Particle and Nuclear Physics

Coordinated by: Institute of Particle and Nuclear Physics
Study branch coordinator: prof. RNDr. Pavel Cejnar, Dr., DSc.

Particle physics (high-energy, subnuclear physics) investigates the structure of matter at the level of elementary particles and their fundamental interactions. Nuclear physics studies the structure of atomic nuclei and, more generally, the behaviour of finite quantum systems of mutually interacting particles. The study programme is based on comprehensive courses of theoretical and experimental particle and nuclear physics, based on extensive courses in quantum mechanics and quantum field theory. Emphasis is placed on mastering the relevant computational techniques and managing the methods of acquisition and evaluation of experimental data, including efficient use of computing and advanced software tools. With the aid of optional courses and the Master's project, students gain deep knowledge in their selected area and choose their orientation toward theory or experiment.

Profile of graduates and study aims:
Graduates have an advanced knowledge of particle and nuclear physics, in both experimental and theoretical domains. With a comprehensive grounding in quantum theory, they understand basic approaches to the description of the microscopic world and know experimental techniques for its study. They find employment mainly in fundamental experimental and theoretical research, but also in relevant applied research, e.g., in detector physics, nuclear medicine etc. Graduates are prepared to creatively develop the field of their scientific focus and to join international research teams. Experience in the application of advanced software tools also opens possibilities for employment in the field of information technologies.

5.1 Recommended Course of Study

Prerequisite for this study programme is a bachelor-level knowledge of general physics, experimental methods, non-relativistic quantum mechanics, calculus and algebra.

First year

NJSF041Experimental and Applied Nuclear Physics 64/0 Ex
NJSF064Nuclear Physics 73/2 C+Ex
NJSF105Elementary Particle Physics 73/2 C+Ex
NJSF068Quantum Field Theory I194/2 C+Ex
NJSF145Quantum Field Theory I194/2 C+Ex
NJSF086Quarks, Partons and Quantum Chromodynamics 62/2 C+Ex
NJSF037Microscopic Theory of Nuclei 64/0 Ex
NJSF085Fundamentals of Electroweak Theory 62/2 C+Ex
NSZZ023Diploma Thesis I 60/4 C

1 Students enrol in only one of these alternating courses.

Second year

NJSF191Seminar on Particle and Nuclear Physics III 30/2 C
NJSF192Seminar on Particle and Nuclear Physics IV 30/2 C
NSZZ024Diploma Thesis II 90/6 C
NSZZ025Diploma Thesis III 150/10 C

5.2 Obligatory Courses

NJSF041Experimental and Applied Nuclear Physics 64/0 Ex
NJSF064Nuclear Physics 73/2 C+Ex
NJSF105Elementary Particle Physics 73/2 C+Ex
NJSF068Quantum Field Theory I194/2 C+Ex
NJSF145Quantum Field Theory I194/2 C+Ex
NJSF086Quarks, Partons and Quantum Chromodynamics 62/2 C+Ex
NJSF037Microscopic Theory of Nuclei 64/0 Ex
NJSF085Fundamentals of Electroweak Theory 62/2 C+Ex
NJSF191Seminar on Particle and Nuclear Physics III 30/2 C
NJSF192Seminar on Particle and Nuclear Physics IV 30/2 C
NSZZ023Diploma Thesis I 60/4 C
NSZZ024Diploma Thesis II 90/6 C
NSZZ025Diploma Thesis III 150/10 C

