What is a Nuclear Cross Section?
Cross Sections
In nuclear physics, a cross-section is a measure of the probability that a specific nuclear reaction (like fusion) will occur. When scientists say the cross-sections get smaller as the atomic number (Z) increases, they mean that it becomes exponentially harder and less likely for two nuclei to successfully fuse and survive as a new, super-heavy element.
Think of the cross-section as the “size of the target” you are trying to hit. As you try to create heavier elements, that target shrinks from the size of a barn door to the size of a needle’s eye.
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| Infographic: The Challenge of Element Synthesis |
Why the Cross-Section Decreases
The production of a super-heavy element is a three-step process, and each step becomes more difficult as the atomic number increases:
- The Capture Stage (Getting Together): To fuse, two nuclei must overcome the Coulomb barrier—the massive electrostatic repulsion between their positively charged protons. As Z increases, this “wall” gets much higher, requiring more energy to overcome.
- The Fusion Stage (Staying Together): Even if the nuclei touch, they often undergo quasifission, where they stick together for a tiny fraction of a second (s) and then fly apart again before ever forming a single “compound nucleus.” The heavier the system, the more likely it is to just bounce off or break apart immediately.
- The Survival Stage (Cooling Down): If they do manage to fuse, the resulting nucleus is “hot” (highly excited). It wants to release that energy, usually by spitting out neutrons. However, for super-heavy elements, the most likely way to release energy is by fissioning (splitting in half). As Z increases, the probability of surviving without fissioning drops toward zero.
The Scale of the Challenge
To put the “shrinking” in perspective, scientists use a unit called the barn (10−24cm2).
- Light elements might have cross-sections in the range of barns or millibarns.
- Super-heavy elements (like Oganesson, Z=118) have cross-sections measured in picobarns ().
| Element | Approx. Cross-Section | Success Rate |
|---|---|---|
| Lower Z | Millibarns (10−3b) | Many atoms per second |
| Element 112 | 1 Picobarn (10−12b) | ~1 atom per week |
| Element 118 | ~0.5 Picobarn | ~1 atom per month |
| Element 120+ | Femtobarns (10−15b) | Predicted ~1 atom per year |
Impact on Research
Because the “target” is so small, researchers have to bombard the target with trillions of ions per second for months at a time just to see a single successful event. This is why discovering a new element now takes years of “beam time” and multi-million dollar particle accelerators.
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