# Electric QuadrupoleMoment Forest NuclPhys I

Electric Quadrupole Moment of a Nucleus

# Pages 104-111

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.

or

then

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.

because

Since

if

if

if

if

potential ar due to charge distribution at

for outside of charged sphere.

is fixed.

= multiple moments

let

= general wave function (l=m for maximum projection)

then

Clebsch Gordon notation:

My notation + example

You can also write in terms of states

ie

= 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

So

After simplifying we get the following for Q:

The Quadrupole moment of a single particle

->

when l=j-1/2

when l=j+1/2

If Q due to unpaired proton

then l=1 s=1/2

A=7

->

exp: -0.04 barns

?????????????? ????? ????? ?????

All of particles in a subshell could contribute to the quadrupole moment.

Max number in subshell =

B.) j=3/2 and N=3

barns