Interaction of Alpha Particles with Matter
Since the electromagnetic interaction extends over some distance, it is not necessary for an alpha particles to make a direct collision with an atom. They can transfer energy simply by passing close by. Alpha particles interact with matter primarily through coulomb forces between their positive charge and the negative charge of the electrons from atomic orbitals. In general, the alpha particles (like other charged particles) transfer energy mostly by:
- Excitation. The charged particle can transfer energy to the atom, raising electrons to a higher energy levels.
- Ionization. Ionization can occur, when the charged particle have enough energy to remove an electron. This results in a creation of ion pairs in surrounding matter.
Creation of pairs requires energy, which is lost from the kinetic energy of the alpha particle causing it to decelerate. The positive ions and free electrons created by the passage of the alpha particle will then reunite, releasing energy in the form of heat (e.g. vibrational energy or rotational energy of atoms). There are considerable differences in the ways of energy loss and scattering between the passage of light charged particles such as positrons and electrons and heavy charged particles such as fission fragments, alpha particles, muons. Most of these differences are based on the different dynamics of the collision process. In general, when a heavy particle collides with a much lighter particle (electrons in the atomic orbitals), the laws of energy and momentum conservation predict that only a small fraction of the massive particle’s energy can be transferred to the less massive particle. The actual amount of transferred energy depends on how closely the charged particles passes through the atom and it depends also on restrictions from quantisation of energy levels.
Stopping Power – Bethe Formula
A convenient variable that describes the ionization properties of surrounding medium is the stopping power. The linear stopping power of material is defined as the ratio of the differential energy loss for the particle within the material to the corresponding differential path length:
,where T is the kinetic energy of the charged particle, nion is the number of electron-ion pairs formed per unit path length, and I denotes the average energy needed to ionize an atom in the medium. For charged particles, S increases as the particle velocity decreases. The classical expression that describes the specific energy loss is known as the Bethe formula. The non-relativistic formula was found by Hans Bethe in 1930. The relativistic version (see below) was found also by Hans Bethe in 1932.
In this expression, m is the rest mass of the electron, β equals to v/c, what expresses the particle’s velocity relative to the speed of light, γ is the Lorentz factor of the particle, Q equals to its charge, Z is the atomic number of the medium and n is the atoms density in the volume. For nonrelativistic particles (heavy charged particles are mostly nonrelativistic), dT/dx is dependent on 1/v2. This is can be explained by the greater time the charged particle spends in the negative field of the electron, when the velocity is low.
The stopping power of most materials is very high for heavy charged particles and these particles have very short ranges. For example, the range of a 5 MeV alpha particle is approximately only 0,002 cm in aluminium alloy. Most alpha particles can be stopped by an ordinary sheet of paper or living tissue. Therefore the shielding of alpha particles does not pose a difficult problem, but on the other hand alpha radioactive nuclides can lead to serious health hazards when they are ingested or inhaled (internal contamination).
The Bragg curve is typical for alpha particles and for other heavy charged particles and describes energy loss of ionizing radiation during travel through matter. For this curve is typical the Bragg peak, which is the result of 1/v2 dependency of the stopping power. This peak occurs because the cross section of interaction increases immediately before the particle come to rest. For most of the track, the charge remains unchanged and the specific energy loss increases according to the 1/v2. Near the end of the track, the charge can be reduced through electron pickup and the curve can fall off.
The Bragg curve also differs somewhat due to the effect of straggling. For a given material the range will be the nearly the same for all particles of the same kind with the same initial energy. Because the details of the microscopic interactions undergone by any specific particle vary randomly, a small variation in the range can be observed. This variation is called straggling and it is caused by the statistical nature of the energy loss process which consists of a large number of individual collisions.
This phenomenon, which is described by the Bragg curve, is exploited in particle therapy of cancer, because this allows to concentrate the stopping energy on the tumor while minimizing the effect on the surrounding healthy tissue.