Asymptotic channels and gauge transformations of the time dependent Dirac equation for extremely relativistic heavy ion collision

We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.

scattering: heavy ion
nuclear reaction: peripheral
Dirac equation: time dependence
Dirac equation: solution
asymptotic behavior
electron: wave function
transformation: gauge
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References(44)

Figures(0)

Electron positron pair production in Coulomb collisions of ultrarelativistic sulphur ions with fixed targets

et al.

- Phys.Rev.Lett. 69 (1992) 1911-1914
•
DOI:
- 10.1103/PhysRevLett.69.1911

Measurement of electron capture from electron positron pair production in relativistic heavy ion collisions

A. Belkacem
(
- LBL, Berkeley
)
,
H. Gould
(
- LBL, Berkeley
)
,
B. Feinberg
(
- LBL, Berkeley
)
,
R. Bossingham
(
- LBL, Berkeley
)
,
W.E. Meyerhof
(
- Stanford U., Phys. Dept.
)

- Phys.Rev.Lett. 71 (1993) 1514-1517
•
DOI:
- 10.1103/PhysRevLett.71.1514

Measurement of electromagnetically produced e+ e- pairs in distant S - Pt collisions

CERES/NA45

Collaboration

•

R. Bauer
(
- Heidelberg U.
)

et al.

- Phys.Lett.B 332 (1994) 471-476,
- Phys. Lett. B332 (1994) 471-476. and CERN Geneva - CERN-PPE-94-076 (94/05,rec.Jun.) 9 p
•
DOI:
- 10.1016/0370-2693(94)91283-1

Electron-positron pair production in Coulomb collisions by 6.4-TeV sulfur ions

C.R. Vane
(
- Oak Ridge
)
,
S. Datz
(
- Oak Ridge
)
,
P.F. Dittner
(
- Oak Ridge
)
,
H.F. Krause
(
- Oak Ridge
)
,
R. Schuch
(
- Royal Inst. Tech., Stockholm
)

et al.

- Phys.Rev.A 50 (1994) 2313-2321
•
DOI:
- 10.1103/PhysRevA.50.2313

- Phys.Rev.Lett. 73 2432

- Phys.Rev.A 51 1253

- Phys.Rev.A 55 842

Capture, ionization, and pair-production processes in relativistic heavy ion collisions in the 1-GeV/nucleon energy range

C. Belkacem
(
- LBL, Berkeley
)
,
H. Gould
(
- LBL, Berkeley
)
,
B. Feinberg
(
- LBL, Berkeley
)
,
R. Bossingham
(
- LBL, Berkeley
)
,
W. E. Meyerhof
(
- Stanford U., Phys. Dept.
)

- Phys.Rev.A 56 (1997) 2806-2818
•
DOI:
- 10.1103/PhysRevA.56.2806

Measurements of positrons from pair production in Coulomb collisions of 33-TeV lead ions with fixed targets

et al.

- Phys.Rev.A 56 (1997) 5, 3682-3686
•
DOI:
- 10.1103/PhysRevA.56.3682

Electron Capture and Ionization of Pb Ions at 33 TeV

et al.

- Phys.Rev.Lett. 80 (1998) 1190-1193
•
DOI:
- 10.1103/PhysRevLett.80.1190

- Phys.Rev.A 58 1253

Electromagnetic Processes in Relativistic Heavy Ion Collisions

- Phys.Rept. 163 (1988) 299
•
DOI:
- 10.1016/0370-1573(88)90142-1

Theory of relativistic ion atom collisions

J. Eichler
(
- Hahn-Meitner Inst.
)

- Phys.Rept. 193 (1990) 165-277
•
DOI:
- 10.1016/0370-1573(90)90018-W

Multiple electron positron pair production in relativistic heavy ion collisions: A Strong field effect

G. Baur
(
- Julich, Forschungszentrum
)

- Phys.Rev.A 42 (1990) 5736-5738
•
DOI:
- 10.1103/PhysRevA.42.5736

Higher-order effects on pair creation by relativistic heavy-ion beams

M.J. Rhoades-Brown
(
- RIKEN BNL
)
,
J. Weneser
(
- Brookhaven
)

- Phys.Rev.A 44 (1991) 1, 330
•
DOI:
- 10.1103/PhysRevA.44.330

Multiplicity distribution of electron - positron pairs created by strong external fields

- Phys.Rev.A 46 (1992) 261-269,
- Phys. Rev. A46 (1992) 261-269 and Darmstadt GSI - Prepr. GSI 91-55 (91/10,rec.Nov.) 17 p
•
DOI:
- 10.1103/PhysRevA.46.261