1000 Solved Problems in Modern Physics

430 8 Nuclear Physics – II

Electric quadrupole moment

For nuclei withJ =0or^12 , electric dipole moment is zero. For spherical nuclei
quadrupole moment is also zero. Only in non-spherical nuclei the quadrupole
moment (Q) exists.
The concept of quadrupole comes from the classical electrostatic potential theory
(Fig. 8.2).

Φ(r,θ)=

1

r

Σ∞n= 0

an

rn

Pn(cosθ) (8.25)

The quantity 2a 2 /eis known as the quadrupole.

Q

e

=

∫

ψ∗(3z^2 −r^2 )ψdτ (8.26)

Fig. 8.2Electric quadrupole
moment for nuclei of various
shapes

Nuclear reactions

x(a,b)ya+x→b+y

Q=(mx+ma−my−ma)c^2 =Eb+Ey−Ea (8.27)

Q=Eb(1+mb/my)−Ea(1−ma/my)−

2

my

(mambEaEb)

(^12)
cosθ (8.28)
Exoergic reactions: Q=+ve
Endoergic reactions: Q=−ve;
Ea(threshold)=|−Q|(1+ma/mx) (8.29)
Elastic Scattering:Q=zero