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Nuclear and Particle
Physics
Lecture 4
Dr Daniel Watts
3rd Year Junior Honours
Course
Thursday January 20th
Main points of Lecture 3 – external nuclear properties
Stable nuclei tend to
populate certain regions of
nuclear chart
n/p ratio of stable nuclei
increases with Z to
counteract electromagnetic
repulsion of protons
External properties
1) Charge – number of protons (ze)
2) Mass - measured in u (1/12 of mass 12C)
3) Size (charge radius – electron scattering
potential radius – neutron scattering)
R = r0 A1/3
V
Coulomb
repulsive
B
0
-V0
r
R
nuclear attractive
Internal properties
Angular momentum J:
nuclei and nuclear particles may possess angular momentum
this property is CONSERVED in nuclear reactions of all kinds
Observable feature:
m projections of angular momentum vector on a spatial axis
Quantum theory
projection is QUANTISED in J
h
Remember
(2J + 1) possible values
-J ≤ m ≤ J
Two types of angular momentum:
1) intrinsic or spin s
2) orbital l
a) integer
⇒ BOSON
b) half-integer ⇒ FERMION
give examples
always integer
l=0
l=1
l=2
l=3
⇒ s-wave (sharp)
⇒ p-wave (principal)
⇒ d-wave (diffuse)
⇒ f-wave (fundamental)
…. continues in alphabetical order
total angular momentum = spin + orb. ang. mom.
For a many-particles system:
obtain: S = s1 + s2 + …
L = l1 + l2 + …
Remember
J=S+ L
this total angular momentum
is always conserved
in all nuclear reactions
Sometimes this NUCLEAR total angular momentum is referred to
as NUCLEAR SPIN J whenever confusion with intrinsic spin in unlikely
How to measure nuclear spins?
through e.g. nuclear reactions
decay modes
angular correlation measurements
4th year
Parity π: fundamental particles may possess an intrinsic parity
property of wave function under inversion of space
coordinates (i.e. under operation) r → -r
if ψ(r) = ψ(−r) ⇒ system is invariant
⇒ POSITIVE or EVEN parity
if ψ(r) = −ψ(−r) ⇒ system is not invariant
⇒ NEGATIVE or ODD parity
positive-parity
word
negative-parity
word
Two types of parity:
1) intrinsic
2) orbital
nucleons have +ve parity (by convention)
πorb = (-1)l
l = orbital angular momentum
l = odd ⇒ parity is odd (negative)
l = even ⇒ parity is even (positive)
total parity = intrinsic x orbital
Remember
πtot = πi x πo
parity is CONSERVED in nuclear and electromagnetic interactions
BUT NOT in weak interactions (e.g. beta decay)
Magnetic moment µ:
associated with the spin is a magnetic dipole moment
electron:
µe ~ -1.0 µB
µB =
eh
2me
Bohr magneton
µN =
eh
2mp
nuclear magneton
(~1/2000 of µb)
For a point like nucleon expect:
µp ~ 1.0µN
µn ~ 0
Experimental measurements:
proton:
µp = 2.79 µN
neutron:
µn = -1.91 µN
Surprise!
the neutron, although uncharged has a non-zero magnetic moment
& proton magnetic moment is anomalously large
consequence of quark sub-structure
(consisting of charged components)
p = 2 up + 1 down
n = 1 up + 2 down
u = + 2/3e
d = - 1/3 e
Important applications of nuclear moments:
(behaviour in e.m. field)
magnetic resonance imaging
nuclear magnetic resonance
… (see Lilley, ch. 9)
Excited states E,J:
nuclei can exist in different excited energy states,
each corresponding to a given configuration of nucleons
excited states have a finite LIFETIME τ and WIDTH Γ
Remember
τΓ~h
Heisenberg’s
uncertainty relation
at low energies levels are DISCRETE
at higher energies level widths Γ become increasingly larger
they eventually overlap forming a CONTINUUM
continuum
high energy
nucleon (or cluster)
low energy
gamma ray
ground state
de-excitation through:
1) γ emission (Eγ = ∆E) with lifetime ∆τ ∼ h /Γ
2) particle emission (if energetically allowed)
each state characterized by a total angular momentum
J=L+S
L = total orbital angular momentum S = total spin
most nucleons combine in pairs
⇓
all nuclei with even N – even Z have J = 0
Excitation level scheme of a real nucleus –
16O
Even N, Even Z nucleus
Spin and parity assignments of the
nuclear excited states
Collectively called a nuclear level scheme
Let’s recap…
charge
mass (u)
e
1.007276
0
1.008556
-e
0.000549
proton
neutron
electron
spin ( h ) parity
½
½
½
+
+
+
e = 1.6022 x 10-19 C
u = 1.6605 x 10-27 kg
931.494 MeV/c2
1 amu (u) = 1/12 mass of neutral
All FERMIONS
12C
⇒ obey Pauli’s exclusion principle
⇒ no two fermions in same quantum state
nuclear radius
R = r0 A1/3
r0 ~ 1.3x10-15 m
nuclear matter has ~ constant density