Magic Numbers Research Articles

Magic Numbers In Computers: Exploring Their Uses And Importance

The phrase, “Not everything that can be counted counts, and not everything that counts can be counted” by Albert Einstein and the recommendation, “We should have a humble reverence for everything that we shall never measure” by Vaclav Havel reveals the fact that numbers never tell the whole story, in information or in any other context and also it never prevents from seeking for numbers, magic or otherwise, which capture the structures and patterns of the information world. Numbers have their own significance and it can be observed that they play a vital role in different aspects of the world viz. numerology, thus it takes the title of “magic”. The concept of magic numbers has its roots in various branches of science, including physics, chemistry, and mathematics. The notion of magic numbers showcases the interdisciplinary nature of the concept, connecting various scientific disciplines through a common thread of special, often symmetric or highly stable numerical values. This research paper investigates the concept of magic numbers in computing, specifically focusing on their applications across various domains within the field. In computing, magic numbers refer to specific numerical values embedded in data structures that play a crucial role in file formats, network protocols, and various software applications. The paper defines magic numbers, examines the historical evolution of magic numbers in computing, investigates their theoretical underpinnings, and explores how they are practically applied in tasks such as file identification, network protocol and software development.

Tetrahedral Clusters Stabilized by Alloying.

A family of nanoclusters of tetrahedral symmetry is proposed. These clusters consist of symmetrically truncated tetrahedra with additional hexagonal islands on the four facets of the starting tetrahedron. The islands are placed in stacking fault positions. The geometric magic numbers of these clusters are derived. Global optimization searches within an atomistic potential model of Pt-Pd show that the tetrahedral structures can be stabilized for intermediate compositions of these nanoalloys, even when they are not the most stable structures of the elemental clusters. These results are also confirmed by density functional theory calculations for the magic sizes 59, 100, and 180. A thermodynamic analysis by the harmonic superposition approximation shows that Pt-Pd tetrahedral nanoalloys can be stable even above room temperature.

Recent progress in configuration–interaction shell model

Since Mayer and Jensen employed the single-particle shell model to interpret the magic numbers, various microscopic nuclear models have been developed to study the nuclear force and structure. The configuration–interaction shell model (CISM), performed in truncated model space with the inclusion of the residual interaction, is one widely-used nuclear structure model. In the last decade, CISM has progressed in investigating the cross-shell excitation in exotic light nuclei, the similarity and difference in mirror nuclei, and the isomerism and seniority conservation in medium and heavy nuclei. Additionally, researchers have attempted to construct effective Hamiltonians for nuclei near [Formula: see text]Sn and [Formula: see text]Pb through a unified way in the CISM framework. In parallel, related models, including the nucleon-pair approximation (NPA) approach, the Monte Carlo shell model (MCSM), the projected shell model (PSM), the Gamow shell model (GSM), etc., have also been extensively developed and validated in the last decade. This paper reviews the recent progress in CISM and some related models.

An investigation into emergency medicine resident cricothyrotomy competency: Is three the magic number?

Cricothyrotomy is a high-stakes emergency procedure. Because the procedure is rare, simulation is often used to train residents. The Accreditation Council for Graduate Medical Education (ACGME) requires performance of three cricothyrotomies during residency, but the optimal number of training repetitions is unknown. Additional repetitions beyond three could increase proficiency, though it is unknown whether there is a threshold beyond which there is no benefit to additional repetition. The objective of this study was to establish a minimum number of simulated cricothyrotomy attempts beyond which additional attempts did not increase proficiency. This was a prospective, observational study conducted over 3 years at the simulation center of an academic emergency medicine residency program. Participants were residents participating in a cricothyrotomy training as part of a longitudinal airway curriculum course. The primary outcome was time to successful completion of the procedure as first-year residents. Secondary outcomes included time to completion as second- and third-year residents. Procedure times were plotted as a function of attempt number. Data were analyzed using descriptive statistics, repeated-measures analysis of variance, and correlation analysis. Preprocedure surveys collected further data regarding procedure experience, confidence, and comfort. Sixty-nine first-year residents participated in the study. Steady improvement in time to completion was seen through the first six attempts (from a mean of 75 to 41 sec), after which no further significant improvement was found. Second- and third-year residents initially demonstrated slower performance than first-year residents but rapidly improved to surpass their first-year performance. Resident mean times at five attempts were faster with each year of residency (first-year 48 sec, second-year 30 sec, third-year 24 sec). There was no statistically significant correlation between confidence and time to complete the procedure. Additional repetition beyond the ACGME-endorsed three cricothyrotomy attempts may help increase proficiency. Periodic retraining may be important to maintain skills.

