Download Nuclear and Particle Physics

Nuclear and Particle
Physics
Lecture 3
Main points of Lecture 2
Particles interact through 4 forces
1) Strong (nuclear) force
2) Electromagnetic
3) Weak
4) Gravitational
} Main forces in nucleus
Responsible for β decay
Negligible in nuclei
Nucleus is a quantum mechanical system. Can be viewed as
particles moving in a spherically symmetric central potential
Solving Schrodinger equation
Possible energies Magnitude and possible
of nucleons are
directions of angular
quantised
momentum (orbital and
spin) are quantised
Dr Daniel Watts
3rd
Year Junior Honours
Course
Monday January 15th
Conservation of
energy , angular momentum
and parity crucial in understanding
nuclear structure and reactions
Angular parts of
solutions are
spherical harmonics
YAm (θ, φ)
parity = ( -1)l
Notes
Notes
The nucleus and its properties
Time evolution of the nuclear chart
A = Z (protons) + N (neutrons)
atomic number
mass number
A
Z
XN
Z ≡ X chemical symbol)
A bit of nomenclature…
NUCLIDE
ISOTOPES
ISOTONES
ISOBARS
ISOMERS
Proton nmber (Z)
Nucleus = central part of an atom
it contains A nucleons (nucleon = proton or neutron)
element with given N and Z
elements with same Z but different N
elements with same N but different Z
elements with same A
elements in metastable (i.e. very long-lived) state
Chart of nuclides
Neutron number (N)
isotones
isobars
isotopes
Notes
Notes
External properties
Charge Ze: protons have +ve charge e = 1.6022x10-19 C
neutrons have zero charge
neutral atom: (A,Z)
contains Z electrons orbiting around nucleus
symbolically:
A
Z
XN
(Z ≡ X chemical symbol)
Mass M: nuclear and atomic masses are expressed in
ATOMIC MASS UNITS (u)
definition: 1/12 of mass of neutral 12C ⇒ M(12C) = 12 u
1u = 1.6605x10-27 kg or 931.494 MeV/c2 (E=mc2)
M(A,Z) < Zmp + Nmn
difference:
∆M = Zmp + Nmn - M(A,Z) ⇒ mass defect (excess)
accounts for BINDING ENERGY of nuclei (see later)
N.B. we typically use ATOMIC and not NUCLEAR masses
⇒ mass of electrons also included
Size R:
nuclear radii are expressed in fermis (fm)
compare with atomic dimensions
1 fm = 10-15 m
1 Å = 10-10 m
matter
essentially
EMPTY SPACE!
Exercise: calculate nuclear matter density
Notes
Notes
… more on nuclear size
What do we define as nuclear size?
Consider the following:
• the nucleus has a net positive charge Ze (Z protons)
• take into account Coulomb
Resulting potential
extends to ∞
as 1/R2
V
nuclear force
has short
(~10-15 m) range
Define:
Coulomb
repulsive
B
+
barrier height B at a distance
from centre R:
B=
0
-V0
r
R
Zze2
R
for incident charge ze
How do we measure nuclear radii?
Charge radius measurement
use electrons as probe ⇒ point like particles, experience
electromagnetic interaction only and not strong (nuclear) force,
probe the entire nuclear volume.
What energy do we need?
Hints:
E ~ pc
p = h/λ
consider required de Broglie wavelength
consider electron fully relativistic
⇒
Remember:
E = =c =
197.3 MeV fm
0.5 fm
~ 400 MeV
=c = 197.3 MeV fm
Study angular distribution of scattered electrons
⇒ observe diffraction effects
⇒ analogy with optics
Optics analogy
nuclear attractive
R = POTENTIAL RADIUS ⇒ related to range of nuclear force
potential radius > charge (or mass) radius
CHARGE RADIUS
assume nucleus behaves
as a circular disk
⇒ related to charge distribution
12C+
eEe=420 MeV
S + eEe=330 MeV
124
1st minimum at θ :
sinθ = 1.22λ
2R
R = CHARGE RADIUS
Notes
Notes
Aside: Babinet’s principle and diffraction
BUT: unlike optical diffraction, minima ≠ 0
⇒ nucleus has blurred edges
DIFFUSENESS of NUCLEAR SURFACE
Charge density distribution
Remember
ρ (r ) =
Screen with
apertures
ρ0
1+ exp⎜⎜ r − R ⎟⎟
⎝ a ⎠
⎛
⎞
R = Radius at half density
a = diffuseness parameter
ρ0 ~ central density
nuclei ~ const. density
Patterns appear
the same
M=Vxρ
A = 4/3πR3 ρ
Remember R = r0 A1/3
Complementary
screen
r0 ~ 1.3 Fm A<50
r0 ~ 1.2 Fm A>50
charge radius ~ mass radius