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We report the first experimental study of the attachment of multiple foreign atoms to a cationic polycyclic aromatic hydrocarbon (PAH). The chosen PAH was coronene, C24H12, which was added to liquid helium nanodroplets and then subjected to electron bombardment. Using mass spectrometry, coronene cations decorated with helium atoms were clearly seen and the spectrum shows peaks with anomalously high intensities ("magic number" peaks), which represent ion-helium complexes with added stability. The data suggest the formation of a rigid helium layer consisting of 38 helium atoms that completely cover both faces of the coronene ion. Additional magic numbers can be seen for the further addition of 3 and 6 helium atoms, which are thought to attach to the edge of the coronene. The observation of magic numbers for the addition of 38 and 44 helium atoms is in good agreement with a recent path integral Monte Carlo prediction for helium atoms on neutral coronene. An understanding of how atoms and molecules attach to PAH ions is important for a number of reasons including the potential role such complexes might play in the chemistry of the interstellar medium. [ABSTRACT FROM AUTHOR]

First principles studies on the geometric structure, stability, and electronic structure of WSin clusters, n = 6-16, have been carried out to show that the observed differing "magic sizes" for WSin clusters are associated with the nature of the growth processes. The WSi12 cluster, observed as a magic species in experiments reacting transition metal ions with silane, is not stable due to a filled shell of 18 electrons, as previously proposed, but due to its atomic structure that arrests further growth because of an endohedral transition metal site. In fact, it is found that all of these clusters, n = 6-16, have filled 5d shells except for WSi12, which has a 5d8 configuration that is caused by crystal field splitting. The stability of WSi15+, observed as highly stable in clusters generated by vaporizing silicon and metal carbonyls, is shown to be associated with a combination of geometric and electronic features. The findings are compared with previous results on CrSin clusters. [ABSTRACT FROM AUTHOR]

Small cationic and anionic clusters of lithium formate were generated by electrospray ionization and their fragmentations were studied by tandem mass spectrometry (collision-induced dissociation with N2). Singly as well as multiply charged clusters were formed in both positive and negative ion modes with the general formulae, (HCOOLi)nLi+, (HCOOLi)nLimm+, (HCOOLi)nHCOO-, and (HCOOLi)n(HCOO)mm-. Several magic number cluster (MNC) ions were observed in both the positive and negative ion modes although more predominant in the positive ion mode with (HCOOLi)3Li+ being the most abundant and stable cluster ion. Fragmentations of singly charged positive clusters proceed first by the loss of a dimer unit ((HCOOLi)2) followed by the loss of monomer units (HCOOLi) although the former remains the dominant dissociation process. In the case of positive cluster ions, all fragmentations lead to the magic cluster (HCOOLi)3Li+ as the most abundant fragment ion at higher collision energies which then fragments further to dimer and monomer ions at lower abundances. In the negative ion mode, however, singly charged clusters dissociated via sequential loss of monomer units. Multiply charged clusters in both positive and negative ion modes dissociated mainly via Coulomb repulsion. Quantum chemical calculations performed for smaller cluster ions showed that the trimer ion has a closed ring structure similar to the phenalenylium structure with three closed rings connected to the central lithium ion. Further additions of monomer units result in similar symmetric structures for hexamer and nonamer cluster ions. Thermochemical calculations show that trimer cluster ion is relatively more stable than neighboring cluster ions, supporting the experimental observation of a magic number cluster with enhanced stability. [ABSTRACT FROM AUTHOR]

