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Physics with Many Positrons- Varenna, 7-17 luglio 2009
Roberto S. BrusaAlfredo Dupasquier
Many experiments with many positrons require high yield of cooled Ps
(see previous and following lectures of this school)
BEC, Anti-hydrogen formation by Ps*-pbar charge exchange,Ps spectroscopy, Ps excitation in Rydberg states
Introductory remarksIntroductory remarks
Physics with Many Positrons- Varenna, 7-17 luglio 2009
•For these experiment high intensity bunched beams are necessarybut Ps must be formed and cooled, confined or in vacuum,
and you need a a 5x5x0.5 mm3 of some material
• Ps can be cooled and in some cases it can reach the
thermal equilibrium with the host (thermalize)
The target material have to fulfill many requirements:
a) To be stable both at RT as at cryogenic T ie:
b) The material must not be damaged by e+ flux or photon fluxthe Ps yield and cooling can be worsened
c) Charging effect must be avoided
Physics with Many Positrons- Varenna, 7-17 luglio 2009
also for laser cooling a Ps pre-cooling would be necessary and a Ps
converter necessary
d) Reasonable goal : it must convert about 10 % of e+ in cooled Ps
If Ps is formed, it could be cooled by lasers, but is final T will depend from its starting T
a two level atom in steady state can spend at most half of its time in the excited state
Physics with Many Positrons- Varenna, 7-17 luglio 2009
a two level atom in steady state can spend at most half of its time in the excited statebecause in P state τ=100µs oPs live 280 ns
In 280 ns about 44 excitation de-excitationare only possible (6.4 ns for process)
smxm
kv
Psrec /105.1 3== h
m
kTk mB
22
2
1
2
1 h= Tm = 0.3 K
If oPs has RT thermal velocity, it can reach at least ~ 10 K
ns
vv
dt
dv recrec 2.3
−=Γ−= 44=Γ∆t
From what we know about Ps formation processes in metals and dielectrics we can point out:
a) In metals , one Ps emission is thermal, it means that high yield are obtained by increasing the temperature, to have Ps emission at low temperature
modification of the surface is needed to change the positron activation energy
b) In silica up to 80% Ps is formed and it can be also emitted in vacuumbut with energy around 1-3 eV, cooling mechanism by collision must be used.
Physics with Many Positrons- Varenna, 7-17 luglio 2009
but with energy around 1-3 eV, cooling mechanism by collision must be used.
Information on Ps collision can be gained by studyingPs thermalization in gases
outlineoutline•I lecture
•Ps thermalization and cooling by collisionsThermalization in gases
•Thermalization in silica oxide powders
•Ps emission at low temperature from modified metal surfaces
Physics with Many Positrons- Varenna, 7-17 luglio 2009
II lecture
•Porous materials: cooling at room temperature
•Porous materials: cryogenic cooling
•oPs pick-off at cryogenic temperature
•oPs emission from nano-channels in silicon
Studies in gas are interesting toobtain information on the thermalization process:
Collisions: elastic ?
anelastic ?
Ps formation in gases
e+ GAS Ps
Collisions in gasesCollisions in gases
Influence the energy loss and theThermalization times
Physics with Many Positrons- Varenna, 7-17 luglio 2009
e+ GAS Ps
Charge exchange process
Positronium is formed with energy
−++ ++→+ ePsYYe
)8.6( −+= + iePs EEE
The energy of interest in Ps thermalization are from few eV (3-6) to meV
Ps beams are limited at Ps energies of 10 eVbecause:
a) Ps yield decreases at threshold energyb) The angular divergence increases
From Surko et al. 2005
Ar
In future, thanks many positrons,measurements with Ps beam from
neutralization of Ps- could be possibleSee for ex. Gartner poster
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Cross sections and oPs thermalization are studied in gases at high pressureinjecting fast positrons from radioactive source
two different systems:
in gases at high pressure : time resolved Doppler broadening DB
in gases confined in silica aerogel (1 atm): ACAR measurements
Open channels in the thermalization process of Ps:
YPsYPs +→+*YPsYPs +→+
Elastic scattering
Inelastic vibrational and rotational excitation(only for molecules)
Channels that can contribute to Ps slowing down
Physics with Many Positrons- Varenna, 7-17 luglio 2009
−+ ++→+ eYYoPs γ2
)()( ↓+→↑+ YpPsYoPs
energyoPsYYoPs +→+
Pick-off quenching
Exchange or conversion quenching
Chemical quenching
Channels that remove Ps
Hypothesis : 1) scattering is spherically symmetric in the centre of mass system 2) Molecular motion completely random
The model looks for an expression giving the energy loss for collision
The Ps slowing down was modeled with the Sauder’s classical elastic scattering model (’68)
If deviation are found , they can be ascribed at inelastic channels
Sauder’s modelSauder’s model
Physics with Many Positrons- Varenna, 7-17 luglio 2009
( )
−
+−=∆
22
22
2
VMvm
Mm
MmE PsPs
Ps
Ps
Whit this hypothesis is possible to average on all possible scattering angles and the energy loss becomes:
M
m
E
E p−≈∆
iKKE −=∆
Psc vnσλ =
( )
−+
−≅ TktEtEmnMm
Mm
dt
tdEbPs
Ps
Ps
2
3)()(2
2)(2
σ3
2VMTkE ==
From the kinetic theory the mean collision rate is
Where n is the number of atoms for cm3 and σ the elastic cross section
PsPsvmtE2
1)( =
cEdt
dE λ∆= Treated as a continuum process
Physics with Many Positrons- Varenna, 7-17 luglio 2009
( ) + Mmdt Ps 22
22
3 VMTkE bth ==
MmM Ps ≈+
thE
E01coth−=β
( )tE
tE
thαβ += 2coth
)(
tcos=σIntegrating with
MmTkn Psb
13σα ≅
The principle of the measurements are based on oPs in m=0 state that annihilate into 2 gammas when mixed with pPs in a magnetic field
(Zeeman effect).
