Understanding Quadrupole Moment of Zero/Half Spin Nuclear Charge

[Rajini]

Hi all,
in many books..they mention..quadrupole moment of nuclear with spin zero or half is zero..
and the reason they give is spherical charge distribution (spherically symmetric.).. is that true?
Or any other better explanation??
thanks

EDit: spherical charge distribution -does this mean-symmetric efg?

 

[ansgar]

you can give your post better names...

you can derive that result for yourself very straightforward, the intepretation is that for nucleus with L = 0 (i.e. J = 0 or 1/2) el_quad = 0 and vice versa.

spherical charge distrubution means that it means, the charger distrubution only depends on the radius.

 

[bcrowell]

As a concrete example, consider 168Er, which is an even-even nucleus that is deformed (prolate). Its ground state has spin and parity 0+. Although the nucleus is deformed, the zero angular momentum of the ground state means that the ground-state wavefunction is a superposition of all possible orientations. Therefore the static quadruple moment <0+|Q|0+> vanishes. However, <0+|Q|2+>, so you do get collective E2 transitions from the first excited state with spin-parity 2+.

 

[Rajini]

Hi,
okay..so something to do with Gordan coefficients..thanks for the hint..
So Q=I(2I-1). Is this relation correct?..If it is correct..is there some book reference for that relation..just to understand further a book would be nice..
thanks again

 

[ansgar]

Here you have it

http://www.phys.washington.edu/users/savage/Class_560/lec560_4/node4.html

 

[Rajini]

Here you have it

http://www.phys.washington.edu/users/savage/Class_560/lec560_4/node4.html

Thanks..Last line is funny!

 

[ansgar]

Thanks..Last line is funny!

hehe yeah