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:: OSEL.CZ :: - How do we describe an atomic nucleus?

:: OSEL.CZ :: – How do we describe an atomic nucleus?

The nucleus is a microscopic organism and belongs to a world where quantum laws apply. This leads to paradoxes that are difficult to imagine with common sense.. It is a system of nucleons, protons, and neutrons that interact through a strong nuclear reaction. The properties of the nuclei are also affected by the electromagnetic interaction, which causes a repulsive force between positively charged protons. While the wattage has an infinite range, the strong nuclear force has a very short range at a distance of about one femtometer. At distances ranging from half a femtometer to one and a half femtometers, they are attractive, at close distances of about half a femtometers, on the contrary, they become disgusting. It is the strong nuclear force that binds the nuclei in the nucleus to each other and defines their properties in a dominant manner. A third reaction is present in the nucleus and it is a weak reaction. It is very weak. However, because, unlike more intense laws, it can violate some conservation laws, it can only convert protons into neutrons and neutrons into protons. Thus it is behind the radioactive decay of beta.

The following fact illustrates, for example, that it is difficult to imagine the nucleus based on our macroscopic and classical experiences. The radius of the nucleons is about the femtometer. The radii of the nuclei become such that the total volume of nucleons in them is tens of percent of their sizes. At the same time, the kinetic energies of the nucleons associated with their movement in the nucleus, known as Fermi motion, correspond to velocities at a percentage level of the speed of light.

The microscopic models for cores thus far only allow describing the light cores, and we are still very far from describing lead.

On the other hand, we also have a very strong interaction between the individual cores, which causes their collective behavior and movement. On the other hand, the nucleons move independently in the force field, which forms all the nuclei in the nucleus as a whole.

In contrast to the electrodynamic reaction, which we can describe as fascinating quantum electrodynamics, we do not yet have an accurate description of the strong nuclear interaction. We do not have an accurate theory and we lack an accurate theory describing the structure of the atomic nucleus. Another problem we face is the fact that the nucleus is a finite multi-particle system and the number of its particles is not so great that we can simply describe it as a continuous environment through statistical methods. We only have models of the kernel, each describing a limited set of properties of the kernel at a certain level of precision.

Phenotypic models of the kernel

We have group models that are based on strong interactions between nucleons and describe the collective properties of the nucleus. For example, the total path of binding energy, the rotation or vibration of the heart. We also have single-particle models describing the independent movement of individual nucleons in the force field that creates all of the nuclei in the nucleus.

The group model is, for example, the drop model, which views the heart as a drop of an incompressible liquid. In a sense, that’s an analogy of a drop of water. It is only necessary to bear in mind that it is an electrically charged droplet due to the charge of protons and consists of two liquids, a proton and a neutron. Also, neutrons and protons are fermions and obey the Pauli exclusion principle. This model well describes the global path of the volume of binding energy per nucleus and thus which nuclei release energy during fusion and which one during fission. It also makes it possible to roughly determine the ratio between the number of protons and neutrons for stable nuclei.

The single particle model, for example, the envelope model. It is based on the fact that nucleons are fermions and there can only be one identical fermion in a single quantum state. It makes it possible to determine the energies of these states, which form groups of states with close energy values, and between which there are large energy differences. These groups of states are called exfoliation, hence the name of the model. Since electrons are also fermions, there is also an envelope model describing the energy states of electrons in the atomic atmosphere. Here the force field creates an electrical charge for the atom’s nucleus. The shell model enables the identification of so-called magic numbers, which is the number of neutrons or protons in which the nuclei have a much higher binding energy, and thus stability. Cores and magic numbers of protons and neutrons are spherical. The model also allows to explain the rotation (momentum moments) of the core and thus the magnetic dipole moments.

The nucleus models mentioned so far use some general physical principles and we look at the nucleus as a whole. We call these models phenomena. The limited number of free parameters present in such virtual models is determined by fit from the experimental data. In a projection model, for example, from a set of measured base weights. Likewise, with the fit of the experimental data, potential shape parameters describing the effect of the total strength of the nucleus on the nucleons in the coat model are obtained.

