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A systematic investigation of superheavy nuclei in the isotopic chains of proton numbers Z=106, 114, 120, and 126 together with isotonic chains of neutron numbers N=162, 172, and 184 is presented in the theoretical framework of relativistic mean-field density functionals based on density-dependent meson-nucleon couplings. Ground-state properties, including binding energy, shape, deformation, density profile, and radius, are estimated to provide compelling evidence of magicity in these even-even nuclei, aligning with the concept of the 'island of stability.' The analysis reveals central depletion in the charge density, indicating a bubble-like structure, primarily attributed to the substantial repulsive Coulomb field and the influence of higher l -states. A thorough examination of potential decay modes, employing various semi-empirical formulas, is presented. The probable α -decay chains are evaluated, demonstrating excellent agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Empirical drops in ground-state nuclear polarizabilities indicate deviations from the effect of giant dipole resonances and may reveal the presence of shell effects in semi-magic nuclei with neutron magic numbers N = 50 , 82 and 126. Similar drops of polarizability in the quasi-continuum of nuclei with, or close to, magic numbers N = 28 , 50 and 82, could reflect the continuing influence of shell closures up to the nucleon separation energy. These findings open a new avenue to investigating magic numbers at high-excitation energies and strongly support recent large-scale shell-model calculations in the quasi-continuum region, which describe the origin of the low-energy enhancement of the photon strength function as induced paramagnetism. The nuclear-structure dependence of the photon-strength function asserts the generalized Brink-Axel hypothesis as more universal than originally expected. [ABSTRACT FROM AUTHOR]

Abstract In this work, we report DFT calculations of the energy formation and stability of multi-vacancies in a unit of Zeolite Template Carbon (C 39 H 9). We label as V n the respective vacancy where n carbon atoms have been removed from the pristine C 39 H 9 structure. The results show that V 2 , V 4 , V 6 and V 9 are the most stable vacancies on the ZTC structure. This result agrees with many other studies. Besides, the most stable vacancy of ZTC structure is when nine carbon atoms are removed (V 9) from the ZTC structure. The formation of pentagon rings in the reconstruction of the ZTC vacancy give drastic effect on the energetics stability. Therefore, the formation of pentagon rings eliminates the dangling bonds thus lowering the energy formation. It is also carried out the decoration of ZTC vacancy with Lithium and Calcium atoms, this is the way to use de ZTC vacancy decorated as a medium for hydrogen storage. The results show that the ZTC vacancy decorated with 3 Lithium atoms can adsorb a maximum of nine hydrogen molecules (3 hydrogen molecules per Lithium atom). This gives a gravimetric storage capacity of 4.44 wt percent (wt. %), which is not enough for meeting DOE gravimetric target. On the other hand, to reach DOE gravimetric target, the study of ZTC vacancy decorated with 3 Calcium atoms is carried out, which can adsorb maximum of fifteen hydrogen molecules (5 hydrogen molecules per Calcium atom), this gives gravimetric storage capacity of 5.81 wt %, which meet DOE gravimetric targets, besides the binding energy of hydrogen molecules on ZTC vacancy decorated with 3 Calcium is calculated. These energies are in the range 0.2453–0.2053 eV/H 2 , which are desirable energies for hydrogen adsorption. This is demonstrated by building isotherm adsorption path. The results show that forming vacancies on ZTC structure decorated with three Calcium atoms (3Ca C 30 H 9) is good candidate as medium for hydrogen storage. Highlights • Creation of vacancy in ZTC structure (C 39 H 9) using DFT calculations. • Decoration of ZTC vacancy with metallic atoms (Ca and Li) using DFT theory. • Adsorption energies of H 2 molecules on 3Ca C 30 H 9 are in range 0.2453–0.2053 eV/H. • Maximum storage capacity of H 2 molecules on 3Ca C 30 H 9 system is 5.81 wt %. • Equilibrium pressure is 20–25 MPa for the 3Ca C 30 H 9 nH 2 system. [ABSTRACT FROM AUTHOR]

