The Nucleus
325
where a is the semi-axis along the axis of rotation and q is the total charge
(Q > 0 implies and elongated or prolate nucleus and Q < 0 implies a flattened
or oblate nucleus).
The nuclear quadrupole moments are determined from their effect on the
hyperfine structure of the atomic spectra. The observed values of Q range from
Q = – 10
–28
m
2
for
123
Sb to 8 × 10
–28
m
2
for
176
Lu, while deuteron has a value of
Q = 2.74 × 10
–31
m
2
.
9.2 NUCLEAR FORCES
The forces that bind nucleons together into a nucleus are very strong forces as
indicated by the large binding energies, and have a very complicated structure.
These forces are described by what is known as strong interactions. Several
important characteristics of these forces follow from a general analysis of the
nuclear properties.
1. The nuclear forces are strong, their magnitude being roughly 100 times
that of electromagnetic forces. This follows from the large nuclear binding
energies.
2. The nuclear forces have a short range. They are dominant over a distance
of about 1 fm but vanish rapidly at distances greater than a few fermis.
This explains the approximate constancy of nuclear density as well as of
binding energy per nucleon. Roughly speaking, the short range of the
forces implies that each nucleon interacts with only a small number of
nearby nucleons.
3. Nuclear forces are independent of the nuclear charges. It is indeed a
striking property that the proton and the neutron have nearly the same
mass. It is convenient to ascribe to the nucleons an isotopic spin (or
isospin for short) τ = 1/2, the τ 2 – 1/2, – 1/2 states corresponding to the
proton and the neutron respectively. The properties of the isospin are
similar to those of the ordinary spin, and the charge independence of the
nuclear forces is equivalently described by the statement that the nuclear
forces are independent of the orientation of the isotopic spin.
4. Nuclear forces are not central forces. In particular, they depend on the
orientation of the spin. This is forcibly demonstrated by the observation
of the deuteron as an S = 1 bound state of a proton and a neutron; no such
bound state is observed in the S = 0 state.
Some important aspects of the nuclear forces are described subsequently.
Yukawa Forces
One of the important modern ideas of forces is that forces between particles
arise from the exchange of particles. The form of the resulting potential can be
deduced from the following arguments.
325
where a is the semi-axis along the axis of rotation and q is the total charge
(Q > 0 implies and elongated or prolate nucleus and Q < 0 implies a flattened
or oblate nucleus).
The nuclear quadrupole moments are determined from their effect on the
hyperfine structure of the atomic spectra. The observed values of Q range from
Q = – 10
–28
m
2
for
123
Sb to 8 × 10
–28
m
2
for
176
Lu, while deuteron has a value of
Q = 2.74 × 10
–31
m
2
.
9.2 NUCLEAR FORCES
The forces that bind nucleons together into a nucleus are very strong forces as
indicated by the large binding energies, and have a very complicated structure.
These forces are described by what is known as strong interactions. Several
important characteristics of these forces follow from a general analysis of the
nuclear properties.
1. The nuclear forces are strong, their magnitude being roughly 100 times
that of electromagnetic forces. This follows from the large nuclear binding
energies.
2. The nuclear forces have a short range. They are dominant over a distance
of about 1 fm but vanish rapidly at distances greater than a few fermis.
This explains the approximate constancy of nuclear density as well as of
binding energy per nucleon. Roughly speaking, the short range of the
forces implies that each nucleon interacts with only a small number of
nearby nucleons.
3. Nuclear forces are independent of the nuclear charges. It is indeed a
striking property that the proton and the neutron have nearly the same
mass. It is convenient to ascribe to the nucleons an isotopic spin (or
isospin for short) τ = 1/2, the τ 2 – 1/2, – 1/2 states corresponding to the
proton and the neutron respectively. The properties of the isospin are
similar to those of the ordinary spin, and the charge independence of the
nuclear forces is equivalently described by the statement that the nuclear
forces are independent of the orientation of the isotopic spin.
4. Nuclear forces are not central forces. In particular, they depend on the
orientation of the spin. This is forcibly demonstrated by the observation
of the deuteron as an S = 1 bound state of a proton and a neutron; no such
bound state is observed in the S = 0 state.
Some important aspects of the nuclear forces are described subsequently.
Yukawa Forces
One of the important modern ideas of forces is that forces between particles
arise from the exchange of particles. The form of the resulting potential can be
deduced from the following arguments.