5.3 Elective Courses

The student needs to obtain at least 25 credits for courses from the following set.
Quantum field theory
NJSF069Quantum Field Theory II194/2 C+Ex
NJSF146Quantum Field Theory II194/2 C+Ex
NJSF139Beyond Standard Model Physics I 42/1 Ex
NJSF140Beyond Standard Model Physics II 42/1 Ex
NJSF082Selected Topics on Quantum Field Theory I 43/0 Ex
NJSF083Selected Topics on Quantum Field Theory II 43/0 Ex
NTMF022Theory of Gauge Fields 43/0 Ex
NJSF084Chiral Symmetry or Strong Interactions 32/0 Ex
NJSF030Quantum Field Theory at Finite Temperature 32/0 Ex
NJSF129Advanced Concepts of Symmetry 52/2 Ex
NJSF142Theory of groups and algebras in particle physics 42/1 Ex
Theory of many-body systems
NJSF196Microcopic Theory of Nuclei II 32/0 Ex
NJSF107Statistical Nuclear Physics 32/0 Ex
NJSF193Collective Dynamics of Manybody systems 32/0 Ex
NJSF031Classical and Quantum Chaos 32/0 Ex
NJSF157Physics of few-body nuclear systems 32/0 Ex
NJSF158Introduction to computational nuclear physics 31/1 Ex
Experimental particle physics
NJSF073Experimental Checks on Standard Model 42/1 C+Ex
NJSF195Strong Interaction at High Energies 32/0 Ex
NJSF102Nuclear Astrophysics 32/0 Ex
NJSF130Cosmic Rays 32/0 Ex
NJSF131Diffraction in particle physics 42/1 Ex
Experimental methods, data evaluation, applications
NJSF070Particle Detectors and Accelerators 32/0 Ex
NJSF159Physics of particle accelerators 42/1 Ex
NJSF101Semiconductor Detectors in Nuclear and Subnuclear Physics 32/0 Ex
NJSF081Software and data processing in particle physics I 31/1 Ex
NJSF109Software and data processing in particle physics II 42/1 Ex
NJSF143Statistical methods in high energy physics 43/0 Ex
NJSF067Data acquisition methods in particle and nuclear physics 42/1 Ex
NJSF138Neural nets in particle physics 42/1 Ex
NJSF024Radioanalytical Methods 32/0 Ex
NJSF008Biological Effects of Ionizing Radiation 32/0 Ex
NJSF141Experimental data evaluation 32/0 Ex
NJSF091Seminar on Particle and Nuclear Physics I 30/2 C
NJSF092Seminar on Particle and Nuclear Physics II 30/2 C

1 Students enrol in just one of these alternating courses.

5.4 Recommended Optional Courses

NJSF079Quantum Field Theory III 94/2 C+Ex
NJSF132Theory of nanosccopic systems I 32/0 Ex
NJSF133Theory of nanoscopic systems II 32/0 Ex

5.5 State Final Exam

Study in the master’s programme is completed by passing the state final exam. It consists of two parts: defence of the master’s (diploma) thesis, and an oral examination. Requirements for the oral part of the state final exam are listed in the following sections.

Necesary conditions for taking the state final exam

earning at least 120 credits during the course of study
passing all compulsory courses
obtaining at least 25 credits for elective courses
submission of a completed master’s thesis by the submission deadline

Requirements for the oral part of the state final exam

The committee asks the student to explain three topics from the following three sectors (one topic from each sector):

A. Quantum theory

1. Formalism of quantum theory
Hilbert space. Pure and mixed states. Compatible and incompatible observables. Discrete and continuous spectra. Open systems. Classical limit.

2. Evolution of quantum systems
Schroedinger equation and the evolution operator. Green operator. Schroedinger, Heisenberg and Dirac representations of time evolution. Evolution generated by a time-dependent Hamiltonian.

3. Symmetries and conservation laws in quantum mechanics
Continuous space-time symmetries and their generators. Space inversion and time reversal. Conservation laws. Scalars, vectors, spinors.

4. Perturbation methods in quantum mechanics
Stationary perturbation theory for a non-degenerate and degenerate spectrum. Non-stationary perturbation method, step and periodic perturbations, Fermi golden rule.

5. Angular momentum in quantum mechanics
Quantization of angular momentum. Addition of two or more angular momenta. Tensor operators, selection rules.

6. Scattering theory
Lippmann-Schwinger equation. Scattering amplitude, Born series. The method of partial waves.

7. Systems of indistinguishable particles
Bosons and fermions. Fock space, occupation number representation. Creation and annihilation operators, n-body operators.

8. Equations of relativistic quantum theory for free particles with spin 0, 1/2 and 1
Klein-Gordon and Dirac equations, solutions with positive and negative energies, continuity equation, symmetry properties. Weyl and Proca equations.

9. Dirac equation for a particle in electromagnetic field
Transition to the Pauli equation and the spin magnetic moment. Hydrogen type atoms and the fine structure of energy spectra.

10. Quantization of free fields and their particle interpretation
Canonical quantization method. Energy and momentum of a quantum field. Particles and antiparticles. Dirac field, anticommutation rules. Electromagnetic and Proca fields. Propagator of a quantum field.

11. Interactions of fields, perturbative expansion of the S-matrix and Feynman diagrams
Examples of interaction Lagrangians, gauge symmetry principle. Dyson expansion in the interaction representation. Feynman diagrams on the tree level. Decay probabilities and cross sections.

12. Foundations of quantum electrodynamics
Scattering of a charged particle in an external electromagnetic field. Second-order processes. Examples of diagrams with a closed loop.