• The density functional theory is used to study electronic structure of quantum dots in magnetic field. • The Kohn-Sham equations for two-dimensional electrons are solved numerically. • The new series of magic numbers for the total angular momentum of electrons are found. • The influence of a charged impurity on the electronic structure of quantum dots has been studied. Density-functional theory is used to study the electronic structure of quantum dots in magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is obtained. The effect of a charged impurity on the electronic structure of a quantum dot has been studied. [ABSTRACT FROM AUTHOR]

[Display omitted] Electronic, structural, and magnetic properties of small Fe n aggregates with n < 15 atoms were investigated in the framework of the density functional theory (DFT). Our results indicate that spin–orbit coupling has little effect on the structural properties. The magnetic moment of each atom in the cluster is greater than the magnetic moment of their bulk material and the average binding energy value rises monotonically with the size of the cluster and approaches the bulk value. As well as Fe 7 and Fe 13 are the two first magic numbers in good agreement with experimental reports. We studied the adsorption of diatomic SO, CO, O 2 , and N 2 molecules on the Fe 7 and Fe 13 nanoclusters. The most stable adsorption sites, binding energies, and the effect of adsorption on the electronic properties of the Fe clusters were studied. The different aspects of the adsorption mechanism were also investigated. The interaction intensity order is SO, O 2 , CO, and N 2 , and the bond length of the molecules increased after adsorption. X@Fe 13 (X = SO, O 2 , CO, and N 2) systems represent higher magnetization compared to the X@Fe 7 systems. The maximum effect of absorption on the magnetization of the Fe 13 cluster was about 2.4% and on the Fe 7 cluster was about 9.6%. These results provide insights into the application of iron-based catalysts and the understanding of the real reactions and experimental reports. [ABSTRACT FROM AUTHOR]

Graphical abstract A pronounced blue-shift of the maximum of the anion yield of negatively charged gold clusters with increasing cluster size is observed and attributed to the need to evaporate helium from the clusters for their observation in the nascent state. Highlights • Size distributions of Au n ± complexes from doped Helium droplets are measured. • Similar magic numbers and structures compared to other methods are observed. • Optimal energy for cation formation shifts downwards with increasing cluster size. • The maximum of the anion formation efficiency shows the opposite behaviour. Abstract We report the mass spectrometric detection of positive and negative cluster ions of gold atoms formed by the pickup of gold by helium nanodroplets (HNDs) near zero K and subsequent exposure to electron impact. Both singly and doubly charged positive cluster ions were observed. Ionization is initiated by the helium ions He+ and He*−, metastable helium atoms He* as well as electron attachment. We focus on the size distributions of the ions, electron energy dependence of ion yield, patterns of stability and the presence of "magic" clusters. As reported previously by others using a variety of other methodologies, a clear oscillation in the intensity of (Au) n +/- is seen, especially for n <21, with odd-numbered clusters being more intense than even-numbered clusters. The distributions peak early around n = 8. There is a suggestion of magic numbers at n = 35 and 58. Efficiencies of formation of the gold cluster anions were monitored as a function of the energy of the electrons; the measured intensity distributions exhibit a shift to higher energies with increasing cluster size that is attributed to the need to evaporate helium from the clusters for their observation in the nascent state. [ABSTRACT FROM AUTHOR]

