Interaction of Atomic Nuclei with Particles

(Transcript of the lesson commentary.)

A puzzle called an atom and the processes in it

At the beginning of the 20th century, a new awareness of the structure of matter, based on several important discoveries, began to take shape. According to new theories, the atom was no longer its smallest indivisible part, but became a gateway to the microworld of subatomic elementary particles. Interest in elucidating the internal structure of atoms was started by Wilhelm Conrad Röntgen with the discovery of X-rays penetrating solid matter. Henri Becquerel subsequently discovered the natural ability of uranium salts to emit radiation without any external energy source and Marie Skłodowska-Curie named this property radioactivity.

Joseph John Thomson and Ernest Rutherford contributed important pieces to the puzzle called the atom. Thomson discovered the negatively charged electrons that were part of the atom while studying cathode rays. And British physicist Ernest Rutherford divided radioactive radiation into three groups on the basis of different penetrability, but mainly using the well-known experiment of bombarding gold foil with alpha particles, he proved that the atom cannot be a homogeneous sphere, but that inside the atom there is a tiny nucleus in which almost all the matter is concentrated and has all the positive charge. Around the nucleus there is a relatively spacious shell of negatively charged electrons.

During chemical reactions, atoms interact with each other at the level of their electron shells and new molecules are created by the reactions. In nuclear reactions, the atomic nuclei themselves interact with particles and new nuclei and new emitted particles are created.

In nuclear physics, nuclear reactions occur when a particle comes close enough to the nucleus to enter the region of the strong nuclear interaction. The result of the reaction is a change in the number and configuration of nucleons in the original nucleus and a change in energy ratios. A frequent accompanying phenomenon of nuclear reactions is the emission of other particles or different types of radiation. By changing the number of neutrons, the nucleus changes to another isotope of the same element. Changing the number of protons always means the transmutation of the original nucleus into the nucleus of another element. Transmutation is actually a dream come true of medieval alchemists.

In general, a nuclear reaction can be written by an equation similar to a chemical reaction. This simple notation means that the original nucleus X is bombarded by a particle P0 and this interaction causes the X nucleus to change to a Y nucleus and the emission of another P1 particle. The parameter E expresses the overall energy balance of the nuclear reaction, both the energy supplied and the energy released during the reaction.

The process of a nuclear reaction is not always unambiguous. Bombarding the same nuclei with the same particles can lead to different interactions and result in different new nuclei emitting different particles. Of course, this diversity of nuclear reaction processes occurs with different probabilities.

The first artificial nuclear transmutation was performed more than 100 years ago by Ernest Rutherford when he bombarded an isotope of nitrogen with alpha particles. The result of the given reaction was an isotope of oxygen and an emitted proton. Today, nuclear transmutations are commonly used primarily to produce artificial radionuclides for the needs of contemporary science, research and technology and for use in health care and a number of industrial fields.

Energy balance of nuclear reactions

In the process of any nuclear reaction, the basic laws of physics must be fulfilled, primarily the law of conservation of the number of nucleons, the law of conservation of electric charge, as well as the laws of conservation of momentum and angular momentum and the laws of conservation of parity and isospin. The law of conservation of kinetic and potential energy in a reaction follows Einstein’s mass-energy equivalence relation.

An important parameter of a nuclear reaction is its energy balance. According to the law of conservation of energy and Einstein’s equivalence relation, the resulting energy of a reaction is given by the difference of the sums of the masses of all particles at rest before and after the reaction.

If the energy balance is negative, the nuclear reaction is endothermic, or in other words endoenergetic, and it is necessary to supply it with this energy, because the kinetic energy of the input particle and the nucleus has been used to change the internal state of the nucleus or to produce new particles. The most common way to introduce energy into a nuclear reaction is to significantly increase the kinetic energy of the incoming particles in accelerators.

A positive energy balance means an exothermic or exoenergetic reaction in which kinetic energy is released, making the transmutation energetically profitable. The energy released is drawn from the binding energy of the nucleus.

Interaction of particles with atomic nuclei

Depending on the kind and kinetic energy of the particle, there are several ways for it to interact with the nucleus. If the particle moves only near the nucleus, the nuclear force does not act on it and there is no interaction. The particle just flies past the nucleus without its movement being significantly affected by the force of the nucleus.

During elastic scattering, the direction of the flying particle’s path changes in the force field of the nucleus in accordance with the laws of conservation of energy and momentum. After the interaction, the particle continues to move with lower energy and momentum, a small part of which was transferred to the more massive nucleus.

In inelastic scattering, some of the particle’s kinetic energy is transformed into other types of energy after the collision with the nucleus. The particle is noticeably slowed down, the nucleus is excited by the absorbed energy and must release it by the emission of a photon or possibly by some other change. In general, inelastic scattering produces secondary ionizing radiation, and if the amount of energy transferred is large enough, inelastic scattering can be accompanied by a nuclear reaction.

The last way of interaction is the capture of the particle by the nucleus. The particle enters the nucleus, creates a compound nucleus and transfers all its energy to it. In the nucleus there is an excitation and a change in the number of nucleons — nuclear transmutation. The release of excess energy is accompanied by the emission of photons or other particles.

