Elements of Modern Physics
328
The second relation, Eq. (9.28), is valid only for the states which are allowed
by Fermi-Dirac statistics for the two protons, i.e. even l for S = 0 and odd l for
S = 1. The electromagnetic interaction will violate charge independence and
introduce small corrections to the above relations.
The model of a nucleon surrounded by a cloud of virtual π-mesons, provides
a qualitative explanation for the magnetic moments of the proton and the neutron.
In this picture, a neutron spends part of the time in the virtual (p + π
–
) state. In
this virtual state, the orbital motion of π
–
gives rise to a substantial negative,
magnetic moment. Similarly a proton spends part of the time in the virtual
(n + π
+
) state. In the (n + π
+
) state, the orbital motion of π
+
gives rise to a large
positive, magnetic moment. These descriptions are in qualitative agreement
with the observed gyromagnetic ratios for the neutron and the proton [Eq. (9.1)].
Strength of Nuclear Interaction
The strength of nuclear interaction can be estimated from the binding energy of
the deuteron. The energy of deuteron may by written as:
E =
2
2
1
2
1
1
2
2
p
n
p
p V
m
m
+
+
(9.29)
If the deuteron is regarded as a sphere of radius r 0 , the uncertainty principle
gives:
E ≈
2
2
0
p
h
V
m r
+
(9.30)
where V is the average potential energy. Taking r 0 ≈ 1 fm and E ≈ – 2 MeV
(binding energy of the deuteron)
V ≈ – 40 MeV
(9.31)
This may be compared with an electrostatic energy of about 1 MeV when
two protons are separated by a distance of about 1 fm. Nuclear interaction is
thus seen to be such stronger than electromagnetic interaction, which explains
the term strong interaction used to describe it.
9.3 MODELS OF THE NUCLEUS
An investigation of the properties of a nucleus with several nucleons is
immensely difficult both because of the complexity of two-nucleon forces and
the absence of a dominant central force. Therefore, model calculations, each of
which has a limited aim of investigating only certain aspects of the nuclear
properties, have to be done. Here, a few nuclear models which together provide
some understanding of the overall structure of the nucleus are considered.
328
The second relation, Eq. (9.28), is valid only for the states which are allowed
by Fermi-Dirac statistics for the two protons, i.e. even l for S = 0 and odd l for
S = 1. The electromagnetic interaction will violate charge independence and
introduce small corrections to the above relations.
The model of a nucleon surrounded by a cloud of virtual π-mesons, provides
a qualitative explanation for the magnetic moments of the proton and the neutron.
In this picture, a neutron spends part of the time in the virtual (p + π
–
) state. In
this virtual state, the orbital motion of π
–
gives rise to a substantial negative,
magnetic moment. Similarly a proton spends part of the time in the virtual
(n + π
+
) state. In the (n + π
+
) state, the orbital motion of π
+
gives rise to a large
positive, magnetic moment. These descriptions are in qualitative agreement
with the observed gyromagnetic ratios for the neutron and the proton [Eq. (9.1)].
Strength of Nuclear Interaction
The strength of nuclear interaction can be estimated from the binding energy of
the deuteron. The energy of deuteron may by written as:
E =
2
2
1
2
1
1
2
2
p
n
p
p V
m
m
+
+
(9.29)
If the deuteron is regarded as a sphere of radius r 0 , the uncertainty principle
gives:
E ≈
2
2
0
p
h
V
m r
+
(9.30)
where V is the average potential energy. Taking r 0 ≈ 1 fm and E ≈ – 2 MeV
(binding energy of the deuteron)
V ≈ – 40 MeV
(9.31)
This may be compared with an electrostatic energy of about 1 MeV when
two protons are separated by a distance of about 1 fm. Nuclear interaction is
thus seen to be such stronger than electromagnetic interaction, which explains
the term strong interaction used to describe it.
9.3 MODELS OF THE NUCLEUS
An investigation of the properties of a nucleus with several nucleons is
immensely difficult both because of the complexity of two-nucleon forces and
the absence of a dominant central force. Therefore, model calculations, each of
which has a limited aim of investigating only certain aspects of the nuclear
properties, have to be done. Here, a few nuclear models which together provide
some understanding of the overall structure of the nucleus are considered.