Roberto S. Brusa Alfredo Dupasquierstatic.sif.it/SIF/resources/public/files/va2009/brusa... ·...

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


•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


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


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.


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


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


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


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


−+ ++→+ 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


( )

−

+−=∆

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


( ) + 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


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


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


From Gidley PRA 67(2003)



( )tE

tE

thαβ += 2coth

)(

thE

E01coth−=β

100 Torr


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


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


Nagashima PRB ‘95, JPB ‘98Saito JPB 2003

∫∞

∞−

∫∞

∞−=

zz

zzps

z

av

dppN

dppNm

p

E

)(

)(2

3

)(

2

exp τ


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


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


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:


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.


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


The perpendicular velocity is measured ⊥v2

22

2

1

t

zmvmE ePs == ⊥⊥

SiOSiO22 powderspowders

Fumed silica0.18 g/cm3

Grain 3.5 nm


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)


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


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


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


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


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


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

Roberto S. Brusa Alfredo Dupasquierstatic.sif.it/SIF/resources/public/files/va2009/brusa... ·...

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