Electric QuadrupoleMoment Forest NuclPhys I
Electric Quadrupole Moment of a Nucleus
As in the dipole calculation we assume that the object is in a state such that its maximum total angular momentum is along the z-axis.
From definition of quadrupole moment for a single charged object/particle.
The origin of this comes from electron-statics.
You expand the electric potential in terms of spherical harmonics.
potential ardue to charge distribution at
for outside of charged sphere.
= multiple moments
= general wave function (l=m for maximum projection)
mean square radius.
Clebsch Gordon notation:
My notation + example
You can also write in terms ofstates
= probability of finding states and with combined total angular momentum L and "z" component M.
Note: : result of taking complex conjugate.
, note that
M=0 and L=2: Orthogonality of's
After simplifying we get the following for Q:
The Quadrupole moment of a single particle
If Q due to unpaired proton
then l=1 s=1/2
exp: -0.04 barns
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All of particles in a subshell could contribute to the quadrupole moment.
Max number in subshell =
B.) j=3/2 and N=3