Neutron Magic Number Research Articles

Critical Impact of Isospin Asymmetry in Elucidating Magicity Across Isotonic Chains of Different Mass Regions Using Relativistic Energy Density Functional

This study provides a comprehensive examination of the surface properties—particularly the symmetry energy and its contributing components—of isotonic chains across various mass ranges, including light, medium, heavy, and superheavy nuclei. We establish a correlation between nuclear symmetry energy and isospin asymmetry in different mass regions along isotonic chains with magic and semi-magic neutron numbers of N = 20, 40, 82, 126, and 172. Our approach integrates the coherent density fluctuation model within the relativistic mean-field (RMF) framework, utilizing both the non-linear NL3 and density-dependent DD-ME2 parameter sets. The methodology employs the Brueckner energy density functional in conjunction with our recently developed relativistic energy density functional (relativistic-EDF). The relativistic parameterization of the EDF at local density facilitates a consistent exploration of isospin-dependent surface properties across the nuclear landscape. In the present work, we successfully reproduce established shell closures and demonstrate that the relativistic approach yields significantly improved predictions for recognized magic numbers, particularly Z = 28 and 50. Additionally, we present compelling evidence for the presence of novel shell and sub-shell closures, specifically at Z = 34, 58, 92, and 118. These findings contribute to a nuanced understanding of nuclear surface properties while serving as a benchmark for future investigations and validations of nuclear models.

Magic Number N = 350 Predicted by the Deformed Relativistic Hartree-Bogoliubov Theory in Continuum: Z = 136 Isotopes as an Example

The investigation of magic numbers for nuclei in the hyperheavy region (Z>120) is an interesting topic. The neutron magic number N=350 is carefully validated by the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), via analysing even-even nuclei around N=350 of the Z=136 isotopes in detail. Nuclei with Z=136 and 340≤N≤360 are all found to be spherical in their ground states. A big drop of the two-neutron separation energy S2n is observed from N=350 to N=352 in the isotopic chain of Z=136, and a peak of the two-neutron gap δ2n appears at N=350. There exists a big shell gap above N=350 around the spherical regions of single-neutron levels for nucleus with (Z=136,N=350). These evidences from the DRHBc theory support N=350 to be a neutron magic number in the hyperheavy region.

The magicity, the radii of neutron orbits 1<i>f</i><sub>7/2</sub>, 2<i>p</i><sub>3/2</sub> and halo-like structure of <sup>52,54</sup>Ca nuclei

The evolution of neutron single-particle spectra of isotones with N = 32 and 34 new magic neutron numbers in the region 16 ≤ Z ≤ 32 was calculated in the dispersive optical model. It was shown that the minimum of the difference between the Fermi energy and the half-sum of the energy levels of the last predominantly occupied state and the first predominantly unoccupied state is achieved in the magic isotones with N = 32 and 34. The calculated root-mean-square radius of the neutron halo-like state 2p3/2 in double magic 52Ca nucleus exceeded the radius of the underlying 1f7/2 state by 0.8 fm. It is consistent with the recent experimental data and theoretical predictions that explain ‟unexpectedly” large root-mean-square charge radius of this nucleus.

Elucidate the nonrelativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

In this paper, we have developed relativistic and nonrelativistic energy density functionals within the local density approximation, transitioning from momentum space to coordinate space. Utilizing the Coherent Density Fluctuation Model, these functionals predict shell and sub-shell closures across isotopic and isotonic chains. Our focus has been on refining fitting procedures and testing these functionals on selected nuclei. Previously, we compared our energy density functionals for E-RMF forces G3 and IOPB-I with the Brückner energy density functional. Our results highlighted significant advantages, particularly in accurately predicting peaks in the symmetry energy curve at magic neutron numbers within heavy and superheavy regions. This success motivates us to extend our fitting procedure for both the relativistic mean field (E-RMF) and nonrelativistic Skyrme–Hartree–Fock (SHF) parameter sets. To further ensure the reliability of our newly fitted functionals, we establish Pearson-type correlations between the symmetry energy and its derivatives.

