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• 1
Application de la spectroscopie à l’étude des décharges électriques dans les milieux denses.
N Bonifaci
CNRS, G2Elab, F-38000Grenoble, FranceNelly.Bonifaci@g2elab.grenoble-inp.fr
Joel Rosato, Jussi Eloranta, Zhiling Li , Vladimir Atrazhev, Vyacheslav Shakatov, Sebastien Flury
• 2
Application:Dischargeinliquid The plasma produced by electrical discharges in liquids are finding important applications in modern technology : Electrical Insulation, High power switching, Electro discharge machning Nanomaterials synthesis, Water sterilization, Plasma medecine
LN2 77 K, 1 bar LN2 77 k 1 bar
Water sterilization
LN2 77 K 1 Bar
superconducting tape Resistive SuperConducting Fault Current Limiter
Liquid N2
G2E. Lab covers the wide spectrum of the electrical engineering science
• Molecular spectra
• Atomic spectra
• Continuum
0
5000
10000
15000
20000
25000
30000
35000
650 700 750 800 850 900 950
Inten
sité
[U.A
.]
longeur d'onde [nm]
8000
10000
12000
14000
16000
18000
20000
22000
350 400 450 500 550 600 650
Inte
nsité
[U.A
.]
longueur d'onde [nm]
365 370 375 380
0
200
400
600
800
1000
1200
1400
380.46 (0-2)
375.5 (1-3)
371.05 (2-4)
Intensité relative
Longueur d'onde (nm)
R. Stringanow and N. S. Sventitskii, Tables of Spectral Lines of Neutral and Ionized Atoms Plenum New York 1968.
NIST ASD Output: Lines http://physics.nist.gov/cgi-bin/ASD/lines1.pl
Atomic Spectral Line Database http://cfa-www.havard.edu/
B. Pearse and A. G. Gaydon The identification of Molecular Spectra Chapman and Hall 1976 G. Herzberg, Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules, 2nd edn. (Van Nostrand, Princeton, NJ, 1950) I. Kovacs, Rotational structure in the spectra of diatomic molecules (Adam Higer Ltd., London, 1969)
OES
Spectral Line Profile
Line width ΔλFWHM Line shift d=λmax-λvacuum Asymmetry Satellite band Forbidden line Self-absorption
Blue wing Red wing
Microscopic probe
Line center
e- e-
700 702 704 706 708 710
P=0,1MPa
λ (nm)
700 702 704 706 708 710
P=1,4MPa
P=2,3MPa
700 702 704 706 708 710
Δλnatural~10-4 Å
Particle Temperature
Gaussian Profile
Natural Broadening
Doppler Broadening
Broadening mechanisms
Instrumental Broadening
Pressure Broadening
72
2 22 7.157 10DkTLn TMc M
λ λ λ−Δ = = ×
T ΔλD
He 10000 0,02 nm Ar 10000 0,0057 nm Hβ 5000 0,025 nm
Gaussian profile
Pressure Broadening
( ) p pp p
C hCV r
r r
ω ν
= ± = ±h
1pm s−Stark Neutral (van der Waals) Resonant
Semi empirical potential
ab initio potential
• 7
Linear Stark -------
Quadratic Stark
-------
Resonant
van der Waals
L-J
W. Behmenburg J. Quant. Spectrosc. Radiat. Transfer 4, (1964) 177 W. R. Hindmarsh, A. D. Petford, G. Smith, Proc Roy Soc A 297 (1967) 296 W. R. Hindmarsh, A. N. Du Plessis et J. M. Farr (1970) J. Phys. B: At. Mol. Opt. Phys. 3, L5-L8 Butaux, F Schuller, R Lennuier J de Phys, 33, (1972), 635.
