Minimum energy of projectile to trigger a nuclear reaction and energy of ejectiles I am studying the following type of nuclear reactions : projectile+target -> ejectile1+ejectile2
I make the assumption that the target is static. This reaction needs energy to be triggered (Q-value<0).
I would like to calculate myself the minimum projectile energy to make the reaction occurs. At first order, E~-Q but it can lead to momentum conservation violation. The exact formula involve the masses of the different nuclei of the reaction but I can't manage to find it. I start from energy and momentum conservation but I'm far from finding the good formula.
1st question : do you have hints or online resources to help me ?
2nd question : once the reaction occurs, a part of the energy can be used as excitation energy of the nuclei. I think the remaining energy is always converted into kinetic energy of the ejectiles, but is it always true ?
 A: Check conditions required for a nuclear reactions. Some easy ones are isotopes of hydrogen or uranium.
Tupical energy per particle when reactions is detectable is about 10KeV, which is somewhere around 1e6 m/s and energy per particle when reaction is significant is around 1 MeV, or about 1e7 m/s. Key word: electron volt, scientific notation.
Problem with your setup is that time of interactions will be extremely small. on the scale of a nanosecond. Even if reaction speed if significant, you will not get noticeable result if reaction time is that short. So, you will need several times larger speed to compensate for a short reaction time.
You might be interested in metric that measures fusion process, they calculate time, density and energy of particles. All three are required. Density in your case will be just a double of solid, matter will pass through. Modern fusion processes can achieve better density. Time of your reaction will be shorter than any other fusion, orders of magnitudes shorter. So you are left with just energy per particle, or speed. But because you've wasted all other properties that are beneficial, your setup will spend the most energy to start a reaction that any other method. Key word: lawson criterion.
Another problem is that as you keep increasing speed, the cross section of the reaction might decrease. This means that chances that particles will just pass through each other increases. Your only chance to fight this effectmis to make the projectile larger and larger. Key word: barn (unit), cross section.
Also keep in mind that these speeds are too high for the atmosphere. 1e4 m/s is already enough to destroy almost any object
Upd: if you want particle beam to drive reaction, check "Accelerator-driven subcritical reactor", if you want neutrons as particles then neutron energy is less important than the chance of capturing this neutron, so the barn unit is the one of highest interest
