Heavy charged particles are all energetic ions with mass of one atomic mass unit or greater, such as protons, alpha particles (helium nuclei) or fission fragments. Especially knowledge of the interaction of fission fragments and alpha particles must be well known in the engineering of nuclear reactors.

Description of Alpha Particles

Alpha Particle - Interaction with MatterAlpha particles are energetic nuclei of helium. The production of alpha particles is termed alpha decay. Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Alpha particles are relatively large and carry a double positive charge. They are not very penetrating and a piece of paper can stop them. They travel only a few centimeters but deposit all their energies along their short paths. In nuclear reactors they are produced for example in the fuel (alpha decay of heavy nuclei). Alpha particles are commonly emitted by all of the heavy radioactive nuclei occuring in the nature (uranium, thorium or radium), as well as the transuranic elements (neptunium, plutonium or americium). Especially energetic alpha particles (except artificially accelerated helium nuclei) are produced in a nuclear process, which is known as a ternary fission. In this process, the nucleus of uranium is splitted into three charged particles (fission fragments) instead of the normal two. The smallest of the fission fragments most probably (90% probability) being an extra energetic alpha particle.

Fission fragment yields

Fission fragment yield for different nuclei. The most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).

Description of Fission Fragments

Nuclear fission fragments are the fragments left after a nucleus fissions. Typically, when uranium 235 nucleus undergoes fission, the nucleus splits into two smaller nuclei, along with a few neutrons and release of energy in the form of heat (kinetic energy of the these fission fragments) and gamma rays. The average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).

Most of these fission fragments are highly unstable (radioactive) and undergo further radioactive decays to stabilize itself. Fission fragments interact strongly with the surrounding atoms or molecules traveling at high speed, causing them to ionize.

Energy from Uranium Fission

Energy from Uranium Fission

Most of energy released by one fission (~160MeV of total ~200MeV) appears as kinetic energy of the fission fragments.

Nature of Interaction of Charged Particles with Matter

Since the electromagnetic interaction extends over some distance, it is not necessary for the light or heavy charged particle to make a direct collision with an atom. They can transfer energy simply by passing close by. Heavy charged particles, such as fission fragments or alpha particles interact with matter primarily through coulomb forces between their positive charge and the negative charge of the electrons from atomic orbitals. On the other hand, the internal energy of an atom is quantised, therefore only certain amount of energy can be transferred. In general, 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.
Fission Fragments

Fission fragments after a nucleus fission. Fission fragments interact strongly with the surrounding atoms or molecules traveling at high speed, causing them to ionize.

Creation of pairs requires energy, which is lost from the kinetic energy of the charged particle causing it to decelerate. The positive ions and free electrons created by the passage of the charged particle will then reunite, releasing energy in the form of heat (e.g. vibrational energy or rotational energy of atoms). This is the principle how fission fragments heat up fuel in the reactor core. 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.

The distance required to bring the particle to rest is referred to as its range. The range of fission fragments in solids amounts to only a few microns, and thus most of the energy of fission is converted to heat very close to the point of fission. In case of gases the range increases to a few centimeters in dependence of gas parameters (density, type of gas etc.)  The trajectory of heavy charged particles are not greatly affected, because they interacts with light atomic electrons. Other charged particles, such as the alpha particles behave similarly with one exception – for lighter charged particles the ranges are somewhat longer.

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:stopping_power_formula

,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.

stopping_power_formula_2

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).

Specifics of Fission Fragments

The fission fragments three two key features (somewhat different from alpha particles or protons), which influence their energy loss during its travel through matter.

  • High initial energy. Results in a large effective charge.
  • Large effective charge. The fission fragments start out with lack of many electrons, therefore their specific loss is greater than alpha’s specific loss, for example.
  •  Immediate electron pickup. Results in changes of (-dE/dx) during the travel.

These features results  in the continuous decrease in the effective charge carried by the fission fragment as the fragment comes to rest and continuous decrease in -dE/dx. The resulting decrease in -dE/dx (from the electron pickup) is larger than the increase that accompanies a reduction in velocity. The range of typical fission fragment can be approximately half that of a 5 MeV alpha particle.

Bragg Curve

Bragg Curve

Bragg Curve is typical for heavy charged particles and plots the energy loss during its travel through matter.
Source: wikipedia.org

The Bragg curve is typical for 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.