( ) 22
CV rr
ω
= ±h
( ) 44
CV rr
ω
= ±h
( ) 33
CV rr
ω
= ±h
( ) 66
CV rr
ω
= −h
2
3 2016r r
e
e fCm c
ω λπ ε
=
2 26
0
12
C e rh
ω αε
=
Semi empirical Potential
( ) 61212 6
CCV rr r
ω⎛ ⎞= −⎜ ⎟
⎝ ⎠h
m6s-1 *2
2 2 *20 2 5 1 ( 1)2 i
nr a n l lz
= + − +
2 26C e rω α= ergcm6
* Hi
i u
En zE E
=−
α atomic polarizability m3
• 8
Blue satellites
R
Vupper
ΔV(R)= Vupper-Vlower
Maximum of ΔV
hν
Internuclear distance R
Maximum
hump
λs
Extrema of ΔV satellites
Vlower
-C6/R6
C3/R3
H G Kuhn : Does your treatment predict satellite line? A Jablonski: The theory does not predict this mysterious effect. 1968
λ0
(repulsive part)
MOLPRO 2009 package http://www.molpro.net Laboratoire de Physique et Chimie Quantique Toulouse
• 9
Stark Van der Waals (-C6/r6) Resonant (+-C3/r3)
Interaction Physical classification
Spectral line Profile
Potentiel ab initio
?
• 10
Historical development
( ) 0dtdtη
ω ω= + 0( )V r
ω ωΔ
= +h
Quasistatic approximation
Line shape formalism based on the Fourier transform of the autocorrelation function
( ) [ ] τωττφπ
ω diP ∫=+∞
0
1 expRe)( ( ( ) ( ))( ) i t te dtη η τφ τ+∞
− −
−∞
= ∫Autocorrelation function (wave train) P. W. Anderson, Phys Rev 76 (1949) 647.
P. W. Anderson, Phys Rev 86 (1952) 809.
Weisskopf (1932), Lindholm (1941), Foley (1946) Holtsmark (1919), Kuhn and Margenau (1937),
Impact approximation Phase shift
11
Spectral Line Profile
11
∫∞
⋅=0
)()0(Re1)( tietdddtI ω
πω
!!
)()0()()( tUdtUtd!!
+=
)())()(()( 0 tUtVtHtdtdUi +=!
time-dependent Schrödinger equation for the evolution operator U(t)
Quantum treatment
Code
d is the dipole moment U(t) evolution operator relative to the electrons
U-matrix
H0 is the Hamiltonian of the unperturbed emitter
12
Spectral Line Profile
12
( ) [ ] τωττφπ
ω diP ∫=+∞
0
1 expRe)(
( ( ) ( ))( ) i t te dtη η τφ τ+∞
− −
−∞
= ∫
Autocorrelation function (wave train)
The autocorrelation function measures the average evolution of the wave train over a time interval τ
from an initial time t
Classical theory Isolated line!!
( )( ) pert pN Vi
te e τηφ τ −−= =
This concerns most of atomic lines emitted from non-
hydrogenic systems.
{ } titi uleetdd ωη −−∝⋅ )()()0(!!
• 13
Perturber density Npert
{ }])'))'((1exp(1[2)(00∫∫ ∫ −−=
+∞ +∞
∞−
τ
πτ dttRVidxbdbVp!
( ) ( )[ ] 2/1202 tv++= xbtR b
R(t)
perturber
classical Perturber trajectory
Emitter
Spectral Line Profile
Rectilinear classical path
b is the impact parameter
( )( ) pert pN Vi
te e τηφ τ −−= =
Vp: collision volume
• 14
Unified theory
( ) ( )( )( )( )
( )( ) ( )( )⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−
∫= ∑ ∫ ∫∑
∞ ∞+
∞−
0~~021'
*''
0'
'
2'
),(0 RdRdeRdxdd
dg eeee
tRdti
ee ee
eeee
fi τρπρτ
τ
α
α
V!
