Title: Lecture 3N
1Lecture 3N Properties of Nuclei
2Binding energy of a nucleus
Total BE of a nucleus is mass of components
mass of nucleus
BE per nucleon is of course BE/A
3Binding energy of 12C
6 H _at_ 1.0078250 6.0469500 amu
6 n _at_ 1.0086654 6.0519924 amu
Sum of parts 12.0989424 amu!!! subtract
12.00000 amu (mass of 12C atom)
BE 0.0989424 amu _at_ 931.48 MeV/amu ? 92 MeV
BE per nucleon 7.6 MeV
4Binding energy per nucleon
5Semi-empirical Mass Formula
Contributions to stability and instability
In a large nucleus, the short-range nuclear
force attracts only immediate neighbours. Each
nucleon provides a BE, av ,which is constant.
For a nucleus of A nucleons B ? avA av
15.5 MeV
Volume term
Surface nucleons do not utilize this fully. The
number of surface nuclei is ? surface area, i.e.
? r2, or A2/3. Surface term like - asA2/3
as 16.8 MeV
Surface term
Coulomb repulsion term
Preference is for NZ. To allow for this
symmetry, a term is inserted of the form. -
asym(A-2Z)2/A asym 23 MeV.
Symmetry term
To allow for pairing a term ? is added. where ?
ap A-3/4for Z and N even ? -ap A-3/4for Z
and N odd ? 0 for A odd ap 34 MeV
Pairing term
6Semi-empirical Mass Formula
7Semi-empirical Mass Formula
Deviations from the formula indicate anomalous
stability for particular values of N and Z (the
magic numbers)
8Nuclear Stability and the Semi-empirical Mass
Formula
9Properties of Nuclei----Angular momentum
Vector j of each nucleon is the result of
coupling its orbital AM l to its intrinsic spin s.
I is the vector sum of the AM vectors j of all
the individual nucleons.
10Properties of Nuclei----Angular momentum
An example showing how I is the result of
coupling the individual nucleon spins j.
11Properties of Nuclei----Angular momentum
An example showing how I is the result of
coupling the individual nucleon spins j.
12Properties of Nuclei----Angular momentum
An example showing how I is the result of
coupling the individual nucleon spins j.
The GS wavefunction of a nucleus also has a
parity ?, that again may be determined by the
wavefunctions of the nucleons. The parity of a
state is (-1)l.
13Properties of Nuclei----Magnetic dipole moment
Many nuclei have an associated intrinsic magnetic
field. This field derives from the motions of the
protons and neutrons that are the substructure of
the nucleus. We will leave detailed discussion
until we study models.
The dipole moment is measured in units of nuclear
magneton ?N, which has a value ?N3.1525 x
10-8 ev/T.
14Properties of Nuclei----Magnetic dipole moment
15Properties of Nuclei----Magnetic dipole moment
16Properties of Nuclei----nuclear deformation
Electric Quadrupole moment
Very few nuclei are spherical only those near
magic numbers
How can the deformation be detected? By the
electric potential set up by protons in the
nucleus.
17Properties of Nuclei----Electric Quadrupole moment
Q 2/5 Z(a2 - b2) ? 6.5ZR2(?R/R)
18Properties of Nuclei----Electric Quadrupole moment
Nuclei with N or Z near magic numbers are
spherical
Shape changes either side of spherical nuclei
Some nuclei have extreme deformations
19Next Lecture
The deuteron The only 2-nucleon nucleus