Overview of Two-Particle Collisions
In nuclear physics and radiation dosimetry, a typical scenario involves a collision between a projectile particle with mass m1, velocity υ1, and kinetic energy (EK)1, and a stationary target particle with mass m2 and velocity υ2 = 0.
The collision outcome depends on several factors such as the mass, velocity, and charge of the projectile and target. After the collision, the system can be modeled as two reaction products: one with mass m3 and velocity υ3 at an angle θ to the projectile's initial direction, and the other with mass m4 and velocity υ4 at an angle ϕ.
Two-particle collisions are categorized into three types:
- Elastic Scattering: No change in the type of particles, and total kinetic energy and momentum are conserved.
- Inelastic Scattering: The target gains some of the projectile's energy in the form of intrinsic excitation.
- Nuclear Reactions: The collision results in new atomic nuclei with different atomic numbers, and energy is either released or absorbed.
Elastic Scattering
In elastic scattering, both momentum and kinetic energy are conserved. The products of the collision are identical to the reactants. Mathematically, this means:
m3 = m1, m4 = m2
After the collision, the total kinetic energy and momentum remain the same as before, which makes this process ideal for certain types of radiation dosimetry and particle physics experiments.
Inelastic Scattering
In inelastic scattering, although the collision products are still the same particles (i.e., m3 = m1 and m4 = m2), the kinetic energy of the projectile is partially transferred to the target, causing it to become excited. This excitation may lead to the emission of gamma rays or other forms of energy.
This type of scattering is important in nuclear spectroscopy and particle detection.
Nuclear Reactions
In nuclear reactions, the collision between a projectile particle and a target results in the formation of new nuclei. The products after the collision have different atomic numbers and mass numbers. This type of reaction can result in the release or absorption of a large amount of energy.
In a typical nuclear reaction, the total energy before and after the reaction must be conserved. The total rest energy is given by:
Etotal = m1c2 + m2c2
and after the reaction,
Etotal = m3c2 + m4c2
The difference in rest energy between the products and the reactants is known as the Q value of the reaction:
Q = (m1 + m2)c2 - (m3 + m4)c2
The Q value can be positive, zero, or negative:
- Q > 0: Exothermic (exoergic) reaction, energy is released.
- Q = 0: Elastic collision, no net energy release.
- Q < 0: Endothermic (endoergic) reaction, energy is absorbed, and the reaction needs an input of energy from the projectile.
The threshold energy EKthr required for an endothermic reaction is given by:
EKthr ≈ (m1 - m3)c2 + Q
If the kinetic energy of the projectile is below the threshold energy, the reaction cannot occur. For exothermic reactions, the energy release makes the process spontaneous.