dee’ Dipole transition moment (ab initio calculation )
Allard N F, Royer A, Kielkopf J F and Feautrier N 1999 Phys. Rev. A 60 1021
( ) [ ]( )1
' '( ) ( ) eV R tkT
ee eed R t d R t e− ⎡ ⎤⎣ ⎦
=%
• 15
Spectral Line Profile
Experimental profile
Lorenztian profile (Voigt profile)
Impact approximation
N<<, core
Red Asymmetric profile
Quasi static approximation
N>>, wing
Unified theory N, ω
The quasistatic and impact approx ima t ions repre sen t important theoretical limits that are in many cases sufficient for practical purposes and have been used to guide and develop new methods that are more generally applicable and, in fact, satisfactorily solve the line b r o a d e n i n g p r o b l e m i n
practically all cases. S. Alexiou / (2009)
Kjj: 0,9-1,8
Stark -------
Resonant
van der Waals
2 3/52/56 0.7v
2ul
vdwPA C N
c Tλ
λπ
⎛ ⎞Δ = Δ ∝⎜ ⎟
⎝ ⎠
A : 8.08 ou 8.16 πµ
kT8v =752,VDW
vdwS λλ
Δ=
Impact Approximation
K: 0,9-1,8
2 20
20
14
ul r rres
r e
e fg PK Ng m c T
λ λλ
π πεΔ = ∝
0resSλ ≈
• 17
Quasistatic Approximation
Stark -------
Resonant
Van der Waals
( )( ) ( )⎟
⎟⎠
⎞⎜⎜⎝
⎛
−
Δ−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
Δ=
ul
qs
ul
qsQSP λλ
λπ
λλ
λλ
421
21
3exp
/
( ) 0=λQSP
ulλλ >
ulλλ ≤
( ) ( ) ζζζλ dPPP QSLorT −Δ= ∫+∞
∞−
H. Margenau Phys. Rev. 48, (1935) 755. H. Margenau Phys Rev 82 (1951) 156.
H. R. Zaidi , Can. J. Physics 55, (1977) 1243.
resQS resQSSλ ε λ≈ Δ
22 2
60.411 ulQS C N
cλ
λ πΔ =
( )1resQS res Nλ λ βΔ = Δ −
• 18
Stark
Hα 656.2 nm, Hβ 486.1 nm
Linear Stark effect Hydrogen lines
H.R. Griem, Plasma Spectroscopy, Academic Press, New York, 1964.1964 H Griem Spectral line broadening by Plasmas London Academic 1974 H. Griem, Principles of Plasma Spectroscopy, Cambridge University Press, 1997.
M. Gigosos et V. Gardeñoso, J. Phys. B: At. Mol. Opt. Phys., vol. 29, no 20, p. 4795, oct. 1996. M. Gigosos , M Gonzalez V. Gardeñoso Spectrochimica Acta Part B 58 (2003) 1489–1504
Table full width at half area
Ne=C(Ne,T)*Δλ3/2 Where C(Ne,T) is in A-3/2 cm-3.
0.68116
23( ) 4.810
estark
Nnmλ ⎛ ⎞Δ = ⎜ ⎟⎝ ⎠
Hα
Hβ
• 20
H-β C6 [ m6s-1] Δλ vdw
4s-2p 7.59*10-43 2.20×10-5PT-7/10
4p-2s 6.85*10-43 2.12×10-5PT-7/10
4d-2p 5.82*10-43 1.98×10-5PT-7/10
H-α C6 [ m6s-1] Δλ vdw
3s-2p 2.75*10-43 2.40×10-5PT-7/10
3p-2s 1.696*10-43 2.20×10-5PT-7/10
3d-2p 1.18*10-43 1.93×10-5PT-7/10
( ) ( )NTN vdweestarklor λλλ Δ+Δ=Δ ,
Hβ quadratic Stark, Hα self –absorption
Example : Helium Gas Linear Stark effect + van der Waals
Quadratic Stark Effect
( ) ωαλ 2)75.01(75.11 rStark
−+=ΔNe, Te
H. R. Griem (1964) Plasmas Spectroscopy , McGraw-Hill Book Compagny, New York. H .R. Griem (1974) Spectral Line Broadening by Plasmas , New York : Academic Press. H. R. Griem (1997) Principles of Plasma Spectroscopy , Cambridge.
( )( )∫
∞
−+=
022341
W1
β
ββπ /
)(Ax
dxJ
p. 97 Griem 1974
Quasistatic Approximation Impact Approximation electrons ions
( ) ( ) ( ) ( )3 2
02 sin expW dβ π β χ βχ χ χ
∞= −∫
ωλ )75,01(2)( rAdS Stark −±=
Holtsmark distribution
• 22
Stark : Line shape Code Quantum treatment, Numerical calculation
Simulation code
LSNS Rosato, J. et al J. Quant. Spectrosc. Radiat. Transfer 2015, 165, 102–107
computer simulation method The particle motion is simulated and the Schrödinger Eq. is solved numerically it is time consuming
SimU Stambulchik, E. et al Phys. Rev. E 2007, 75, 016401
….. Models
PPP Frequency Fluctuation Model Rapid calculations for neutral and charged emitters
QC-FFM Stambulchik, E.et al Phys. Rev. E 2013, 87, 053108.
