Understanding the concept of cross section

The cross section is a tiny area, measured in barns ($10^{-28} \mathrm{m^2}$), which relates to the probability of a reaction.

But I have trouble interpreting that number.

For example how can I calculate, when two deuterons collide what's the chance that they fuse? I read in forums that they much more likely scatter.

• have a look at this kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4.html ? – anna v May 21 '14 at 17:47
• A cross section is a way to describe the probability of an event. If scatter is more likely than fusion, then the scatter cross section will be greater than the fusion cross section. In other words - cross section is defined for a specific interaction (although you could sum them for all possible types of interactions and come up with a "total" cross section for "any interaction", I suppose) – Floris May 21 '14 at 19:55
• Cross sections are usually related to scattering events. But they can be expressed in terms of scattering operators (S-matrix) and T-operators and the latter can be considered as functions of the complex energy. There can be poles which can be related to bound states or resonances. The latter play a role in processes such as fusion. – Urgje May 21 '14 at 20:55
• @Floris So basically if two events possible and one has the cross section of 2 barns and the other has 8 barns, that means that the former event has 20% and and the latter has 80% probability? – Calmarius May 21 '14 at 22:26
• If you add the word relative I think you are right. For total probability you need to know how much material is in your beam. – Floris May 22 '14 at 3:20