Problems and Solutions in Nuclear and Particle Physics (1st Edition, 2019) by Sergio Petrera

,Contents




1 Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Initial Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Nuclear Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Nuclear Binding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Nuclear Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Nuclear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Fundamental Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Hadrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Weak and Electro-Weak Interactions . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Experiments and Detection Methods . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Interaction of Radiation with Matter . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Detection Techniques and Experimental Methods . . . . . . . . . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Appendix: Solutions of Exercises and Problems . . . . . . . . . . . . . . . . . . . . 43




ix

,Notes




Data

Each problem can be taken as stand-alone. This means that all input data are
provided in the text: For example, the relevant particle masses are usually given in
the text. The reader may notice that their accuracies can change on a case-by-case
basis. This feature is a consequence of the origin of the text, since these problems
were used for examinations and I preferred to give all the needed input data at the
accuracy required for each specific case. On the other hand, it also allows the reader
to pick up problems randomly without requiring a sequential reading.
The problems are mainly numerical and require values of physical constants,
especially for conversion purposes. Whenever these values are not reported in the
text, the reader can refer to the PDG Review of Particle Physics [2] which provides
an up-to-date collection of constants, units, atomic, and nuclear properties. This
review is much more than a simple collection and can be considered as a “must” for
dealing with any nuclear and particle physics case.
Nuclear physics data are available from several sources. Some examples are the
National Nuclear Data Center (NNDC) at Brookhaven National Laboratory [3] and
the IAEA Nuclear Data Section [4].



Units

We use the International System of Units (SI), except for energy, mass, and
momentum which are specified in terms of eV. This mixed system can be easily
handled and the system-specific electromagnetic constants disappear promptly,
using the SI definition of the fine structure constant a and the value of 
hc in mixed
units.
In nuclear physics, kinematical expressions are mostly non-relativistic. In par-
ticle physics, the relativistic treatment is instead mandatory. As adopted in many


xi

, xii Notes

books, in all kinematical expressions c is omitted (i.e., c = 1), making them simpler
to be handled. Once the energy scale of the problem is set, e.g., GeV, the right units
are easily restored with the rule that momenta, energies, and masses are finally
given in GeV=c, GeV, and GeV=c2 respectively. For all the other quantities (e.g.,
velocity, time, distance, etc.), the light velocity c is kept in the equations.




Other References

There are several excellent books that deal with either nuclear or particle physics.
Less frequently does one see textbooks presenting these two areas of physics in a
unified manner, especially at the undergraduate level. The books Nuclear and
Particle Physics by W. S. C. Williams [5], Particles and Nuclei by B. Povh et al. [6],
Nuclear and Particle Physics by B. R. Martin [7], and Introduction to Nuclear and
Particle Physics by A. Das and T. Ferbel [8] provide the kind of combined expo-
sition more appropriate to the level of the problems proposed here. Finally, a very
useful collection of solved problems, including also different topics, is Problems
and Solutions on Atomic, Nuclear and Particle Physics by Yung-Kuo Lim [9].