( )
)(36)1(1
1
1
2
22
320,1
kG
Bx
x
xy
yy
≅++
=
Γ+Γ+
=Γ γγ
Principle of the measurementsPrinciple of the measurements
Physics with Many Positrons- Varenna, 7-17 luglio 2009
At the used field of about 3 kG 64% of oPs is mixed and its lifetime is reduced at 52 ns
pPs lifetime is practically un-changed at this field
)1(1 x++
Effect: narrowing of DB annihilation spectraand characteristic feature in ACAR spectra
Delayed Time window 30- 50 nsTo avoid prompt events.
Time resolved Doppler broadening Time resolved Doppler broadening
0 < t <30 prompt events:e+, pPs, annihilations
Physics with Many Positrons- Varenna, 7-17 luglio 2009
t>30 oPs mixed
The oPs average kinetics energy is computed from the FWHMof the narrow peak assuming a Maxwell Boltzman distribution of isotropic velocity for thermalized Ps
EPs= (1.028 FWHM)2
Physics with Many Positrons- Varenna, 7-17 luglio 2009
From Gidley PRA 67(2003)
From Gidley PRA 67(2003)
Physics with Many Positrons- Varenna, 7-17 luglio 2009
( )tE
tE
thαβ += 2coth
)(
thE
E01coth−=β
100 Torr
From Gidley PRA 67(2003)
Ps within 10% Eth 2τ=2/ΓN2 ~ 180 nsHe ~ 120 ns H2 ~ 50 ns
Isobutane C4H10 ~ 32 nsNeopentane C5H12 ~ 26 ns
Normalized density thermalization rate
thPsPs v
M
m
nσα ≅=Γ
tE
Earc αβ +=
0coth
Measure in silica aerogel 0.1 g/cm3
Mean grains diameter of aerogel 5 nm mean distance between the grain 70 nm
In the measurements the scattering with the walls of the grainsmust be take into account
The Sauder’s model is modified
L
vPss =λa collision frequency with the grain is added
ACAR in silica aerogel ACAR in silica aerogel
Psc vnσλ =to
Physics with Many Positrons- Varenna, 7-17 luglio 2009
thE
E01coth−=β( )tE
tE
thαβ += 2coth
)(
Ls =λa collision frequency with the grain is added
sMLs
2=
Ms effective mass of surface atoms
Psc vnσλ =
MmTkn Psb
13σα ≅
to
Psbm mTks
M
n3*
+= σα
Without field With 0.29 T magnetic field
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Nagashima PRB ‘95, JPB ‘98Saito JPB 2003
∫∞
∞−
∫∞
∞−=
zz
zzps
z
av
dppN
dppNm
p
E
)(
)(2
3
)(
2
exp τ
Physics with Many Positrons- Varenna, 7-17 luglio 2009
dte
dtetE
Et
t
av
∫∞ −
∫∞ −
=
0
0)(
)(τ
τ
τ
∫∞
∞−
∫∞
∞−=
zz
zzps
z
av
dppN
dppNm
p
E
)(
)(2
3
)(
2
exp τ
With E(t) from an improved formula of the type
( )[ ])(2
3)()(2
)(sffTktEtEm
dt
tdEbPs +
−−≅ σ
Both the experiments seems to indicate that the thermalization of PsIs only determined by elastic scattering.
Also in the complex molecules.
