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1.0 Slides: Practical
applications of nuclear physics (PDF)

1.1 Slides: Phys-340a course overview,
low-energy nuclear physics (PDF)

1.2 Slides: nuclear accelerators (PDF)
1.2 Notes (PDF)

1.3 Notes: nuclear units and constants of nature, with examples (PDF)

1.4 Notes: de Broglie wavelength
of electron and heavy-ion beams (PDF)

2.0 From quarks to nuclei

2.0a Notes: the four fundamental
interactions, leptons and hadrons, quarks, standard model (PDF)

QCD and lattice gauge theory:
masses of hadrons (Frank Wilczek, Physics Today, 2000)

2.0b Slides: from quarks
to nuclei (PDF)

2.0c Notes: the nuclear quantum
many-body problem (PDF)

2.1 Basic experimental facts

2.1a Slides: nuclear chart
and decay modes (PDF)
2.1a Notes (PDF)

Nuclear chart, proton and neutron driplines. Alpha, beta, and gamma decay.
Radioactive

decay law: decay rate, half-life, mean life, and level width. Gamov's
explanation

(1928) of alpha emission via potential barrier tunneling. Spontaneous
fission:

charge and mass distribution of fission fragments, fission half-lives.
The frontier

of superheavy elements, exp. evidence for Z=117. Proton and neutron
radioactivity

at the driplines, cluster emission. The "terra incognita" of neutron-rich
nuclei.

Location of neutron dripline for light isotopes.

2.1b Slides: nuclear
densities and binding energies (PDF)
2.1b Notes (PDF)

Nuclear charge densities and rms radii (elastic electron scattering).
Nuclear

binding energies. Liquid drop model and Bethe-Weizsaecker
semi-empirical

mass formula. NOTE: nuclei are not classical liquids! Reason:
pair

correlation function for fermions ("Pauli repulsion"),
see Section 4.2 for details.

2.1c Slides: nuclear astrophysics (PDF)
2.1c Notes (PDF)

Type II Supernovae, iron core collapse, production of neutrons and
neutrinos

via electron capture by protons. Supernova explosion driven by
high-energy

neutrinos. Synthesis of heavier nuclei via the rapid neutron capture
process

(r-process). Neutron stars. The rapid proton capture process
(rp-process)

in nova explosions.

2.1d Slides: RIB facilities (PDF)

2.2 Basic theoretical concepts

2.2 Notes: Binding energies and Q-values (PDF)

Q-value formalism for nuclear reactions (using energy conservation).

Applications: energy release in nuclear fission and fusion,

neutron separation energies and location of neutron dripline (homework),

threshold energies for heavy-ion fusion reactions (homework).

2.2.1 Notes (PDF)

Structure of nuclear many-body Hamiltonian: one-body, two-body, and three-body
operators.

Many-particle Schroedinger equation. Quantum systems of identical
particles,

symmetric and anti-symmetric many-particle wave functions. Fermions,
bosons and

Pauli's spin-statistic theorem. Phenomenological one-body Hamiltonians
(e.g. nuclear

shell model): total energy and many-body wave function (Slater determinant).
Spin and isospin

formalism (Pauli matrices and state vectors). Free nuclear Fermi gas
model

(Fermi momentum and Fermi energy as function of density, relation between
Fermi energy

and total energy, explanation of symmetry energy in liquid drop model).

3.1 Single-particle motion: shell models

3.1a Notes: spherical shell model (PDF)
3.1b Slides (PDF)

Exp. evidence for nuclear shell structure: "magic numbers"
(discontinuities

in binding energies, first excited 2+ states). Spherical shell
model

with spin-orbit force due to strong interaction. Calculation of
single-particle

energy levels and wave functions, explanation of "magic numbers"
due to

shell gaps. Contour plots of single particle probability densities
("nuclear

orbitals"). Electric multipole (EL) transitions and Weisskopf unit.

3.1c Notes: deformed shell model (PDF)
3.1d Slides (PDF)

Deformed shell model ("Nilsson model"): qualitative description
of deformed

nuclear ground states, "shape isomers" and "shape coexistence".

3.2 Collective motion

3.2a Slides: collective motion; rotation, vibration, giant resonances (PDF)

3.2b Notes: surface vibrations, rotations (PDF)

3.2c Notes: rot/vib bands, superdeformation, giant resonances (PDF)

Double- and triple-humped fission barriers and fission isomers of actinide nuclei:

macroscopic-microscopic method (liquid drop + deformed shell model).