The issue of magicity of 1442Si28 has been a contentious one. Fridmann et al., through studies of two-proton knockout reaction 1644S28 → 1442Si28, presented strong evidence in support of magicity and sphericity of 1442Si28. However in complete conflict with this, Bastin et al., gave equally strong empirical evidence, to show that the N = 28 magicity had completely collapsed in 1442Si28 to make it well deformed. The consensus at present though is in favour of the validity of the latter experiment. However, our QCD based theoretical model supports the result of Fridmann experiment. They had explored the amazing persistence of the unique exotic nucleus 1442Si28 as a stable structure within the nucleus 2048Ca28; even after stripping off six-protons through the isotonic chain: 2048Ca28 → 1846Ar28 → 1644S28 → 1442Si28. Thus it is the novel and unexpected stability of proton shell closure at Z=14 in 1442Si28, which is playing such a dominant role in ensuring its magicity, while the neutron magic number N = 28, goes into hiding or actually disappears. Recently, SAA has shown that the fusion experiment of a beam of halo nucleus 6He with the target nucleus 238U, actually provided strong evidence that the "core" of the halo nucleus has the structure of a tennis-ball (bubble) like nucleus, with a "hole" at the centre of its density distribution. This provides us with clear-cut support for our Quantum Chromodynamics based model of clusters of tritons in neutron-rich nuclei. Here we show that our QCD based model, provides support to Fridmann et al., showing that, 1442Si28 has a spherically magic structure of 14 1³H2 (14-tritons) with a tennis-ball (bubble) like structure with "hidden" N=28 neutrons. [ABSTRACT FROM AUTHOR]

The alpha decay chain properties of Z = 122 isotope in the mass range 298? A 350, even-even nuclei, are studied using a fission-like model with an effective combination of the cubic plus proximity potential in the pre and post-scission regions, wherein the decay rates are calculated using improved transfer matrix method, and the results are in good agreement with other phenomenological formulae such as Universal decay law, Viola-Seaborg, Royer, etc. The nuclear ground-state masses are taken from WS4 mass model. The next minimum in the half-life curves of the decay chain obtained at N=186,178 & 164 suggest the shell closure at N=184, 176 & 162 which coincides well with the predictions of two-centre shell model approach. This study also unveils that the isotopes 298-300, 302, 304-306, 308-310, 312,314122 show 7α, 5α, 4α, 3α, 2α and 1α decay chain, respectively. All the other isotopes from A = 316 to 350 may undergo spontaneous fission since the obtained SF half -lives are comparatively less. The predictions in the present study may have an impact in the experimental synthesis and detection of the new isotopes in near future. [ABSTRACT FROM AUTHOR]

The role of the shell model in pairing interaction in nuclei is investigated by calculating the pairing energies of O-O (odd-odd), O-E (odd-even), E-E (even-even) and E-O (even-odd) isotopes of four elements namely; 15P, 25Mn, 40Zr and 60Nd. The pairing energies were computed using the values of binding energy (B) obtained from AME2016 atomic mass evaluation. The graphs of the pairing energies against the mass numbers revealed an increase of the pairing energies with the occurrence of periodic humps adjacent to the neutron magic numbers. The rise in the pairing energies is attributed to the bound states of heavy nuclei arising from the neutron-neutron pairs in the shell structures beyond the Fermi-surface, while in the light and intermediate nuclei, the rise in the pairing energies is due to the increase in the number of nucleons occupying the surface region. These neutron-neutron pairs formed beyond the Fermi-surface of nuclei of heavy elements have greater pairing energies, which contribute to greater binding energies associated with the heavy elements found in the neutron stars. It is concluded that the shell model can predict the existence of isotopes of heavy elements in the neutron stars and the criterion to ascertain their existence lies on the pairing energies. Calculations show that the isotopes with highest peaks among the heavy elements can predict the most abundant isotopes of the heavy elements in the neutron stars, for instance, 90Zr, 91Zr, 142Nd, 145Nd, 146Nd, 148Nd and 150Nd nuclei. [ABSTRACT FROM AUTHOR]

The tensor force is implemented into the time-dependent Hartree–Fock (TDHF) theory so that both exotic and stable collision partners, as well as their dynamics in heavy-ion fusion, can be described microscopically. The role of tensor force on fusion dynamics is systematically investigated for Ca 40 + Ca 40 , Ca 40 + Ca 48 , Ca 48 + Ca 48 , Ca 48 + Ni 56 , and Ni 56 + Ni 56 reactions which vary by the total number of spin-unsaturated magic numbers in target and projectile. A notable effect on fusion barriers and cross sections is observed by the inclusion of tensor force. The origin of this effect is analyzed. The influence of isoscalar and isovector tensor terms is investigated with the T IJ forces. These effects of tensor force in fusion dynamics are essentially attributed to the shift of low-lying vibration states of colliding partners and nucleon transfer in the asymmetric reactions. Our calculations of above-barrier fusion cross sections also show that tensor force does not significantly affect the dynamical dissipation at near-barrier energies. [ABSTRACT FROM AUTHOR]