0
1
2
3
4
5
Inte
gral
cro
ss s
ectio
n [1
0-16 c
m2 ]
H2 N2 CO
ν=0 1
first vibrational quantum
e-e+
Surko 2005
e- CO
Physics with Many Positrons- Varenna, 7-17 luglio 2009
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0
Electron Energy [eV]
But Ps is neutral and its interaction is a van der Walls interaction effective atshort distance
interaction positronium
Static Zero
Polarization Zero
Exchange Yes
86)(
R
B
R
ARV +−=
1E-3 0,01 0,1 10,01
0,1
1
10
Ps
inte
ract
ion
time
t x1
0-14 s
Ps energy [eV]
t = a/vPs a= 3 A
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Ps energy [eV]
Vibrational period in molecules ~ 10-14 s Rotational period in molecules ~ 10-12 s
Study of Ps thermalization in gases seems to show that inelastic scattering collisions, if present, are not much effective in cooling Ps
Time resolved DB and ACARTime resolved DB and ACARfor thermalization in powders and aerogelfor thermalization in powders and aerogel
Method:
Physics with Many Positrons- Varenna, 7-17 luglio 2009
From Takada et al. RPC 2000Materials:
Cab-O-Sil or fumed silica
Aerogel , very light material [ ] OnHSiOOHnSi n 224 2)( +→
HClSiOOHSiCl 42 2224 +→++
In magnetic field B
(-OH group on the walls)
Silica powders
ACAR time resolved DB-time resolved
a
vTE
dt
tdE Ps)()( ∆=
70 nm
5.6 nm
M= 355a.mu.
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Th
Average Ps energy as a function of the time t in powders. Closed circles results onCab-O-Sil (ρ=1 g/cm3) with time resolved ACAR. Open Circles results on silicaaerogel (ρ=0.1 g/cm3).The line is a fit with the Sauder’s elastic model.
Time of flightTime of flight
Physics with Many Positrons- Varenna, 7-17 luglio 2009
The perpendicular velocity is measured ⊥v2
22
2
1
t
zmvmE ePs == ⊥⊥
SiOSiO22 powderspowders
Fumed silica0.18 g/cm3
Grain 3.5 nm
Physics with Many Positrons- Varenna, 7-17 luglio 2009
2
22
2
1
t
zmvmE ePs == ⊥⊥F(t) is multiplied for:
exp (t/142 ns) – oPs decay1/t –time spent by oPs in front to the detector
t3 – for the change of variables
Mills-1989t=0
SiOSiO22 powderspowders
non thermal Ps emission was found
4.2 K 2% thermal at 19 keV positron implatation30 % below 10 meV (76 K)
77 K at 10 keV 54 % below 64 meV (490 K)
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Mills-1989
AluminumAluminum
Vacuum
e+Ps e+
Solid eVEE ba 8.6−+= −φ
To obtain thermal desorption at low temperature the surface must be modified
to lower the activation energy Ea
After Lynn ’80, monolayer of Owas found to promote Ps desorption
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Mills ‘91
the Ps formation and yield is strongly dependent on the Al + O system preparation and the right O2 exposure conditions at lowtemperaturethe oxygen phase at the Al surface can change as a function of the sample temperature and the adsorbed oxygen.
Practical problems with such a source of cool Ps
Physics with Many Positrons- Varenna, 7-17 luglio 2009
the oxygen coverage is destroyed by heating the sampleafter the oxygenation process and probably the oxygen overlayer is also sensible to photonsflux that can dissociate the chemical surface bonding betweenphysisorbed oxygen and Al
eVEE ba 8.6−+= −φ
Ni +alkaliNi +alkali--metalmetal
Physics with Many Positrons- Varenna, 7-17 luglio 2009
Gidley 88
Ps formation measured by lifetime and peak to valley ratioTotal Ps yield at 325 K up to 65 % was obtained by covering the Ni surfaceand the yield increased by increasing the sample temperature up to 525 K.
The linear extrapolation of Ea as a function of the coverage predict spontaneous emission of Ps (Ea=0) at 0.9 monolayer of Na on Ni (100)
summarysummary
Ps collision at energies below few eV in gases seems to be mostly elastic and very sensitive to the mass of the single atoms more
than to the structure of the molecules
Ps cool down in silica powders and silica aerogel quite efficiently.The cooling rate depends
from the size of the open volumes between the grains. Effective mass
Physics with Many Positrons- Varenna, 7-17 luglio 2009
from the size of the open volumes between the grains. Effective mass always larger than the mass of the SiO2 and -HO atoms on the surface
Ps was found to cool at 77 K in Si powder kept at 4 K
Metals are requiring more study. Works date ’88-’91Possible modification of the
surface for activating Ps desorption at low temperature must be search for.
•I lecture
•Ps thermalization and cooling by collisionsThermalization in gases
•Thermalization in silica oxide powders
•Ps emission at low temperature from modified metal surfaces
Physics with Many Positrons- Varenna, 7-17 luglio 2009
II lecture
•Porous materials: cooling at room temperature
•Porous materials: cryogenic cooling
•oPs pick-off at cryogenic temperature
•oPs emission from nano-channels in silicon