Microscopic models of the nucleus

Another type of model is microscopic models. In this case, we proceed from elementary principles at the microscopic level. We’ll use the knowledge of the interaction of a pair of nucleons, for example, from experiments with scattering of protons onto protons or nuclei. Then we take the number of protons and neutrons corresponding to a certain number of these nucleons in the nucleus that we want to describe. And let’s see what the system in which we know the interaction of nucleons looks like. Of course, we must also add the electric force acting between the protons. One problem that we face in this way is to define and interpret three-particle and multi-particle interactions that do not appear when a pair of nucleons are dispersed. The calculations are called the ab initio approaches. It is an attempt to use it to describe the structure of the excited states of the nucleus, first those of relatively low energy. So is the path of nuclear reactions at relatively low energies.

If we want to determine the structure of the nuclei, their bottom energy and their excited states, it is necessary to solve the equation of motion of a system for a certain number of nucleons, which interact with each other through a certain basic interaction. For the non-relativistic system of nucleons in the nucleus, this equation of motion in the quantum world is what is called the Schrödinger equation. In such a case, they allow the energy to find the eigenvalues ​​of the Hamiltonian nuclear shown in this equation, and then a complete description of the nuclear quantum system is provided by the functions of the obtained nuclear wave.

The nuclear Hamiltonian is represented in the mathematical operations by a matrix. However, their size grows very rapidly with the number of nucleons in the nucleus that we want to describe and with the number of excited states that we want to describe or influence them in the described states. Even for light and medium-heavy cores, the matrix describing Hamiltonian reaches very high dimensions and soon surpasses the capabilities of today’s largest supercomputers.

Groups that deal with the aforementioned microscopic models and perform mathematical operations from scratch should have access to the largest of today’s largest supercomputers. Most of them are international groups of leading theoretical nuclear physicists. For related computer centers, working with them is an opportunity to test the capabilities of the machine in solving tasks within their capabilities. One of the supercomputers that are also in use is a supercomputer from the ORNL laboratory in the United States of America. It is a gigantic computer center that has long been at the forefront of the arrangement of computing power and capabilities.

One of the leading theoretical nuclear physicists in this field is his colleague Peter Navratel, who in the early 1980s and 1990s began working in the field of nuclear modeling in our country in the Department of Theoretical Physics of the Institute of Nuclear Physics AS CR. . Then for a long time he moved to South Africa, and then to the USA and Canada. He currently works at TRIUMF Lab in Vancouver. It remains a pioneer in this field for a long time, which can be documented as well Job review Summarizing the progress in describing nuclei by microscopic models.

Use symmetries to simplify mathematical operations

At present, the tradition of nuclear modeling continues in our institute, especially in the field of microscopic models, a group led by Tomáš Dytrych, which collaborates extensively with foreign theoretical physicists. It deals with describing light and medium heavy cores using models with ab initio approach. It searches for symmetries that make it possible to simplify mathematical operations by selecting the dominant states. It turns out that the specific nature of the strong nuclear reaction is reflected in the surprisingly simple structure of the basic and low excited states of A nuclei in the region from light to medium-heavy nuclei. The newly discovered simple structure by the aforementioned group is related mathematically to a symmetric group and determines the predominant collective properties of the nucleus. An article about their results was published last year in a magazine article Physical review letters And the previous formula for it ArXiv Server. Besides other novelties, this interesting finding also appears in the annual report of the ASCR Institute for Nuclear Physics.

The use of this symmetry and extrapolation for heavier systems makes it possible to define, for example, the microwave functions of relatively heavy cores, which are still not available in the current capabilities of even the most powerful supercomputers. Thus it is possible to make key predictions to interpret the data obtained in experiments with increasingly difficult cores. We can use these experiments as laboratories to study the basic properties and symmetries of particles that interact through a strong nuclear reaction. Here we can search for the effect of the quark structure of nucleons and the quantum color dynamics behind the strong nuclear force, as well as aspects of the new strange physics behind the Standard Model of matter and interactions. We recently wrote about the search for new physics in other areas of nuclear and particle physics in Oslo. For example, using very subtle Measurement of the magnetic dipole moment of a muon Or while studying a lot Rare decay of particles containing heavy quarks On the LHC Accelerator.