8.1 Basic Concepts and Formulae 429
Charge symmetryof nuclear forces: p−p=n−n force
Charge Independenceof 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)
whereQe is the charge of the particle in terms of electron charge,T 3 is the third
component ofT, andBis the baryon number.
Thus,nandpof similar mass form an isospin doublet of nucleon. For proton,
T 3 =+^12 and for neutronT 3 =−^12. 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 conventionnand pare 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
2 mpc)
(8.22)
whereJis the nuclear spin andgis the nuclear g factor.
In Rabi’s experiment the resonance technique is used. In a constant magnetic
fieldB, the magnetic moment precesses with Larmor’s frequencyνgiven by
v=μB
Jh(8.23)
If an alternating magnetic field of frequencyfis superimposed there will be a
dip in the resonance curve when
v=f. (8.24)