# Understanding Quadrupole Moment of Zero/Half Spin Nuclear Charge

• Rajini
In summary, the conversation discusses the concept of the quadrupole moment of a nuclear with spin zero or half being zero due to its spherical charge distribution. It is also mentioned that this result can be derived easily using Gordon coefficients and that the relation Q=I(2I-1) holds true. A book reference for further understanding is also provided.
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?

Last edited:
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.

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+.

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

Here you have it

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

ansgar said:
Here you have it

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

Thanks..Last line is funny!

Rajini said:
Thanks..Last line is funny!

hehe yeah

## 1. What is a quadrupole moment in nuclear physics?

A quadrupole moment is a measure of the distribution of electric charge within an atomic nucleus. It takes into account not only the total charge of the nucleus, but also the shape and orientation of the charge distribution. This is an important factor in understanding the behavior of nuclei in certain experiments.

## 2. How is the quadrupole moment of a nucleus calculated?

The quadrupole moment of a nucleus is calculated by using the electric field generated by the nucleus. This field is determined by the distribution of charge within the nucleus, which can be measured experimentally. The quadrupole moment is then calculated using a mathematical formula that takes into account the shape and orientation of the charge distribution.

## 3. What is the significance of a zero or half spin nuclear charge in relation to the quadrupole moment?

The spin of a nucleus plays a significant role in determining its quadrupole moment. In general, a zero or half spin nuclear charge will result in a more spherical charge distribution, leading to a smaller quadrupole moment. This is because these spin values correspond to nuclei with a more symmetric distribution of charge, as opposed to nuclei with higher spin values that may be more elongated or asymmetric.

## 4. How does the quadrupole moment affect the stability of a nucleus?

The quadrupole moment is one factor that can affect the stability of a nucleus. A larger quadrupole moment can indicate a less stable nucleus, as it may be more prone to shape changes or deformations. However, there are other factors that also play a role in nuclear stability, such as the number of protons and neutrons in the nucleus and the strength of the nuclear force.

## 5. What are some practical applications of understanding the quadrupole moment of zero/half spin nuclear charge?

Understanding the quadrupole moment of zero/half spin nuclear charge can have a variety of practical applications. For example, it can be used to study the structure and behavior of nuclei in nuclear physics experiments. It can also be used in medical imaging techniques, such as nuclear magnetic resonance imaging (MRI), which relies on the behavior of nuclei with specific quadrupole moments in a magnetic field. Additionally, knowledge of the quadrupole moment can help in the development of nuclear energy and weapons technology.

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