Frequency Fluctuation Model
Zest Gilleron, F et al Atoms 2018, 6, 11
Quasi-static description of ions and impact approximation for electrons
……
Calisti, A et al Phys. Rev. A 1990, 42, 5433–5440.
• 23
Stark (C2/r2, C4/r4) Van der Waals (-C6/r6) Resonant (+-C3/r3)
Interaction Physical classification
Spectral line Profile
Potentiel ab initio Code MOLPRO
http://www.molpro.net
Classical theory Quantum treatment
Unified theory Impact approximation Quasitatic approximation
• 24
Examples
1. Self-healing of a metallized polypropylene film 2. Positive streamers in liquid nitrogen 3. Streamers in chlorinated alkane and alkene liquids 4. Helium cryoplasma
• 25
Modeling of the spectroscopic emission lines of Aluminum emitted by a self-healing of a
metallized polypropylene film.
Rel
ativ
e in
tens
ity
394 396 398
0.2
0.4
0.6
0.8
1
Wavelength (nm)
Simulation
Experiment
394.5 and 396.15 nm
• 26
385 390 395 400 405 410
0.0
0.2
0.4
0.6
0.8
1.0
Rel
ativ
e in
tens
ity
Wavelength (nm)
Self-healing Hollow cathode
lamp of Al
385 390 395 400 405
0.0
0.2
0.4
0.6
0.8
1.0
Rel
ativ
e In
tens
ity
Wavelength (nm)
Confined discharge
Modeling of the spectroscopic emission lines of Aluminum emitted by a self-healing of a
metallized polypropylene film.
T=6500-7000K Ng=0,8-1 1026 m-3
Ne=2-3 1024 m-3
Two distinct phases
The streamer propagation Streamer reaches the plane Re-illumination
Weak emitted light Intense emitted light
~100 streamers 1 streamer
Streak photograph of filamentary
streamer propagating up to plane
time
d
Positive filamentary streamers in liquid nitrogen
80mm, 102kV
0,4/1400µs 100-200 mA
Light emitted by one positive streamer in LN2 when it stops
on the insulating plane
Intense NI Atomic line (3s4P-3p4S0 and 3s4P-3p4P transition)
Experimental Results
Tbreakdown T=0 No N2 emission time
Positive filamentary streamers in liquid nitrogen
When one positive streamer stops on the insulating plane, a large current pulse and a bright emitted light are recorded at tb
Re-illumination
Broadening of Atomic line of NI
Re-illumination
Positive filamentary streamers in liquid nitrogen
Propagation velocity : 10-30 km/s
735 740 745 750 755
0,0
0,2
0,4
0,6
0,8
1,0
Normalized
Intens
itya.u.
λ(nm)
Tb= 2.6µs v=30km/s
Tb= 6.4µs v=12,4km/s
Tb= 8.6µs v=9,3km/s
Ne~1,5x1024 m-3
Ng~6x1026 m-3
Simulation of atomic line Re-illumination
Positive filamentary streamers in liquid nitrogen
735 740 745 750 755
0,0
0,2
0,4
0,6
0,8
1,0
Intens
itya.u.
λ(nm)
s imula teds pec trumexperimenta ls pec trum
Tb=2,6µs
2 3 4 5 6 7 8 9 10 11
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
neutrald
ensity1026
m-3
elec
tron
den
sity1024
m-3
B reakdowntime(µs )
e lec tronic dens ityneutra ldens ity
Re-illumination
R= 124 µm
Ng (2.6µs) > Ng (8.6µs) ?
