# Information on Graduate Course Requirements

## Choosing First Year Graduate Subjects

The Department does not require PhD students to take any subjects other than those needed to satisfy the specialty and breadth requirements described below. However, many students begin by taking some combination of graduate Classical Mechanics (8.309), graduate Quantum Mechanics (8.321 and 8.322), graduate Electricity and Magnetism (8.311), and graduate Statistical Mechanics (8.333). Not only have these subjects been proven to give students a broad view of basic physics, but each of them (with the exception of 8.322) may be used to satisfy the related part of the Written General Exam.

First-year students concerned with the level of their undergraduate preparation are encouraged to consider taking senior-level undergraduate subjects such as Electricity and Magnetism (8.07), Statistical Mechanics (8.08) and Classical Mechanics (8.09). Some first-year students may wish to sample basic graduate subjects in specialty areas: Atomic and Optical Physics (8.421 or 8.422), Solid State Physics (8.511), Systems Biology (8.591J), Plasma Physics (8.613J), Introduction to Nuclear and Particle Physics (8.701), and Astrophysics (8.901 or 8.902). These subjects may later be counted towards one’s specialty or breadth requirements. While planning their first year program, students should keep in mind that the normal subject load for those with full time RAs is two academic subjects, or about 24 units. A student with an RA will also register for Pre-Thesis Research (8.391 in the fall; 8.392 in the spring and summer terms), for 12 or more units, depending on the rest of the course load.

### NUPAX Graduate Student Classes

Graduate students who belong to the NUPAX division are required to take two specialty classes and two breadth requirements. The full academic responsibilities for graduate students are discussed in greater detail on the main Physics website (http://web.mit.edu/physics/current/graduate/doctoral.html). Students are encouraged to visit the website for more information about these requirements.

NuPAX offers three courses in experimental nuclear and particle physics: 8.701, 8.811, and 8.711. The graduate courses 8.811 and 8.711 assume that students have completed a rigorous introductory course in nuclear and particle physics. The level of undergraduate particle and nuclear physics varies greatly depending on institution and instructor. Students should review the example final for 8.701 to determine placement. The purpose of each of the three courses is summarized, and detailed topics are outlined, below.

**Introduction to Particle and Nuclear Physics – 8.701**

- Graduate or advanced undergraduate introduction to particle and nuclear physics.
- Satisfies breadth requirement for graduate students not in NuPAT or NuPAX.
- Prepares undergraduates for Physics GRE subject exam.
- NuPAX students should take this course in the fall of their first year.

- Graduate overview of topics in nuclear physics.
- Satisfies breadth requirement for NuPAT.
- Undergraduates should have completed 8.701 before taking 8.711.
- NuPAX students should take this course in the spring of their first year.

- Graduate overview of topics in particle physics.
- Satisfies breadth requirement for NuPAT.
- Undergraduates should have completed 8.701 before taking 8.811.
- NuPAX students should take this course in the fall of their second year or in consultation with the instructor and their graduate advisor.

#### Introduction to Particle and Nuclear Physics – 8.701

##### Subjects and Topics

**Course Overview: Introduction to Nuclear and Particle Physics**

- Properties of particles and nuclei
- Development of standard model
- Feynman calculations
- Experimental techniques

**Basics**

- Relativity Review
- Relativistic kinematics
- Lagrangians
- Noether’s Theorem
- Fermi’s Golden Rule
- Decay Rates
- Cross-sections

**Electromagnetism**

- Dirac Equation
- QED
- Feynman diagram calculations

**Weak Interactions**

- Beta Decay
- P Violation and Wu Experiment
- Chirality
- Flavor and CKM
- CP Violation and Cronin & Fitch
- Higgs Mechanism

**Strong Interaction**

- Properties of mesons, baryons, quarkonia
- QCD, color, asymptotic freedom
- Parton distribution functions, sum rules
- PDF connection to experiment

**Nuclear Physics**

- Nuclei basics
- Shell model
- Alpha Decay, quantum tunnelling
- Beta Decay, Fermi theory
- Solar cycle, binding per nucleon
- Nuclear reactors and weapons

**Experiment**

- Accelerators
- Spectroscopy, Partial Wave, Dalitz plots
- electron-proton scattering, GE & GM, structure functions
- Deep in-elastic scattering

#### Nuclear Physics – 8.711

##### Subjects and Topics

**Course Overview: Experimentalist’s top down view of nuclei**

- Fundamental particles and interactions
- Modern NP (quarks, nucleons, Nuclei, Astro)
- Pions, isospin and NN interaction
- Low energy properties of nuclei and nuclear saturation
- Nuclear Decays

**Effective Many Body Methods**

- Fermi gas
- Nuclear properties and observables (excited states, spins, parities, EM moments, …)
- Mean-field approximation and the Shell-Model
- Single particle excited states and EM transitions
- Bohr-Mottelson collective model
- Phonons, nuclear deformations, rotational modes
- Nuclei far from stability, pairing interactions and modification of magic numbers

**Nuclear Astrophysics**

- History of the universe,
- Big Bang Nucleosynthesis
- Solar Fusion
- Element production via s-process and r-process in neutron stars.

**NN Interaction and Ab-Initio Many-Body Methods**

- The Deuteron
- Phenomenological potentials (AV18)
- NN scattering and phase shifts
- QCD and chiral EFT
- Many-body methods [MC, CC, SRG, Corr. Operators]
- Beyond the mean-field approximation (long and short-range correlations, clustering)

**Electron Scattering**

- Elastic scattering
*Continued**…..*- Quasi-Elastic scattering
- Polarization observables
- Deep Inelastic Scattering
- Parity violation

**Nucleon Structure**

- Form Factors
- Structure functions
- Spin structure
- TMD / GPD etc
- Nuclear medium modification

**Nuclear Decay and Fundamental Symmetries**

- Beta decay and electron capture (nuclear modeling and standard model tests)
- Neutrino Oscillations
- Double-Beta decay (emphasis on gA quenching and matrix elements)

**Heavy Ion Collisions**

- Anisotropic flow
- QCD phase diagram

**Nuclear Energy**

- Nuclear reactors
- Nuclear weapons

**Detectors (Integrated as appropriate in the above topics)**

- Interactions of particle with matter
- Nuclear detectors

#### Particle Physics – 8.811

##### Subjects and Topics

**Course Overview: Particle Physics at the Energy, Intensity and Cosmology Frontiers**

- Standard Model
- Detectors and Accelerators
- Cosmology
- Particle Astrophysics

**Standard Model**

- Symmetries
- Advanced Feynman diagrams
- Higgs Mechanism
- Extending the SM with GUTs

**Neutrino Physics**

- Neutrino Oscillations
- Sterile Neutrinos
- Matter Effects
- See-saw Models

Cosmology

- Basic formalism
- Inflation
- CMB, Supernova, Lensing, LSS

Dark Matter

- Dark Matter and Structure
- WIMPs
- Axions
- Model building

Cosmic Rays

- Origin of Cosmic Rays
- Propagation and GZK cutoff
- Neutrino Production

Experiment *(Some presented with above topics)*

- Accelerators
- Detectors at colliders
- Specialized detectors