Neutron Magic Number Research Articles

New results on nuclear magicity and possible extension of the nuclear landscape

In nuclear theory, there is always a quest for possible extensions of the nuclear landscape and extending our knowledge to the limits of nuclear existence. In this study, we examine the stability and structural properties of a wide range of nuclei in super- and ultra-heavy region in a phenomenological semi-microscopic approach. we calculated the shell correlation energy, residual pairing correction energy, two-nucleon separation energy and two-nucleon energy gap for 3670 even–even nuclei along [Formula: see text]-stability line and two-neutron driplines in the ranges [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text], respectively. To assure reliability and confidence of the new results in the ultra-heavy region, we extended the search space to include heavy and super-heavy nuclei. We report 83 double magic nuclei and address the predominance of proton and neutron magic numbers. Our calculations reproduced known results on nuclear magicity and present strong evidences on islands of stability and magic numbers in super- and ultra-heavy regions. We also address shifts in nuclear magicity along the nuclear landscape close to the [Formula: see text]-stability line and close to the neutron rich regions.

New α-Emitting Isotope ^{214}U and Abnormal Enhancement of α-Particle Clustering in Lightest Uranium Isotopes.

A new α-emitting isotope ^{214}U, produced by the fusion-evaporation reaction ^{182}W(^{36}Ar,4n)^{214}U, was identified by employing the gas-filled recoil separator SHANS and the recoil-α correlation technique. More precise α-decay properties of even-even nuclei ^{216,218}U were also measured in the reactions of ^{40}Ar, ^{40}Ca beams with ^{180,182,184}W targets. By combining the experimental data, improved α-decay reduced widths δ^{2} for the even-even Po-Pu nuclei in the vicinity of the magic neutron number N=126 are deduced. Their systematic trends are discussed in terms of the N_{p}N_{n} scheme in order to study the influence of proton-neutron interaction on α decay in this region of nuclei. It is strikingly found that the reduced widths of ^{214,216}U are significantly enhanced by a factor of two as compared with the N_{p}N_{n} systematics for the 84≤Z≤90 and N<126 even-even nuclei. The abnormal enhancement is interpreted by the strong monopole interaction between the valence protons and neutrons occupying the π1f_{7/2} and ν1f_{5/2} spin-orbit partner orbits, which is supported by the large-scale shell model calculation.

Moving away from singly-magic nuclei with Gorkov Green’s function theory

Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, $NN$+$3N\text{(lnl)}$ and NNLO$_{\text{sat}}$. An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers $N=28,32,34$ emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlation in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.

Systematic study on $$\alpha $$-decay half-lives: a new dependency of effective sharp radius on $$\alpha $$-decay energy

Within the framework of the proximity formalism, we present a systematic study to analyze the effects of the $$\alpha $$ -decay energy through the effective sharp radius parameter on the $$\alpha $$ -decay half-lives of 227 nuclei in the range $$61 \le Z \le 99$$ . Wentzel-Kramers-Brillouin (WKB) calculations with the proximity potential Zhang 2013 are carried out to obtain the theoretical values of the $$\alpha $$ -decay half-lives. In this work, we introduce a new $$Q_{\alpha }$$ -dependent (QD) form of the effective sharp radius which significantly reduces the standard deviation of estimated half-lives using the Zhang 2013 model in comparison with the corresponding experimental data in our selected mass range. We evaluate the validity of this simple formula using the Geiger-Nuttall (G-N) plots and semi-empirical formulas. The modified form of the Zhang 2013 model is also found to work well in $$\alpha $$ -decay studies of superheavy nuclei (SHN) with $$Z=117-120$$ . Our results reveal that the calculated half-lives for the use of new proposed form of the effective sharp radius in the proximity potential can reproduce the closed-shell effects at neutron magic number $$N=126$$ and $$N=184$$ .

