Theoretical Nuclear and Subnuclear Physics

The following sections are included:

• Preface

• Contents

The following sections are included:

• Attractive

• Short-range

• Spin dependent

• Noncentral

• Charge independent

• Exchange character

• Hard core

• Spin-orbit force

• Summary

• Meson theory of nuclear forces

The following sections are included:

• Nuclear radii and charge distributions

• The semiempirical mass formula

• Nuclear matter

The following sections are included:

• Isotopic spin

• Second quantization

• Variational estimate

• Single-particle potential

The following sections are included:

• Bethe-Goldstone equation

• Effective mass approximation

• Solution for a nonsingular square well potential

• Solution for a pure hard core potential

• Justification of the independent-particle model

• Justification of the independent-pair approximation

The following sections are included:

• General canonical transformation to particles and holes

• Single-particle shell model

• Spin-orbit splitting

The following sections are included:

• Two valence particles: general interaction and δ⁽³⁾(r) force

• Several particles: normal coupling

• The pairing-force problem

The following sections are included:

• Multipole analysis

• Photon in an arbitrary direction

• Transition probabilities and lifetimes

• Reduction of the multipole operators

• Static moments

• Electron scattering to discrete levels

The following sections are included:

• Extreme single-particle model

• Nuclear current operator

• Relativistic corrections to the current

The following sections are included:

• Tamm-Dancoff approximation (TDA)

• Random phase approximation (RPA)

• Reduction of the basis

The following sections are included:

• The [15] supermultiplet in TDA

• Random phase approximation (RPA)

• The [1] supermultiplet with S = T = 0

• Application to nuclei

Many calculations of nuclear spectra starting from realistic single-particle properties and two-nucleon interactions have been carried out (see, for example, [Ba75b, Sp81, Na84, Br87, Br88, Ku90]). It is impossible to summarize all these results here. Rather, we present just one example of an attempt to calculate the excited states of a real nucleus. The calculation focuses on the negative-parity T = 1 states of ; these are the states excited in inelastic electron scattering at large angles and high momentum transfer through the large isovector magnetic moment of the nucleon [Eqs. (7.77) and (8.30)]. The calculation in the TDA is due to Donnelly and Walker [Do70] (see Fe71])…

The first five problems review the analysis in nonrelativistic quantum mechanics of the scattering of a spinless particle by a spherically symmetric potential (see [Bl52, Mo53, Sc68, Fe80]). In these problems the notation is employed…

A principal goal of nuclear physics is to develop a consistent, economic understanding of the main features of the structure of ordinary nuclei that can be extrapolated to new regions of baryon density, temperature, neutron/proton ratio, strangeness content, and momentum transfer…

The following sections are included:

• A simple model

• Lagrangian

• Relativistic mean field theory (RMFT)

• Nuclear matter

• Neutron matter equation of state

• Neutron star mass vs. central density

The following sections are included:

• Relativistic Hartree theory of finite nuclei

• Nucleon scattering

The following sections are included:

• Motivation

• Feynman rules

• An application — relativistic Hartree approximation (RHA)

The following sections are included:

• RPA calculation of collective excitations of closed-shell nuclei

• Electromagnetic interaction

The following sections are included:

• Relativistic mean field theory (RMFT)

• Numerical results

• Finite temperature field theory in QHD-I

The following sections are included:

• Quarks and color

• Quantum chromodynamics (QCD)

• Properties of QCD

• Phase diagram of nuclear matter

The following sections are included:

• Some general considerations

• Pseudoscalar coupling and σ exchange

• Feynman rules for baryon, scalar, and pion contributions to S_fi

• Particle-exchange poles

• Threshold behavior

• Decay rate for φ → π + π

The following sections are included:

• Isospin invariance — a review

• The chiral transformation

• Conserved axial current

• Generators of the chiral transformation

The following sections are included:

• Spontaneous symmetry breaking

The following sections are included:

• A low-mass scalar

• The Δ(1232)

The following sections are included:

• Model hadronic field theories – revisited

• Spontaneously broken chiral symmetry – revisited

• Effective field theory

• Effective lagrangian for QCD

• Effective lagrangian and currents

• RMFT and density functional theory

• Parameters and naturalness

• An application

• Pions – revisited

In this chapter we present a brief overview of density functional theory. The discussion is based on [Ko99, Ar00, Fe71, Se01, Va02]. We first review the statistical mechanics of a non-relativistic, uniform assembly [Fe71]…

The first seven problems review some basic results from advanced quantum mechanics: properties of the Dirac equation and introduction to the relativistic quantum theory of fields. We use , γ₄ = β with . Also σ_μν = [γ_μ, γ_ν]/2i and the Maxwell field tensor is F_μν = ∂A_ν/∂x_μ − ∂A_μ/∂x_ν. The relation to the conventions of Bjorken and Drell is discussed in detail in appendix D.2…