P Gournay and O Lesaint 1994
Rm=130µm
21µs
Tb=2.6 µs Tb=8.6 µs Time
streamer channel radius
Collapse of gaseous filament
R= 78 µm
Tb The plasma column has expanded Ng
Expansion of gaseous filament
Positive filamentary streamers in liquid nitrogen Laser beam
Photodiode
10 µm
200 µm
t0
h
8 µm
tc tmax
gmax
100 ns
100µm 50 µm
A
B
C
Positive filamentary streamers in liquid nitrogen
2000 K- 3000 K Internal Pressure of the gas ~200 B V=30 km/s Internal Pressure of the gas ~30 B V=10 km/s Ne=1-5 1023 m-3
• 33
Spectral analysis of the light emitted from streamers in chlorinated alkane and
alkene liquids
Trot =3000-4000 K P=86-136 bar Ne=4-8 1023 m-3
725,6 nm
20-30 km/s
• 34
Optical Emission from Helium Cryoplasma Discharge in dense fluids (liquids or high-pressure gases :1-100 bar)
Corona-discharge
Liquid Helium
Gas liquid
Temperature: 300 K Density N: 2 1019 cm-3
4.2 K 2 1022 cm-3
T
Ø pure liquid Ø intense luminescenceØ helium is atomic.Ø Low electronic mobility.Ø physical and Thermodynamic
propertiesØ interaction potential ab initio He*-
He and He2*- He
V ~ kV DC, I ~ 0,1-50µA
P=0,1-100mW,
gap distance~5-8 mm
Rtip ~ 0,1-2µm
Important input parameters for the collision-radiative model in the theoretical study of the corona-discharges
Goal: Determine Ne ,Te, T, NHe
• 35
4.2 K 11 K 150 K 300 K
Helium Cryoplasma
• 36
Temperature : Rotational temperature measurements
300 K (P) 4.2 K (P)
N2, N2+
He2
150 K (P) 11 K (P)
N2, N2+
He2
He2 He2
388 389 390 391 392 393
0,0
0,2
0,4
0,6
0,8
1,0
B2Σ+u-- X2Σ+g
Inte
nsity
(u.a
)
λ(nm)
Exper Simulation
P=0.04MPaNegativeTrot=250K
N+2
He
(0-0)
T=150K
630 635 640 645 650
0.0
0.2
0.4
0.6
0.8
1.0 T =150KP =0.04MP a
Δλ=0.1nmS =0.28nmT
r=165K
Intensité(u.a)
λ(nm)
E xpérienceS imula tion
Trot=240 K Trot=200 K
N2+
He2
The rotational line of Nitrogen molecular bands was a probe to thermodynamic temperature at non equilibrium plasma. The values of
• 37
Temperature : Rotational temperature measurements
3300 K (P)(P) 4.2 K
0,0 0,3 0,6 0,9 1,2 1,5 1,8 2,1 2,4
300
330
360
390
420
450
480
510
H e2659,5nm
N2
+391nm
H e2639,6nm
Trot(K)
P res s ure P ,MP a
300K
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,940
60
80
100
120
140
160
180
200
220
240
260
T rot(K)
659,5nm639,6nm
P res s ure P ,MP a
11K
150 K (P) 11 K (P)
300-500 K 240-280 K 80-240 K Trot= 31 P +370 Trot= 33 P +263 Trot= 208 P +62
0,0 0,2 0,4 0,6 0,8 1,0200
220
240
260
280
300
320
T
rot(K
)
H e2639,6nm
N2391nm
H e2659,5nm
P res s ure P ,MP a
150K
N2+ He2
N2+
He2 He2
• 38
?
