Recombination from the Negative Continuum Anton Artemyev and Andrey - PowerPoint PPT Presentation

Recombination from the Negative Continuum Anton Artemyev and Andrey Surzhykov Physikalisches Institut, University of Heidelberg Helmholtz Nachwuchsgruppe VH-NG-421 "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Recombination from the Negative Continuum Introduction : Electron-positron pair production in ion-ion collisions Two-center Dirac problem Negative continuum dielectronic recombination Theoretical background Differential and total NCDR cross sections Outlook : Further NCDR studies Scenarios for future experiments and “visibility” of the process "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Relativistic ion-atom collisions Dynamically induced strong fields result in a large number of atomic processes. Positive Energy Continuum - e + mc 2 Transfer Excitation Ionization 0 Pair Production - mc 2 e + We wish to consider process of Negative Energy Continuum electron-positron pair creation. "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008 47 (20 CERN C

Pair production in heavy ion collisions projectile + mc 2 + mc 2 target 0 0 Electron-positron pair production in ion- - mc 2 ion collisions (at moderate energies) - mc 2 has attracted much interest during last e + years. e + target projectile Theoretical description of such a process Au 79+ + U 92+ requires an analysis of two-center Dirac problem: Coupled-channel methods Numerical integration on the grid D. C. Ionescu and A. Belkacem, Phys. Scr. T80 (1999) 128 "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Recombination from the Negative Continuum Introduction : Electron-positron pair production in ion-ion collisions Two-center Dirac problem Negative continuum dielectronic recombination Theoretical background Differential and total NCDR cross sections Outlook : Further NCDR studies Scenarios for future experiments and “visibility” of the process "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Negative continuum dielectronic recombination In the negative continuum dielectronic recombination + mc 2 a free (or quasi-free) electron is captured by a heavy ion via the creation if a positron-electron pair. 0 - mc 2 + + − → − + + + Z ( Z 2 ) X e X e e + projectile "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

DR vs. NCDR Negative continuum dielectronic Dielectronic recombination (DR) recombination (NCDR) + mc 2 + mc 2 0 0 - mc 2 - mc 2 e + projectile projectile Ion in initial state can be bare. Few-electron ion in initial state (before the capture). Non-resonant process. There is threshold of the process. Resonant process. "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

NCDR: Basic theory (1) outgoing positron (p f , m f ) = Differential cross section: incoming electron (-p f , -m f ) ( ) σ π 4 bound electrons d 2 2 = τ p 2 Ω f if d v f i incident electron With the transition amplitude: ( ) ω − r r ( ) exp i ( ) π δ − τ = Ψ α − ψ ψ α α 1 2 2 i E E 1 , − − − i f if f 1 2 r r p m p m i i f f 1 2 electron-electron interaction (Feynman gauge) Electron-electron interaction operator includes not only Coulomb term but also magnetic interactions. "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

NCDR: Basic theory (2) outgoing positron (p f , m f ) = incoming electron (-p f , -m f ) bound electrons Final-state wavefunction of helium- like ion is provided within the Independent Particle Model: incident electron ψ ψ r r ( ) ( ) ( ) ∑ Ψ = n j m 1 n j m 1 r r a a a b b b ( , ) N j m j m JM ψ ψ r r f 1 2 a a b b ( ) ( ) m , m n j m 2 n j m 2 a a a b b b a b e 1 ∝ r 12 Z ∝ e Good approximation for high-Z ions! r Z ∝ 2 r nucleus 1 "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

NCDR cross sections θ laboratory frame θ projectile frame initial state final state ( ) σ π ( ) 4 We like to study differential (in d 2 2 θ = τ p 2 , T positron angle) NCDR cross section Ω f p f if d v for the various collision energies. f i ε ≥ + 2 E s mc Threshold for the process: i 1 2 total energy (with rest mass) "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Differential cross sections in projectile frame Calculations have been carried out within the projectile frame. One need to perform Lorentz transformation to evaluate differential cross section in the laboratory frame. A. N. Artemyev et al ., Phys. Rev. A 67 (2003) 052711 "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Lorentz transformation Example: γ p = 2 One has to transform the positron emission angle: ′ θ sin θ = ( ) tan ′ ′ γ θ + β β cos / p p Note: in the laboratory frame there exists a maximal value of the angle θ for which emission is possible! ′ ′ β γ ( ) ′ θ = β < β sin , β γ max p p p J. Eichler and W. Meyerhof, Relativistic atomic collisions (1995) And the differential cross section: Ω′ σ σ d d d = Ω′ Ω Ω d d d Note: when the emission angle reaches its maximum, the differential cross section (in lab. frame) becomes infinite! "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Differential cross sections in laboratory frame Despite the singularity, the integral of the differential cross section over the angle in both frames converges and yields the same value (i.e. the total NCDR cross section). Calculations have been done for the value: σ ( ) θ + ∆ θ d ∫ ∆ σ θ = π θ θ 2 sin d θ θ d A. N. Artemyev et al ., Phys. Rev. A 67 (2003) 052711 "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Total NCDR cross sections Capture into 1s 2 state The NCDR cross section increases rapidly above the threshold and has a maximum slightly above the energy e + U 92+ needed to create a free electron- positron pair. e + Pb 82+ + + − → − + + + + − Z ( Z 1 ) X e X e e RR T p : 1.8 GeV ... 5.5 GeV Capture into ground state of (initially) U 92+ The NCDR cross sections are by (about) six orders of magnitude NCDR smaller than the RR cross sections. "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Capture into excited ionic states (1) Calculation have been also performed for the NCDR into excited states of (finally) helium-like ions. T kin = 1200 keV + mc 2 ′ ′ β γ θ = sin 0 β p γ max p - mc 2 e + projectile A. N. Artemyev et al ., NIMB 235 (2005) 270 A. N. Artemyev et al ., to be published The maximum scattering angle will be different for NCDR into bound states with different angles. "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Capture into excited ionic states (2) Calculation have been also performed for the NCDR into excited states of (finally) helium-like ions. Capture into excited states enhance the total NCDR + mc 2 cross section by about 25 %. 0 - mc 2 e + projectile A. N. Artemyev et al ., NIMB 235 (2005) 270 A. N. Artemyev et al ., to be published "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Recombination from the Negative Continuum Introduction : Electron-positron pair production in ion-ion collisions Two-center Dirac problem Negative continuum dielectronic recombination Theoretical background Differential and total NCDR cross sections Outlook : Further NCDR studies Scenarios for future experiments and “visibility” of the process "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

The role of Compton profile So far calculations have been performed for the “delta-function- like” energy distribution of the incoming electrons and ion beam. If incident electrons or ions have some energy distribution that is expected to remove the singularity in the differential cross section. A. N. Artemyev et al ., NIMB 235 (2005) 270 A. N. Artemyev et al ., to be published Experiments at: target atom Electron target (cooler) ? Jet target ? projectile ion Foil target ? "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008

Scenarios for the future experiments Probable scenario is “coincidence experiment” in which emitted positron is detected in coincidence with X (Z-2)+ ion. The “signature” of the process is: forward positron emission (in lab. frame) associated with projectiles that captured two electrons. Competitive processes? (RDEC and DREC, pair production) Can we employ positron angular distributions to separate out experimentally competitive processes? "The physics of supercritical electromagnatic fields“ GSI, 18 July 2008