The following sections are included:

• Yang-Mills theory — a review

• Quarks and color

• Confinement

• Asymptotic freedom

The following sections are included:

• Propagator and the path integral

• Partition function and the path integral

• Many degrees of freedom and continuum mechanics

• Field theory

• Relativistic quantum field theory

The following sections are included:

• Some preliminaries

• QED in one space and one time dimension

• Lattice gauge theory

• Summary

The following sections are included:

• Counting

• Ising model — review

• Mean field theory (MFT)

• Lattice gauge theory for QED in MFT

• An extension

• Some observations

The following sections are included:

• Internal space

• Gauge invariance

• Continuum limit

• Gauge-invariant measure

• Summary

The following sections are included:

• Mean-field approach

• Evaluation of required integrals for SU(2)

The following sections are included:

• The (lī) interaction in QED

• Interpretation as a V_lī(R) potential

• Nonabelian theory

• Confinement

• Continuum limit

• Results for

• Determination of the glueball mass

The following sections are included:

• Nonabelian theory

• Basic observation

• Strong-coupling limit (σ → 0)

• Strong-coupling SU(2)

• Strong-coupling SU(3)

• Strong-coupling U(1)

The following sections are included:

• Mean values

• Monte Carlo evaluation of an integral

• Importance sampling

• Markov chains

• The Metropolis algorithm

The following sections are included:

• Fermions in U(1) lattice gauge theory

• Gauge invariance

• Continuum limit

• Path integrals

• Problem — fermion doubling

• Possible solution to the problem of fermion doubling

• Chiral symmetry on the lattice

The following sections are included:

• Bag model

• Quark model state vectors

• Matrix elements

• Transition magnetic moment

• Axial-vector current

• Large N_C limit of QCD

The following sections are included:

• General analysis

• Bjorken scaling

• Quark-parton model

• Momentum sum rule

• EMC effect

The following sections are included:

• Evolution equations in QED

• Splitting functions

• Weizsäcker-Williams approximation

• QCD — Altarelli-Parisi equations

The following sections are included:

• The quark gluon plasma

• Relativistic heavy ions

• Transport theory

• Summary

Please refer to full text.

The following sections are included:

• Lepton fields

• V – A theory

• β-decay interaction

• Leptons

• Current-current theory

• μ-decay

• Conserved vector current theory (CVC)

• Intermediate vector bosons

• Neutral currents

• Single-nucleon matrix elements of the currents

• Pion decay

• Pion-pole dominance of the induced pseudoscalar coupling

• Goldberger-Treiman relation

The following sections are included:

• Spinor fields

• Leptons

• Point nucleons

• Weak hypercharge

• Local gauge symmetry

• Vector meson masses

• Spontaneous symmetry breaking

• Particle content

• Lagrangian

• Effective low-energy lagrangian

• Fermion mass

The following sections are included:

• Weak multiplets

• GIM identity

• Covariant derivative

• Electroweak quark currents

• QCD

• Symmetry group

• Nuclear currents

• Nuclear domain

The following sections are included:

• Multipole analysis

• Nuclear current operator

• Long-wavelength reduction

• Example – “allowed” processes

• The relativistic nuclear many-body problem

• Summary

The following sections are included:

• Neutrino reactions

• Charged lepton (muon) capture

• β-decay

• Final-state Coulomb interaction

• Slow nucleons

The following sections are included:

• One-body operators

• Unified analysis of electroweak interactions with nuclei

• Applications

• Some predictions for new processes

• Variation with weak coupling constants

• The relativistic nuclear many-body problem

• Effective field theory

The following sections are included:

• Quark mixing in the electroweak interactions: two-families — a review

• Extension to three families of quarks

• Feynman rules in the quark sector

The following sections are included:

• Some background

• Solar neutrinos

• Neutrino mixing

• Some experimental results

The following sections are included:

• Cross section

• General analysis

• Parity violation in

• Cross sections

• An example — from a 0⁺ target

Please refer to full text.

The following sections are included:

• Appendix A Part 1
  • Meson exchange potentials
  • is a rank-j irreducible tensor operator

• Appendix B Part 2
  • Pressure in MFT
  • Thermodynamic potential and equation of state
  • π-N scattering
  • The symmetry SU(2)_L ⊗ SU(2)_R
  • π-π scattering
  • Chiral transformation properties

• Appendix C Part 3
  • Peierls' inequality
  • Symmetric (T, S) = (½, ½) state
  • Sum rules

• Appendix D Part 4
  • Standard model currents
  • Metric and convention conversion tables
  • Units and conventions

• Bibliography

• Index