# INTRODUCTION TO NUCLEAR AND PARTICLE PHYSICS

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INTRODUCTION TO NUCLEAR
AND PARTICLE PHYSICS

Katrin Becker
Department of Physics, University of Utah
Salt Lake City, UT 84112-0830
1. Introduction

The goal of elementary particle physics is to ﬁnd and understand the funda-
mental laws of nature which govern how matter interacts. We call an interaction
anything that changes the state of matter. We believe that this matter, this means
the world around us, is constructed from a few building blocks called elementary
particles. If we know precisely how the microscopic world is constructed, then,
at least in principle, we know how macroscopic and chemical processes behave.
Everything can in principle be explained as an interaction of elementary particles.

In order to understand the world of elementary particles we have to understand
the world at very small distances. But this is equivalent to considering physics at
very high energies. Indeed, this follows from Heisenberg’s uncertainty principle
which states

¯
∆p · ∆x ≈ h.

This means that a particle which we would like to use the probe a distance ∆x
should at least have an momentum
h¯
∆p ≈        .
∆x
This means that we need high energies to analyze the world of the smallest particles.
This means that elementary particle physics is the same as high energy physics.

In elementary particle physics energies are usually measured in eV (electron
volt) or multiples of it. One eV is the energy gained by an electron if it is acceler-
ated by a potential diﬀerence of 1V (volt):

1 eV = 1.60 × 10−19 C × 1V = 1.60 × 10−19 J (joule).

Multiples of eV are also commonly used. So for example

106 eV = 1 M eV,        109 eV = 1 GeV         and     1012 eV = 1 T eV.

In order to introduce the units for the mass m and the total momentum we will

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need a very important equation which follows from special relativity and which we
will explain in more detail in a later lecture, namely

E 2 = p2 c2 + m2 c4 .

This means that the total energy of a particle consists of a rest energy, namely mc2 ,
which is independent of the momentum and one part depending on the momentum.
A particle without mass, like the photon, will have an energy

E = pc,

while a particle without momentum, this means a particle at rest, will have an
energy

E = mc2 .

From here we see that mass will have units eV /c2 or multiples of it. While the
momentum has units eV /c. Most of the time we will set c = 1 which means that
energy, mass and momentum will all have the same units. As an example the rest
mass of the proton is given by Mp = 938.28 M eV, which is approximately 1 GeV .
The size of the proton is approximately 10−13 cm. In order to discover what is
inside the proton we have to test even smaller distances, which would correspond
to even higher energies. The diﬀerent orders of magnitude can be seen in the ﬁgure
below.

Atom                Nucleus                      Proton           Neutron

-8                     -12                        -13                -15
10        cm            10 cm                     10         cm      10         cm

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Today we know that the world around is constructed from a few atoms. Using
some basic laws of quantum mechanics it is actually possible to get an approximate
value for the size of the hydrogen atom. If we try to describe the atom using the
laws of classical physics, we would ﬁnd that the atom is unstable since the electron
is performing an accelerated motion in the electrical ﬁeld generated by the proton.
As a consequence the electron would emit its energy in the form of radiation.
The atom would be unstable with a lifetime of less than 10−9 s. But quantum
mechanically the situation is completely diﬀerent. Indeed, an atom is only stable
if it is described with the laws of quantum mechanics.

In order to see this we will use Heisenberg’s uncertainty relation which states

¯
∆p · ∆x ≈ h.

If the size of the hydrogen atom is determined by a radius R then we know the
position coordinate of the electron with a certainty ∆x ≈ R. This means that the
electron must have a momentum which ﬂuctuates about the classical value (which
corresponds to a vanishing momentum) with

¯
h
p = ∆p ≈     .
R

If R is very small, the momentum is very big, and the electrostatic attraction
of the proton is not suﬃcient to keep the electron at a distance R from the proton.
Using the above result for the momentum we can approximate the total energy of
the electron which is given by the kinetic energy and the potential energy due to
the electric ﬁeld of the proton, namely

h2
¯     e2
E(R) =        − .
2me R2  R

This function E(R) is plotted in the ﬁgure below and it will have a minimum R0
at dE(R)/dR = 0.

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E(R)

R0                          R

This implies
h2
¯
R0 =           ≈ 5 · 10−9 cm.
me e 2

The energy of the electron at the minimum is

e2
E(R0 ) = −        ≈ −13.6 eV.
2R0

Since a smaller energy is not possible, this implies that the electron can no longer
collapse with the proton. This computation gives a simple way of approximating
the size of the hydrogen atom.

The deuteron is composed of a proton and a neutron and it has a size of
approximately RN ≈ 10−13 cm. With this information we can approximate the
kinetic energy of the nucleons (with mass mN ) to be

h2
¯
Ekin =        2 ∼ 20 M eV.
2mN RN

This implies that there must be a very strong attractive potential which overcomes
the huge kinetic energy. That strong attractive potential comes of course from the
strong force.

