Exploring nuclear structure through experimentation and logic

<sec>The atomic nucleus is an extremely complex quantum many- body system composed of nucleons, and its shape is determined by the number of nucleons and their interactions. The study of atomic nuclear shapes is one of the most fascinating topics in nuclear physics, providing rich insights into the microscopic details of nuclear structure. Physicists have observed significant shape coexistence phenomena and stable triaxial deformation in isotopes of Zn, Ge, Se, and Kr. This paper aims to delve deeper into the influences of shape coexistence and triaxiality on the ground-state properties of atomic nuclei, as well as to verify new magic numbers. We employ the density-dependent meson-exchange model within the framework of the relativistic Hartree-Bogoliubov (RHB) theory to systematically study the ground-state properties of even-even Zn, Ge, Se, and Kr isotopes with neutron numbers <i>N</i> = 32–42. The calculated potential energy surfaces clearly demonstrate the presence of shape coexistence and triaxial characteristics in theseisotopes. By analyzing the ground-state energy, deformation parameters, two-neutron separation energy, neutron radius, proton radius, and charge radius of the atomic nucleus, we discuss the closure of nuclear shells. Our results reveal that at <i>N</i> = 32, there is anotable abrupt change in the two-neutron separation energy values of <sup>62</sup>Zn and <sup>64</sup>Ge. At <i>N</i> = 34, a significant decrease in the two-neutron separation energy values of <sup>68</sup>Se and <sup>70</sup>Kr is observed, accompanied by an abrupt change in their charge radii. Meanwhile, at <i>N</i> = 40, clear signs of shell closure are observed. The maximum specific binding energy may be correlated with the emergence of spherical nuclear structures. The shell closure not only enhances nucleon binding energy but also suppresses nuclear deformation through symmetry constraints. Our findings support <i>N</i> = 40 as a new magic number, and some results also suggest that <i>N</i> = 32 and <i>N</i> = 34 can be new magic numbers. Notably, triaxial deformation plays a crucial role here. Furthermore, we explore the potential correlation between triaxiality and shape coexistence in the ground-state properties of atomic nuclei and analyze the physical mechanisms behind these changes.</sec><sec>The discrepancies between current theoretical predictions and experimental data reflect the limitations of modeling higher-order many-body correlations (e.g. three-nucleon forces) and highlight challenges in experimental measurements for extreme nuclear regions(including neutron-rich and near-proton-drip-line regions). Future studies will combine tensor force corrections, large-scale shell model calculations, and high-precision data from next-generation radioactive beam facilities (e.g. FRIB and HIAF) to clarify the interplay among nuclear force parameterization, proton-neutron balance, and emergent symmetry, thereby providing a more comprehensive theoretical framework for studying the nuclear structures under extreme conditions.</sec>

A consideration of the effects of radiation on the hemopoietic tissues brings one into a controversial field. This is necessarily so, since various modes of subjecting the blood and the hemopoietic tissues to radiation have been used. Further, results in one species do not always agree with those in other species and hence confusion is frequently caused by an attempt to apply to one species what has been found to occur in another. Difficulties of the above type are so commonly encountered in the older literature on the subject that it has been decided not to include here any survey of this literature. Excellent reviews are available for those who want them. One of the most recent is that by Shields Warren in 1942. The types of radiant energy under consideration in this discussion are either electromagnetic energy waves, such as roentgen and gamma rays, or particulate matter having mass, such as alpha and beta particles, protons, and neutrons. While the former are devoid of mass (other than energy mass) and electrical charge, they may for convenience be considered as bullets of energy called quanta. The alpha particle is the nucleus of the helium atom, having a unit positive charge of two and a unit mass of four. The beta particle (electron) has a negative charge of one and a unit mass of 1/1840. The proton is a component of all atomic nuclei and comprises the entire mass of the hydrogen nucleus. It has a unit positive charge of one and unit mass of one. The neutron is a component of all atomic nuclei with the exception of the hydrogen nucleus. It is neutral in charge and has a unit mass of one. The positron and mesotron are omitted from this discussion for simplification. An unstable atomic nucleus (one having excess energy) may return to a more stable state by the release of energy in the form of an alpha particle, an electron, a proton, a neutron (neutron only during fission process), a gamma ray, or by a combination of several of these forms of energy. An unstable atom may release its excess energy in the form of light, heat, or roentgen rays, or by a combination of two or more of these forms. Materials being subjected to these radiations may be considered as being bombarded with quantas of energy without mass and by particulate matter having both mass and energy. All living cells, whether of man, animal, or plant, are capable of injury from these various types of radiant energy. The extent, location, and type of injury which may be sustained are dependent upon the kind of radiation under consideration, its physical properties, its mode of application, (whether external or internal), its intensity, duration of exposure, and the character and function of the cells of the species of animal or plant being subjected to irradiation. In other words, the degree and character of the biological changes resulting from irradiation are dependent upon many complicating factors and often subject to difficulties of interpretation.