MolecularexcimersHe2*
630 635 640 645 650
0.0
0.2
0.4
0.6
0.8
1.0
T =4.2K
Intens
ité(u
.a)
λ(nm)
P =0.1MP aP =0.6MP aP =1.4MP a
L IQ U ID E
Strongly Blue Shifted
Temperature : Rotational temperature measurements
R
D1Σu+-B1Πg
(659nm)
d3Σu+-b3Πg
(639,6nm)
P
No boltzmann distribution High degree of rotational excitation
Trot=800 K
P(18)
• 39
Electron number density : Ne
300 K (P) 4.2 K(P)
Hα : 656 nmHβ : 486 nm
He I : 492 nm He 492 nm
Forbidden line 1s4f-1s2p
150 K 11 K
300 K
• 40
The 4th Spectral Line Shapes in Plasmas code comparison workshop– Baden – March 20th to 24th, 2017
Code comparison code workshops http://plasma-gate.weizmann.ac.il/slsp/
corona discharge in helium 300 K
492 nm line
• 41
Code comparison code workshops
Comparison of the FWHM of the H-β Line
• 42
H-β Line in a Corona Helium Plasma: A Multi-Code
Line Shape Comparison
RR Sheeba, M Koubiti, N Bonifaci, F Gilleron, C Mossé… - Atoms 2018, 6(2), 29; https://doi.org/10.3390/atoms6020029
• 43
Broadening of the Neutral Helium 492 nm Line in a Corona Discharge:
Code Comparisons and Data Fitting
1.5 bar 300 K
RR Sheeba, M Koubiti, N Bonifaci, F Gilleron, JC
Pain… - Atoms 2018, 6(2), 19; doi:10.3390/atoms6020019
• 44
A New Procedure to Determine the Plasma Parameters from a Genetic Algorithm Coupled with
the Spectral Line-Shape Code PPP
C Mossé, P Génésio, N Bonifaci, A Calisti- Atoms 2018, 6(4), 55; https://doi.org/10.3390/atoms6040055
• 45
A New Procedure to Determine the Plasma Parameters from a Genetic Algorithm Coupled with
the Spectral Line-Shape Code PPP
• 46
492 493
0
1
2
3
4
5
6
Spe
ctrum(arb.units)
e xperimenta ls pec trumadjus tment,N
e= 1 .8x1015cm -3
λ(nm)
H e I492nmP = 1 ba r
Electron number density : Ne 492 nm
Line Shape Modeling for the Diagnostic of the Electron Density in a Corona Discharge
J Rosato, N Bonifaci, Z Li, R Stamm - Atoms, 2017
Te= 104 K
300 K Computer simulation method
• 47
Electron number density : Ne
300 K (1-10 bar) 4.2 K (P)
1015-1016 cm-3
Forbidden line
Self-absorption allowed line
In Progress
150 K 11 K
• 48
Neutral Perturbers Density : NHe
300 K (P)
Blue satellite
Unified line shape semi-classical theory (N. Allard et al Phys Rev A 60 p1021 1999)
706 nm(3S-3P)
Main line disappears
696 698 700 702 704 706 708 710 712 7140.0
0.2
0.4
0.6
0.8
1.0
Intens
ity(arb.units)
λ(nm)
P = 10ba rP = 16ba rP = 24ba rP = 32ba rP = 39ba rP = 59ba r
T = 300K
Fourier Transform of the dipole autocorrelation function
4.2 K
706 nm(3S-3P)
( ) ( )( )e HeN g sαφ τ−
=
• 49
Neutral Perturbers Density : NHe
He*-HePotential
Blue satellite
• 50
Neutral Perturbers Density : NHe
50
N=2.4 1020 cm3
N=3.8 1020 cm3
N=4.8 1020 cm3
The agreement for a pressure of 1 and 16 Bar is excellent
Comparison between experiment and theory
ResultsforHeline706nm(3S-3P)at300K
N ALLARD, et al EPL 88 (2009) 53002
N ALLARD, et al EPJ D 61 (2011) 365-372
P=10 Bar P= 16 Bar P= 20 Bar
ω (cm-1) ω (cm-1) ω (cm-1) ω (cm-1)
• 51
Neutral Perturbers Density : NHe
300 K (P) 706 nm
Discrepancyobservedathighpressures
width
Comparisonbetweenexperimentandtheory
Width Shift
Unified Theory
• 52
Computer simulation method
Neutral Perturbers Density : NHe
• 53
Neutral Perturbers Density : NHe
685 690 695 700 705 710 715 720-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
Inte
nsity
λ (nm)
P=0.1MPa P=0.6MPa P=1.6MPa P=3.5MPa
Strongly
Blue shifted symmetrical
Gaussian profile 696 698 700 702 704 706 708 710 712 7140.0
0.2
0.4
0.6
0.8
1.0
Intens
ity(arb.units)
λ(nm)
P = 10ba rP = 16ba rP = 24ba rP = 32ba rP = 39ba rP = 59ba r
T = 300K
4.2 K
706 nm
• 54
Neutral Perturbers Density : NHe
Unified semiclassical theory
Allard, N. F. 2012, J. Phys. Conf. Ser., 397, 012065
4. 2 K 706 nm
Line Shape calculations
• 55
Interpretation ? 4.2 K
630 635 640 645 650
0.0
0.2
0.4
0.6
0.8
1.0
T =4.2K
Intens
ité(u
.a)
λ(nm)
P =0.1MP aP =0.6MP aP =1.4MP a
L IQ U ID E
685 690 695 700 705 710 715 720-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
Inte
nsity
λ (nm)
P=0.1MPa P=0.6MPa P=1.6MPa P=3.5MPa
• 56
The mobility decreases rapidly when transitioning from the gas to the liquid phase
The repulsive interaction occurring between e- and helium atoms.
