Time–dependent simulations ofelectron emission in grazingion–surface collisions
Darıo MitnikInstituto deAstronomıay Fısica del Espacio
Departamento deFısicaUniversidad deBuenos Aires
Argentina
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Darıo MitnikJorge MiragliaMarıa GravielleIAFE – UBA
Andres ArnauInigo AldazabalUPV – EHU
DIPC
Vıctor PonceCAB
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Grazing ion–surface collision
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Capture to the Continuum:The Convoy Peak
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Continuum Capture: The Convoy Peak
G.B. Crooks and M.E. Rudd,
Phys. Rev. Lett. 25, 1599
(1970).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Convoy Peak is (de)accelerated?
M.S. Gravielle and J.E.
Miraglia, Phys. Rev. A 67,
042901 (2003)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Convoy Peak is (de)accelerated?
G.R. Gomez et al., Phys.
Rev. B 58, 7403 (1998)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Outline
I Development of theoretical strategies for ab initio calculationsof ion–surface collisions
I Development of numerical methods for solving theTime–dependent Schrodinger Equation
I Study of the Convoy Peak Shift
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Outline
I Development of theoretical strategies for ab initio calculationsof ion–surface collisions
I Development of numerical methods for solving theTime–dependent Schrodinger Equation
I Study of the Convoy Peak Shift
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Outline
I Development of theoretical strategies for ab initio calculationsof ion–surface collisions
I Development of numerical methods for solving theTime–dependent Schrodinger Equation
I Study of the Convoy Peak Shift
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The track potential
I The incident projectil is at the origin of the laboratory frameof reference, at t = 0
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The track potential
I The charge density when the ion is in position {0,Y (Z ),Z (t)}
n(z , t) = n0e−α|Y (Z)|e−
β|z−Z(t)|vz
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The track potential
I The track potential is
V (x , y , z , t) =
∫ Z(t)
−∞du
n(u, t)√x2 + y2 + (u − z)2
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The track potential
I Change of coordenates: The origin at the ion
x ′ = x
y ′ = y − Y (Z )
z ′ = z − Z (t)
V (x ′, y ′, z ′, t) =
∫ Z(t)
−∞du
n(u, t)√x ′2 + (y ′ + Y )2 + (u − (z ′ + Z ))2
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The track potential
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Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential + Coulomb
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential + Coulomb
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential + Coulomb
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential + Coulomb
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Track Potential + Coulomb
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The time–dependent Schrodinger equation
The time–dependent Schrodinger equation
idΨ(r, t)
dt= H(r, t)Ψ(r, t)
has the solution
Ψ(r, t + ∆t) = exp[−i∆tH]Ψ(r, t)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Simple case: radial potential
if the potential V = V (r) → variable separation
ψnlm(r) = Rnl(r)Yml (r) ≡ Pnl(r)
rY m
l (r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Simple case: radial potential
The radial part of the Hamiltonian becomes
H(r) = −1
2
∂2
∂r2+
l(l + 1)
2r2+ V (r)
≡ T + V (r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Simple case: radial potential
and the time–independent Schrodinger equation is
H(r)Pnl(r) = EnlPnl(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Simple case: radial potential
the time evolution of this solution is given by
ψnlm(r, t) = exp[−i∆tH]Rnl(r , t0)Yml (r)
= exp[−i∆tEnl ]Pnl(r , t0)
rY m
l (r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Schrodinger equation
In our case, the track potential
I Is a time–dependent potential
I Is not a central potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Schrodinger equation
In our case, the track potential
I Is a time–dependent potential
I Is not a central potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The Schrodinger equation
In our case, the track potential
I Is a time–dependent potential
I Is not a central potential
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Expansion of the track potential inspherical harmonics
V (r, t) = V (r , θ, φ, t) =∑lm
Vlm(r , t)× Y ml (θ, φ)
where
Vlm(r , t) ≡∫ 2π
0∂φ
∫ π
0∂θ sin θ Y m
l∗(θ, φ)V (r, t)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Expansion of the track potential inspherical harmonics
V (r, t) = V (r , θ, φ, t) =∑lm
Vlm(r , t)× Y ml (θ, φ)
where
Vlm(r , t) ≡∫ 2π
0∂φ
∫ π
0∂θ sin θ Y m
l∗(θ, φ)V (r, t)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–ChannelsUsing the expansion
ψ(r) =∑l1,m1
Pl1,m1(r)
rY m1
l1(r),
the time–independent Schrodinger equation becomes
H(r)ψ(r) = [T + V (r)]∑l1,m1
Pl1,m1(r)Ym1l1
(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–ChannelsUsing the expansion
ψ(r) =∑l1,m1
Pl1,m1(r)
rY m1
l1(r),
the time–independent Schrodinger equation becomes
H(r)ψ(r) = [T + V (r)]∑l1,m1
Pl1,m1(r)Ym1l1
(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channelsand using the potential expansion
V (r) =∑l2,m2
Vl2,m2(r)Ym2l2
(r),
the Schrodinger equation is