The classical part of a new microscopic model of nuclear structure based on high spatial symmetry is proposed. The isomorphic model, as it is called, is a model of the closed-shell nuclei up to 208Pb at the ground state. In brief, it assumes stable dynamic equilibrium of nucleons on spherical shells, which results in shells having average shapes represented by high symmetry polyhedra derived from one another, whose vertices represent average nucleon positions. Properties successfully examined by application of this classical part alone are nuclear shells and magic numbers, nuclear radii, nuclear density, and ground-state moments of inertia of rotating nuclei based on a closed-shell approximation. Through the presentation of this new model, we wish above all to show that symmetry, used as the basis for a nuclear structure model, is highly successful, just as in other areas of physics and chemistry.

Study of the Shell Evolution Effect on the Nuclei around the 78Ni Core Structure

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

The consequences, for good and ill, of that annus mirabilis of discovery and invention are still very much with us.

A scaled test on the damage and vibration behavior of reinforced concrete nuclear containment subjected to a large aircraft impact

Atomic nuclei have a shell structure in which nuclei with 'magic numbers' of neutrons and protons are analogous to the noble gases in atomic physics. Only ten nuclei with the standard magic numbers of both neutrons and protons have so far been observed. The nuclear shell model is founded on the precept that neutrons and protons can move as independent particles in orbitals with discrete quantum numbers, subject to a mean field generated by all the other nucleons. Knowledge of the properties of single-particle states outside nuclear shell closures in exotic nuclei is important for a fundamental understanding of nuclear structure and nucleosynthesis (for example the r-process, which is responsible for the production of about half of the heavy elements). However, as a result of their short lifetimes, there is a paucity of knowledge about the nature of single-particle states outside exotic doubly magic nuclei. Here we measure the single-particle character of the levels in (133)Sn that lie outside the double shell closure present at the short-lived nucleus (132)Sn. We use an inverse kinematics technique that involves the transfer of a single nucleon to the nucleus. The purity of the measured single-particle states clearly illustrates the magic nature of (132)Sn.

238U material is component in fuels of nuclear reactor core. Understanding properties and structure of 238U nucleus is necessary before simulating and designing nuclear reactor. Besides that, the study of nuclear reaction is necessary to identify the specific characteristics of nucleus, it is the most effective experimental method up to now. However, in order to explain the properties of nuclear structure, in addition to study of the nuclear reaction, nuclear structure models and its theory must be used. There are many nuclear structure models to solve those properties of nucleus. This paper presents application of the Collective Model to determine some rotational bands of 239U nucleus, using Prompt gamma neutron activation analysis method (PGNAA). Experiment is performed at channel No.2 of Dalat Research Reactor (DRR), using Filtered Thermal Neutron Beam and Compton Suppression Spectroscopy with High – Purity Germanium detector (HPGe). The results have found 11 rotational bands of 239U nucleus. This work is very necessary for the research of nuclear structure which controls material technology by itself.

PHYSICAL CONSIDERATIONS A short time after radium was discovered, it was found that objects in the neighborhood of open radium preparations acquired a radioactivity of their own. This activity was very short lived if the object was removed from the vicinity of the radium but could be renewed at will by bringing it back. This mysterious phenomenon is readily explained when the sequence of radioactive changes is known. Radium itself is a metal, belonging to the same chemical group as barium and calcium. The nucleus of the atom is, however, unstable, and at some (entirely unpredictable) time it suddenly ejects a portion of itself. This portion, which is called an alpha ray or alpha particle, is exactly like the nucleus of a helium atom. In any given quantity of radium, every instant a certain percentage of all the atoms present undergo this transformation, the rest remaining completely unchanged. The apparent