Applications of different machine learning methods on nuclear charge radius estimations

Theoretical models come into play when the radius of nuclear charge, one of the most fundamental properties of atomic nuclei, cannot be measured using different experimental techniques. As an alternative to these models, machine learning (ML) can be considered as a different approach. In this study, ML techniques were performed using the experimental charge radius of 933 atomic nuclei (A ≥ 40 and Z ≥ 20) available in the literature. In the calculations in which eight different approaches were discussed, the obtained outcomes were compared with the experimental data, and the success of each ML approach in estimating the charge radius was revealed. As a result of the study, it was seen that the Cubist model approach was more successful than the others. It has also been observed that ML methods do not miss the different behavior in the magic numbers region.

Density-functional study of electronic structure of quantum dots in high magnetic fields

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.

Probing the effect of magnesium doping on the structural and electronic properties of boron clusters

In this paper, a global search for the lowest energy structure of Mg2Bn0/- (n = 1–12) clusters is performed based on Density functional theory combined with the particle swarm optimization algorithm program CALYPSO. The geometry, stability, charge transfer, and bonding properties of the clusters were analyzed at the B3LYP/def2-tzvp level. Then Mg2B8 with high symmetry D4h was found to be the magic numbers cluster among them. The doped clusters Mg2Bn0/− were compared with the pure boron clusters Bn+20/− (n = 1–12) at the same level. The following results are obtained: as the number of boron atoms increases, the boron clusters doped with Mg atoms change from a two-dimensional planar or quasi-plane structure to a three-dimensional structure. The doped magnesium atoms are always positively charged in the convex capped position. And the doping of Mg atoms drives the overall stabilization of the boron clusters and makes the clusters more compact. There is a large amount of charge transfer between the Mg atom and the B atom, and the main orbitals involved are the S and p orbitals. There are strong interactions between the two atoms of boron and magnesium. Through the analysis of the bonding properties, it was found that the s-p hybridization mode between MgB is the main reason for the enhanced cluster stability.

Neutron rearrangement of the magic number 90Zr-core determined by the matter density difference between 90Zr and 92Zr

Matter density distributions and root-mean-square matter radii for 90Zr and 92Zr were determined through fitting the small-angle differential cross sections of proton elastic scattering at 0.8 GeV with the Glauber model. With the obtained neutron densities, a neutron rearrangement beyond the expectation for the magic number 90Zr-core was found from 90Zr to 92Zr by adding two valence neutrons. By considering the surface-peaked term, the rearrangement was reproduced by the shell model calculations with the realistic Woods-Saxon potentials. It indicates that the surface-peaked term related to surface nucleon interactions plays an important role in describing the nucleon rearrangement, since the surface-peaked term would improve the description of the radial wave functions.

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm.