3.2d Slides: fission barriers and fission isomers in macroscopic-microscopic model (PDF)

4.1 The nucleon-nucleon (N-N) interaction

4.1a Notes: N-N interaction (PDF)

4.1b Notes: N-N interaction (PDF)

4.1c Slides: N-N interaction (PDF)

Structure of N-N interaction potential based on invariance principles,

dependence on spin and isospin, strong spin-orbit term, tensor

interaction and one-pion exchange potential, multiple meson exchanges.

The Argonne v-18 N-N potential: plots of radial functions. Angular momentum

eigenstates for N-N scattering, phase shift analysis of measured p-p and n-p

differential scattering cross sections (Nijmegen data set).

4.2 Nuclear many-body theory in "occupation number representation"

4.2a Notes (PDF)

Creation and annihilation operators for fermions, anti-commutators.

State vector corresponding to single Slater determinant. One-body operators

and ground state expectation values: calculate ground state density and

total kinetic energy. Two-body and three-body operators: nuclear many-body

Hamiltonian and total ground state binding energy.

4.3 Brief discussion of "ab initio" calculations for light nuclei

4.3a Slides: "ab initio" calculations
for light nuclei (PDF)

a) Green's function Monte-Carlo with Argonne-v18 + NNN interaction.

b) "No-core" shell model results.
c) Coupled cluster theory.

4.4 Ground state mean field theory: static and constrained Hartree-Fock (HF)

4.4a Slides: static Hartree-Fock formalism (PDF)

Pair correlation function for nucleons (Pauli "exchange hole"), average distance

between nucleons. Independent particle motion in mean-field potential.

Derivation of HF equations from variational principle. Mean field "Hartree"

potential and Fock exchange term, need for effective interactions (Bruckner G-matrix),

Bethe-Goldstone equation for G-matrix. Phenomenological effective interactions:

Skyrme interactions, Skyrme energy density functional and mean field.

4.4b Slides: static Hartree-Fock numerical results (PDF)

Contour plots of mass density distributions for spherical and deformed nuclei,

plots of mean field potentials for protons and neutrons, HF single-particle

energies, total binding energies, and rms-radii. Constrained HF calculations:

potential energy surface and fission barrier, cranked HF calculations: rotational bands.

4.5 Beyond the mean field: residual interactions

4.5a Slides: residual interactions and BCS pairing

Pairing due to short-range residual interaction, structure of BCS ground state

for nuclei, pair occupation probability, spectral distribution of pairing,

HF + BCS pairing Hamiltonian, modification of ground state density.

4.6 Ground state mean field theory with pairing: Hartree-Fock-Bogoliubov (HFB)

4.6a Slides: static HFB theory and numerical results (PDF)

HFB formalism: quasi-particle transformation, generalized variational principle,

mean-field and pairing field Hamiltonian, HFB equations in coordinate space,

normal density and pairing density. Mean field potential and Fermi energies

for stable nuclei and near the 2n-dripline. Contour plots of normal density

and pairing density for protons and neutrons, 2n-separation energies and location

of 2n-dripline for Zr isotopes, pairing gaps, quadrupole moments.

HFB nuclear mass table: S2n and ground state deformations for all nuclei.

HFB with (Q20,Q30) constraints: potential energy surface for 238U fission,

and single-particle energies for 224Ra.

4.7 Random Phase Approximation (RPA): theory of collective excitations

4.7a Slides: Nuclear RPA theory and numerical results (PDF)

Microscopic theory of excited states: particle-hole excitations built on the HF

ground state. Collective motion = coherent superposition of large number of

p-h excitations. TDHF --> linear response theory --> RPA equations. Discussion

of early RPA calculations for 208Pb: quadrupole and octupole surface vibrations

and giant multipole resonances. Recent results: splitting of GDR in deformed nuclei

(example 238U), and quasiparticle RPA (=QRPA) calculations for exotic neutron-rich nuclei.

4.8 Time-dependent Hartree-Fock (TDHF): dynamic theory of nuclear reactions

4.8a Slides: Unrestricted TDHF: fusion and deep-inelastic reactions (PDF)

4.8b TDHF animations: the reaction 48Ca + 132Sn at Ecm = 130 MeV for two different impact parameters

Heavy-ion fusion at b = 4.45 fm (MPEG4 movie, 122 kb)

Deep-inelastic reaction at b = 4.6 fm (MPEG4 movie, 74 kb)

4.8c Density-constrained TDHF theory (DC-TDHF)

DC-TDHF: heavy-ion potentials and sub-barrier fusion

Fusion of stable and neutron-rich nuclei, "hot" and "cold" fusion leading to superheavy elements.

4.9 Summary and Outlook

4.9a Slides: Glimpses of the Future (PDF)

Last update: Dec 3, 2014

Volker Oberacker

Vanderbilt University

Volker Oberacker

Vanderbilt University