The shape resonance model was developed by Gamow [Ga] and by Gurney and Condon [GC] to describe the decay of an unstable atomic nucleus by alpha-particle emission. The idea is very simple. The atomic nucleus is modeled by a potential barrier of finite width which traps the alpha particle. A typical situation is shown in Figure 16.1. According to quantum theory, the wave function for the alpha particle, initially localized in the potential well between the barriers, will oscillate between the barriers. However, because the barriers have finite thickness, as measured by the Agmon metric, the wave function penetrates the barriers, and hence the particle has a nonzero probability of escaping to infinity. In fact, the probability that the particle will escape to infinity in infinite time is 1. To say this another way, there are typically no bound states for this model, and consequently a decay condition such as (16.1) holds: The wave function will eventually leave every bounded region. The classical limit of this model is clear: The barriers are infinitely high, so the distance in the Agmon metric across the barrier is infinite. This forces the wave function to vanish in the classically forbidden region, and the alpha particle is in a bound state. As we will show by a rescaling of the Schrodinger operator, this is equivalent to taking Planck’s constant to zero. The semiclassical regime, therefore, is described by very large potential barriers relative to the energy of the alpha particle. We describe the alpha particle as a quantum resonance of a Hamiltonian H(λ) = -△ + λ2 V, where V has the “shape” of a confining potential barrier of finite thickness determined by λ. We will work in the large λ regime.

The nuclear shell model is a benchmark for the description of the structure of atomic nuclei. The magic numbers associated with closed shells have long been assumed to be valid across the whole nuclear chart. Investigations in recent years of nuclei far away from nuclear stability at facilities for radioactive ion beams have revealed that the magic numbers may change locally in those exotic nuclei leading to the disappearance of classic shell gaps and the appearance of new magic numbers. These changes in shell structure also have important implications for the synthesis of heavy elements in stars and stellar explosions. In this review a brief overview of the basics of the nuclear shell model will be given together with a summary of recent theoretical and experimental activities investigating these changes in the nuclear shell structure.

This chapter surveys the nuclear landscape to display a few typical patterns of nuclear spectra as well as some of the systematic changes in these patterns over sequences of nuclei. The goal is to let the reader see exactly what kinds of data characterize atomic nuclei and nuclear structure and are the most useful as tests of various nuclear models. Nuclear data refer to the vast, varied, and rich reservoir of information about atomic nuclei — from the deuteron to the actinides — obtained by a wide range of techniques. The simplest information is the mass of atomic nuclei. A more useful form for these is nuclear binding energies, which focus on the interactions between nucleons in the nucleus when the masses of the individual nucleons are subtracted. Still more useful (in many cases) are nucleon separation energies, or the energy required to remove the last, outermost nucleons from the nucleus.

The magic neutron number N = 20 arises after 2 quanta of the harmonic oscillator and persists, albeit weakened, after considering a more realistic potential including the spin-orbit interaction. The N = 20 shell gap can be found between the 0d3/2 and 0f7/2 orbitals.It has become clear that magic numbers are not a fixed property throughout the nuclear chart, but can evolve as a function of Z and N due to (residual) proton-neutron interactions, which can lead to a quenching of certain magic numbers and the appearance of others. The archetypical example of these very rapid changes in nuclear structure is the so-called 'island of inversion', comprising the very neutron-rich nuclei near N ∼ 21 and Z ∼ 11.Historically it was found that these nuclei are more bound than expected and subsequent experimental observations pointed toward an abrupt onset of collectivity with deformed ground states. The most striking observations are highly collective E2 transitions between low-lying states, in particular the low energy of the first Jπ = 2+ state of 32Mg and the very large B(E2; 0+gs → 2+1). These properties can best be explained by the dominance of intruder configurations, i.e. configurations outside the sd-shell.The interest in this region of the nuclear chart has grown enormously over time, due to the ever better accessibility of these nuclei at RNB facilities. I will review the current experimental understanding of these nuclei on a few selected examples and will give an outlook on the experimental progress to be expected in the near future.Furthermore an outlook and future plans concerning in-beam γ-ray spectroscopy at RIKEN is given.

One of the common methods used to investigate the nuclear structures of atomic nuclei is the nuclear shell model. Similar to the placement of atomic electrons into orbits, in the nuclear shell model, protons and neutrons are thought to fill the orbits within the nucleus, following the principle of Pauli's exclusion. These orbits are grouped to form shells, which are said to be closed if all possible places in a shell are full. Atomic nuclei with closed shells are very stable and valence nucleons that are more than these nuclei are included in the nuclear shell model calculations. In this study, the nuclear shell model was used to investigate the nuclear structure of even-even Ne nuclei by considering the 16O core as a closed-shell nucleus. Single-particle orbits d5/2, s1/2 and d3/2 are taken into account and different parameter sets are used for two-body interactions between valance nucleons. The results were compared with each other and with current literature values. It was seen that the closest results to the experimental values were obtained with parameter sets of usdb and sdnn. In the 18Ne isotope with magic neutron number, it was seen that the first excited level energy was found to be large as expected. Then, this excitation energy decreases for the 20Ne and 22Ne nuclei and rises again when the orbits become full.