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

The magic number: three women on the board

Purpose This study aims to unpack the progress of board gender diversity among the 3,000 largest US listed firms by market capitalization (i.e. Russell 3000 Index). This study extrapolates four classifications of firms based on the number of women in the boardroom: zero women, one or two women, three plus women and gender balanced. The purpose of this study is to examine where progress has and has not been made, why firms plateau and an agenda for the future. Design/methodology/approach This study first provides a summative overview of the literature on the benefits of board gender diversity. It then examines progress according to the four classifications, each of which have theoretical underpinnings for whether or not firms can reap the strategic benefits of gender-diverse boardrooms. Findings Several indices of US publicly traded companies now have women holding between 30% and 33% of the seats in the boardroom. By examining the spread of women on boards according to the four classifications, this study extrapolates three key insights: firms experiencing tokenism (i.e. one or two women in the boardroom) do not have enough women to reap the strategic benefits of diverse boardrooms; firms that have reached a critical mass (three women in the boardroom) are at an impasse and may risk plateauing; and gender-balanced firms are elevated to the status of being role models for other firms. Calls for action and associated action plans accompany these insights. Practical implications This study reminds managers and directors of the strategic benefits of gender-diverse boards and offers three critical insights that boards can use to classify what stage they are at on the path toward board gender equality. Based on their classification, calls for action and action plans offer guidance to firms. Originality/value This study shifts away from focusing on the average percentage of board seats held by women across all firms and offers new insights on the progress that firms have made according to the number of women in their boardroom.

A study on light charged particle accompanied ternary fission of 253Cf

We investigated 253Cf ternary fission followed by a light-charged particle (LCP) accompanied ternary fission. The many LCPs, include 4He, 6Li, 9Be 10B, 12C, 14N, 16O, 19F 20Ne, 23Na 24Mg, 26Al, 28Si, 30P 32S, 35Cl, 40Ar, 39K and 40Ca. Using Coulomb potential and proximity potential, the overall potential has been investigated. In estimating potential, deformations and angle of orientation were taken into account. Using cold valley plots, the driving potential at its lowest level is determined. Using WKB integral, the penetration probability is evaluated. When the fission fragment combinations include equal or close to the magic number of protons or neutrons, the minimal driving potential, maximum penetration probability, and maximum logT1/2 are observed. Therefore, 138Ba+4He+111Ru are the most likely fission fragment combination when 253Cf undergoes LCP followed ternary fission. Therefore, 4He particle-emission coupled with two likely fission fragments are the most likely fission fragments if the nuclei 253Cf undergo LCP-accompanied ternary fission. The significance of this finding may thus be seen in the ternary fission half-lives.

Association between glycated hemoglobin and functional outcomes in patients with intracranial large artery atherosclerotic disease-related acute ischemic stroke: identifying the magic number.

This study aimed to investigate the effect of the glycated hemoglobin A1c (HbA1c) level on the functional outcome (FOC) in patients with intracranial large artery atherosclerotic disease (ICLAD)-related acute ischemic stroke (AIS). This retrospective study enrolled patients with ICLAD-related AIS who were admitted to King Fahd University Hospital between January 2017 and September 2021. Patients were divided into two groups based on the optimal cutoff HbA1c level determined using receiver operating characteristic curve analysis-those with HbA1c ≤6.9% and those with HbA1c >6.9%. Demographic and other clinical characteristics were compared between the two groups using chi-square tests. The association between HbA1c and 90-day FOC was assessed using the chi-square test and odds ratios (ORs). Multivariate analysis was performed to adjust for confounding factors. A total of 140 patients were included in the analysis. A significant association was observed between the HbA1c level and FOC. Compared to patients with HbA1c ≤6.9%, patients with HbA1c >6.9% were more likely to have an unfavorable FOC [p = <0.001, OR = 2.05, 95% confidence interval (CI) = 1.33-3.14]. The association between HbA1c >6.9% and unfavorable FOC was sustained even after adjusting for confounding factors (p = 0.008) and atherosclerosis risk factors (p = 0.01). HbA1c >6.9% was also associated with higher ORs for in-hospital complications (p = 0.06, OR = 1.34, 95% CI = 1.02-1.77) and mortality (p = 0.07, OR = 1.42, 95% CI = 1.06-1.92) although these associations did not attain significant p-values. HbA1c >6.9% was significantly associated with unfavorable FOC in ICLAD-related AIS. However, further studies with larger sample sizes are required to verify whether HbA1c is an independent predictor of poor FOC. Nevertheless, targeting HbA1c <7% should be the goal of physicians when managing patients at high risk of ICLAD.