Practitioners may face difficulties in the interpretation of fire codes since they often present so called “magic numbers”, i.e. numbers available in the codes which are listed for providing the design of building fire safety, for which the derivation and justification are not explained. The present paper discusses the need for a transparent regulatory approach, in which legislators publicly justify each of the choices made during the development of the fire codes. This approach has been used for the first time during the development of the Italian Fire Safety Code DM03/08/15, where the process adopted for the development of the code requirements has been publicly released in parallel with the code itself. This is deemed to facilitate the interpretation of the fire code, avoiding mis-use and preventing criticism on lack of transparency. To address this issue, the Italian legislators have conducted a process of reconstructing the assumptions adopted for the definition of magic numbers in other International codes (i.e., British Standard 9999) in order to identify suitable specifications for the national context under consideration. This includes the performance of a series of calculations rather than a mere historical examination of their basis. As a first attempt towards an increased transparency in fire code development at an International level, this paper publicly summarizes the process adopted by the Italian legislators for the development of the new Italian fire code, focusing on the exemplary case of the calculations performed for the definition of the requirements concerning stair design (i.e. vertical evacuation). This is presented by comparing the deemed-to-satisfy provisions of the Italian code with the ones given in the British Standard 9999. The process of developing fire codes is discussed together with the benefits associated with transparency in the assumptions adopted for their definition. [ABSTRACT FROM AUTHOR]

Clusters composed of a few to a few hundred atoms are the ultimate nanoparticles where every atom and every electron count. Over the past 50 years clusters have evolved as a new field of matter intermediate between atoms and bulk. In this retrospective we trace the role mass spectrometry has played in this emerging field with emphasis on how extremely intense mass peaks indicating a high abundance of clusters led to the discovery of magic numbers in alkali metal clusters, the fullerenes in carbon clusters, and “Met-Cars” in transition-metal carbide clusters. Magic numbers in alkali metal clusters in turn helped bridge the gap between two disparate fields, atomic physics and nuclear physics. Studies of mass spectra combined with theory and a variety of other experimental techniques have since led to a fundamental understanding of the structure–property relationships of clusters, thus broadening the scope of cluster science. Clusters not only serve as a bridge between atoms and bulk and between atomic and nuclear physics, but also as a bridge across many disciplines. Although this retrospective is focused on atomic clusters, briefly discussed is the solvation phenomenon, a subject to which mass spectrometry has and continues to make a large contribution. [ABSTRACT FROM AUTHOR]

Evaluation of nuclear binding energies from theory close to available measurements of a very high number of superheavy elements (SHE) based on α-decay energies Qα, arrived at a closing shell with a significant neutron number 184. Within the option of several discussed magic numbers for protons of around 120, Bagge's numbers 126 and 184 fit well and are supported by the element generation measurements by low energy nuclear reactions (LENR) discovered in deuterium loaded host metals. These measurements were showing a Maruhn--Greiner maximum from fission of compound nuclei in an excited state with double magic numbers for mutual confirmation. [ABSTRACT FROM AUTHOR]

Abstract: For at least 60years, scientists have known that certain numbers of protons or neutrons in nuclei formed closed shells of some kind, producing additional stability to nuclei that possess these properties. The most stable nuclei, or nuclei exhibiting enhanced stability, are called doubly magic. Only recently, Lucas has explained that the magic numbers are really composites of several sub shells filling, rather than being single shells. In addition, his theory leads to a conclusion that protons and neutrons fill sub shells in a different way. This is because the protons are charged particles, and by Coulomb repulsion they try to get as far away from each other as possible, hence tending to occupy the outer regions of nuclei. Neutrons, being uncharged but possibly polarizable, tend to occupy both outer and inner shells and to possibly increase the number in an outer shell when the nuclei are heavy in a similar way to electrons filling in inner shells in the Lanthanide and Actinide series. Using these ideas, and following a simple modification of Lucas’ geometrical packing scheme, individual candidates for new magic proton numbers and new magic neutron numbers have been identified. Amazingly, these new magic numbers correspond to the experimentally identified superheavy element distribution to a very large extent, and even correspond to magic numbers suggested using very sophisticated theoretical physics methods and computations. As an added bonus, the newly suggested magic numbers correspond to the long lived Thorium and Uranium isotopes, and to the Fermium isotopes, which may help explain the shape of the Peninsula of Heavy isotopes. They also suggest going back to reassess somewhat lighter isotopes to see if some magic effects have been missed. [ABSTRACT FROM AUTHOR]