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for single-nucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic mean-field model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach. [ABSTRACT FROM AUTHOR]

Shell closures and their associated magic numbers of nucleons provide a unique means for studying the structure of exotic nuclei far from stability. An experiment was recently performed at the National Superconducting Cyclotron Laboratory to measure resonant elastic proton scattering on 46 Ar in inverse kinematics in the region containing isobaric analogue states of 47 Ar, an N = 29 nucleus with one neutron above the N = 28 shell closure. Four candidate resonances were observed: one corresponding to the 3 / 2 − ground state of 47 Ar, another corresponding to its 1 / 2 − first excited state, and two that likely correspond to states in the 47 K compound nucleus. The observed properties of the ground state resonance were compatible with values from the literature, but a significantly lower spectroscopic factor was found for the 1 / 2 − state resonance. [ABSTRACT FROM AUTHOR]

The low-energy structures of Al8Sim(m= 1–6) have been determined by using the genetic algorithm combined with density functional theory and the Second-order Moller-Plesset perturbation theory (MP2) models. The results show that the close-packed structures are preferable in energy for Al–Si clusters and in most cases there exist a few isomers with close energies. The valence molecular orbitals, the orbital level structures and the electron localisation function (ELF) consistently demonstrate that the electronic structures of Al–Si clusters can be described by the jellium model. Al8Si4corresponds to a magic number structure with pronounced stability and large energy gap; the 40 valence electrons form closed 1S21P61D102S21F142P6shells. The ELF attractors also suggest weak covalent Si–Si, Si–Al and Al–Al bonding, and doping Si in aluminium clusters promotes the covalent interaction between Al atoms. [ABSTRACT FROM AUTHOR]

In-flight separators have played a significant role in the physics of exotic nuclei. In the last decade, in particular, this field has expanded rapidly with the advent of the new-generation (3rd-generation) in-flight-separator facility, the RI-beam Factory (RIBF) at RIKEN that was commissioned in 2007. In addition, new experimental methods, techniques and state-of-the-art detectors at in-flight separators have developed rapidly, which has contributed considerably to this progress. One can now reach very far from the stable nuclei towards the drip lines, and even beyond in some cases. Hundreds of new isotopes have been identified, and new exotic isomers have been observed. β decays and relevant γ decays, including isomeric states, have clarified many new aspects of nuclear structures. A variety of direct reactions, making the best use of in-flight rare isotope (RI) beams at intermediate/high energies, have been applied for a wide range of rare isotopes. New experimental results using these methods have shown that one needs a new framework to understand structures and dynamics of exotic nuclei, such as new or lost magic numbers, novel neutron halo/skin structures and relevant reactions/excitations. A wide range of reactions associated with nucleo-synthesis in the Universe and the equation of state (EoS) of neutron-rich nuclear matter have also been studied through experiments using rare isotopes available at in-flight separators. This review article focuses its attention on how recent experimental techniques have been developed and applied to exotic nuclei at in-flight separators. We also make remarks on prospects for the near future: in the era when the 3rd-generation RI-beam facilities based on in-flight separators are being completed world-wide. [ABSTRACT FROM AUTHOR]

Recent mass spectrometry measurements carried out for the coronene (C 24 H 12 ) cation coated with helium atoms have revealed special stabilities associated with ’magic numbers’ at sizes 38, 41, and 44, the latter being interpreted as the signature of a complete first solvation shell. In the present contribution we examine by means of path-integral molecular dynamics simulations employing a polarizable potential the equilibrium structures of such clusters and how they differ from the classical global minima. Our results confirm the special energetic stability of the suggested sizes and the highly symmetric geometric arrangement of the helium atoms around the aromatic cation. However, they also indicate that the helium atoms in the vicinity of the aromatic plane are highly fluxional and not associated with a unique local minimum in the energy landscape. Above the size of 44, the shell expands but remains stable with no immediate evidence for a second shell. [ABSTRACT FROM AUTHOR]

In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken Ca with a single neutron in the Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov-Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for O, Ca, Ca and Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei. [ABSTRACT FROM AUTHOR]

