The article talks about what the Mossbauer effect is. It also reveals such concepts as a quantum, the level of energy in an atom and atomic nucleus, a solid body and collective quasiparticles in it.
Math fun
The breakthrough in physics that occurred in the first decade of the twentieth century required serious knowledge in mathematics from scientists. Many discoveries were deduced, as they say, at the tip of a pen: at first they were calculated theoretically and only then discovered in practice.
For example, the presence of gravitational waves, predicted by Einstein in 1910, could only be experimentally confirmed in 2016. The fusion of two neutron stars gave rise to a tremor of space, which terrestrial physicists have grasped and recorded, ushering in an era of gravitational dimensions in the science of mankind. No wonder gravity is mentioned here: it is for such studies that the Mossbauer effect is of importance. But this is more an exception than a rule. Most often, theorists and experimenters stepped on each other's heels: one study gave rise to the need for its mathematical description, and side conclusions were the assumption of new, not yet obtained dependencies. The Mossbauer effect turned out to be one of these phenomena. The assumption of Max Planck, expressed at the end of 1900, also became such a “side effect”. It stated that in the world of electrons and atomic nuclei all quantities can take only discrete values, that is, quantize. Moreover, in his own opinion, this was just a mathematical trick that made the calculations more convenient. Until the end of his life, he believed that a quantum, or the smallest possible portion, such as light, was only a suitable way of describing it, without any serious physical meaning.
Quantum world
However, other scientists interested in an adequate description of what is happening on an atomic scale examined the potential of such a conclusion and took it as an axiom that everything is quantized. Electrons around nuclei can only be in certain orbits, atomic nuclei themselves can have only specific energy levels. Jumping between them, the nuclei give rise to gamma rays. The Mossbauer effect claims that this action should give rise to a kind of return, but this does not happen. In general, all quantities that describe the behavior of the nanoworld are subject to quantization - that is, they are discrete. However, do not forget that the momentum, which in the macrocosm is expressed as the product of mass and velocity, is for the elementary particle something fundamentally different, which means that it is also quantized. So in science, the report in which Max Planck deduced his famous formula containing the value of h, or minimal action, opened a new era. It was an era of quantum physics. The Mossbauer effect, the interpretation that was subsequently given to this phenomenon, became one of the most important milestones of twentieth-century science.
The discovery of the Mossbauer effect
As we noted above, theoretical conclusions went hand in hand with experiment. Some practical conclusions were proved on installations assembled literally “on the knee” and from improvised materials. Scientists should not only be able to derive formulas, but also solder flasks, saw boards, work with metal and assemble plants. Of course, the heads of the laboratories only generalized the results of their wards. However, each experimenter was also an engineer, since the instruments were developed for specific purposes and directly in the research process. The Mossbauer effect was no exception. Its discovery would not have taken place if the stubborn doctoral student Rudolf Mossbauer had not changed the measurement method by cooling the installation, instead of heating it, as advised by the supervisor.
Solid
The theory that we will tell readers in this section at first glance seems understandable. However, as you know, lightness is always achieved by incredible efforts. And so that we can now tell in simple words what the Mossbauer effect is for dummies, literally, whole laboratories once worked.
By solid is usually meant a substance in a crystalline state. The atomic nuclei in this case form a strict periodic lattice, while the electrons are generalized to one degree or another. Of course, a very specific metallic bond is formed in metal crystals, due to which the nuclei exist, as it were, separately from the generalized electrons. The electronic cloud lives by its independent laws, not paying attention to the behavior of the crystal lattice. In crystals, where more traditional ionic and covalent bonds are present, electrons are more closely related to “their” nuclei. However, even there they move more freely between neighboring nodes than in gas or liquid.
The properties of a solid are determined not only by the chemical elements that enter them, but also by the symmetry of the arrangement of atoms relative to each other. In the classic carbon example, one structure produces soft graphite, and the other the hardest natural material, diamond. So the type of connection and the symmetry of the unit cell means a lot to a solid. It is the properties of a solid body that reveal what the Mossbauer effect is. Its nature is explained by the following: all atoms in a solid are connected.
Collective quasiparticles
Now imagine a fairly large three-dimensional lattice. Salt is most suitable for the model: Na and Cl are located at the vertices of the cubes, replacing each other. If you somehow capture one atom and pull it, move it from the usual place of equilibrium, thanks to a fairly tight bond, adjacent atoms will stretch after it. Calculations show that a change in the position of one core has at least some significant effect on third-order neighbors. This means that if you “grab” sodium, adjacent chlorine atoms will follow, followed by sodium atoms and another farthest layer of chlorine. This impact will obviously spread in all directions. Usually they say that the perturbations of the fourth-order neighbors are negligible. However, they are not equal to zero.
Therefore, if you somehow “knock” the crystal harder (for example, direct a laser or a beam of electrons at it), the crystal lattice will go “waves”. Such collective movements, when many neighboring atoms of the crystal simultaneously experience a shift, for example, up or down, are called phonons. In order to describe in an accessible manner what the Mossbauer effect is for dummies, we will not go into details and just tell you that phonons, as it turned out, behave like elementary particles. For example, their energy is quantized, they have a wavelength, momentum, and they are able to interact with each other. Thus, phonons are called collective quasiparticles. Their quantity and quality is determined by the structure of the solid in which they arise. This can be calculated by knowing the size, symmetry, and types of atoms of the unit cell. The appearance of phonons is also affected by the lengths and types of bonds between ions in the crystal lattice.