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Atoms consist of a positively charged nucleus which is surrounded by nega-
tively charged electrons. The nucleus and the electrons are hold together by the
electromagnetic interaction. Also the interaction between atoms, which governs
all of chemistry, is electromagnetic. The atomic nucleus consists of protons and
neutrons. These protons and neutrons are hold together by the strong interaction.
Nowadays we believe that protons and neutrons are not elementary but are con-
structed from some basic building blocks which are called quarks. We will discuss
in great detail the quark model of elementary particles during these lectures. The
quarks are hold together through the strong force. The particles mediating this
strong force are called gluons. Gluons are the quanta of the strong force in the
same way as the photons are the quanta of the electromagnetic interaction. All
strong interacting particles are called hadrons.

There are some particles that do not feel the strong interaction, like electrons,
muons, τ -leptons and neutrinos. These particles form the family of the leptons
which interact weakly and if they have electric charge also electromagnetically.
But they feel no strong forces.

Hadron and leptons are the building blocks of matter. They are like lego pieces
which combined in diﬀerent ways give rise to all the atoms and molecules we know.
The u and d quarks are the constituents of the atomic nucleus which together with
the electrons builds the atoms. The electron neutrino appears as a byproduct in the
β-decay. The rest of the elementary particles can be produced in some high energy
accelerators but until this day the reason why the additional particles appear is
still a mystery. Maybe some modern ideas like superstring theories have something
towards the end of this lectures.

But it turns out that this is not the whole story yet since each of the particles
in the table below appears together with its antiparticle. As we will later see
antiparticles have exactly the same properties as the particles except the additive
quantum number (like electric charge) which have opposite sign. So for example

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the antiparticle corresponding to the electron is called positron. A positron has
the same mass and spin as the electron but opposite electric charge. Antiparticles
do not appear in nature since they would immediately annihilate together with the
corresponding particle. But they can be produced artiﬁcially.

Above we have discussed the constituents of matter. But we also know that
there are particles mediating the diﬀerent forces. These are the following

The electromagnetic interaction is mediated by the photon.

As we have seen the strong forces are mediated by gluons.

As we will later see in these lectures the weak forces are responsible for the
β-decay. The particles mediating the weak force are the W -bosons and the
Z-bosons.

Then we also have gravitation. This force is much weaker than the other
forces in nature. So for example the gravitational interaction between a
proton and an electron is 1039 times weaker than the electrical interaction.
Since in these lectures we are interested in subatomic processes we can safely
ignore the gravitational interaction.

To indicate the relative magnitudes of the diﬀerent forces one can compare the
relative forces between two protons that are just in contact. They are given in the
following table

strong     1
electromagnetic     10−2
weak     10−7
gravity    10−39

The list of known elementary particles can be seen in the ﬁgure below

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Some elementary particles like protons, neutrons and electrons appear abun-
dantly in nature while others can only be obtained artiﬁcially. The main sources
of more exotic particles

cosmic rays are elementary particles (mostly protons) which bombard the
earth and which through the interaction with the upper atmosphere produce
showers of secondary particles which are mostly muons. The particles in the
cosmic rays can have enormous energies (up to 1021 eV has been observed
for the primary cosmic rays). So in principle they would be ideal to perform
elementary particle experiments. The only problem with cosmic rays is that
their rate is very low and with a detector of reasonable size one would have
to wait a very long time before measuring an event.

elementary particles (like neutrinos) can appear as a byproduct of nuclear re-
actions. So for example the sun generates its power by transforming hydrogen
to helium. As a byproduct of this transformation neutrinos are generated.

elementary particles can, of course, also be produced in particle accelerators.
The idea behind these accelerators is to collide very high energetic particles
(electrons, protons or their antiparticles) and look at the resulting debris by
using a detector. There are diﬀerent types of particle accelerators. They
can, for example, be rings in which particles circulate in opposite directions
and at some point are brought to a head on collision. The most powerful
machine of this type is the Large Hadron Collider (LHC), which will operate

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in the year 2007 in CERN and at this moment is under construction. The
LHC will collide beams of protons at an energy of 14 T eV .

Once these elementary particles are produced we would, of course, like to detect
them. In order to do this many kinds of particle detectors are used. If the particles
are charged they can be easily detected since they ionize atoms along their path.
If one applies an electric ﬁeld then the charges can be separated and the currents
can be measured. Particles without electric charge are more diﬃcult to detect.
Neutral particles can only be detected when they react to produce two particles
with the same charge but with opposite sign (an example of this can be seen in
the ﬁgure below which represents an image taken by a bubble chamber). In these
detectors a strong magnetic ﬁeld is usually applied. This will make the charged
particles move in circular paths. The form of the path will allow us to determine
the sign of the charge.

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More details about these accelerators and detectors can be found in the part I
section of Frauenfelder and Henley.

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