Three-dimensional tracking multi-segmented proportional gas counter for [formula omitted]-decay spectroscopy of unstable nuclei

We report on the performance of a recently developed high-efficiency, low-background, three-dimensional tracking multi-segmented proportional gas counter (3DT-MSPGC), intended for β-decay spectroscopy of neutron-rich nuclei in the vicinity of neutron magic number N=126 at the KEK Isotope Separation System (KISS) facility. The 3DT-MSPGC uses two concentric cylindrical layers of proportional gas counters (16 per layer, 32 in total) featuring resistive anode wires (3 kΩ/cm). By independently measuring the charge deposition from both ends of each counter, we constrain β particle trajectories and determine where they intersect with the central axis of the 3DT-MSPGC. New compact charge-sensitive pre-amplifier modules, along with shaping amplifier and fast-timing amplifier modules, were developed to deduce the hit position by precisely measuring the charge deposition and timing. We have studied the performance of the 3DT-MSPGC in on- and off-line experiments. A longitudinal position resolution of ≤3.5 mm (FWHM) was achieved for each counter. The determination of the event trajectories allowed for suppression of background events, resulting in the background-event rate reaching 0.020(3) count-per-second (cps) while still maintaining a high-detection efficiency. This reduction of background is shown to improve the signal-to-noise ratio in determination of the half-life of 196Ir by a factor of 2.3(6), resulting in a significant improvement in achievable precision.

Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of N\u2009=\u200932

Nuclear charge radii are sensitive probes of different aspects of the nucleon–nucleon interaction and the bulk properties of nuclear matter, providing a stringent test and challenge for nuclear theory. Experimental evidence suggested a new magic neutron number at N = 32 (refs. 1–3) in the calcium region, whereas the unexpectedly large increases in the charge radii4,5 open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with β-decay detection, we were able to extend charge radii measurements of potassium isotopes beyond N = 32. Here we provide a charge radius measurement of 52K. It does not show a signature of magic behaviour at N = 32 in potassium. The results are interpreted with two state-of-the-art nuclear theories. The coupled cluster theory reproduces the odd–even variations in charge radii but not the notable increase beyond N = 28. This rise is well captured by Fayans nuclear density functional theory, which, however, overestimates the odd–even staggering effect in charge radii. These findings highlight our limited understanding of the nuclear size of neutron-rich systems, and expose problems that are present in some of the best current models of nuclear theory.

Test of nuclear mass models

The reliability and prediction ability of 8 global nuclear mass models is systematically analyzed in terms of the accuracy of the model and the new neutron magic number predicted by experiments based on the ground-state nuclear mass data from AME2016. The root-mean-square (RMS) deviations of nuclear mass predicted by 8 nuclear mass models are calculated by subregion, and find that the Bhagwat and WS4 models possess better accuracy to describe the existing experimental data. By analyzing the trend of the neutron shell energy gap varying with neutron number, it is found that the KTUY, WS3 and WS4 models can well represent the mutation behavior caused by the new magic number &lt;i&gt;N&lt;/i&gt; = 32, and it is predicted that &lt;i&gt;N&lt;/i&gt; = 32 is likely to be a new magic number in the Cl isotope chain and Ar isotope chain. By analyzing the variation trend of α decay energy in the superheavy region, it is found that the FRDM12, WS3 and WS4 models can reproduce the phenomena of subshell with &lt;i&gt;N&lt;/i&gt; = 152 and &lt;i&gt;N&lt;/i&gt; = 162 well, and predict the relatively long life of nuclei at the neutron number &lt;i&gt;N&lt;/i&gt; = 184 for the isotope chain with proton number &lt;i&gt;Z&lt;/i&gt; = 108—114. The comprehensive analysis shows that the mass model with good accuracy cannot reproduce shell evolution behavior. For example, the Bhagwat model has the same accuracy as the WS4 model, but it cannot reproduce the mutation behavior of the new magic number &lt;i&gt;N&lt;/i&gt; = 32, 152 and 162. But the KTUY model and FRDM12 model can reproduce the new magic number behavior of &lt;i&gt;N&lt;/i&gt; = 32, 152 and 162, respectively, although the RMS deviation is slightly larger. The RMS deviation of WS4 model is small and can describe the shell evolution behavior in the nuclear mass well.

Experimental Challenges of the First Mass Measurement Campaign at the Rare-RI Ring

With the recent commissioning of the Rare-RI Ring (R3), nuclear mass measurement of rare isotopes (RIs) produced at the RI Beam Factory (RIBF) at RIKEN has become possible. The R3 spectrometer is based on the Isochronous Mass Spectrometry technique that allows for reaching a mass measurement precision of 10−6 within less than 1 ms. With the newly established self-triggered individual injection method, R3 specialized in mass measurements of extremely short-lived nuclei with low production yields.In this paper, we report the first mass measurement campaign conducted at the R3 addressing nuclei in the vicinity of N=50 and N=82 neutron magic numbers, with a particular focus on the challenges of this new facility.