Double-magicity of proton drip-line nucleus 22Si with ab initio calculation

New magic numbers have been discovered in the neutron-rich region of the nuclear chart. However, there has been a lack of research on proton-rich nuclei. 22O, the mirror nucleus of 22Si, is a double-magic nucleus bearing a high E(21+). Whether 22Si exhibits double-magic characters is an intriguing topic. To investigate this matter, we utilized ab initio valence space in-medium similarity renormalization group for 22Si/22O, and their nearby nuclei. Our ab initio calculations provide good descriptions for the double magicity of 22O, as well as the shell evolution of N=14 and Z=14 through E(21+). The computed E(21+) indicate that the closure of Z=14 sub-shell in proton-rich nuclei is weaker than the N=14 sub-shell closure in their mirror nuclei. Particularly, the calculated E(21+) of 22Si is 800 keV lower than the one of 22O. To further explore the magicity of 22Si, the mirror energy difference (MED) of 26Si/26Mg, 24Si/24Ne, as well as 22Si/22O are calculated. The results demonstrate that the calculated MEDs agree well with available experimental data, and the E(21+) values of 22,24,26Si are all lower than their respective mirror nuclei due to the Thomas-Ehrman shift with large s1/2 occupation. Moreover, our calculation provides that the many-body configurations of the low-lying state of 22Si/22O are nearly identical despite the fact that the states bearing large MED. In conclusion, our ab initio results suggest that 22Si is a double magic nucleus, similar to its mirror nucleus 22O, albeit with a lower E(21+).

Dependence of the fission half-lives of heavy nuclei on the highest proton magic number within a macro-microscopic approach

Dependence of the fission half-lives of heavy nuclei on the highest proton magic number within a macro-microscopic approach

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

α decay half-lives of nuclei W, Re, Os, Ir and Pt in the range 157≤A≤193 using the modified generalised liquid drop model (MGLDM)

The α-decay half-lives for the isotopes of nuclei W, Re, Os, Ir and Pt in the range have been studied by using the Modified Generalised Liquid Drop Model (MGLDM). The half-lives predicted for some even–even nuclei by using the deformed Two Potential Approach (TPA) [Comm. Theo. Phys. 74, 055301 (2022)] are considered and included for the comparison. Additionally, we have analysed the α-decay half-lives using eight ℓ-dependent empirical formulae, and compared the results with the experimental data. The standard deviation and the average deviation for by using MGLDM is obtained as 0.6025 and 0.5403, respectively. Also, the results of MGLDM match well with predictions of TPA, with standard deviation of 0.47 and 0.44 respectively. A dip in the half-life curve or a peak in the decay energy curve at 82, a magic neutron number of the daughter nuclei of increases the viability of the calculations. Also, the linear nature of Geiger-Nuttall law, Universal law, the relation connecting and and the New Geiger-Nuttall law helps to calculate the half-lives of newly synthesized and unknown isotopes, making MGLDM more reliable.

Surprising Charge-Radius Kink in the Sc Isotopes at N=20.

Charge radii of neutron deficient ^{40}Sc and ^{41}Sc nuclei were determined using collinear laser spectroscopy. With the new data, the chain of Sc charge radii extends below the neutron magic number N=20 and shows a pronounced kink, generally taken as a signature of a shell closure, but one notably absent in the neighboring Ca, K, and Ar isotopic chains. Theoretical models that explain the trend at N=20 for the Ca isotopes cannot reproduce this puzzling behavior.

Three is the magic number: Distance measurement of NGC 3147 using SN 2021hpr and its siblings

