The Nucleus
319
where g p = 2.793, g n = 1.913. A Dirac particle without any structure would be
expected to have g p = 1 and g n = 0. The observed values for the magnetic moments
suggest a complicated structure for the proton and the neutron. It may be noted
that these magnetic moments are smaller than the electronic magnetic moments
by a factor of about m e /m p .
While the proton is stable (some recent theories however, predict that the
proton decays with a lifetime of about 10
31
– 10
32
years), the neutron decays,
n
p e v
→ + +
(9.2)
where v is the antineutrino (neutrino v and its antiparticle antineutrino v are
zero-mass, spin 1/2, neutral particles, see Sec. 10.1), with a half-life of about 11
minutes. The decay process is known as the neutron β-decay. Protons and
neutrons are together known as nucleons.
Binding Energies
Since nuclear forces are strong, nuclear binding energies are a significant fraction
of nuclear masses. Thus, nuclear binding energies can be obtained from the
masses.
The binding energy E b of a nucleus of mass m A , containing Z protons and
(A – Z) neutrons, is
E b = c
2
[Zm p + (A – Z)m n – m A ]
(9.3)
This is the minimum energy required to separate the nucleus into its
constituent nucleons. A nucleus with Z protons and A nucleons is said to have a
charge or atomic number Z and mass number A, and is designated by
A
Z X
where X stands for the chemical symbol of the nucleus (e.g. one has
1
2
3
1
1
1
H, H, H
nuclei with 0, 1, 2 neutrons respectively). Nuclei with the same number of
protons but different number of neutrons are known as isotopes e.g.
1
2
1
1
H, H etc.
or 16 17
8
8
O, O , etc. Nuclei with the same number of neutrons but different number
of protons, are called isotones, e.g.
4
5
2
3
He, Li , and nuclei with the same A but
different Z are called isobars, e.g.
5
5
2
3
He, Li . One also has some nuclei which
are excited states of a stable nucleus, but which have a very long lifetime (say
τ > 0.1 s). These are called isomers.
A very useful concept in nuclear physics is the binding energy per nucleon,
E b /A. It starts from a very low value of E b /A ≈ 1.1 MeV for the deuteron
(E b ≈ 2.225 MeV), rapidly increases to 7.1 MeV for the α-particle, i.e.
4
2 He,
reaches a peak value of about 8.7 MeV for A ≈ 56. For nuclei with larger A, it
319
where g p = 2.793, g n = 1.913. A Dirac particle without any structure would be
expected to have g p = 1 and g n = 0. The observed values for the magnetic moments
suggest a complicated structure for the proton and the neutron. It may be noted
that these magnetic moments are smaller than the electronic magnetic moments
by a factor of about m e /m p .
While the proton is stable (some recent theories however, predict that the
proton decays with a lifetime of about 10
31
– 10
32
years), the neutron decays,
n
p e v
→ + +
(9.2)
where v is the antineutrino (neutrino v and its antiparticle antineutrino v are
zero-mass, spin 1/2, neutral particles, see Sec. 10.1), with a half-life of about 11
minutes. The decay process is known as the neutron β-decay. Protons and
neutrons are together known as nucleons.
Binding Energies
Since nuclear forces are strong, nuclear binding energies are a significant fraction
of nuclear masses. Thus, nuclear binding energies can be obtained from the
masses.
The binding energy E b of a nucleus of mass m A , containing Z protons and
(A – Z) neutrons, is
E b = c
2
[Zm p + (A – Z)m n – m A ]
(9.3)
This is the minimum energy required to separate the nucleus into its
constituent nucleons. A nucleus with Z protons and A nucleons is said to have a
charge or atomic number Z and mass number A, and is designated by
A
Z X
where X stands for the chemical symbol of the nucleus (e.g. one has
1
2
3
1
1
1
H, H, H
nuclei with 0, 1, 2 neutrons respectively). Nuclei with the same number of
protons but different number of neutrons are known as isotopes e.g.
1
2
1
1
H, H etc.
or 16 17
8
8
O, O , etc. Nuclei with the same number of neutrons but different number
of protons, are called isotones, e.g.
4
5
2
3
He, Li , and nuclei with the same A but
different Z are called isobars, e.g.
5
5
2
3
He, Li . One also has some nuclei which
are excited states of a stable nucleus, but which have a very long lifetime (say
τ > 0.1 s). These are called isomers.
A very useful concept in nuclear physics is the binding energy per nucleon,
E b /A. It starts from a very low value of E b /A ≈ 1.1 MeV for the deuteron
(E b ≈ 2.225 MeV), rapidly increases to 7.1 MeV for the α-particle, i.e.
4
2 He,
reaches a peak value of about 8.7 MeV for A ≈ 56. For nuclei with larger A, it