Calculation of nuclear charge radii with a trained feed-forward neural network

A feed-forward neural network model is trained to calculate the nuclear charge radii. The model trained with input data set of proton and neutron number $Z,N$, the electric quadrupole transition strength $B(E2)$ from the first excited 2$^+$ state to the ground state, together with the symmetry energy. The model reproduces well not only the isotope dependence of charge radii, but also the kinks of charge radii at the neutron magic numbers $N=82$ for Sn and Sm isotopes, and also $N=126$ for Pb isotopes. The important role of $B(E2)$ value is pointed out to reproduce the kink of the isotope dependence of charge radii in these nuclei. Moreover, with the inclusion of the symmetry energy term in the inputs, the charge radii of Ca isotopes are well reproduced. This result suggests a new correlation between the symmetry energy and charge radii of Ca isotopes. The Skyrme HFB calculation is performed to confirm the existence of this correlation in a microscopic model.

Microscopic description of structural, surface, and decay properties of Z=124, 126 superheavy nuclei

A systematic investigation has been carried out for even-even isotopic series of two superheavy nuclei with Z=124 and Z=126 in the region 160≤N≤220, and 162≤N≤218, respectively, within the framework of covariant density functional theory (CDFT). Based on the potential energy curves calculated using the explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models, many sensitive observables have been analyzed to understand the structural evolution, shape coexistence, and to predict the possible candidates for neutron shell-closure within the isotopic series of Z=124 and Z=126. The shell correction energy and nuclear symmetry energy have been evaluated within the Strutinsky shell correction approach and the Coherent Density Fluctuation Model (CDFM), respectively. All the sensitive observables i.e. two-neutron separation energy, its differential, neutron-pairing energy, single-particle energy levels, and total shell-correction energy reproduce known spherical neutron magic numbers, and present evidence on new deformed neutron magic numbers at N=168, 174 and 178. The symmetry energy shows a direct correlation with the shape of the system. The α-decay chain of four isotopes 124298,302 and 126300,304 have been studied within three different semi-empirical approaches named UNIV2, SemFIS2 and ImSahu, and compared with the available experimental data, FRDM2012 and the WS4 mass model. All the models, DD-ME2, DD-PC1, FRDM2012, and WS4 have predicted around 8α to 10α decay before spontaneous fission (SF) can start.

A unified view of the first-excited 2+ and 3− states of Cd, Sn and Te isotopes

Symmetries are known to play an important role in the low lying level structure of Sn isotopes, mostly in terms of the seniority and generalized seniority schemes. In this paper, we revisit the multi-j generalized seniority approach for the first excited $2^+$ and $3^-$ states in the Cd ($Z=48$), Sn ($Z=50$) and Te ($Z=52$) isotopes, where the Cd and Te isotopes represent two-proton hole and two-proton particle nuclei, thus involving both kind of particles (protons and neutrons) in contrast to Sn isotopes. Interestingly, the approach based on neutron valence space alone is able to explain the B(E2) and B(E3) trends respectively for the $2^+$ and $3^-$ states in all the three Cd, Sn and Te isotopes. The new results on the inverted parabolic behavior of B(E3) values in Cd and Te isotopes are understood in a manner identical to that of Sn isotopes by using the generalized seniority scheme. No shell quenching is supported by these calculations; hence, the neutron magic numbers, $N=50$ and $N=82$, remain robust in these isotopic chains. It is quite surprising that the generalized seniority continues to be reasonably successful away from the semi-magic region, thus providing a unifying view of the $2^+$ and $3^-$ states.

Investigating the Properties of Nuclei with an Extreme Excess of Neutrons in the Vicinity of Neutron Magic Number N = 184

The properties of the ground state of even–even nuclei in a wide range of mass numbers are studied in an approximation of a self-consistent relativistic and nonrelativistic mean field of nuclei. Special attention is given to nuclei beyond the theoretically known neutron drip line, which form a peninsula of nuclei stable with respect to the emission of one or two neutrons in (N, Z) space at N = 184.

