α particle preformation and shell effect for heavy and superheavy nuclei

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84-92 isotopes and N = 126,128,152,162,176,184 isotones.The calculated results show clearly that the shell effects play a key role in α particle preformation.The closer the proton and neutron numbers are to the magic numbers,the more difficult the formation of the α cluster inside the mother nucleus is.The preformation factors of the isotopes reflect that N = 126 is a magic number for Po,Rn,Ra,and Th isotopes,but for U isotopes the weakening of the influence of the N =126 shell closure is evident.The trend of the factors for N = 126 and N = 128 isotones also support this conclusion.We extend the calculations for N = 152,162,176,184 isotones to explore the magic numbers for heavy and superheavy nuclei,which are probably present near Z = 108 to N = 152,162 isotones and Z = 116 to N = 176,184 isotones.The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei.This is useful for future experiments.     

Alpha decay chains from superheavy nuclei

Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. Whether these fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo α-decay in a very short time, remains an open question. α-decay half lives of nuclei with 130≥Z≥100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survived Sg nuclei with Z=106, N=162 is predicted to have the highest α-decay half life (∼3.2 h) in the Z=106-108, N=160-164 region called small island/peninsula. Superheavy nuclei with Z>118 are found to have α-decay half lives of the order of microseconds or less.     

The study of superheavy elements at SHIP: Results and plans

The nuclear shell model predicts that the next doubly magic shell closure beyond ²⁰⁸Pb is at a proton number between Z=114 and 126 and at a neutron number N=184. The outstanding aim of experimental investigations is the exploration of this region of spherical “superheavy elements.” This article describes the experiments that were performed at the GSI SHIP. They resulted in an unambiguous identification of elements 107 to 112. They were negative thus far in searching for elements 113, 116, and 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism are also presented.     

Magic numbers in superheavy elements

The energy density method is used to study the magic character of neutron and proton numbers corresponding to N > 126 and Z > 82. It is found that N = 184 and N = 228 are the next neutron magic numbers. For the protons, however, no sign of a shell closure appears for 82 < Z ? 130. Some simple criteria for the β^? - and α-stability of N = 184 and N = 228 isotones are also discussed.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

A pilgrimage through superheavy valley

We searched for the shell closure proton and neutron numbers in the superheavy region beyond Z = 82 and N = 126 within the framework of non-relativistic Skryme–Hartree–Fock (SHF) with FITZ, SIII, SkMP and SLy4 interactions. We have calculated the average proton pairing gap Δ_p, average neutron pairing gap Δ_n, two-nucleon separation energy S _2q and shell correction energy E _shell for the isotopic chain of Z = 112–126. Based on these observables, Z = 120 with N = 182 is suggested to be the magic numbers in the present approach.     

A relativistic mean-field study of magic numbers in light nuclei from neutron to proton drip-lines

In an axially deformed relativistic mean-field calculation of single-particle energy spectra ofN = 8 (Li-Mg) andN = 14,16 (C-Mg) isotonic chain and the one- and two-neutron separation energies of various isotopes of Li-Mg, new magic numbers are found to exist atN = 6 andN = 16 and/orN = 14, which are in addition to theN = 8 andN = 20 magic numbers. In neutron-rich nuclei, the shell gap atN = 6 is larger than atN = 8 and a large gap is observed forN = 16 or 14 for the neutron-rich andN = 14 for proton-rich nuclei. Large shell gaps are also found to exist atN = 14 and 16 orN = 16 alone for nuclei near theβ-stability line. The above results are independent of the parameter sets TM2, NL3 and NL-SH used here. Similarly, new large shell gaps are predicted atZ = 616 and/or 14 for protons.     

Superheavy nuclei — cold synthesis and structure

The quantum mechanical fragmentation theory (QMFT), given for the cold synthesis of new and superheavy elements, is reviewed and the use of radioactive nuclear beams (RNB) and targets (RNT) is discussed. The QMFT is a complete theory of cold nuclear phenomena, namely, the cold fission, cold fusion and cluster radioactivity. Also, the structure calculations based on the axially deformed relativistic mean field (DRMF) approach are presented which predict new regions of spherical magicity, namely Z=120 and N=172 or 184, for superheavy nuclei. This result is discussed in the light of recent experiments reporting the cold synthesis of Z=118 element.     

Search of Possible Double Magic Nuclei in the Superheavy Valley Using Relativistic Mean Field Density Depending Coupling Models

The magic nature and the stability of the various possible stable combinations of the nucleons (proton and neutron) are scrutinized with the help of density dependent relativistic mean filed model (DDRMF). To analyze the parameter dependence of our calculation three different parameters namely, DD-ME1, DD-ME2 and PKDD are used to calculate relevant properties of finite nuclei. In the present context S_2n and δ_2n are taken as the befitting quantities for the magic nature, and the existence of these predicted magic nuclei are justified from E_B/A and λ. Finally the stability is studied by calculation of α-decay and β-decay half lifetime. Our calculation shows that certain combinations of nucleons i.e. Z = 114, 120 and 126 with N = 172, 184 and 198 respectively are best pair in their immediate neighbors to synthesize experimentally.     

Pairing with a delta interaction in the energy density nuclear mass formula

The variations of the average pairing strength in the (N, Z) plane are studied with a δ-interaction in the frame of the self-consistent energy density formalism. It is found that the same δ-interaction with constant strength can be used for protons and neutrons in spherical nuclei near the stability line. This interaction is used to study the extrapolation of the average pairing strength to deformed nuclei, to the superheavy region and to the regions of the drip lines. The consequences of the results for the stability of superheavy nuclei and for magic numbers far from the stability region are examined.     

