PHYS 560: Theoretical Nuclear Physics (Winter 2021)
(NB: The lectures in Winter quarter will be conducted remotely using Zoom. I will be using an iPad Pro
with a stylus to interact with the class via Zoom. Sessions will be recorded and made available.)
MT 12:30-1:50pm zoom
Instructor: Silas Beane B457 OH: Friday noon zoom and by appointment
TA: Francis Walsh OH: by appointment
Subject matter
This course will consist of an introduction to non-relativistic effective field theory
methods and applications for few- and many-particle systems in nuclear and atomic physics.
Tentative list of topics (subject to change):
Effective field theory (EFT) basics
General comments -- scale separation
Finite-range potentials
Nuclear and atomic scales
Non-relativistic field theory
Lagrangians and Hamiltonians
EFT strategy
Symmetries: Galilean invariance, etc.
Power counting
Two-body problem -- review
Scattering theory
Effective range theory (ERT)
NN system
Bound states
EFT description of two-body system
Regularization and renormalization
Fixed points of the renormalization group (RG)
Corrections and ERT
Comparison with other methods
Dibaryon/dimer formalism
External currents
Including long-range forces
Coulomb corrections
Perturbative pions (KSW expansion)
Non-perturbative pions (Weinberg expansion)
One-pion exchange potential
Singlet channel
Triplet channel - the deuteron
Interlude: singular potentials in quantum mechanics
Three-body system
General scaling of operators
Neutron-deuteron and He-dimer systems
Asymptotic integral equation
Spin-doublet (and three-boson) system and the limit cycle
Efimov effect
Many-fermion systems
Fermi liquid theory and EFT
Dilute Fermi gas
Unitary Fermi gas
BCS instability and EFT
Weakly interacting Bose gas
Bose-Einstein condensation and EFT
Goldstone mode and EFT
Energy density
The effect of geometry
Prerequisites
Note that this is an advanced graduate course in physics. Graduate-level quantum mechanics is an essential prerequisite.
Useful Review References
1) Building light nuclei from neutrons, protons, and pions, By Daniel R. Phillips. 10.1007/s10582-002-0079-z.
2) Effective field theory and the Fermi surface, By Joseph Polchinski. hep-th/9210046.
3) Five lectures on effective field theory, By David B. Kaplan. nucl-th/0510023.
4) Introduction to effective field theory, By Eric Braaten.
5) Universality in few-body systems with large scattering length, By E. Braaten and H.W. Hammer. 10.1016/j.physrep.2006.03.001 .
6) The few-atom problem, By D.S. Petrov.
7) Dick Furnstahl's nuclear physics notes
8) Effective theories of dense and very dense matter, By Thomas Schäfer. nucl-th/0609075
Useful Original Sources
1) Two nucleon systems from effective field theory, By David B. Kaplan, Martin J. Savage, Mark B. Wise. 10.1016/S0550-3213(98)00440-4.
2) Effective field theory of short range forces, By U. van Kolck. 10.1016/S0375-9474(98)00612-5.
3) Rearranging pionless effective field theory, By Silas R. Beane, Martin J. Savage. 10.1016/S0375-9474(01)01088-0.
4) Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces, By Steven Weinberg. 10.1016/0550-3213(91)90231-L.
5) Effective field theory for dilute Fermi systems, By H.W. Hammer, R.J. Furnstahl. 10.1016/S0375-9474(00)00325-0.
6) Field redefinitions at finite density, By H.W. Hammer, R.J. Furnstahl, N. Tirfessa. 10.1016/S0375-9474(00)00687-4 .
7) The potential of effective field theory in NN scattering, S.R. Beane, T.D. Cohen, D.R. Phillips. 10.1016/S0375-9474(98)00007-4
8) Two-particle states on a torus and their relation to the scattering matrix, M. Lüscher. 10.1016/0550-3213(91)90366-6
9) Two nucleons on a lattice, S.R. Beane et al. 10.1016/j.physletb.2004.02.007
Homework, exams and grades
Your grade for this course will be based on the homework, which will be assigned approximately once every two weeks. I encourage you to work
on the homework in groups. However, the work that you hand in must be your own, and you must list your collaborators on your manuscript as well
as any references you have used (if you find a solution to a problem on the web, you must cite the url, if you find the solution in a book, you
must cite the book, etc.). The homework assignments will (generally) be due on Friday in the TA's emailbox.
Religious Accommodations
Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW’s policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy (https://registrar.washington.edu/staffandfaculty/religious-accommodations-policy/). Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form (https://registrar.washington.edu/students/religious-accommodations-request/).
Calendar