Correlation of pick-o annihilation cross section
and the collisional cross section for Ps-atom/molecule collisions
Ken Wada and Toshio Hyodo
Institute of Materials Structure Science, High Energy Accelerator Organization (KEK),
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
Abstract
Positronium quenching through its collisions with gaseous atoms and molecules is discussed.
quenching parameter,
1
Ze ,
at room temperature are practically proportional to the geometric collisional cross-sections estimated from the radius of
the positronium and those of the atoms and molecules derived from the viscosity. This suggests that the probabilities of the pick-o quenching of the
thermalized positronium per collision with various atoms and molecules are almost constant.
Positron annihilation in gases
Experimental values of 1Ze
The annihilation rate of the positron in gaseous
media,
λ+ ,
σgeom
It is convenient to normalize
it to the density of the gas,
n.
1
Ze (≡ 1 Ze (pick-o))
for the
atoms and molecules are shown below against
gas, unless the density is too high or the temperature is too low.
Pick-o quenching
The values of
is proportional to the density of the
in a linear scale.
1
The
Ze
values for
O2 was obtained by decomposing with the age-
If we further
momentum correlation (AMOC) technique [10],
normalize it by the Dirac annhilation rate for
and those for Kr and Xe with an eective use of
unit electron density at the positron,
πr0 2 c,
a
a magnetic eld [7].
dimensionless parameter is introduced:
The
λ+
.
Ze =
πr0 2 c n
experimental values of Ze
(1)
spread widely
across seven orders of magnitude. Using detailed
experimental and theoretical works from the last
two decades, especially those focusing on the energy dependence, most of the values has been
explained well with both the long- and shortrange correlation eects and the formation of
temporary positron-molecule bound states due
to vibrational Feshbach resonances [1].
of
ented
of
Experimental values are cited from refs.[3-6] and oth-
σgeom , is π(a0 +
d/2)2 . Here a0 is the Bohr radius and d is the diameter
of the molecule estimated from its viscosity, η , by the
√
2
equation π(d/2)
= M v/8 2η . M and v are the mass
ers. Geometric collisional cross-section,
and the averaged speed of the molecule, respectively.
Quenching channels
The right vertical axis indicates the pick-o
Pick-o quenching: All gases.
Spin conversion quenching through electron exchange: O2 and NO [3,5]. It takes
inhat
of
ize
endel
of
nts
her
the
nal
It is found that the values of the normalized pick-o
FIG. 14. Scaling of Z
with
/(E
E ). The same symbols
spin-singlet) self-annihilates into 2γ at a rate
of
1/125 ps−1
while ortho-Ps (o-Ps, spin-triplet)
1/142 ns−1 in vacuum.
of o-Ps measured in a
self-annihilates into 3γ at
The annihilation rate
λtotal , is greater than the selfannihilation rate, λ3γ , due to collisional quenchgaseous medium,
o-Ps
NO2 ,
is rst bound to or be
Spin conversion quenching through spinorbit interaction: Kr (1 Ze = 0.478(3)), Xe
(1.26(1)), and probably CH3 I (2.1(2)) [4,6].
Decomposition required to isolate
λpick-o
only.
o-Ps
Theoretical calculation of
1
Ze
density,
n,
and the Dirac rate,
4πr0 c,
σgeom
are roughly
for the real scatter-
ing cross-section, the linear dependence of the
plots indicates that the pick-o quenching probability per collision,
P,
does not vary much
among those atoms and molecules, namely,
σpick-o /σgeom ∼ 6.0 × 10−7 .
This suggests that
the instantaneous overlap of the wave function
o-Ps
positron and that of the taregets'
electrons which are in a spin-singlet state relative to the positron does not vary much among
σpick-o /σgeom
The small value
indicates that
∼ 1.7 millions
The experimental values of
o-Ps
collisions on
1
Ze
are roughly
section. This suggests that the pick-o quenching probabilities per collision for the
There are other quenching processes in addition
There are only a few calculations for He [8], one
to the pick-o.
for Ne, Ar, Kr, and Xe [9], and none for any
cluding all quenching processes with the sub-
others.
script 1 as
many-body eects, as was done for He to ex-
λquench
,
1 Ze =
4πr0 2 c n
(4)
o-Ps
Inclusion of the enhancement due to
The ratio of the cross-section for the pick-o annihilation to the collisional cross-section is [12]
σpick-o /σgeom ∼ 6.0 × 10−7 .
plain experimental result [11], may resolve the
discrepancies between calculations and experiments.
References
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with
atoms and molecules are almost constant.
(3)
We introduce a parameter in-
pick-o
proportional to the geometric collisional cross-
for unit
λpick-o
.
Ze =
2
4πr0 c n
P ∼
Conclusion
spin-singlet electron density, viz,
1
Ze
average.
The pick-o quenching rate,
2
If we take
quenching occurs in
molecules which is in a spin-singlet state relative
is conventionally normalized to the gas
section.
of
(2)
λpick-o ,
1
those atoms and molecules.
annihilates with the electron in the
to the positron.
is the relative speed of the centers of
mass of the molecule and the Ps.
of the
In the case of pick-o quenching, the positron
of the
as
proportional to the geometric collisional cross-
ings where
λtotal = λ3γ + λquench .
vrel
Ze
of the target is non-singlet.
in a resonant state with these molecules.
Among positronium (Ps) atoms, para-Ps (p-Ps,
Here,
1
The experimental values of
Br2 , and I2 [3]. The
Ps quenching in gases
lated to
place only when either the initial or nal state
Chemical or attachment quenching:
cited from ref. [2].
σpick-o , which is reσpick-o = 4πr0 2 c 1 Ze /vrel .
quenching cross-section,
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(5)