Lifetime of positronium
Lab report
Friedrich Kurz, Guillem Cucurull, Kaya Vogler
Contents
1 Introduction 2
2 Theory 2
3 Experimental setup 3
4 Experimental method 5
4.1 Energy measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2 Time measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 Data Analysis and Results 9
5.1 Time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.2 Positronium Lifetime in POM . . . . . . . . . . . . . . . . . . . . . . 10
5.3 Positron Lifetime in Aluminium . . . . . . . . . . . . . . . . . . . . . 11
5.4 Energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6 Discussion 13
1
, 1 Introduction
This lab aims to measure the lifetime of positronium. Positronium is a particle
which consists of an electron and a positron. For the experiment, a radioactive
source undergoing β + decay is used. The β + particles (or positrons) bond to an
electron to form positronium, which then annihilates. We use known energies of
photons emitted in the various steps of the experiment to determine the lifetime of
the positronium.
In the first part of the experiment, the source is placed in an aluminium container,
in which electrons are free. We measure a 1275 keV photon emitted during the source
decay to mark the ’start’ time of the positron’s lifetime. In the next step we measure
a 511 keV photon which is emitted during the annihilation of the positron with an
electron. The time difference between these two events gives us a measurement for
the lifetime of the positron in aluminium.
In the second part, the source is placed in a polyoxymethylene (POM) container,
in which the electrons are not free. This means that bound positronium states can
be formed, as the positrons lose energy when they collide with the material. The
positronium later annihilates (decays) in the same way as in the first part of the
experiment, and we can again measure the time difference between the 1275 keV
photon being detected and a 511 keV photon being detected to determine the lifetime
of the bound positronium.
2 Theory
Positronium can exist in two different states: para- and ortho-positronium. Para-
positronium is the state in which the spin of the electron is antiparallel to the spin
of the positron. In ortho-positronium the two spins are parallel. Both of these states
are unstable and will annihilate after a short time. In the case of para-positronium,
the annihilation will emit 2 photons, the ortho-positronium will emit 3. It is well
known that the photons emitted in the decay of para-positronium each have an
energy of 511keV.
Para-positronium has a much shorter lifetime than ortho. Due to parity conser-
vation under electromagnetism, there can only be odd numbers of photons emitted
from ortho-positronium decays and only even numbers for para. Due to this, the
decay width for ortho-positronium is smaller than that for para; and thus the life-
time, which is inversely proportional to the decay width, must be greater for ortho
than for para. In vacuum, the lifetimes of the two states have been determined as
shown in Tab.2
para-positronium 1.25· 10-10 s
ortho-positronium 1.42· 10-7 s
Table 1: Positronium lifetimes in vacuum
In material, the lifetime of the ortho state is much shorter. This is because it is
able to change into para-positronium through collisions with atoms in the material.
2
Lab report
Friedrich Kurz, Guillem Cucurull, Kaya Vogler
Contents
1 Introduction 2
2 Theory 2
3 Experimental setup 3
4 Experimental method 5
4.1 Energy measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2 Time measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 Data Analysis and Results 9
5.1 Time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.2 Positronium Lifetime in POM . . . . . . . . . . . . . . . . . . . . . . 10
5.3 Positron Lifetime in Aluminium . . . . . . . . . . . . . . . . . . . . . 11
5.4 Energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6 Discussion 13
1
, 1 Introduction
This lab aims to measure the lifetime of positronium. Positronium is a particle
which consists of an electron and a positron. For the experiment, a radioactive
source undergoing β + decay is used. The β + particles (or positrons) bond to an
electron to form positronium, which then annihilates. We use known energies of
photons emitted in the various steps of the experiment to determine the lifetime of
the positronium.
In the first part of the experiment, the source is placed in an aluminium container,
in which electrons are free. We measure a 1275 keV photon emitted during the source
decay to mark the ’start’ time of the positron’s lifetime. In the next step we measure
a 511 keV photon which is emitted during the annihilation of the positron with an
electron. The time difference between these two events gives us a measurement for
the lifetime of the positron in aluminium.
In the second part, the source is placed in a polyoxymethylene (POM) container,
in which the electrons are not free. This means that bound positronium states can
be formed, as the positrons lose energy when they collide with the material. The
positronium later annihilates (decays) in the same way as in the first part of the
experiment, and we can again measure the time difference between the 1275 keV
photon being detected and a 511 keV photon being detected to determine the lifetime
of the bound positronium.
2 Theory
Positronium can exist in two different states: para- and ortho-positronium. Para-
positronium is the state in which the spin of the electron is antiparallel to the spin
of the positron. In ortho-positronium the two spins are parallel. Both of these states
are unstable and will annihilate after a short time. In the case of para-positronium,
the annihilation will emit 2 photons, the ortho-positronium will emit 3. It is well
known that the photons emitted in the decay of para-positronium each have an
energy of 511keV.
Para-positronium has a much shorter lifetime than ortho. Due to parity conser-
vation under electromagnetism, there can only be odd numbers of photons emitted
from ortho-positronium decays and only even numbers for para. Due to this, the
decay width for ortho-positronium is smaller than that for para; and thus the life-
time, which is inversely proportional to the decay width, must be greater for ortho
than for para. In vacuum, the lifetimes of the two states have been determined as
shown in Tab.2
para-positronium 1.25· 10-10 s
ortho-positronium 1.42· 10-7 s
Table 1: Positronium lifetimes in vacuum
In material, the lifetime of the ortho state is much shorter. This is because it is
able to change into para-positronium through collisions with atoms in the material.
2