In the last 35 years, a large amount of data on the changes in the mean-square charge radii, δ〈 r 〉, around the lead region has been gathered. Isotopic chains are often normalised and compared to reduce the impact of systematic uncertainties of the extracted δ〈 r 〉 from the isotope shifts. However, this biased picture can obscure other interesting effects that are apparent in absolute scale. In this contribution, we review the extent of the knowledge on the δ〈 r 〉 in the lead region in addition to observations on the absolute scale. [ABSTRACT FROM AUTHOR]

A method is developed to consider the particle-phonon coupling (PC) effects in the calculation of the odd-even double mass differences (DMD) in semi-magic nuclei starting from the free NN potential. The PC correction δΣ to the mass operator Σ is found in g -approximation, g being the vertex of creating the L-phonon. The tadpole term of the operator δΣ is taken into account. The method is based on a direct, without any use of the perturbation theory, solution of the Dyson equation with the mass operator Σ(ε) = Σ + δΣ(ε) for finding the single-particle energies and Z-factors. In its turn, they are used as an input for finding different PC corrections to the DMD values. Results for a chain of even semi-magic nuclei Pb show that the inclusion of the PC corrections makes agreement with the experimental data significantly better. [ABSTRACT FROM AUTHOR]

The ratio of conductances through carbon-ring based molecules are calculated for various positions of source-drain electrode leads on the molecule. These ratios are usually integers the so-called magic numbers. We find that deviations of the magic number ratios are either zero or quadratic in ratios of tight-binding model parameters. [ABSTRACT FROM AUTHOR]

ABSTRACT Cluster-cluster reaction rate constants are obtained from measurements of coalescence in nozzle-beam expansions. Coalescence is described by the Smoluchowski equations, modified to accommodate changes in volume and temperature. The asymptotic form of the cluster size distribution can reveal the scaling of the second-order rate constants Kjk with the sizes of colliding particles. Scalings derived in the past are demonstrably incorrect and physically unjustifiable. Here, we use the physically reasonable scaling, Kjk = K11 jμkμ, to study H2 coalescence in a nozzle beam. Experimental size distributions fit the predicted asymptotic form, Nk = Akae− bk, very well, with deviations identifying magic numbers. We obtain the base agglomeration cross section K11 and the parameter μ, and thus all the rate constants, for H2. By comparing with products of geometric cross section and relative velocity, we find sticking coefficients. Experimental results for a nozzle-beam expansion of He are analyzed similarly, to yield K11 and μ, and hence sticking coefficients, for He. These are compared to those for H2. [ABSTRACT FROM AUTHOR]

The system of Kohn-Sham equations is solved self-consistently for the two-dimensional, spatially separated electrons and holes. We find the series of magic numbers for the total angular momentum of the electrons and holes in a strong magnetic field. The change of the angular momentum of the charge carriers is shown to lead to the persistent current oscillations. [ABSTRACT FROM AUTHOR]

This paper reports on a curiosity concerning magic numbers in neutral molecular clusters, namely on magic numbers related to the photoelectron anisotropy in angle-resolved photoelectron spectra. With a combination of density functional calculations and experiment, we search for magic numbers in Na(H2O)n, Na(NH3)n, Na(CH3OH)n, and Na(CH3OCH3)n clusters. In clusters of high symmetry, the highest occupied molecular orbital can be delocalized over an extended region, forming a symmetric charge distribution of high s character, which results in a pronounced anisotropy in the photoelectron angular distribution. We find magic numbers at n = 6 and 4 for sodium-doped dimethyl ether and ammonia clusters, respectively, but not for sodium-doped water and methanol clusters, which is likely a consequence of the degree of hydrogen bonding and the number of structural isomers. [ABSTRACT FROM AUTHOR]

