. A Foldy-Wouthuysen nonrelativistic reduction of a pseudoscalar field theory leads to several ambiguities in the pion production operator H′. The extent to which these ambiguities are reflected in the (p, π⁺) differential cross section is studied, for the particular case of 185 MeV protons incident on ¹²C. The results indicate that the O(1/m³) terms (m is the nucleon mass) in the production operator have as important an effect on the differential cross section as the O(1/m²) nucleon recoil term. The freedom of carrying out a further unitary transformation on H′ is found to have a substantially larger effect on the cross section than does the uncertainty associated with the relativistic transformation properties in the external nucleonnucleus potential. The size of these several effects suggests that the DWBA pionic stripping theory in its present form cannot serve as a sensitive probe of nuclear structure. Our results indicate the need for a more consistent relativistic theory of (p, π⁺) reactions.     

Frame Independent Nonlocality for Three Qubit State

Bell’s inequality is investigated for the three qubit GHZ state in relativistic regime. Two different relativistic spin operator are considered. One of them is defined by Lee and Ee (New J. Phys. 6:67, 2004). and the other which is the Pauli-Lubanski pseudovector used by Kim and Son (Phys. Rev. A 71:014102, 2005). It is shown that for both spin operator Bell’s inequality is still maximally violated in a Lorentz-boosted frame.     

On the reduction of the Dirac equation to non-relativistic form: the dipole-dipole interaction in the hydrogen atom

Finite nucleus models are used in the calculation of the dipole-dipole part of the second-order hyperfine energy in the ground state of the hydrogen atom. The results are used as a guide to bring the non-relativistic calculation for a point nucleus into agreement with the relativistic calculation. This necessitates the introduction of delta function operators in the dipole-dipole operator and the zeroth-order hamiltonian. It is concluded that the reduction of the Dirac equation to non-relativistic form is valid for the hyperfine interaction up to order mc ²α⁶.     

Nucleon polarization and the nuclear charge operator

Effects of nucleon polarization on the nuclear charge operator have been evaluated in a constituent quark model. At momentum transfer q ≈ 4 fm^?1 monopole, dipole and quadrupole excitations are of equal importance. In a harmonic oscillator model for ³He all multipolarities give negative contributions, leading to an overall contribution comparable to the relativistic pair effect. The influence of realistic wave functions, coupling constants and off-shell form factors is discussed.     

Electromagnetic and Axial Form Factors of Octet and Decuplet Baryons

We report from a study of the elastic electromagnetic and axial form factors of all lowest baryon states with flavors up, down, and strange along relativistic constituent-quark models. We consider the baryons as relativistic bound states of three constituent quarks and solve the eigenvalue problem of the invariant mass operator. The corresponding eigenstates are employed to calculate manifestly covariant form factors within the point form of Poincaré-invariant quantum mechanics. The electromagnetic and axial current operators are constructed along the spectator model in point-form relativistic dynamics. We have thus obtained covariant predictions for the electroweak form factors, for momentum transfers up to Q ² ~ 4 GeV², as well as the electric radii, magnetic moments, and axial charges. The theoretical results in general agree very well with existing phenomenological data. In cases, where no experimental information is yet available, the results are well compatible with data from lattice quantum chromodynamics.     

The transparency of nuclei to nucleons and pions in a relativistic Glauber approximation

We present a selection of results obtained within the context of a relativistic eikonal model. First, results of relativistic Glauber calculations for the nuclear transparency extracted from photon-induced pion production are presented. Second, computed differential cross-sections for the ¹² C(p, 2p) are compared to data.     

The I2(B) predissociation by solving an inverse atoms-in-molecule problem

The valence electronic states of the iodine molecule are analysed by means of a simple atoms-in-molecule model which accounts for the lowest ²P states of iodine atoms and approximates the spin-orbit interaction by its atomic part. For this model, an inverse problem is solved, i.e. non-relativistic potential energy curves and diabatic couplings are determined by a least-squares fit to known relativistic potential energy curves. The resulting adiabatic wave functions are used to calculate the electronic matrix elements responsible for natural, hyperfine and magnetic predissociation of the iodine molecule in the B0⁺ _u: state. The results are in reasonable agreement with experimental data, being stable enough with respect to the variation of input relativistic potentials. They also indicate the importance of diabatic couplings between the non-relativistic states of the same symmetry.     

Point-form quantum field theory and meson form factors

We comment on canonical quantization of relativistic field theories on a Lorentz-invariant surface of the form x ² = τ². By this choice of the quantization surface all components of the four-momentum operator become interaction dependent, whereas the generators of Lorentz transformations stay free of interactions – a feature characteristic for Dirac’s “point-form” of relativistic dynamics. In the sequel we demonstrate how field theoretical concepts may enter the framework of relativistic quantum mechanics. To this aim we employ a Poincaré-invariant approximation scheme, which allows to reduce a field theoretical many-body problem to a multichannel problem for a Bakamjian-Thomas-type mass operator. As an application of this multichannel formalism we will discuss the scattering of an electron by a (confined) quark-antiquark pair. It will be sketched how an electromagnetic meson form factor can be extracted from the one-photon exchange optical potential.     

Polarization potentials in heavy-ion scattering

A polarization potential is defined in terms of the Feshbach projection operator formalism to represent the effect upon the elastic channel of the coupling to non-elastic channels in heavy-ion scattering. The polarization potential represents coupling to specific surface degrees of freedom of the particular reaction considered and it is contrasted to the complementary global approaches for the volume potential such as the folding model and the proximity potential. The coupled channels method is used both as a source of exact model solutions for comparison with the various approximate potential forms and also as a numerical means of constructing trivially equivalent local potentials. The imaginary Coulomb polarization potential is due in lowest order to quadrupole coupling to the lowest collective 2⁺ state of a nucleus. It is considered in detail since it provides the insight of closed analytical forms in various approximations. Multistep coupling to higher states, energy loss and off-energy shell effects are also considered analytically. The real Coulomb polarization potential due to the virtual excitation of multipole giant resonances, and the polarization potential arising from relativistic corrections, are investigated in detail. Polarization potential components due to nuclear coupling are investigated numerically. Analytical cross section approaches are contrasted with the polarization potential approach and with coupled channels.     

Relativistic quantum particle in a time-dependent homogeneous field

A model of the relativistic quantum particle under the action of a time-dependent force is considered. This exactly solvable model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space is one-dimensional Lobachevsky space. We have explicitly constructed the wave functions and propagators for this model in both x- and p-representations. We have also found a solution of a definite class of partial differential and finite-difference equations, which can be interpreted as the operator identities.     

Evidence for a relativistic electron-pair model of nuclear particles

A positroniumlike, relativistic electron-pair model previously found to describe the properties of the pion and hadron resonances is tested for its prediction of the hadron-to-muon production ratioR in high-energye ⁺ e ^– collisions. It is found that the model leads to the observed magnitude ofR and its stepwise increase with energy. The model predicts a series of further rises ofR as the available energy is increased, beginning at about 7.9 Gev.     

Zeeman-Effekt im Grundzustand von atomarem Kohlenstoff

The Landé factors of the ground state levels³ P ₁ and³ P ₂ of atomic carbon are calculated. The Hamilton operator proposed by Abragam and Van Vleck takes account of relativistic effects up to the second order. Additionally, corrections to the orbital and spin moments of the electrons are applied. The deviation from Russell-Saunders coupling is treated in perturbation theory. The results $$\begin{gathered} g_J ({}^3P_1 ) = 1.501069 \hfill \\ g_J ({}^3P_2 ) = 1.501056 \hfill \\ \end{gathered} $$ differ from the experimental values by about 10^?5.