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channelsand using the potential expansion
V (r) =∑l2,m2
Vl2,m2(r)Ym2l2
(r),
the Schrodinger equation is
[T + V (r)]∑l1,m1
Pl1,m1(r)Ym1l1
(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channelsand using the potential expansion
V (r) =∑l2,m2
Vl2,m2(r)Ym2l2
(r),
the Schrodinger equation is
[T +∑l2,m2
Vl2,m2(r)Ym2l2
(r)]∑l1,m1
Pl1,m1(r)Ym1l1
(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
The term ∑l2,m2
Vl2,m2(r)Ym2l2
(r)∑l1,m1
Pl1,m1(r)Ym1l1
(r)
is expanded as∑l1,m1
Pl1,m1(r)∑l2,m2
Vl2,m2(r)Ym1l1
(r)Y m2l2
(r) =
=∑l1,m1
∑l2,m2
Pl1,m1(r)Vl2,m2(r)∑l3,m3
Sm3,m1,m2
l3,l1,l2Y m3
l3(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
∑l1,m1
∑l2,m2
Pl1,m1(r)Vl2,m2(r)∑l3,m3
Sm3,m1,m2
l3,l1,l2Y m3
l3(r)
where
Sm3,m1,m2
l3,l1,l2= (−1)m3
√(2l1 + 1)(2l2 + 1)(2l3 + 1)
4π×
×(
l3 l1 l20 0 0
) (l3 l1 l2−m3 m1 m2
)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
The Schrodinger equation
[T +∑l2,m2
Vl2,m2(r)Ym2l2
(r)]∑l1,m1
Pl1,m1(r)Ym1l1
(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
The Schrodinger equation
T∑l1,m1
Pl1,m1(r)Ym1l1
(r) +
+∑l1,m1
∑l2,m2
Pl1,m1(r)Vl2,m2(r)∑l3,m3
Sm3,m1,m2
l3,l1,l2Y m3
l3(r) =
= E∑l1,m1
Pl1,m1(r)Ym1l1
(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
multiplying and integrating
∫∂ rY m3
l3(r) T
∑l1,m1
Pl1,m1(r)Ym1l1
(r) +
+
∫∂ rY m3
l3(r)
∑l1,m1
∑l2,m2
Pl1,m1(r)Vl2,m2(r)∑l3,m3
Sm3,m1,m2
l3,l1,l2Y m3
l3(r) =
=
∫∂ rY m3
l3(r) E
∑l1,m1
Pl1,m1(r)Ym1l1
(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Coupled–Channels
we obtain coupled equations for every channel
TPl3,m3(r) +∑l1,m1
∑l2,m2
Vl2,m2(r)Sm3,m1,m2
l3,l1,l2Pl1,m1(r) =
= E∑l1,m1
Pl3,m3(r)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
ResultsStarting from the 1s state of hydrogen
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p1 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p1 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p1 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p1 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p1 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p0 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p0 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p0 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p0 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the 2p0 state of hydrogen
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Propagation of the Schrodinger equation in imaginary time
τ ≡ it
∂Φ(r, τ)
∂τ= −HΦ(r, τ)
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
The solution of this equation
Φ(r, τ) = e−HτΦ(r, 0)
is expanded in the stationary eigenvectors
Φ(r, τ) =∞∑
q=1
aqe−Eqτψq(r).
In the limit τ →∞, Φ tends to the ground state:
limτ→∞
Φ(r, τ) = ψ1(r).
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Starting from the 1s hydrogenic function, the relaxed ground stateis obtained by an imaginary time propagation
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Starting from the 1s hydrogenic function, the relaxed ground stateis obtained by an imaginary time propagation
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Starting from the 1s hydrogenic function, the relaxed ground stateis obtained by an imaginary time propagation
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Starting from the 1s hydrogenic function, the relaxed ground stateis obtained by an imaginary time propagation
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
The relaxation method
Starting from the 1s hydrogenic function, the relaxed ground stateis obtained by an imaginary time propagation
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the relaxed ground state
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the relaxed ground state
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the relaxed ground state
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the relaxed ground state
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Results
Starting from the relaxed ground state
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Capture in the Continuum
Assuming that the electron is captured in a low–energy continuumstate
Φ(r , 0) =1
(ωπ)1/4exp
[−(r − a)2
2ω2
]exp [−iki r ]
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation with Coulombic potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Projection to continuum states
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Propagation: Coulombic + Track potential
Replay Movie
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Projection to continuum states
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions
1. We are trying to simulate a grazing ion–surface scatteringprocess
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX
Preliminars Outline Track Schrodinger Track expansion Coupled–Channels Results 2p Relaxation Continuum Projection Propagation
Conclusions1. We are trying to simulate a grazing ion–surface scattering
process
2. We developed numerical solutions of the time–dependentSchrodinger equation
3. As a first step, we assume an electron captured on acontinuum state of the projectil
4. A track potential represents the effect of the surfaceinteraction on the electronic state
5. We analyze the effect of the track potential on the electronvelocity distribution
6. Our method is able to detect a deceleration of theconvoy–electron peak, due to the surface interaction, inquantitative agreement with the experimental data
Darıo Mitnik (IAFE – UBA) Time–dependent ion–surface collisions ISIACXX