8.1 Basic Concepts and Formulae
429
Charge symmetry of nuclear forces: p − p = n − n force
Charge Independence of nuclear forces: p − p = p − n = n − n force
Isospin: A fictitious quantum number (T) which is used in the formalism of charge
independence The charge
Q
e
= T 3 +
B
2
(8.19)
where
Q
e
is the charge of the particle in terms of electron charge, T 3 is the third
component of T , and B is the baryon number.
Thus, n and p of similar mass form an isospin doublet of nucleon. For proton,
T 3 = +
1
2
and for neutron T 3 = −
1
2
. For strong interaction of other particles refer to
Chap. 10. Although there is no connection between isospin and ordinary spin, the
algebra is the same. For a system of particles, the notation for isospin will be I.
Nuclear spin (J)
Odd A nuclei : J =
1
2
,
3
2
,
5
2
, . . .
(8.20)
Even A nuclei : J = 0, 1, 2, . . .
(8.21)
Nuclear parity: By convention n and p are assigned even(+) intrinsic parity. In
addition parity comes from the orbital angular momentum (l) and is given by (−1)
l .
Thus, for deuteron which is mainly in the s-state, this part of parity is +1. Parity
is multiplicative quantum number, so that for deuteron, P = +1.
Hyperfine structure of spectral lines
Fine structure of spectral lines is explained by the electron spin, while the hyperfine
structure is accounted for by the nuclear spin.
Nuclear magnetic moment (μ)
μ = gJ
e
2m p c
(8.22)
where J is the nuclear spin and g is the nuclear g factor.
In Rabi’s experiment the resonance technique is used. In a constant magnetic
field B, the magnetic moment precesses with Larmor’s frequency ν given by
v =
μB
Jh
(8.23)
If an alternating magnetic field of frequency f is superimposed there will be a
dip in the resonance curve when
v = f.
(8.24)
429
Charge symmetry of nuclear forces: p − p = n − n force
Charge Independence of nuclear forces: p − p = p − n = n − n force
Isospin: A fictitious quantum number (T) which is used in the formalism of charge
independence The charge
Q
e
= T 3 +
B
2
(8.19)
where
Q
e
is the charge of the particle in terms of electron charge, T 3 is the third
component of T , and B is the baryon number.
Thus, n and p of similar mass form an isospin doublet of nucleon. For proton,
T 3 = +
1
2
and for neutron T 3 = −
1
2
. For strong interaction of other particles refer to
Chap. 10. Although there is no connection between isospin and ordinary spin, the
algebra is the same. For a system of particles, the notation for isospin will be I.
Nuclear spin (J)
Odd A nuclei : J =
1
2
,
3
2
,
5
2
, . . .
(8.20)
Even A nuclei : J = 0, 1, 2, . . .
(8.21)
Nuclear parity: By convention n and p are assigned even(+) intrinsic parity. In
addition parity comes from the orbital angular momentum (l) and is given by (−1)
l .
Thus, for deuteron which is mainly in the s-state, this part of parity is +1. Parity
is multiplicative quantum number, so that for deuteron, P = +1.
Hyperfine structure of spectral lines
Fine structure of spectral lines is explained by the electron spin, while the hyperfine
structure is accounted for by the nuclear spin.
Nuclear magnetic moment (μ)
μ = gJ
e
2m p c
(8.22)
where J is the nuclear spin and g is the nuclear g factor.
In Rabi’s experiment the resonance technique is used. In a constant magnetic
field B, the magnetic moment precesses with Larmor’s frequency ν given by
v =
μB
Jh
(8.23)
If an alternating magnetic field of frequency f is superimposed there will be a
dip in the resonance curve when
v = f.
(8.24)