Ab initio study of Z(N) = 6 magicity* *This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 12175280, 12250610193, 12375143, 11975282, 11705240, 11435014), the Natural Science Foundation of Gansu Province, China (Grant Nos. 20JR10RA067, 23JRRA675), the Chinese Academy of Sciences "Light of West China" Program, the Key Research Program of the Chinese Academy of

The existence of magic numbers of protons and neutrons in nuclei is essential for understanding the nuclear structure and fundamental nuclear forces. Over decades, researchers have conducted theoretical and experimental studies on a new magic number, Z(N)=6, focusing on observables such as radii, binding energy, electromagnetic transition, and nucleon separation energies. We performed ab initio no-core shell model calculations for the occupation numbers of the lowest single particle states in the ground states of Z(N)=6 and Z(N)=8 isotopes (isotones). The results of our calculations do not support Z(N)=6 as a magic number over a range of atomic numbers. However, 14C and 14O exhibit the characteristics of double-magic nuclei.

Nuclear shape evolution in even-even Pd isotopic chain

The covariant density functional theory is utilized to examine the evolution of shape in even–even 96−130 Pd isotopes by using the density-dependent meson-exchange DD-ME2 and the density-dependent point-coupling DD-PC1. This research is carried out by considering the evolution of the ground-state shapes derived from calculations of the axial and triaxial potential energy surfaces. The shape transition in the palladium isotopic chain is very clearly manifested. In addition, various ground-state properties, such as binding energy, charge radius, two-neutron separation energy, and two-neutron shell gap have been calculated and have been observed to adequately match the existing experimental data. Moreover, a robust shell closure is distinctly observed at the magic neutron number N = 82.

THE STUDY OF ELECTRIC QUADRUPOLE TRANSITION (E2) IN 58Ce AND 60Nd NUCLEI

Transition strengths 2w.u. M(E2) for gamma transition from first excited 21+statesto the ground states that produced by pure electric quadrupole emission in even –even nuclei of 58Ce and 60Nd have been calculated as a function of neutron number(N). The life times for 21+ excited states together with the intensities of γ0- transitionsmeasurements are used in calculations. The results thus obtained have shown that;the nuclei with magic neutron number such as 58Ce140 and 60Nd142 have minimumvalue for 2w.u. M(E2) . The reduced transition probabilities B(E2) are alsocalculated and compared with the experimental data and other theoretical models.PACS:- 27.60-j, 23.20-g, 23.20.Ck, 23.20.Gq

Matrix‐Product State Approach to the Generalized Nuclear Pairing Hamiltonian

AbstractIt is shown that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix‐product state) despite the presence of long‐range interactions. The ground state can be obtained using the density‐matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used Bardeen‐Cooper‐Schrieffer (BCS) approach, and does not suffer from any mean‐field artifacts. This framework is applied to compute the even‐odd mass differences of all known lead isotopes from to in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. Pairing with non‐zero angular momentum is also considered and the lowest excited states in the full configuration space of one major shell is determined, which is demonstrated for the , isotones. To demonstrate the capabilities of the method beyond low‐lying excitations, the first 100 excited states of with singlet pairing and the two‐neutron removal spectral function of are calculated, which relate to a two‐neutron pickup experiment.

Shape evolution and shape coexistence in even-even Mo isotopic chain

The phenomena of shape evolution and shape coexistence within the Molybdenum isotopic chain are investigated using the covariant density functional theory with the parameterizations DD-ME2 and DD-PC1. Furthermore, various ground state properties of this chain are investigated, including binding energy, two-neutron separation energy, charge radii, and two-neutron shell gap. A robust agreement is observed when comparing with the available experimental data. The ground state deformation of Mo isotopes evolves smoothly and correlates with the continuous and gradual changes observed in the physical properties. A noticeable phenomenon of shape coexistence can be observed in certain isotopes, marked by the simultaneous existence of both a triaxial and an oblate axial minimum. A pronounced and well-defined shell closure is prominently evident at the neutron magic number N=82.

