Physics with Cold Polarised
Positronium
David B. Cassidy & Allen P. Mills
Department of Physics and Astronomy,
University of California, Riverside, USA
cassidy@physics.ucr.edu
Jefferson Lab March 2009
Positronium
Although electrons and positrons mutually annihilate each
other, they can co-exist for a short time in a bound state
called positronium (chemical symbol Ps)
Ps can exist in different configurations depending on the
relative spin states of the positron and the electron. These are
known as para-positronium (p-Ps), with total spin s = 0 and
ortho positronium (o-Ps) with s = 1.
0,0 
1


2
 

1,0 
1


2
 

1,1  
1,1  
How long does positronium live?
The Ps lifetime against annihilation depends on the number of
photons the atom decays into. For s=1 this must be an odd
number and for s = 0 it must be even
The Ps decay rates are
1 mc 2 5
2 ( p  Ps) 
2 n 3
2 6
2
mc

3 (o  Ps) 
( 2  9)
9
n 3
The ground state Ps vacuum lifetimes (inverse of the
decay rate) are
τp-Ps = 125 ps
τo-Ps = 142 ns
Energy levels of hydrogen and positronium
En ( H )  
H 
e 4
2n 2

1
 13.6eV
2
n
me M
 me
me  M
me2
m
 Ps 
 e
2me
2
1
E n ( Ps)   2  6.8eV
n
Gross energy levels are half
that of H. The large Ps
magnetic moment makes the
hyperfine splitting much
larger than is the case for H
R. Ley, Appl. Surf. Sci. 194 301(2002)
How do we make Ps atoms?
Porous silica (and similar materials)
It’s actually quite easy to
make Ps atoms: positrons
directed onto a silica film
will pick up an electron and
make Ps in the bulk which
may then diffuse to the
surface or internal voids.
In some samples Ps may
also become trapped in a
surface state where they can
interact with other Ps atoms
and form Ps2 molecules.
e+
Ps
SEQ
a-SiO2
Ps2
We can also make Ps on a metal surface:
Single crystal
metal (Al(111))
Incident
Positron pulse
~ 2 keV
Positron
trapped in a
surface state
t ~0.5 ns
e+ emission
Direct/thermal
Ps emission
Positron does
not diffuse to
surface and
annihilates in
the bulk
What can happen when Ps atoms
interact with each other?
• Nothing
o-Ps + o-Ps → o-Ps + o-Ps
• Spin exchange quenching (SEQ)
o-Ps(m=1) + o-Ps(m = -1) → 2 p-Ps + 2Eh
• Positronium molecule (Ps2) formation
X+ o-Ps(m = 1) + o-Ps(m = -1) → X+ Ps2 + Eb
A decoupled
Surko trap
Target
chamber
Trap
Accumulator
Buncher
Source
Nitrogen buffer gas
SF6 cooling gas (~ 1 x 10-8 Torr)
e+ lifetime ~ 2 seconds
e+ lifetime > 500 seconds
Neon moderator
efficiency ~ 20%,
efficiency ~ 80%
> 106 e+/sec
4 Hz duty cycle
Maximum 108 e+
> 50,000 e+/pulse
Typical pulse, 5 x 107 e+
50 mCi 22Na
source
RSI 77, 073106 (2006)
Pulse out ~ 15 ns FWHM
The positron beam density can be
controlled via the “rotating wall”
electric field in the accumulator
 
 
5.0
4.5
n2D ~ 3×1010 cm-2
Inlet
1 2 3 4 5 6 7 8 9
stage 1&2
gate
4.0
Stage 3: multi-ring trap
electrodes
3.0
4.5
5.0
5.5
5.0
4.5
n2D ~ 8×109 cm-2
4.0
3.5
30
Inlet
4.0
4.5
5.0
x (mm)
5.5
gate
200
20
100
10
0
0
3.0
Stage 3
Stage 1 & 2
2
4
6
distance along accumulator axis (inches)
8
dump voltage (V)
4.0
Accumulation voltage (V)
y (mm)
3.5
2 kV buncher produces sub-ns pulses
magnet coil
HV pulse
input
buncher rings
positrons
5 cm
0
-2
-40
Buncher on
Buncher off
-80
-4
-6
-120
-8
-20
-10
0
10
time (ns)
20
30
40
50
PMT output (mV)
PMT output (mV)
0
PMT output (arb. untis)
Lead fluoride and lead tungstate detectors
10
0
PbF2 on H3378-50 PMT
PbWO4 on XP 2020 PMT
Primary light feedback
pulse (~ 5%)
Al(111) target
secondary light feedback
pulses (~ 0.5%)
10
-1
Ion afterpulses
10
-2
10
-3
Prompt peak and
later times recorded
with different scope
gain
NIM A 580 1338 (2007)
-50
0
50
100
150
200
250
time (ns)
300
350
400
450
500
We can analyze each waveform separately, and/or we can automatically determine
the parameter fd which is a measure of the amount of o-Ps created
" delayed fraction" f d  20ns V (t )
PMT Anode signal (V)
150ns