Zone Theory
Since a solid generalizes all its electrons, then the orbitals (and hence their energies) must also generalize. First you need to remember that electrons belong to this class of particles called fermions. Fermi, Dirac, and Pauli jointly found out that only one particle of this kind can be in one state in a given system. If we return to the example of salt, then each crystal with which we sprinkle soup or meat contains an incredible amount of sodium and chlorine ions. And each of them has the same number of electrons that rotate in identical orbits. How to be? A solid body goes out of position as follows: the energy of each electron orbiting around the nucleus is slightly different from the energy of any other electron belonging to the same orbit of another atom. Thus, it turns out: in the crystal there are incredibly many energy levels that differ so little from each other that they form a compressed zone. The perturbations introduced by phonons are small, since one atom does not oscillate very much. Only collective movement as a whole is of significance. Therefore, the phonon energy, as it were, “dissolves” in the energy of the zone. This is the basis for the Mossbauer effect.
Electromagnetic scale
The movement of charged particles is accompanied by the appearance of an electromagnetic field. This fact poses, for example, the question of why one planet and satellite has it, while the other does not. Electromagnetic waves are usually divided into classes according to their frequency and, accordingly, energy. These two characteristics are interconnected and also depend on the wavelength. What is the Mossbauer effect can be briefly told only if the reader understands where gamma radiation is located on the electromagnetic scale. So, open the scale of the radio waves. Theoretically, the limit of their wavelength is the size of the universe. However, the energy of such radiations would be so small that it cannot be detected. The terahertz radiation frequency is slightly higher. However, both it and radio waves are observed under very specific conditions: drag of electrons in a magnetic field, bending vibrations of polymers, motion of excitons in a solid. The next part of the electromagnetic spectrum is more understandable - infrared radiation. It transfers energy in the form of heat. The energy of visible radiation is even higher. The part of the spectrum that the human eye perceives is very small compared to the entire scale.
Red light carries the least energy, and purple - the greatest. In this regard, the paradox is known: colder water is indicated in blue, whose energy is higher than that of red radiation. The following ultraviolet portion of the electromagnetic scale already has a high enough frequency to penetrate into a solid. Despite the fact that people, like other living creatures of our planet, do not perceive ultraviolet light, its importance for the normal functioning of biological organisms is enormous. The main source of ultraviolet research is the sun. X-ray has a higher energy and ability to penetrate many substances. The source of such radiation is the drag of electrons in electromagnetic fields. In this case, electrons can be both bound, that is, belong to atoms, and free. In medical devices are devices on free electrons. And finally, the hardest and shortest wavelength is gamma radiation.
X-ray and gamma
The Mossbauer effect and its application in physics and technology require distinguishing between gamma rays and x-rays. In terms of energy and, accordingly, wavelength, they overlap in a very wide spectrum. That is, there is both gamma and X-rays with a wavelength of 5 picometers. Differ ways to obtain them. As already explained above, x-ray radiation occurs when electrons are decelerated. In addition, in some processes (including nuclear ones) an electron disappears from the inner shell of a fairly heavy atom, such as uranium. In this case, other electrons tend to take its place. Such transitions become the source of x-ray radiation. Gamma rays are the result of transitions of the nucleus itself from a more excited state. This radiation has great penetrating power and ionizes the atoms with which it interacts. Moreover, when a gamma ray collides with the nucleus of an atom, so-called recoil must be present. However, it turned out in practice that there is no recoil during the interaction of a gamma quantum with the nucleus of an atom belonging to a solid. This is explained by the fact that additional energy seems to be “smeared” over the electronic zones of the crystal, generating a phonon.
Isotopes
The Mossbauer effect and its application are closely related to one surprising fact: the phenomenon does not affect all chemical elements of the periodic table. Moreover, it is essential only for certain isotopes of substances. If the reader suddenly forgot what isotopes are, recall. It is known that any single atom is electrically neutral. This means that there are as many positive protons in the nucleus as there are electrons in the shell. However, the nucleus also contains neutrons, particles without charge. If you change their number in the nucleus, electroneutrality will not be violated, however, the properties of such an atom will slightly change. In addition, it happens that the heavier isotope is radioactive and prone to decay, while ordinary matter is quite stable. A very specific list of elements and their isotopes, which are characterized by the Mossbauer effect. The detection of 57 Fe, for example, is usually trusted precisely with this phenomenon.
The benefits of quantum effects
It is often difficult to make an experiment that confirms one or another hypothesis related to the microworld. In addition, it is not clear what benefit the same Mossbauer effect can bring? His application, however, is quite wide. A study of the properties of crystalline substances, amorphous solids, and finely ground powders takes place, including using this quantum phenomenon. Such data are required both in sections that are far enough from practice (theoretical physics), and in disciplines very close to man, for example, medicine. Thus, the Mossbauer effect and its application should be considered as an example of a theoretical discovery, which brings many benefits even in everyday life.