Prediction of Decay Modes for Superheavy Nuclei with Magic Number of Neutrons and Protons

The Cubic plus Yukawa plus Exponential (CYE) model has been used to study the different decay properties of Superheavy nuclei 298,310114, 306,318122, 308,310124, 310,322126 and compared them with the available theoretical and experimental values. Here, the half-lives of several clusters have been computed that have not yet been detected experimentally. Hopefully, this will assist future research in this area. As a result of comparing the three different decay modes (α-decay, cluster radioactivity and spontaneous fission), it was possible to predict the predominant decay modes of Superheavy nuclei.

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.

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.

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.

Shape evolution of nuclei in the region of (A≈30) using covariant density functional theory

Shape evolution of even–even isotopes of Ne, Mg, Si, S, Ar and Ca in the vicinity of [Formula: see text] mass region of the nuclear chart is studied using covariant density functional theory. It will be studied based on finite range NN-interaction force represented by NL3∗ and DD-ME2 and zero finite range NN-interaction force represented by DD-PC1. Both [Formula: see text]Mg and [Formula: see text]Si exhibit shape coexistence and the ground state shape which is found to be both oblate and prolate. The spherical shape is obtained for the Ca isotopes, and for nuclei that have magic neutron numbers [Formula: see text] and 20. The rest of the isotopic chain has only one minimum and alternates between prolate and oblate shapes. Physical properties are calculated at the location of ground state deformation with neutron number ([Formula: see text]) and proton number ([Formula: see text]), such as the binding energy, two-neutron separation energies, proton, neutron and charge radii. In general, a smooth change in these properties is found, except near [Formula: see text] and 20 one can see a sharp change, which reflects the sudden change in the ground state deformation in the neighboring nuclei. A very good agreement is found with the available experimental data, HF and FRDM models

Neutron multiplicity measurement and investigation of nuclear dissipation and shell effects in Si30+W182,184,186 reactions

Background: Enhanced prescission neutron multiplicity (${\ensuremath{\nu}}_{\mathrm{pre}}$) over statistical model calculations assuming Bohr-Wheeler fission width is explained using Kramers' fission width incorporating dissipative effects. The dissipation strength obtained from such studies reported significant effect of the neutron shell closure of $N=126$ of the fissioning system as well as nuclear temperature. The dependence of dissipation strength on shell effect and temperature is also attributed to the choice of input parameters in the statistical model calculations.Purpose: We investigate the role of $N/Z$, shell effect, collective enhancement of level density (CELD), and excitation energy on ${\ensuremath{\nu}}_{\mathrm{pre}}$ in reactions forming isotopes of the Ra nucleus.Methods: The neutron multiplicity excitation function is measured for the $^{30}\mathrm{Si}+^{182,184,186}\mathrm{W}$ reactions populating $^{212,214,216}\mathrm{Ra}$ nuclei using the National Array of Neutron Detectors (NAND) at the Inter-University Accelerator Centre, New Delhi. Among these compound nuclei, $^{214}\mathrm{Ra}$ has a major neutron shell closure of $N=126$. Measured ${\ensuremath{\nu}}_{\mathrm{pre}}$ are analyzed within the framework of a statistical model incorporating dynamical hindrance in nuclear fission due to dissipation, shell corrections in the fission barrier and level density, and CELD.Results: Experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ show a marginal isotopic dependence at all excitation energies. ${\ensuremath{\nu}}_{\mathrm{pre}}$ values do not show any noticeable effect of neutron magic number $N=126$. Dissipation strength of $\ensuremath{\beta}=8\phantom{\rule{4pt}{0ex}}{\mathrm{zs}}^{\ensuremath{-}1}$ ($5.27\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$) reasonably reproduces the experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ excitation functions for all three nuclei in the measured energy range. Appreciable variations in presaddle neutron emissions are observed when shell effect or CELD is excluded in the calculations. Even though both the shell and CELD are found to impact primarily in the presaddle sector, they alter the excitation energy and multiplicity in the saddle-to-scission sector as well in a complementary manner.Conclusions: A temperature independent dissipation coefficient is observed to reproduce the experimental results in this study throughout the excitation energy range measured. Shell corrections in fission barrier and level density parameters and CELD in fission and particle evaporation widths also influence the neutron multiplicities. The observed effect of CELD in the presaddle phase is attributed to the large enhancement of level density at the saddle due to its large deformation and consequent enhancement of fission width.