Jelliumatic shell model (JSM), a variant of jellium model (JM), is proposed in an attempt to rationalize the electron counts of four metal clusters that 'violate' the global jelliumatic model (GJM): (1) for the spherically shaped [CuH(SCNR)], the global jelliumatic electron ( gje) count of 30 is partitioned into three electronic shells of {[H]@[CuH]@[CuH(SCNR)]} with 2, 8, and 20 jelliumatic shell electrons ( jse); each shell conforms to JM for a spherical shape; (2) for the [CuH{SP(OPr)}] cluster, the gje of 22 can be divided into two electronic shells of {[CuH]@[CuHL]} with jse of 10 and 12, respectively; each shell satisfies JM for a prolate ellipsoidal shape; (3) for the [CuH{SP(OPr)}] cluster, with an overall prolate molecular shape, the gje of 40 can be subdivided into three electronic shells of {[CuH]@[CuH]@[CuHL]} with 16, 12, and 12 jse, in harmony with an oblate ellipsoidal shape for the [CuH] core and prolate ellipsoidal shapes for the [CuH] and [CuHL] shells, respectively; and (4) for the spherical-shaped intermetalloid {[Sn]@[Cu]@[Sn]} and {[As]@[Ni]@[As]} clusters, the gje of 108 can be apportioned into three electronic shells (charges as shown) with 8, 8, and 92 jse with each shell being in compliance with JM for a spherical shape. [ABSTRACT FROM AUTHOR]

We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented. [ABSTRACT FROM AUTHOR]

Multiple organic functionalities can now be apportioned into nanoscale domains within a metal-coordinated framework, posing the following question: how do we control the resulting combination of "heterogeneity and order"? Here, we report the creation of a metal-organic framework, MOF-2000, whose two component types are incorporated in a 2:1 ratio, even when the ratio of component types in the starting solution is varied by an order of magnitude. Statistical mechanical modeling suggests that this robust 2:1 ratio has a nonequilibrium origin, resulting from kinetic trapping of component types during framework growth. Our simulations show how other "magic number" ratios of components can be obtained by modulating the topology of a framework and the noncovalent interactions between component types, a finding that may aid the rational design of functional multicomponent materials. [ABSTRACT FROM AUTHOR]

We review the theory behind abundance of experimentally observed nanoclusters produced in beams, aiming to understand their magic number behavior. It is shown how use of statistical physics, with certain assumptions, reduces the calculation of equilibrium abundance to that of partition functions (PFs) of single clusters. Methods to practically calculate these PFs are introduced. The formalism is general and potential independent, but is only applicable to equilibrium or close-to-equilibrium scenarios and the interactions for which the PFs can be accurately calculated. As an illustration, we compute the abundance of Lennard-Jones clusters at low temperatures, which reveals their experimentally observed magic number behavior. This shows that purely energetic and thermodynamic reasons can cause the magic numbers. We then briefly review kinetic approach to the problem and comment on the interplay between chemical, mechanical and thermodynamic stability of the clusters in more generality. [ABSTRACT FROM AUTHOR]

In this paper we construct an approach to extract the Wigner energy [Bw(N,Z) = -W(A)|N-Z|-d(A)δN,Zπnp] by using local mass relations, in the first-order approximation. We obtain W(A) = (42.7 ± 1.2)/A MeV, d(A) = (28.7 ± 1.5)/A MeV. By using the Wigner energies such obtained as well as empirical pairing and symmetry energies, the resultant binding-energy difference between the lowest T = 0 and T = 1 states of odd-odd N = Z nuclei is in good agreement with experimental data. [ABSTRACT FROM AUTHOR]

Recent observation of the 6+ seniority isomers and measurements of the B(E2) values in the 134-138Sn isotopes lying close to the neutron drip line have raised some questions about the validity of the currently used effective interactions in the neutron-rich region. Simpson et al. [Phys. Rev. Lett. 113, 132502 (2014)] had to modify the diagonal and nondiagonal νf7/2² two-body matrix elements of the Vlk interaction by ~150 keV in their shell model calculations in order to explain the data of 136Sn. In contrast, we are able to explain the observed energy levels and the B(E2) values after marginal reduction of the same set of matrix elements by 25 keV in the RCDB (renormalized CD-Bonn) interaction. The observed mismatch in reproducing the data of 136Sn is due to the seniority mixing. Further, we do not find it necessary to consider the core excitations, and the RCDB interaction seems better suited to explain the data beyond N = 82 magic number. [ABSTRACT FROM AUTHOR]