Abstract: The structures and stabilities of gold ion-doped argon clusters Au+Ar n (n =1–6) are investigated by using the quantum-chemical theory. In the lowest-lying geometries, the argon atoms tend to arrange around the central gold ions. Comparatively stable complexes are considered to consist of four and six argon atoms. The octahedral Au+Ar6 is the first shell closure of title clusters. The most stable structure of Au+Ar4 is distortedly tetrahedral rather than planar. [Copyright &y& Elsevier]

Abstract: The decay energy spectrum for neutron unbound states in 24O (, ) has been observed for the first time. The resonance energy of the lowest lying state, interpreted as the level, has been observed at a decay energy above 600 keV. The resulting excitation energy of the level above 4.7 MeV, supplies strong evidence that 24O is a doubly magic nucleus. The data is also consistent with the presence of a second excited state around 5.33 MeV which can be interpreted as the level. [Copyright &y& Elsevier]

Abstract: The main purpose of the present manuscript is to review the structural evolution along the isotonic and isotopic chains around the “traditional” magic numbers 8, 20, 28, 50, 82 and 126. The exotic regions of the chart of nuclides have been explored during the last three decades. Then the postulate of permanent magic numbers was definitely abandoned and the reason for these structural mutations has been in turn searched for. General trends in the evolution of shell closures are discussed using complementary experimental information, such as the binding energies of the orbits bounding the shell gaps, the trends of the first collective states of the even–even semi-magic nuclei, and the behavior of certain single-nucleon states. Each section is devoted to a particular magic number. It describes the underlying physics of the shell evolution which is not yet fully understood and indicates future experimental and theoretical challenges. The nuclear mean field embodies various facets of the nucleon–nucleon interaction, among which the spin-orbit and tensor terms play decisive roles in the shell evolutions. The present review intends to provide experimental constraints to be used for the refinement of theoretical models aiming at a good description of the existing atomic nuclei and at more accurate predictions of hitherto unreachable systems. [Copyright &y& Elsevier]

Abstract: Metal-rich (n ∼27) clusters were produced by the supersonic cooling expansion of laser-induced KI plasma. The obtained mass spectroscopic peaks show the unique magic numbers at n =9, 13, and 22 for K1(KI) n ; n =8, 12, and 21 for K2(KI) n ; n =8, 12, 16, and 21 for K3(KI) n ; n =7, 9, 11, and 13 for K4(KI) n ; and n =12 and 21 for K5(KI) n . These magic numbers are fairly different from those of other reported metal-rich and clusters. It is interesting to note that clusters have the same magic numbers at n =12 and 21 and possess structures that are closely related to the 3×3×3 and 3×3×5 cubic structures with the excess electron at the side anion vacancy or the center anion vacancy. [Copyright &y& Elsevier]

Abstract: The electronic and structural properties of clusters (Mo n S m ) of the layered semiconductor MoS2 are studied using density-functional based methods. For small Mo n S m clusters the evolution of structural elements, resembling the corresponding structure motifs of the layered bulk compound MoS2 was found. Among the small clusters a highly symmetric Mo4S6 cluster features an outstandingly high stability and a large HOMO–LUMO gap. This cluster can be characterized as a “magic cluster”. With increasing cluster size the stabilization of platelet structures is indicated. In the platelet structures the edges determine the deviation from the bulk properties. The binding energies increase smoothly with increasing cluster size towards the bulk limit. Small clusters and platelet structures have a HOMO–LUMO gap comparable with the gap of the semiconductor bulk material, whereas larger platelet structures show a metallic-like behavior. [Copyright &y& Elsevier]

Selected topics in present days nuclear structure physics studied by reactions of RI beams are presented. They are change in nuclear radii, single particle orbitals, and shapes. Dynamical changes are shown for nuclei far from the stability line in particular in p-sd shell. Among the future reaction study, a thick target method for a storage ring is presented. A possibility to obtain the highest luminosity for an internal target experiment is proposed. [Copyright &y& Elsevier]