Exotic Nuclear Structure of Neutron-rich Zn Isotopes

Nuclear structure of unstable nuclei, in particularly the nuclei near the magic number, has been one of the hot topics of nuclear physics study. Near the neutron magic number N=40, 50, rich nuclear structure phonomania appeared in the nickel region, in particularly for the neutron-rich isotopes, have stimulated intensive investigation from both theoretical and experimental aspects. In order to gain a better understanding of the nuclear structure in the nickel region, we choose to study the properties of neutron-rich Zn(Z=30) isotopes. In this paper, after a simple introduction of the laser spectroscopy experiment of Zn isotopes at CERN-ISOLDE, we reviewed the nuclear spins, magnetic moment, electric quadrupole moment and root mean square charge radius of the ground and long-lived isomeric states of 62–80Zn isotopes. Based on these properties, together with shell-model calculation from different interactions, we discussed systematically the nuclear structure phenomena, such as the shell structure evolution, magicity, deformation and shape coexistence, and the cross-shell excitation of correlated nucleons. At the end, on the basis of the current experimental data and nuclear structure information, as well as the theoretical prediction of energy level evolution of N=51 isotones in nickel region, we propose to measure the basic properties of 81,82Zn nuclei at the collinear resonance ionization spectroscopy setup at ISOLDE-CERN.

Correlation Between the Behavior of $${\alpha}$$-Decay Half-Life Time and $$\boldsymbol{Q}$$ Values with Neutron Number Variation of Daughter Nuclei

$$\alpha$$ decay of 2000 parent heavy and superheavy nuclei, with atomic numbers in the range $$Z=80$$ to $$Z=122$$ , is considered. We calculated the half-life time, $$T_{\alpha}$$ , of each nucleus using the density-dependent cluster model with M3Y-effective nucleon–nucleon interaction. The $$Q_{\alpha}$$ values needed for calculation of $$T_{\alpha}$$ were extracted from four different mass tables used frequently in $$\alpha$$ -decay calculation. These tables are WS4, WS3, FRDM(2012), and DZ tables. The present study shows to what extent the behavior and value of $$T_{\alpha}$$ , as the nucleon number varies, depends on choosing the mass table used to extract $$Q_{\alpha}$$ values. For this purpose, we studied the variation of log $$T_{\alpha}$$ and the corresponding $$1/Q_{\alpha}$$ with the neutron number of the daughter nucleus, $$N_{d}$$ , using the four different mass tables. The results show that the log $$T_{\alpha}$$ variation follows the corresponding $$1/Q_{\alpha}$$ variation. The two mass tables WS3 and WS4 predict almost the same log $$T_{\alpha}$$ variation and agree in the magic and semi-magic numbers. For FRDM(2012) and DZ tables the variation of log $$T_{\alpha}$$ with $$N_{d}$$ follows the same $$1/Q_{\alpha}$$ variation but the magic numbers deduced from these two tables do not agree with each other and almost differ from those predicted from WS3 and WS4. FRDM(2012) tables predict the main deep minimum at $$N_{d}=128$$ instead of the magic neutron number $$N_{d}=126$$ .

Ne İzotoplarının Nükleer Yapı Özelliklerinin Nükleer Kabuk Modeli ile İncelenmesi

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

The transuranic elements and the island of stability.

Since the 1930s the synthesis of nuclides too unstable to exist naturally on Earth has stretched the periodic table to 118 elements. While the lighter transuranic elements have found uses, the isotopes of those past lawrencium, the superheavy elements, are too unstable to exist outside the laboratory. In the 1970s, leading element discoverers Glenn Seaborg at the University of California, Berkeley, USA, and Georgy Flerov, at the Joint Institute for Nuclear Research in Dubna, USSR, took interest in a supposed 'island of stability', leading from the nuclear shell model of Maria Goeppert Mayer and Hans Jensen, and predicted elements with so-called magic numbers of protons and neutrons would be far more stable. This review shall look at the historical developments that led to the field of element discovery, the attempts to discover superheavy elements in nature based on the island of stability, and the subsequent successful synthesis of elements and the implications of their half-lives and properties. This article is part of the theme issue 'Mendeleev and the periodic table'.

