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ABSTRACTMonolayer-protected noble metal clusters, also called nanoclusters, can be produced with the atomic precision and in large-scale quantity and are playing an increasingly important role in the field of nanoscience. To outline the origin and the perspectives of this new field, we overview the main results obtained on free metal clusters produced in gas phase including mainly electronic properties, the giant atom concept, the optical properties, briefly the role of the metal atom (alkali, divalent, noble metal) and finally the atomic structure of clusters. We also discuss the limitations of the free clusters. Then, we describe the field of monolayer-protected metal clusters, the main results, the new offered perspectives, the added complexity, and the role of the ligand beyond the superatom concept.

Applications of configuration-mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new “outposts” are highlighted: 28O, 42Si, 60Ca and 78Ni. Topics include shell gaps, single-particle properties, islands of inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.

Abstract أعادة رؤية فى إحدى قلادات توت عنخ آمون Ar]] في صندوق على هيئة الخرطوش عُثر عليه في كنز مقبرة الملك توت عنخ آمون KV 62 بطيبة، تم العثور على أروع قلادةمحلاه بشكل القمر وزهور اللوتس متناغمة مع براعمها، وهناك دلالات توضح أن الملك كان يرتديها أثناء حياته، هذا البحث سوف يقدم رؤية جديدة لهذه القلادة ورمزيتها الدينية، وسيكشف القوة السحرية لهذه القلادة. [En] In a cartouche-shaped box found in the treasury of king Tutankhamun’s tomb KV 62 in Thebes, one of the most wonderful moon-shaped necklaces with lotus flowers matching their buds was discovered. Some signs show that the King wore this necklace throughout his lifetime. This research paper presents a revised view of this necklace and its religious symbolism and explores its magic power.

We consider an N fermion system at low temperature T in which we encounter special particle number values Nm exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the Nm. For a quantum state described by the matrix ρ, its purity is expressed by Trρ2 and then the degree of mixture is given by 1−Trρ2, a quantity that coincides with the entropy Sq for q=2. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.

Abstract Hollow nanostructures are at the forefront of many scientific endeavors. These consist of nanoboxes, nanocages, nanoframes, and nanotubes. We examine the mathematics of atomic coordination in nanoboxes. Such structures consist of a hollow box with n shells and t outer layers. The magical formulas we derive depend on both n and t. We find that nanoboxes with t = 2 or 3, or walls with only a few layers generally have bulk coordinated atoms. The benefits of low-coordination in nanostructures is shown to only occur when the wall thickness is much thinner than normally synthesized. The case where t = 1 is unique, and has distinct magic formulas. Such low-coordinated nanoboxes are of interest for a myriad variety of applications, including batteries, fuel cells, plasmonic, catalytic and biomedical uses. Given these formulas, it is possible to determine the surface dispersion of the nanoboxes. We expect these formulas to be useful in understanding how the atomic coordination varies with n and t within a nanobox.

Background. The root-mean-square charge radii are the important characteristics of atomic nuclei which might be measured experimentally. In this research, we study the experimental data on the root-mean-square charge radii of the spherical nuclei available in the literature. The purpose of this analysis is to establish what is the manifestation of the neutron shells in the considered observable and to find regularities in the behavior of the charge radii when a shell is crossed. Materials and methods. The present analysis is performed by means of calculation of the relative charge radius for a given element x = x (N, Nsh , Z ). This value is equal to the charge radius of an isotope with neutron number N over the charge radius of the isotope t with the closed neutron shell N = Nsh . Results. As the result, we have found manifestation of the shells Nsh = 8, 28, 50 and 82. It turns out that the well-known shells with the neutron numbers 20 and 126 do not show up. Conclusions. It is shown that the values of relative charge radius form groups corresponding to different values of Nsh . On the basis of the revealed regularity, the charge radius is predicted for isotope 30 S which is absent among the experimental data.

Abstract We correct magic formulas for body centered cubic (bcc) structures. The logical rational for this is further corroborated by calculations of the radial distribution function (RDF) for several crystal structures. We add results for truncated cubes which may be found in nature.

Abstract Size and surface properties such as catalysis, optical quantum dot photoluminescense, and surface plasmon resonances depend on the coordination and chemistry of metal and semiconducting nanoclusters. Such coordination-dependent properties are quantified herein via “magic formulas” for the number of shells, n, in the cluster. We investigate face-centered cubic, body-centered cubic, simple cubic clusters, hexagonal close-packed clusters, and the diamond cubic structure as a function of the number of cluster shells, n. In addition, we examine the Platonic solids in the form of multi-shell clusters, for a total of 19 cluster types. The number of bonds and atoms and coordination numbers exhibit magic number characteristics versus n, as the size of the clusters increases. Starting with only the spatial coordinates, we create an adjacency and distance matrix that facilitates the calculation of topological indices, including the Wiener, hyper-Wiener, reverse Wiener, and Szeged indices. Some known topological formulas for some Platonic solids when n=1 are computationally verified. These indices have magic formulas for many of the clusters. The simple cubic structure is the least complex of our clusters as measured by the topological complexity derived from the information content of the vertex-degree distribution. The dispersion, or relative percentage of surface atoms, is measured quantitatively with respect to size and shape dependence for some types of clusters with catalytic applications.

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 NA(p,2p)CA−1 quasi-free scattering reactions to measure the proton component of the 21+ state of 16,18,20C. The experimental findings support the notion of a moderate reduction of the proton 1p1/2−1p3/2 spin-orbit splitting, at variance to recent claims for a prevalent Z=6 magic number towards the neutron dripline.

Cryptographic algorithms installed on Internet of Things (IoT) devices suffer many attacks. Some of these attacks include the differential linear attack (DL). The DL attack depends on the computation of the probability of differential-linear characteristics, which yields a Differential-Linear Connectivity Table (DLCT). The DLCT is a probability table that provides an attacker many possibilities of guessing the cryptographic keys of any algorithm such as Serpent. In essence, the attacker firstly constructs a DLCT by using building blocks such as Substitution Boxes (S-Boxes) found in many algorithms’ architectures. In depth, this study focuses on securing IoT devices against DL attacks used on Serpent algorithms by using three magic numbers mapped on a newly developed mathematical function called Blocker, which will be added on Serpent’s infrastructure before being installed in IoT devices. The new S-Boxes with 32-bit output were generated to replace the original Serpent’s S-Boxes with 4-bit output. The new S-Boxes were also inserted in Serpent’s architecture. This novel approach of using magic numbers and the Blocker Function worked successfully in this study. The results demonstrated an algorithm for which its S-Box is composed of a 4-bit-output that is more vulnerable to being attacked than an algorithm in which its S-Box comprises 32-bit outputs. The novel approach of using a Blocker, developed by three magic numbers and 32-bits output S-Boxes, successfully blocked the construction of DLCT and DL attacks. This approach managed to secure the Serpent algorithm installed on IoT devices against DL attacks.

The absence of magic numbers in bosonic 4He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.