Kinetic Energy Release Distributions (KERDs) have been measured for the C2 evaporation from a series of fullerenes including C80+ and its endohedral compounds, Sc3N@C80+ and Ti2@C80+. We have employed Finite Heat Bath Theory (FHBT) to analyze the measured KERDs and to deduce the C2 binding energies. We re-evaluated previously measured binding energies for C82+, La@C82+, and Tb@C82+ in the light of recent findings that fragmentation of fullerene ions proceeds via a very loose transition state. This procedure demonstrates a substantial increase in the binding energy on going from C82+, to La@C82+ & Tb@C82+. The KERDs for all three ions, C80+, Sc3N@C80+, and Ti2@C80+ are nearly overlapping and the C2 binding energies are equal within experimental error. The binding energy deduced for C80+ is surprisingly high. C82+ on the other hand has nearly the same stability as C78+. These results indicate that C80 is a magic number. The results will be discussed in the light of proposed structures for the various compounds and the reliability of data deduced from KERDs. [Copyright &y& Elsevier]

We have adopted the newly developed technique of growing cationic clusters in size-to-charge selected helium nanodroplets (HNDs), with subsequent removal of helium in a collision cell, to record high-resolution mass spectra of Ne n +. Growth in singly charged HNDs leads to mass spectra that feature the same anomalies in the cluster ion abundance as in previous work, namely maxima at n = 14, 21, 55/56, 75. Several other, weaker but statistically significant anomalies are observed at n = 9, 26, 29, 33, 35, 69, 82, 89. However, when neon clusters are grown in larger HNDs, which are likely to be multiply charged, we observe a different set of magic numbers, at n = 7, 13, 19, 26, 29, 34, 55, 71, 81, plus many other numbers for larger clusters, up to n = 197. A transition from the first to the second set is observed in a limited size range if the collision pressure is increased. The most likely reason for the existence of two different sets of magic numbers appears to be the existence of two distinct structural families. Image 1 • Magic numbers in mass spectra of neon clusters reveal local anomalies in their stability. • Helium nanodroplets are charged and size-to-charge selected before doping them with neon. • Two different sets of magic numbers appear; one of them fully agrees with earlier reports. • The other set closely tracks anomalies observed for heavier noble gases. • The presence of two sets suggests the existence of two structural isomers that do not interconvert. [ABSTRACT FROM AUTHOR]

Abstract: Recently, Lucas has explained that the magic numbers are really composites of several sub shells filling, rather than being single shells. In addition, his theory leads to the conclusion that protons and neutrons fill sub shells differently, because the protons tend to occupy outer shells first, while neutrons tend to occupy both outer and inner shells. Using a simple modification of Lucas’ geometrical packing scheme, new magic proton and neutron numbers were postulated for the superheavy nuclei, which matched the island of stability distribution to a large extent. These magic numbers were also tested against some nuclei in the peninsula of isotopes, and found to be relevant. Now, in consideration of a suggestion made many years ago by Linus Pauling, new magic numbers between 50 and 82 are postulated in the continent of isotopes, and compared to experimental data. These new numbers have strong support among the three elements considered by Pauling, namely Cadmium, Tin and Tellurium, and the results suggest that the range of isotopes found, their stability, and their lifetimes are strongly affected by the new magic numbers. In addition, if 58 nucleons are taken to be magic, then the double hump fission distribution for heavy isotopes may be explained semi-quantitatively. [Copyright &y& Elsevier]

Abstract: In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher–Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher–Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters. [Copyright &y& Elsevier]

The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the Z = 6 spin-orbit shell gap towards the neutron dripline. To do so, we employed N A (p,2p) C A − 1 quasi-free scattering reactions to measure the proton component of the 2 1 + state of 16,18,20C. The experimental findings support the notion of a moderate reduction of the proton 1 p 1 / 2 − 1 p 3 / 2 spin-orbit splitting, at variance to recent claims for a prevalent Z = 6 magic number towards the neutron dripline. [ABSTRACT FROM AUTHOR]