# Nuclear Fission - the double-humped barrier

#### Samy89

Hey Guys,

iam trying to understand the following graphic:

Firstly, the fission was defined by Bethe-Weizsäcker-Equation and the deformation by the distortion parameter epsilon.

So if the deformation increases, than the probability of fission will increase.
Now they induce the correction term and shows the results of that by this graphic. Does anyone know why there are two minima?

#### benit13

Hey Guys,

iam trying to understand the following graphic:

Firstly, the fission was defined by Bethe-Weizsäcker-Equation and the deformation by the distortion parameter epsilon.

So if the deformation increases, than the probability of fission will increase.
Now they induce the correction term and shows the results of that by this graphic. Does anyone know why there are two minima?
I'm not sure I understand the graphic either and I certainly don't have a specific answer, but I'll attempt an answer anyway.

Generally speaking, shell effects in the nuclear-shell model are associated with the quantum numbers and the nature of interactions between the different nucleons. For example, the nucleons in the s-shell contribute to the nuclear radius in a different way to the nucleons in the p-shell. It's also not just a case of whether the number of nucleons gives rise to filled shells or unfilled shells, but there can also be clustering. Alpha-clustering is the idea that certain nuclei tend to be configured in a way that tries to emulate multiples of helium nuclei (also known as molecular nuclei). The classic examples $$\displaystyle ^{12}C$$, $$\displaystyle ^{16}O$$ and the other $$\displaystyle \alpha$$-nuclei, but there's probably effects in others too. These nuclei are known to have interesting and unusual effects not seen in very heavy nuclei.

As a consequence of these effects, it should perhaps be unsurprising that the deformation caused by an excitation of a nucleus is non-monotonic with energy. There are other examples of systems in physics where adding energy gives rise to less deformation.

I can't really give more advice without knowing more about the context (like Fig. 13.2 or the surrounding text in the book).

#### Samy89

thanks. It helped to understand the non-monotic behaviour of the nucleus if their is a reaction which indicates a deformation.

To connect this into the graphic which is from "Krane - Introductory Nuclear Physics - Figure 13.16":

The Energy is the Barrier Energy from the core(?) and it has two minimas, where the deformation induces a formation which leads to some low-states of single nucleons which wouldnt be filled without deformation(?)

#### benit13

thanks. It helped to understand the non-monotic behaviour of the nucleus if their is a reaction which indicates a deformation.

To connect this into the graphic which is from "Krane - Introductory Nuclear Physics - Figure 13.16":

The Energy is the Barrier Energy from the core(?) and it has two minimas, where the deformation induces a formation which leads to some low-states of single nucleons which wouldnt be filled without deformation(?)
Ahhh, yes. I think I have a copy of Krane. I'll have a read later!

1 person

#### neila9876

nucleus vs polymer

I think of something and browse the internet. I got a chart about the deformation of high polymer. It shows the breaking of the main covalent bond. (Zhurkov Theory). The solid line has two minima too.
I even doubt if it's appropriate for me to post this here...