He localizes electrons in «bubbles»
Re ~20 Å P=0.1 MPa T= 4.2 K
e-
R~20Å
He atom
Electron bubbles in liquid 4He
Microscopic cavity: « Bubble » PRREE eltot32
344 πσπ ++=
surface energy PV energy L He is characterized by its density and surface tension parameter
P is the He pressure
• 57
Atomic–bubble model
A. Hofer, P. Moroshkin, S. Ulzega, D. Nettels, R. Müller-Siebert, and A. Weis, Phys. Rev. A 76 , 022502 (2007)
Alkali-metal atoms implanted in condensed He reside innanosize spherical cavities
These bubbles are formed around each impurity atom due to the Pauli principle that forbids any overlap between the closed S shells of He atoms and the valence electron of the impurity
Schematic model of a Cs atom inside a spherical He bubble.
Ralkali ~ 5–7 Å
• 58
He* He2* Rydberg electron
Interpretation:
Microscopic void around the He*3s and He2*3d
Repulsion between Rydberg e- and surrounding atoms in the ground state forms bubble
?
• 59
He*(3s)
Atomic bubble
Bulk helium
New autocorrelation function with « bath » interaction
( ) ( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ Δ−−=Φ ∫
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−
rdrtrVi
ei
fi
3
/1exp ρτ
!
Difference pair potential b e t w e e n t h e s t a t e s corresponding to the emission line
Molpro code
Liquid density in the electronic ground state around 3s calculated using Bosonic Density
Functional Theory DFT
• 60
Bubble Radius (Rb) depends on applied
pressure (P).
1 bar
Liquid density around He*(3s3S)
Liquid density around 3s3S calculated using DFT
Empty cavity around excited atom (emitter)
Phys. Rev. A 85 042706 (2012).
3S
• 61
706.5 nm He* line (3S-3P)
the line position is extremely sensitive to the He*(3s) - He pair potential
Experimental (continuous) vs theoretical (dashed)
Line shift
DFT b1, b2
• 62
He2*(d3Σu)-He ab initio potential
J. Eloranta and V. A. Apkarian J. Chem. Phys. 115, 752 (2001). N Bonifaci, Z Li, J Eloranta and S L Fiedler J. Phys. Chem. A, 120 (45), pp 9019–9027 2016
Linear He2 (3d) - He
He(3s)-He
630 635 640 645 650
0.0
0.2
0.4
0.6
0.8
1.0
T =4.2K
Intens
ité(u
.a)
λ(nm)
P =0.1MP aP =0.6MP aP =1.4MP a
L IQ U ID E
T-orientation He2 (3d) - He
• 63
Liquid density around He2 d3Σu+
R=12,7 Å 1 Bar R= 10,8 Å 24 Bar
DFT
Shift
He2(3d-3b)
AAo
&o
• 64
Conclusion
Impact theory Unified semiclassical theory Localized bubble state
300 K 4.2 K
The good agreement observed between the simulations and the experimental fluorescence data suggests that both He2 and He emit from a liquid environment at 4 K.
NHe, Ne, T Liquid Helium
He 3s Bubble R~10 Å
He2 d3Σu+
Bubble
R~10-13 Å
• 65
Outlook: Comparison between Andronikashvili's and the molecular probe approaches.
Andronikashvili’s experiment Molecules He2*/liquid He
Macroscopic Microscopic
Two-fluid model Local two-fluid model
Observable: torsional frequency Observable : OES
Interaction of He2*molecules with helium nanoscopic probes
Tλ=2,17 K
4 K 1 K Superfluid phase
300 K
Thank you for your attention
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