Sequences of single-particle energy levels of even–even SHN with Z = 116−132 based on α-decay systematics

The [Formula: see text]-decay half-lives, [Formula: see text], for five heavy and nine superheavy even–even nuclei with [Formula: see text] and [Formula: see text], respectively, have been calculated within the density-dependent cluster model. The [Formula: see text]-nucleus potential was derived by employing the double-folding model with a realistic [Formula: see text] interaction whose exchange part has a finite-range. We considered several isotopes for each [Formula: see text]-value. The behavior of [Formula: see text] against the neutron number variation for different isotopes of each element is investigated. We found a clear similarity in the behavior of [Formula: see text] for the isotopes of a number of successive elements. The proton pair in the emitted [Formula: see text] particle, for these elements, comes from the same proton energy level. Also, the behavior of [Formula: see text] with the parent neutron number, for different isotopes of an element, was found to be governed by the existence of neutron magic number or neutron-level closure. The possibility to correlate the behavior of [Formula: see text] for several isotopes of a specific element with the proton and neutron energy levels of this element is investigated. Moreover, the behavior of [Formula: see text] when adding successive proton pairs to fill the energy level at different neutron numbers is studied. This work can be considered as a significant step forward to correlate the behavior of [Formula: see text] with the energy levels.

Realistic analytical approach for α decay and clustering

We approximate the realistic $\ensuremath{\alpha}$-core nuclear interaction between the inner turning point and Coulomb barrier, derived within the double folding procedure, by a parabolic dependence. It turns out that the corresponding harmonic oscillator frequency is concentrated in a narrow interval around $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}\ensuremath{\approx}$ 9 MeV for all analyzed transitions from even-even and odd-mass $\ensuremath{\alpha}$ emitters. The penetrability through the nuclear barrier has an exponential dependence on the ratio between the fragmentation potential and this harmonic oscillator frequency. On the other hand, the Coulomb penetrability has the standard dependence on the Coulomb parameter. Our analysis revealed that the reduced width, extracted by using the nuclear plus Coulomb penetrability factors, exponentially decreases versus the number of $\ensuremath{\alpha}$ clusters along all analyzed $\ensuremath{\alpha}$ lines, except one region where it increases by approaching the neutron magic number ${N}_{\mathrm{mag}}=126$. In that case, the number of valence proton pairs is much smaller than the number of valence neutron pairs. The reduced width exponentially depends on the magic neutron-proton asymmetry above doubly magic nuclei. These dependencies allow us to propose a systematics for reduced widths in terms of the quartet number and magic asymmetry evaluated above the closest doubly magic nuclei.

Skyrmions, Tetrahedra and Magic Numbers

Abstract Michael Atiyah’s interest in Skyrmions and their relationship to monopoles and instantons is recalled. Some approximate models of Skyrmions with large baryon numbers are then considered. Skyrmions having particularly strong binding are clusters of unit baryon number Skyrmions arranged as truncated tetrahedra. Their baryon numbers, $B = 4 \,, 16 \,, 40 \,, 80 \,, 140 \,, 224$, are the tetrahedral numbers multiplied by four, agreeing with the magic proton and neutron numbers $2 \,, 8 \,, 20 \,, 40 \,, 70 \,, 112$ occurring in the nuclear shell model in the absence of strong spin-orbit coupling.

Simulation study of nuclear shell model using sine basis

Single-particle energy states for a neutron and a proton are obtained by solving the time-independent Schrödinger equation for the mean-field Woods–Saxon potential along with the spin-orbit term. The wavefunctions are expanded as a linear combination of simple sine-wave basis states, which are eigenfunctions of the infinite spherical-well potential. The requisite algorithm based on matrix diagonalization is implemented in Free Open Source Software (FOSS) Scilab. Initial values for the simulation were taken from model parameters given in the book on Nuclear Structure by Bohr and Mottelson, which were then optimized to obtain the best convergence with the available experimental energy values of various nuclei with magic proton and neutron numbers. The level scheme, as well as the energy values for doubly magic nuclei 82208Pb and 2040Ca, which are obtained using our simulation, is presented in this paper. Finally, energy level diagrams for neutrons and protons with respect to mass number A were arrived at, based on those obtained for various magic nuclei. The evaluation method, which is based on the sine-wave basis, is akin to Fourier analysis. When done with the aid of FOSS Scilab, this technique becomes easily accessible to students at the under-graduate (UG) level and may be studied through small projects.