The synthesis and properties of superheavy nuclei produced in the 48Ca+244Pu, 248Cm reactions

We present the results of the experiments aimed at producing hypothetical long-lived superheavy elements located near the spherical shell closures with Z>-114 and N>-172. For the synthesis of superheavy nuclei a combination of neutron-rich reaction partners, such as ²⁴⁴Pu and ²⁴⁸Cm targets and a ⁴⁸Ca projectile have been used. The sensitivity of the present experiment exceeded by more than two orders of magnitude previous attempts to synthesize superheavy nuclides in reactions of ⁴⁸Ca projectiles with actinide targets. We observed new decay sequences of genetically linked α-decays terminated by spontaneous fission. The decay properties of the synthesized nuclei are consistent with the consecutive α-decays originating from the parent nuclides ^288,289114, produced in the 3n and 4n-evaporation channels, and ²⁹²116 — in the 4n-evaporation channel with cross sections of about a picobarn. The present observations can be considered an experimental evidence of the existence of the “island of stability” of superheavy elements and are discussed in terms of modern theoretical approaches.     

Decay Mechanism of 290,292114* Superheavy Nuclei Formed in 48Ca-Induced Reactions

We calculate the neutron-evaporation residue cross sections σ _3n , σ _4n , and σ _5n in the hot-fusion reactions ⁴⁸Ca+^242,244Pu →^290,292114 ^? over a wide range of compound-nucleus excitation energies ( $E_{\text{CN}}^{*}$ = 34–53 MeV). We work with the dynamical cluster-decay model (DCM), with a single parameter, the neck-length parameter ΔR. To calculate neutron-evaporation cross sections, we choose the superheavy proton magic Z = 126 and neutron magic N = 184. Among the 3n, 4n, and 5n production cross sections for ^{290, 292}114^?, only the 3n decay cross sections of ²⁹²114^? correspond to spherical fragmentation. The 4n and 5n cross sections of ²⁹²114^? and 3n, 4n, and 5n cross sections of ²⁹⁰114^? could only be fitted after the inclusion of quadrupole deformations β _2i within the optimum orientation approach. Changes in the angular momentum and N/Z ratio do not significantly influence the fragmentation paths of ^{290, 292}114^? superheavy nuclei. Larger barrier modification is required for the lower angular momentum states and lighter neutron clusters. The contribution of the fusion–fission component is also computed for the compound nucleus ²⁹²114^? in the energy range $E_{\text{CN}}^{*}$ = 27–47 MeV.     

On the stability of superheavy nuclei against fission

We use the methods, which we developed in a previous paper, for the calculation of potential energy surfaces and lifetimes for superheavy nuclei. Two regions of relative stability against spontaneous fission, which are connected with the magic proton numbersZ=114 andZ=164 and which will both become accessible for experiments in the near future, are discussed. Especially the nuclei aroundZ=164 are investigated here at the first time. The lifetimes for α-decay are also estimated and appear to be long enough for experimental work. Furthermore, we have investigated the dependence of the fission barrier on the level-distributions at the fermi-surface. At the end we discuss the difficulties in the usual microscopic calculations for the fission process and show a way to overcome the limitations and inconsistencies of the usually used Strutinsky-type calculations.

     

Impact of nuclear structure on production and identification of new superheavy nuclei

Using the microscopic-macroscopic approach based on the modified two-center shell model, the low-lying quasiparticle spectra, ground-state shell corrections, mass excesses and Q _α -values for even Z superheavy nuclei with 108 ≤ Z ≤ 126 are calculated and compared with available experimental data. The predicted properties of superheavy nuclei show that the next doubly magic nucleus beyond ²⁰⁸Pb is at Z ≥ 120. The perspective of using the actinide-based complete fusion reactions for production of nuclei with Z = 120 is studied for supporting future experiments.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

Additional results concerning nuclei in the terminal parts of the r-process path

An investigation of the nuclear stability of heavy neutron-rich nuclei, on the basis of more recent model refinements and the microscopic-macroscopic method, gives additional support to an earlier suggestion regarding the unlikelihood of the synthesis of superheavy elements by the r-process. The use of microscopically calculated inertial masses gives some probability for a moderate longevity around Z = 110, N = 172.     

The analysis of reactions leading to synthesis of super heavy elements within the dinuclear system concept

The dinuclear system concept of complete fusion of nuclei has been applied to the analysis of superheavy elements synthesis. The optimal excitation energy of compound nuclei and production cross sections in the cold synthesis of heavy elements with charge Z=102–112 have been calculated. The possibility of synthesizing the element with magic number Z=114 in cold and hot fusion reactions has been considered.     

Shell evolution in neutron-rich nuclei: the single particle perspective

The isospin dependence of spin-orbit(SO)splitting becomes increasingly important as N/Z increases in neutron-rich nuclei.Following the initial independent-particle strategy toward explaining the occurrence of magic numbers,we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term.It is found that new magic numbers N=14 and N=16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling,whereas the traditional magic number,N=20,may disappear.The magic number N=28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting,corresponding to the strength of the SO coupling term.Meanwhile,the N=50 and 82 shells may persist within the single particle scheme,although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei.Besides,an appreciable energy gap appears at N=32 and 34 in neutron-rich Ca isotopes.All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model.The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrèchart.     

Evidences for magicity in superdeformed shapes

Many empirical evidences that point to the existence of preferred magic nucleon numbers for superdeformed (SD) shapes are presented in this paper. We use a simple premise based on the 4-parameter formula fitted using observed γ-rays of SD bands. In particular, plots of γ-ray energy ratios, nuclear softness parameter values and the number of SD bands for given N and Z are used to pinpoint the magicity (N, Z numbers) that are most favoured as the SD magic numbers. This analysis also leads to several new predictions on the occurrence of SD bands specially in neutron-rich nuclei.