Most studies on the determination of the alpha-decay preformation factor have used decay formulae. The preformation factor is known to contain abundant information on the nuclear structure. The successful determination of the preformation factor through the cluster formation model (CFM) motivates this study to determine the factor for nuclei near the magic numbers and present results in an analytic study based on different comparisons and observations. The difference between preformation factors obtained from CFM and from the decay formula method is significant. The formula method is used for the entire process of alpha decay as a transition between two states, whereas CFM is applied for the initial state of alpha formation. The preformation factor obtained using CFM and clusterization state representation was first compared with that obtained from the decay formula. Results were used to investigate alpha formation in even-even heavy nuclei, including 72 < Z < 92 and 92 < N < 142, near the magic numbers Z = 82 and N = 126. The values of the preformation factor were discussed and explained in detail according to the clusterization state representation to describe the most possible states of ground-state nuclei. The alpha clustering described through CFM is found to be consistent with that described using the decay formula for the open-shell nuclei of N < 126. The presence of more nucleons in the open-shell nuclei results in lower probability for alpha clustering and lower value of the preformation factor. However, few nucleons beyond the closed shell can cause higher probability for alpha clustering and larger value of the preformation factor. The maximum and minimum of the alpha-cluster formation occur in the nucleus of the double-shell closure (with N = 126 and Z = 82 and in the nucleus of two protons and two neutrons more. This formation probability is sensitive to the subshells, leading to the possibility of more clusterization states, including core-cluster, core-cluster1-cluster2, and core-alpha-alpha structures. The cluster states deduced from the formation probability can be used in future studies to extend the Ikeda diagram to the heavy nuclei. [ABSTRACT FROM AUTHOR]

Relative stability of geometric magic-numbergold nanoclusters with high point-group symmetry (Ih, D5h, Oh) and sizeup to 3.5 nm, as well as structures obtained by global optimizationusing an empirical potential, is investigated using density functionaltheory (DFT) calculations. Among high-symmetry nanoclusters, our calculationssuggest that from Au(147) to Au(923), the stability follows the order Ih> D5h> Oh. However, at the largest size of Au(923), the computedcohesive energy differences among high-symmetry Ih, D5hand Ohisomersare less than 4 meV/atom (at PBE level of theory), suggesting thelarger high-symmetry clusters are similar in stability. This conclusionsupports a recent experimental demonstration of controlling morphologiesof high-symmetry Au(923) clusters (Plant, S. R.; Cao, L.; Palmer, R. E.J. Am. Chem. Soc.2014, 136, 7559). Moreover,at and beyond the size of Au(549), the face-centered cubic-(FCC)-basedstructure appears to be slightly more stable than the Ihstructure with comparable size, consistentwith experimental observations. Also, for the Au clusters with thesize below or near Au(561), reconstructed icosahedral and decahedralclusters with lower symmetry are slightly more stable than the correspondinghigh-symmetry isomers. Catalytic activities of both high-symmetryand reconstructed Ih-Au(147)and both Ih-Au(309) clustersare examined. CO adsorption on Au(309) exhibits less sensitivity onthe edge and vertex sites compared to Au(147), whereas the CO/O2coadsorption is still energetically favorable on both goldnanoclusters. Computed activation barriers for CO oxidation are typicallyaround 0.2 eV, suggesting that the gold nanoclusters of ∼2nm in size are highly effective catalysts for CO oxidation. [ABSTRACT FROM AUTHOR]

We construct two new Hartree–Fock–Bogoliubov mass models, labeled HFB-28, HFB-29, which in addition to the generalized Skyrme form containing t 4 and t 5 terms, also include now a modified spin–orbit force. This alternative spin–orbit force allows for an unconventional isospin and/or density dependence relative to the traditional form included in Skyrme functionals. The new forces underlying these models are fitted to essentially all mass data and at the same time to a realistic equation of state of neutron matter. The inclusion of the modified spin–orbit terms allows us to reduce the rms deviation with respect to all the 2353 known masses with Z , N ≥ 8 by 20 keV, leading to a final model error of 0.52 MeV. It is shown that the newly optimized spin–orbit forces do not conform with the one deduced from the relativistic mean field theory, and consequently that the relativistic spin–orbit force might not be optimum to reproduce experimental masses. The spin–orbit splittings are shown to be reduced and in better agreement with empirical values when including a density-dependent form of the spin–orbit interaction. However, the new mass models with such modified spin–orbit terms still fail to reproduce the kink seen in the isotopic shift of the K or Pb charge radii around the neutron magic numbers, despite the fact that such generalizations of the spin–orbit terms were also introduced to improve the description of the isotopic shifts. Shell effects, in particular far away from stability, are shown to remain unaffected by the new spin–orbit terms, except at the N = 184 magic number. [ABSTRACT FROM AUTHOR]