150ns
 20 ns
V (t )
-1
10
-2
10
-3
10
fd
-4
10
0
fd
50
time (ns)
100
150
Single atom positronium decay in voids
• Single shot lifetime
spectra measure the
amount and the decay
rate of o-Ps.
• In porous materials the
decay rate, , depends on
the pore size (pick-off).
• Ps decays
dn
exponentially→
dt
A
A < B
 n
B
How do lifetime spectra change if Ps
atoms interact with each other?
• If SEQ occurs, o-Ps atoms
are converted to p-Ps atoms
and decay rapidly ( ~ 8 ns-1)
• If Ps2 molecules are formed
these will also decay rapidly
( ~ 4 ns-1)
• Present resolution cannot tell
the difference.
• Decay becomes non-linear:
Ordinary (pick-off) decay due to
Ps-Ps
decay
interactions
dn
 n(1   n)
dt
parameter  describes
strength of SEQ and/or
Ps2 formation
If there is a Ps surface state then heating the sample will
thermally desorb Ps, leading to an increase in the Ps fraction
Indicates no Ps surface state
Sample has a Ps surface state
Ps2 formation allowed
Ps2 formation suppressed
20
fd (%)
18
12
Random pores
Aligned pores
Fit
10
8
200
300
400
500
600
Temperature (K)
We were lucky with our samples: they were each
suitable for one process and unsuitable for the other
PMT Anode signal (V)
-1
Randomly distributed Pores
10
System response
Low density beam
High density beam
-2
10
-3
10
-4
10
V (mV)
1.5
1.0
High - Low density
fit
Ps2
0.5
0.0
0
50
100
time (ns)
150
180 K
384 K
517 K
Ps-Ps interactions indicated
by density dependent
changes in lifetime spectra:
the “quenching” effect
1
f d (n2 D )  f d (n2 D ) 
m
1.0
1.5
Quenching data
Y(T) (scaled)
Z
2
Z
-2
cm )
-0.2
f
d
( n2 D )
1
2.5
3.0
-2
Form of Q(T)
indicates that
the Ps-Ps
interactions
occur via two
surface state
atoms
( Z  1  Y (T ))
0
200
m
2.0
10
20
-14
0.0
n2D (10 cm )
30
Q (10
0.2
-0.4
Q  df d / dn 2 D
10
fd (%)
0.4
300
400
Temperature (K)
500
Nature 449 196 (2007)
New system recently installed: higher Ps density
Accumulator beam imaging
chamber
pumping restriction
movable
phosphor
screen
rotatable 10-850 K
cold head
electrostatic
buncher lenses
magnetic field
termination
retractable LEED/Auger
spectrometer
cryo pump
The (near) future……
Production of a BoseEinstein condensate of
positronium
This requires spin
aligned Ps at high
densities
1
2/3
BEC transition temp Tc  (n)
m
Critical temperature Tc (K)
1000
Ps BEC
(after remoderation)
100
10
Ps-Ps interactions
SEQ, Ps2
(present work)
Stimulated annihilation
(after multi-cell trap)
1
Ps laser cooling
recoil limit
0.1
15
10
16
10
17
10
18
10
19
10
-3
Ps density (cm )
20
10
21
10
How can we observe the formation of a Ps BEC?
Doppler broadening of
thermal Ps ensemble will
be much narrower for the
condensed atoms. Can be
observed by laser
absorption
The lifetime difference
between thermal and
condensed Ps will be
negligible.
Ps BEC Atom Laser
Concluding remarks
• Ps2 formation observed, 60 years after it was
predicted…
• Observation via timing data and sample properties is
compelling, but indirect
• Excited state of Ps2 allows for a definitive
spectroscopic measurement
• New area of multi-positronium physics now possible.
Beyond Ps2, Ps BEC formation should also be
achievable using similar techniques, but polarised
beam needed.
Thank you for your attention