Cluster radioactivity - preformed cluster model

[logearav]

cluster radioactivity --- preformed cluster model

In cluster radioactivity,
heavy nuclei decay to form Helium, Carbon, Nitrogen, Silicon etc. I came across the term Preformed cluster model. What is preformed cluster model? Members, could you please throw some light on this?

 

[sambristol]

The preformed cluster method was developed by R K Gupta and others as a calculation tool.

You will be familiar with it as an extension of the usual way of calculating alpha decay half life.

In this model you consider the emitted nucleus (the cluster) as existing inside the parent nucleus hence preformed cluster.

You then calculate the probability of the cluster quantum tunnelling out of the parent nucleus. When this is multiplied by a measure of the rate at which the cluster is rattling around inside the parent you get the rate of decay and hence the half life.

So you can see the analogy with the Gamov model of alpha decay where the preformed cluster is He⁴.

The method works best for clusters of high binding energy (He⁴, C¹² etc) but even so care needs to be paid to the form of the nuclear potential assumed. With alpha decay you can get remarkably good
results with a very crude model for the nuclear potential but this is not the case for heavier clusters.

Hope this helps

Regards

Sam

 

[logearav]

Thanks a lot Mr. Sam for your reply. You said "cluster rattling around inside the parent". I construe this as the time taken by the cluster or attempts made by the cluster to come out of the parent nuclei. Am i correct?

 

[sambristol]

Opps Yes When I said 'rattling around' it was a crude description but just about as crude as Gamow in his original papers (see G. Gamow Ziet fur Phys. 51,204 and 52,510 both from 1928 if you read German and can interpret the Gothic script used as a typeface in those days )

The idea is the cluster (ie the nucleus to be emitted) bangs around in a sphere of radius 1.3 * 10 ^-15 *A ^1/3 metres where A is the atomic weight (eg 238 in uranium ²³⁸)

(this remarkably accurate result works to a high degree of accuracy for all but the most tightly bound nuclei – on a more sophisticated level it tells us the strong force in nuclei becomes saturated )

The kinetic energy of the cluster is assumed by Gamow to be the difference in the binding energy of the parent nucleus and the products (an assumption I personally have never been comfortable with). Hence you can calculate the velocity and therefore the transit time of the cluster in the nucleus thus the time factor to multiply with quantum tunnelling probability.

Regards

Sam

 

[logearav]

Thanks again Mr. Sam. Do cluster radioactivity comes under the category " Strong interaction"?

 

[sambristol]

The simple answer is NO


I could write a textbook on the 'strong nuclear force' but by the time it got into the bookshops it would be out of date.

The strong force (in an nucleus) is a 'left over' of the force holding the protons and neutrons together (both made up of 3 quarks – the strong force holding them)

It only has relevance to cluster decay in that the cluster must be tightly bound to have any observable probability of decay.


Regards

Sam