Comparative study on charge radii and their kinks at magic numbers

Isotope dependences of charge radii, i.e., isotope shifts, calculated by the Skyrme Hartree-Fock, the relativistic mean-field, and the relativistic Hartree-Fock calculations are compared against the experimental data of magic and semimagic nuclei. It is found that the tensor interaction plays a role in reproducing the ``kink'' behavior, irregularity of isotope shifts at the neutron magic number, in the relativistic Hartree-Fock approach. With several Skyrme models, it is found that the kink behavior can be reproduced with the spin-orbit interaction having nonzero isovector channel. The single-particle orbitals near the Fermi energy are crucial to determine the kink size. The effects of the symmetry energy and the pairing interaction are also discussed in relation to the kink behavior.

α and 2α decay of nuclei in the region 94≤Z≤101 using the modified generalized liquid drop model

The \ensuremath{\alpha} decay and $2\ensuremath{\alpha}$ decay of various isotopes of Pu, Am, Cm, Bk, Cf, Es, Fm, and Md in the mass region $A=218$ to 273 are investigated using the modified generalized liquid drop model (MGLDM) and universal decay law. The comparison of experimental alpha decay half-lives with the predicted half-lives proves the consistency of our calculations. As a result we broadened our investigation to also include a study of double alpha decay of these isotopes. There is a considerable interest in performing research on double alpha decay, as seen by the proposal submitted at CERN to investigate the double alpha radioactivity of $^{224}\mathrm{Ra}$. In view of this, the decay half-lives of most probable $2\ensuremath{\alpha}$ emitters, calculated using MGLDM by employing different preformation factors, are presented which can be beneficial for upcoming experimental investigations on this topic. A peak or dip in \ensuremath{\alpha} and $2\ensuremath{\alpha}$ decay half-life is witnessed which indicates the stability of parent or daughter isotopes correspondingly. Minimum and maximum half-lives for decay are observed when the daughter and parent nuclei, respectively, contain a magic number of neutrons. From our study, 126 and 162 are found as magic/semimagic numbers. A linear plot is obtained while plotting ${\mathrm{log}}_{10}{T}_{1/2}$ of all the isotopes against $Z{Q}^{\ensuremath{-}1/2}$, which emphasizes that our estimations are reliable.

Presolar grain isotopic ratios as constraints to nuclear physics inputs for s-process calculations

The isotopic abundances in presolar SiC grains of AGB origin provide important and precise constraints to those star nucleosynthesis models. By comparing the values of the s-element abundances resulting from calculations with the ones measured in these dust grains, it turns out that new measurements of weak-interaction rates in ionized plasmas, as well as of neutron-capture cross sections, are needed, especially in the region near the neutron magic numbers 50 and 82.

Isotopic yields and spontaneous fission half-lives of 279Ds and 281Ds superheavy isotopes

In this paper, Isotopic yield and half-lives of cold spontaneous fission for [Formula: see text] and [Formula: see text] superheavy isotopes are studied. The interacting potential between fragments includes mean field proximity and Coulomb potentials. Fission [Formula: see text]-value, driving potential, [Formula: see text] and partial penetration probability of each possible individual fragmentation are calculated using [Formula: see text] approximation. According to the tunneling effect, the most favored pair of fragments is produced for the highest [Formula: see text]-value or the lowest driving potential. A few fragmentation with higher [Formula: see text]-value are selected for each atomic number Z. It is found that for [Formula: see text] isotope, the highest relative yield belongs to the [Formula: see text]Te + [Formula: see text]Ce fragmentation while for [Formula: see text], the combination [Formula: see text]Te + [Formula: see text]Ce has lowest driving potential and highest yield due to presence of fragments with magic or near magic proton and neutron numbers ([Formula: see text] and [Formula: see text]). By calculating yield of each fragmentation, its partial fission decay constant and then by summing over all decay constants for possible fragmentation, the fission decay constant for each superheavy isotope is obtained. Furthermore, half-life of each superheavy isotope is also estimated. Finally, the calculated half-lives using this method are compared with the experimental data. Good agreement achieved between our calculated half-lives and the experimental data.