This paper inquires into the concavity of the map $$N\mapsto v_s(N)$$ from the integers $$N\ge 2$$ into the minimal average standardized Riesz pair-energies $$v_s(N)$$ of $$N$$ -point configurations on the sphere $$\mathbb {S}^2$$ for various $$s\in \mathbb {R}$$ . The standardized Riesz pair-energy of a pair of points on $$\mathbb {S}^2$$ a chordal distance $$r$$ apart is $$V_s(r)= s^{-1}\left( r^{-s}-1 \right) $$ , $$s \ne 0$$ , which becomes $$V_0(r) = \ln \frac{1}{r}$$ in the limit $$s\rightarrow 0$$ . Averaging it over the $$\left( \begin{array}{c} N\\ 2\end{array}\right) $$ distinct pairs in a configuration and minimizing over all possible $$N$$ -point configurations defines $$v_s(N)$$ . It is known that $$N\mapsto v_s(N)$$ is strictly increasing for each $$s\in \mathbb {R}$$ , and for $$s<2$$ also bounded above, thus 'overall concave.' It is (easily) proved that $$N\mapsto v_{-2}^{}(N)$$ is even locally strictly concave, and that so is the map $$2n\mapsto v_s(2n)$$ for $$s<-2$$ . By analyzing computer-experimental data of putatively minimal average Riesz pair-energies $$v_s^x(N)$$ for $$s\in \{-1,0,1,2,3\}$$ and $$N\in \{2,\ldots ,200\}$$ , it is found that the map $$N\mapsto {v}_{-1}^x(N)$$ is locally strictly concave, while $$N\mapsto {v}_s^x(N)$$ is not always locally strictly concave for $$s\in \{0,1,2,3\}$$ : concavity defects occur whenever $$N\in {\mathcal {C}}^{x}_+(s)$$ (an $$s$$ -specific empirical set of integers). It is found that the empirical map $$s\mapsto {\mathcal {C}}^{x}_+(s),\ s\in \{-2,-1,0,1,2,3\}$$ , is set-theoretically increasing; moreover, the percentage of odd numbers in $${\mathcal {C}}^{x}_+(s),\ s\in \{0,1,2,3\}$$ is found to increase with $$s$$ . The integers in $${\mathcal {C}}^{x}_+(0)$$ are few and far between, forming a curious sequence of numbers, reminiscent of the 'magic numbers' in nuclear physics. It is conjectured that these new 'magic numbers' are associated with optimally symmetric optimal-log-energy $$N$$ -point configurations on $$\mathbb {S}^2$$ . A list of interesting open problems is extracted from the empirical findings, and some rigorous first steps toward their solutions are presented. It is emphasized how concavity can assist in the solution to Smale's $$7$$ th Problem, which asks for an efficient algorithm to find near-optimal $$N$$ -point configurations on $$\mathbb {S}^2$$ and higher-dimensional spheres. [ABSTRACT FROM AUTHOR]

The principal building block of the atomic nucleus is the deuteron which is formed by the addition of a neutron to a proton with both spin vectors parallel and directed along the line of centers, which is also the axis of a linear vortex in a primordial ideal fluid filling all space as postulated by the hydrodynamic theory of particles and fields previously published in this journal. Two deuterons with opposite spin vectors lying on the same axis can combine to form an alpha particle (helium nucleus). Many nuclei consist of compact clusters of alpha particles with parallel axes giving rise to atomic mass numbers divisible by 4, which are called magic numbers because these nuclei are unusually stable and abundant. There is a repulsive magnetic force and a repulsive Magnus force between deuterons with spin vectors parallel and orthogonal to the line of centers, but when the spin vectors are antiparallel there is an attractive magnetic force and an attractive Magnus force between the deuterons. As a result deuterons tend to assemble into flat layers with deuterons located at the vertices of concentric polygons with odd numbers of sides (3, 5, 7, etc.) centered on a single deuteron on an axis of rotational symmetry. A similar layer of deuterons with opposite spin vectors will be located beneath the first layer to give a sequence of nested polygons with alpha particles at the vertices. [ABSTRACT FROM AUTHOR]