Download Chapter 5, Lecture 1 - University of Hawaii Physics and Astronomy

Front page of the NY Times on Friday February 24, 2017
Kim Jong Un
Nuclear Physics question: What kind of bomb is this ?
Midterm results were encouraging:
average score was 85.6
Notes:
Dx = gb ct
since Dx=g vt
+ -
e e ® ¡(4S) ® BB
Question: What is the quark
content of a B meson ?
B0 = bd; B- = bu
Midterm problem and one homework
problem based on PEP-II accelerator
Dx = gb ct
since Dx=g vt
Hard to flip the helicity of an
electron than a muon
Leptons are left-handed in the V-A weak
interaction. Anti-leptons are right-handed.
Flipping a helicity requires boosting to the rest
frame of a particle. The electron is nearly
massless.
Re-read p.99-102 of Bettini
M = ml fpfp l(1- g 5 )p g mn l
m
See the V-A
coupling here
Lamb shift (master energy level diagram)
Review: The hydrogen atom: Schrodinger Equation
Use this potential in the Schrodinger
Equation
2
-1 e
U(r) =
4pe 0 r
Use the separation of
variables technique and
spherical coordinates
y (r,q ,f ) = R(r)Q(q )F(f )
The hydrogen atom:
3-D Schrodinger Equation
y (r,q ,f ) = R(r)Q(q )F(f )
Question; What three quantum numbers
appear in the solution ?
Ans: n, l, m
Review Question: What are the energy levels ?
-13.6eV
En =
n2
This result agrees
with the Bohr model
!
What happens to the l, m
quantum numbers ?
Here l=0,1,2,….n-1
This result does not agree
with the Bohr model.
Question: Why ? What
happens for n =1 ?
Here m=0,±1, ±2,…. ±l
The energies of the l, ml levels are degenerate !
Magnetic moments (from the Bohr model to QM)
Let’s calculate the magnetic dipole moment in
the Bohr model (assume electron moves with
velocity v at a radius r around the nucleus)
2p r
q
ev
T=
;I = =
v
T 2p r
ev
evr
2
m = IA =
pr =
2p r
2
evr emvr
e
m=
=
=
L
2
2m 2m
This is the “Bohr
magneton”
mB = 5.788 ´10-5 eV / T = 9.274 ´10 -24 J / T
Magnetic moments from orbital ang. momentum
Now let’s put aside the Bohr model and get
the precise results from QM
U = - mz B
-e
mz =
Lz
2m
Here ml=0,±1,±2…±l
This result explains the Zeeman effect.
mB = 5.788 ´10-5 eV / T = 9.274 ´10 -24 J / T
• Hierarchy of effects:
• Fine structure (spin-orbit coupling): this
involves the interaction of orbital magnetic
moment and the spin magnetic moment of
the electron. Need the Dirac equation.
• Hyperfine structure: Interaction of nuclear
spin magnetic moment and electron spin
magnetic moment.
Question: Can you give a simple argument for the relative
size of these effects ?
Ans: Key is the mass term in the nuclear
magnetic moment.
The Lamb shift is
somewhat smaller.
The 21 cm line of hydrogen in Radio Astronomy
Question: What is the physical
origin of the famous 21cm line ?
(first detected in 1951)
The spins of the nucleus and
electron are shown. A “spin
flip” transition is the origin of
the 21cm photon (5.87μ eV)
Lamb shift (master energy level diagram)
What happens to atomic energy levels
in a B field ?
For l>0, the levels are split according to the
ml value. This is called the Zeeman effect.
Block diagram of the Lamb shift experiment
Note a deficit of 2S1/2
electrons is
detected.
Oven to
dissociate
single H
atoms.
Bombard with
electrons to
excite a few
atons to the
2S1/2 state
Separation of ml levels
by B field.
(2S1/2, m=+1/2) state is
metastable (10-4s).
Pumping by RF to
excite it to the
(2P3/2, m=-1/2, +1/2.
+3/2) states, which are
not stable.
Lamb used a metal
to detect the 2S1/2
states; these
dexcite and
produce a
conduction
electron
Data from the Lamb shift experiment.
Adapted from Lamb, W. E. Jr. & Retherford, R.C. (1947); Phys. Rev. 72 241
Willis E. Lamb, 1955 Nobel
Prize in Physics (shared with
Polykarp Kusch (g-2 for the
electron))
E(2S1/2 ) - E(2P1/2 ) = 0
This expectation is
not confirmed.
E(2S1/2 ) - E(2P1/2 ) = 1057,8 ± 0.1 MHz
Question: What is the significance of the deviation of red points (data)
from atomic physic expectations (black dashed lines) ?
QED Feynman (x vs t) diagrams
Question: Are we done ?
Question: Are we done ?
Question: How is the diagram on the right compatible with
energy conservation ?
Isn’t it forbidden ?
Question: Are we done ?
Question: Are we done now ?
Ans: No. There is an infinite series of finite
diagrams to sum-up.
Nobel Prize in 1965,
Feynman, Tomonga and
Schwinger for QED
Feynman Diagrams for other
fundamental interactions
Components of Feynman diagrams.