Coupled-channel equations and gauge transformations

Rumrich, Klaus; Greiner, Walter; Soff, G.

doi:10.1016/0375-9601(90)90863-j

Cited by 10 publications

(13 citation statements)

References 2 publications

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“…We already mentioned that for a complete set of basis states the coupled-channel equations are asymptotically gauge independent. Rumrich, Soff, and Greiner [44] proved this explicitly in the representation of the coupled channels. In addition, an example has been given for the gauge dependence when using a truncated basis.…”

Section: !?mentioning

confidence: 83%

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Ionization and pair creation in relativistic heavy-ion collisions

1993

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Ionization, pair creation, and electron excitations in relativistic heavy-ion collisions are investigated in the framework of the coupled-channel formalisrn. Collisions between heavy projectiles and pb8*+ are considered for various bombarding energies in the region E =500 up to 2000 MeV/u. Useful symmetry relations for the matrix elements are derived and the influence of gauge transformations onto the coupled-channel equations is explored. PACS nurnber(s): 34.90. +q, 36.10.Dr,

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Section: !?mentioning

confidence: 83%

“…(54) have to be transformed. In the following we want to investigate whether in this case the asymptotic gauge invariance remains fulfilled [44]. is valid, i.e., the asymptotic gauge invariance is fulfilled.…”

Section: !?mentioning

confidence: 99%

Ionization and pair creation in relativistic heavy-ion collisions

1993

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“…The integrand is a component of a 4-vector current density, which is a conserved quantity (see appendix E). This transition current [35], ( J (k,j) , J (k,j) 0 ), is defined by…”

Section: B the Amplitudesmentioning

confidence: 99%

“…Gauge transformations should also be applied with care when used in calculations employing truncated basis sets [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

1998

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We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using lightfront variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.

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“…The main concern of this paper is with the lack of gauge invariance of the predictions of coupled-channel time-dependent solutions of the Schrödinger equation governing relativistic Coulomb excitation. Some related discussions of this subject have been given by Baltz, Rhoades-Brown, and Weneser [12], Rumrich and Greiner [13] and Kobe and Kennedy [14].…”

Section: Lorentz Gauge Coulomb Gaugementioning

confidence: 99%

Gauge dependence of calculations in relativistic Coulomb excitation

Bayman

Zardi

2005

Phys. Rev. C

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Before a quantum-mechanical calculation involving electromagnetic interactions is performed, a choice must be made of the gauge to be used in expressing the potentials. If the calculation is done exactly, the observable results it predicts will be independent of the choice of gauge. However, in most practical calculations approximations are made, which can destroy the gauge invariance of the predictions.We compare here the results of coupled-channel time-dependent relativistic Coulomb excitation calculations, as performed in either Lorentz or Coulomb gauges. We find significant differences when the bombarding energy per nucleon is ≥ 2 GeV, which indicates that the common practice of relying completely on the Lorentz gauge can be dangerous.

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Coupled-channel equations and gauge transformations

Cited by 10 publications

References 2 publications

Ionization and pair creation in relativistic heavy-ion collisions

Ionization and pair creation in relativistic heavy-ion collisions

Light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

Gauge dependence of calculations in relativistic Coulomb excitation

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