B. Physics of elementary particles

1. Classification of elementary particles
Leptons, hadrons, interaction mediators. Approximate SU(3) symmetry, hadron multiplets. Quark model. Colour of quarks, its experimental evidence. Quarks u, d, s. Heavy quarks c, b. Decays of hadrons (neutron, pion, strange particles).

2. Properties of hadrons and their experimental determination
Spin, magnetic moment, spatial-, charge- and G-parity, isospin, strangeness, hypercharge. Conservation laws for individual interaction types. Examples of experiments.

3. Properties of leptons
Weak and electromagnetic interactions of leptons: mion pair production in electron-positron annihilation, scattering of neutrinos, decays of muons and tau leptons. Helicity of neutrinos, neutrino oscillations, P and CP violation. Neutrino experiments.

4. Methods of measurement and identification of particles in experiments
Measurement of energy, momentum, time of flight, Cherenkov and transition radiation, invariant mass of decay products. Examples of detection techniques in particle discoveries.

5. Experiments with particle accelerators
Linear and circular particle accelerators, colliders, luminosity. Present-day accelerators. Particle production in hadronic and leptonic collisions.

6. Conceptual foundations of the standard model of electroweak interactions
Gauge invariance. Yang-Mills field. The Higgs mechanism.

7. Types of particle interactions in the standard model of electroweak interactions
Interactions of vector bosons, interactions of the Higgs boson, neutral and charged currents. Discovery of vector bosons W and Z, discovery of the Higgs boson.

8. Mixing in the quark sector of the standard model
Generation of masses through the Yukawa interactions. Cabibbo-Kobayashi-Maskawa matrix, CP violation. Discovery of quarks c, b, t.

9. Systems of neutral mesons
Oscillation and regeneration. Direct and indirect CP violations and their signatures.

10. Structure of nucleons and the parton model
Elastic scattering of electrons on the proton, formfactors. Deep inelastic scattering, structure function, Bjorken scaling. Formulation of the parton model and the concept of parton distribution function.

11. Applications of the parton model
Basic processes in the parton model: hadron production in electron-positron annihilation, Drell-Yan process. Fragment function, deep inelastic scattering, measurement of parton distribution functions. Jet production, discovery of gluon.

12. Quantum chromodynamics
QCD Lagrangian and the gauge invariance principle. Running coupling constant, asymptotic freedom, colour confinement. Description of quarkonia. Infrared and collinear singularities, jets, evolution equation for parton distribution functions.

C. Nuclear physics

1. Characteristics of nuclei and their experimental determination
Binding energy, von Weizsaecker formula. Spin, parity. Magnetic dipole and electric quadrupole moments. Deformation parameters.

2. Nuclear decays and radioactivity
Beta decay, spectra of electrons/positrons, selection rules, electron capture. Alpha decay, decay chains. Gamma decay, elements of the theory of electromagnetic transitions, their types and multipolarities, selection rules.

3. Nucleon-nucleon interactions
Phenomenological and microscopic nucleon-nucleon potentials, symmetry principles, isospin, meson exchanges and their quark interpretation. Effective interactions in nuclear environment. Deuteron.

4. Mean field and single-particle motions in nuclei
Hartree-Fock construction of the mean field. Spin-orbit coupling, magic numbers. Nilsson model, deformation.

5. Pairing of nucleons and its consequences
Short-range residual interactions. Bardeen-Cooper-Schrieffer theory of superconductivity. Signatures of pairing in nuclei.

6. Collective motions of nuclei
Rotational and vibrational spectra of nuclei and their phenomenological and microscopic description. Giant resonances. Nuclear fission.

7. Nuclear reactions and highly excited states
Direct and compound-nucleus reactions, examples, typical properties, elements of their theoretical description. Population of excited states, statistical modelling of their decays, yrast line.

8. Passage of ionizing radiation through matter
Processes during the passage of heavy and light particles through matter. Interaction of gamma particles. Passage of neutrons.

9. Principles of detection of nuclear radiation
Spectrometry of charged and neutral particles. Basic types of particle detectors and their characteristics.

10. Application of nuclear physics in material analysis and dating
Measurement of elemental and isotopic abundances. Nuclear probes in materials. Nuclear methods of age determination.

11. Application of nuclear physics in medicine
Methods of imagining based on nuclear radiation, functional tomography. Radiotherapy and hadron therapy.

12. Nuclear energy
Nuclear fission and fusion. Nuclear reactor, tokamak. Nuclear processes in stars.


Charles University, Faculty of Mathematics and Physics
Ke Karlovu 3, 121 16 Praha 2, Czech Republic
VAT ID: CZ00216208

HR Award at Charles University

4EU+ Alliance