Context. The nearby spiral galaxy NGC 3147 hosted three Type Ia supernovae (SNe Ia) in the past decades that have been the subjects of intense follow-up observations. Simultaneous analysis of their data provides a unique opportunity for testing different methods of light curve fitting and distance estimation. Aims. The detailed optical follow-up of SN 2021hpr allows us to revise the previous distance estimations to NGC 3147 and compare the widely used light curve fitting algorithms to each other. After the combination of the available and newly published data of SN 2021hpr, its physical properties can also be estimated with higher accuracy. Methods. We present and analyse new BV griz and Swift photometry of SN 2021hpr to constrain its general physical properties. Together with its siblings, SNe 1997bq and 2008fv, we cross-compared the individual distance estimates of these three SNe given by the Spectral Adaptive Lightcurve Template (SALT) code, and we also checked their consistency with the results from the Multi-Color Light Curve Shape (MLCS) code. The early spectral series of SN 2021hpr was also fit with the radiative spectral code TARDIS to verify the explosion properties and constrain the chemical distribution of the outer ejecta. Results. After combining the distance estimates for the three SNe, the mean distance to their host galaxy, NGC 3127, is 42.5 ± 1.0 Mpc, which matches with the distance inferred by the most up-to-date light curve fitters, SALT3 and BayeSN. We confirm that SN 2021hpr is a Branch-normal Type Ia SN that ejected ~1.12 ± 0.28 M⊙ from its progenitor white dwarf and synthesized ~0.44 ± 0.14 M⊙ of radioactive 56Ni.

A systematic study of α-decay half-lives for Ac, Th, Pa, U and Np isotopes with A = 205–245 using the modified generalized liquid drop model

The Modified Generalized Liquid Drop Model (MGLDM) has been used for calculating the ground-to-ground states of [Formula: see text]-decay half-lives for various Ac, Th, Pa, U and Np isotopes in the mass number range of [Formula: see text]. To account for the nuclear proximity energy, the potential of Blocki et al. 74 [J. Blocki, J. Randrup, W. J. Swiatecki and C. F. Tsang, Ann. Phys. NY 105 (1977) 427] is used. The experimental [Formula: see text] values are used to evaluate the [Formula: see text]-decay half-lives. It can be observed that the logarithm of [Formula: see text]-decay half-life increases with increasing neutron number ([Formula: see text]), with evident minimum at the magic number 126, where the neutron shell is closed. The calculated results are compared with available experimental data and with the predictions of different empirical formulae such as, ARF, MARF, Royer, AKRE, Akrawy, NRB, VS, MVS, YQZR and MYQZR. It is found that the MGLDM is able to predict the experimental half-lives with a standard deviation of 0.6892 (the lowest one among all the other applied empirical formulae), and is therefore suitable for predicting the [Formula: see text]-decay half-lives for unknown and new heavy nuclei.

Shell evolution and emerging paradigm changes

The shell structure conceived by Mayer and Jensen in 1949 has been shown to be quite appropriate for stable and near-stable nuclei, but substantial deviations from it have also been observed more recently for exotic nuclei with notable neutron excess. Such changes of the basic picture of the nuclear shell structure, called the shell evolution, seem to be the subject studied most extensively and most elaborately by RI beam experiments worldwide. An overview of the shell evolution is presented in this talk, from both theoretical and experimental perspectives. The shell structure is shown to be varied, for instance, from the one presented by Mayer and Jensen, by particular types of the monopole components of the effective nucleon-nucleon interaction in nuclei. Among various contributions, the importance of the tensor force is illuminated here, with an outstanding example: the emergence of new neutron magic number 34 in neutron-rich Ca isotopes. The mechanism of the shell evolution produces significant impacts also on the nuclear shapes. Type II shell evolution shifts the excitation energies of intruder deformed bands, for instance, in some Ni isotopes. In other more general cases, the monopole interaction is shown to produce unexpected crucial effects on the patters of rotational bands of heavy deformed nuclei. In fact, the shape of the ellipsoidal deformation is investigated by large-scale shell model calculations, which is nothing but the Monte Carlo Shell Model. The unique role of the monopole component of the tensor force is clarified: the interplay between this monopole interaction and the quadrupole interaction provides us with various patterns of triaxial shapes for many nuclei, such as 166Er, one of the traditional prolate deformed heavy nuclei. Thus, the prolate preponderance hypothesis by Aage Bohr is investigated for its microscopic validity. Some of the nuclear paradigms are changing now in this way, due to emerging aspects of nuclear-force effects.