134 research outputs found
Spin in relativistic quantum theory
We discuss the role of spin in Poincar\'e invariant formulations of quantum
mechanics.Comment: 54 page
Comparison of Relativistic Nucleon-Nucleon Interactions
We investigate the difference between those relativistic models based on
interpreting a realistic nucleon-nucleon interaction as a perturbation of the
square of a relativistic mass operator and those models that use the method of
Kamada and Gl\"ockle to construct an equivalent interaction to add to the
relativistic mass operator. Although both models reproduce the phase shifts and
binding energy of the corresponding non-relativistic model, they are not
scattering equivalent. The example of elastic electron-deuteron scattering in
the one-photon-exchange approximation is used to study the sensitivity of
three-body observables to these choices. Our conclusion is that the differences
in the predictions of the two models can be understood in terms of the
different ways in which the relativistic and non-relativistic -matrices are
related. We argue that the mass squared method is consistent with conventional
procedures used to fit the Lorentz-invariant cross section as a function of the
laboratory energy.Comment: Revtex 13 pages, 5 figures, corrected some typo
Poincare Invariant Three-Body Scattering
Relativistic Faddeev equations for three-body scattering are solved at
arbitrary energies in terms of momentum vectors without employing a partial
wave decomposition. Relativistic invariance is incorporated withing the
framework of Poincar\'e invariant quantum mechanics. Based on a Malfliet-Tjon
interaction, observables for elastic and breakup scattering are calculated and
compared to non-relativistic ones.Comment: 4 pages, 2 figures. Proceedings of the workshop "Critical Stability
of Few-Body Quantum Systems" 200
On the Bargmann space approach to the extended coupled cluster method for simple anharmonic systems
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
Relativistic instant-form approach to the structure of two-body composite systems
A new approach to the electroweak properties of two-particle composite
systems is developed. The approach is based on the use of the instant form of
relativistic Hamiltonian dynamics. The main novel feature of this approach is
the new method of construction of the matrix element of the electroweak current
operator. The electroweak current matrix element satisfies the relativistic
covariance conditions and in the case of the electromagnetic current also the
conservation law automatically. The properties of the system as well as the
approximations are formulated in terms of form factors. The approach makes it
possible to formulate relativistic impulse approximation in such a way that the
Lorentz-covariance of the current is ensured. In the electromagnetic case the
current conservation law is ensured, too. The results of the calculations are
unambiguous: they do not depend on the choice of the coordinate frame and on
the choice of "good" components of the current as it takes place in the
standard form of light--front dynamics. Our approach gives good results for the
pion electromagnetic form factor in the whole range of momentum transfers
available for experiments at present time, as well as for lepton decay constant
of pion.Comment: 26 pages, Revtex, 5 figure
Point-Form Analysis of Elastic Deuteron Form Factors
Point-form relativistic quantum mechanics is applied to elastic
electron-deuteron scattering. The deuteron is modeled using relativistic
interactions that are scattering-equivalent to the nonrelativistic Argonne
and Reid '93 interactions. A point-form spectator approximation (PFSA)
is introduced to define a conserved covariant current in terms of
single-nucleon form factors. The PFSA is shown to provide an accurate
description of data up to momentum transfers of 0.5 , but falls
below the data at higher momentum transfers. Results are sensitive to the
nucleon form factor parameterization chosen, particularly to the neutron
electric form factor.Comment: RevTex, 31 pages, 1 table, 13 figure
Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems
We study a square-lattice spin-half Heisenberg model where frustration is
introduced by competing nearest-neighbor bonds of different signs. We discuss
the influence of quantum fluctuations on the nature of the zero-temperature
phase transitions from phases with collinear magnetic order at small
frustration to phases with noncollinear spiral order at large frustration. We
use the coupled cluster method (CCM) for high orders of approximation (up to
LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to
calculate ground-state properties. The role of quantum fluctuations is examined
by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral
transition within the same model. We find clear evidence that quantum
fluctuations prefer collinear order and that they may favour a first order
transition instead of a second order transition in case of no quantum
fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.
Deep inelastic scattering and final state interaction in an exactly solvable relativistic model
In the theory of deep inelastic scattering (DIS) the final state interaction
(FSI) between the struck quark and the remnants of the target is usually
assumed to be negligible in the Bjorken limit. This assumption, still awaiting
a full validation within nonperturbative QCD, is investigated in a model
composed by two relativistic particles, interacting via a relativistic harmonic
oscillator potential, within light-cone hamiltonian dynamics. An
electromagnetic current operator whose matrix elements behave properly under
Poincar\'e transformations is adopted. It is shown that: i) the parton model is
recovered, once the standard parton model assumptions are adopted; and ii) when
relativistic, interacting eigenfunctions are exactly taken into account for
both the initial and final states, the values of the structure functions,
averaged over small, but finite intervals of the Bjorken variable , coincide
with the results of the parton model in the Bjorken limit.Comment: 26 pages, to appear in Phys. Rev. C (May 1998
Relativistic Corrections to the Triton Binding Energy
The influence of relativity on the triton binding energy is investigated. The
relativistic three-dimensional version of the Bethe-Salpeter equation proposed
by Blankenbecler and Sugar (BbS) is used. Relativistic (non-separable)
one-boson-exchange potentials (constructed in the BbS framework) are employed
for the two-nucleon interaction. In a 34-channel Faddeev calculation, it is
found that relativistic effects increase the triton binding energy by about 0.2
MeV. Including charge-dependence (besides relativity), the final triton binding
energy predictions are 8.33 and 8.16 MeV for the Bonn A and B potential,
respectively.Comment: 25 pages of text (latex), 1 figure (not included, available upon
request
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