Nuclear reactions are complex processes dependent on the properties of the incoming particles and on the structure of the bombarding target nuclei. After a particle penetrates the nucleus, their interaction can take place either by a direct process, in which the particle collides with one of the nucleons of the nucleus and knocks it out or puts it in a higher energy state, or by the process of the formation of a compound nucleus, when the particle loses so much energy after several collisions with nucleons that it is no longer able to leave the nucleus and remains bound in it. The excited compound nucleus subsequently transitions to the basic state by the emission of gamma rays or particles.

Cross-section of nuclear reactions

The probability that a flying particle will interact with a nucleus in a particular way can be graphically expressed using the cross section of a given nuclear reaction. We could imagine the cross-section as a circular area in front of the shelled core. If the particle flies through this surface, the given nuclear reaction will occur, if it flies outside the surface, the reaction will not occur. The larger the cross section, the greater the probability that the reaction will proceed in a given particular way.

Mathematically, the number of particles reacting with nuclei in a given way can be expressed as the product of the surface density of the atomic nuclei of the target substance, the total number of particles directed at the target and the cross-section of the given nuclear reaction. It follows that the  nuclear reaction cross-section is given by the ratio of the number of nuclear reactions to the total number of bombarding particles, multiplied by the reciprocal of the surface density of nuclei in the target substance.

The cross-section is usually not related to the geometric cross-section of the target nucleus, but it is significantly influenced by the specific internal mechanisms of the given reaction, or the energy and electric charge of the flying particle. For positively charged particles, due to repulsive forces, the cross-section of the given reaction can decrease. For other particles, on the contrary, it can increase.

If the same particle can cause different nuclear reactions on the same target nucleus, each of these reactions has its own cross-section and thus also its own probability that it will take place in that way. Cross-sections in these cases do not depend at all on the dimensions of the bombarded cores.

For simplicity, the unit of the cross-section of the nuclear reaction is not the inadequately large square meter, but the more practical barn, which approximately corresponds to the geometric cross-section of the atomic nucleus of uranium. More precisely, 1 barn equals 10−28 m2. The barn unit originated in the early days of nuclear technology, when researchers were hitting uranium nuclei with tiny neutrons, compared to barn-sized nuclei. It was probably apt, so the unit of cross-section remained.

Classification of nuclear reactions

The most common division of nuclear reactions is the classification according to which particle they were triggered by. The cause of the reaction can be neutrons, protons or other heavier positively charged ions. Reactions caused by electrons or gamma radiation are less common.

Reactions in which nuclei are bombarded with neutrons take place most readily. A neutron has no electric charge and therefore is not repelled by the nucleus and can enter it even with a relatively low energy. The basic neutron reaction is the simple radiative capture of a neutron by a nucleus. It is called radiative because the newly formed compound nucleus passes from an excited to a normal state by emitting a photon. One neutron will be added to the new nucleus, so an isotope of the same element will actually be formed. Isotopes created by the radiation capture of a neutron often undergo β radioactive transformation.

Of course, neutrons can also cause other nuclear reactions during collisions with nuclei, mostly associated with the emission of other particles, but these reactions take place mainly at higher neutron kinetic energies. The neutron capture cross-section by the nucleus is largest for slow neutrons. With increasing neutron energy, the cross-section decreases, then it reaches the resonance region, where sharp resonance maxima and minima are related to the occupation of discrete energy levels of nucleons in the nucleus, and finally, for higher neutron energies, the cross-section decreases significantly.

Proton-induced nuclear reactions are possible only when the protons are accelerated sufficiently in cyclotrons or linear accelerators so that the flying proton overcomes the repulsive electric forces of the positively charged nucleus and enters it. Depending on the energy of the accelerated proton, a number of nuclear reactions can take place, from simple radiation capture to the emission of a proton, neutron, deuteron or alpha particle. In proton-initiated reactions, nuclear transmutation occurs and the resulting nuclei often show β radioactivity. The cross-section of proton-induced reactions first increases with increasing proton energy, but after reaching a certain maximum value, it decreases again at the same rate.

Nuclear reactions can also produce heavier particles such as deuterons or alpha particles or other positively charged ions in the target nucleus. The most common reactions of the accelerated heavy isotope of hydrogen — deuteron are the processes of detachment and absorption of a neutron or proton from a deuteron in the field of the atomic nucleus. These reactions are used to prepare radionuclides and are also an efficient source of neutrons. Similar reactions also take place during the bombardment of target nuclei with alpha particles. Even heavier nuclei, also referred to as multiply charged ions, can only be used as projectiles to effect a nuclear reaction if they are accelerated to very high kinetic energies. The range of reactions in this case is quite wide, not excluding the splitting of target nuclei into two lighter nuclei, or, on the contrary, the formation of new superheavy nuclei when bombarding heavy nuclei.

For the sake of completeness, we can add that nuclear reactions can also be triggered by electrons or strong gamma radiation (so-called photonuclear reactions), but it must be added that they are not so common and in both cases it is necessary for the electrons and quantity of gamma radiation to have considerable energy. When bombarding target nuclei with a stream of accelerated electrons, we can observe mainly their elastic scattering, then inelastic scattering accompanied by braking radiation and the excitation of atomic nuclei. At very high energies, electrons can penetrate nuclei and cause nuclear reactions in them. High-energy gamma radiation can also cause a nuclear reaction in the target nucleus, during which a neutron or proton is knocked out of the nucleus. But the condition is that the radiation energy is greater than the binding energy of the nucleons in the target nucleus.