Biomedical Engineering Reference
In-Depth Information
125 ps. In order to conserve charge-parity, the decay of ground-state Ps proceeds by
an odd number of
-rays for ortho-Ps or an even number for para-Ps . Thus, a unique
signal of ground-state ortho-Ps is the coincident detection of three
-rays whose
energies must total the sum of twice the rest mass energy of the electron (1.022
MeV) and any initial kinetic energy. As with 'direct' annihilation, which occurs
principally by the emission of two
-rays, decay via a higher number of photons
is reduced by several orders of magnitude. At the coarsest level of description, Ps
is structurally similar to atomic hydrogen, with the Bohr energy levels halved as a
result of the lower mass of the positron in comparison to the proton. Beyond this
similarity, the fine structure is quite different (e.g. [
10
]) due to the ratio of magnetic
moment of the positron to that of the proton (
), which elevates the hyperfine
structure observed in Ps to the order of the fine structure observed in H [
11
].
In addition to the formation of Ps, the positron may ionize a target directly by
releasing one (or more) electron(s). Overall, the total ionization cross-section (
658
Q
i
)
C Q
ti
C Q
ann
C Q
n
C
Q
i
D Q
Ps
C Q
i
is defined by:
, where the elements of the
sum are the cross-sections for Ps formation, direct ionization, transfer ionization,
annihilation and multiple ionization, respectively.
1
i
For atomic targets, this can be
Q
i
C Q
i
approximated to
, the cross-sections for the other processes
often being comparatively negligible [
4
]. At their maxima, the probabilities for Ps
formation and direct ionization account for roughly half of the overall scattering
probability.
Q
Ps
8.2.2
Ionization of atoms
The atomic targets examined in this section are used to introduce key features
of positron-impact ionization before considering molecules. (A recent review of
positron-impact ionization of the inert atoms can be found in [
4
]).
Figure
8.1
a shows the partitioning of
Q
i
for He into the contributions from the
two dominant ionization processes, Ps formation and direct ionization, and serves
to highlight some common features for atoms. While at high energies electron data
may be used to approximate corresponding positron results,
2
at energies below
1 keV major differences arise due to the diverse nature of the interactions and
reactions of the different projectiles. These include exchange for electrons (and Ps—
see Section
8.3
), the equal and opposite static interaction for electrons and positrons,
as well as the possibility of electron capture and annihilation for positrons (and
Ps). In general, the total ionization cross-section by positron impact exceeds that
by electrons at low and intermediate energies, primarily due to Ps formation. For
low-
Q
i
also exceeds that for electrons due to polarization effects [
20
],
a situation which is reversed at the lowest impact energies due to a combination
Z
atoms,
1
Ionization-excitation events are a subset of the above-identified ionization events.
2
As per the charge-sign independence of the cross-sections within the First Born Approximation.
