Shell Closure Effects Research Articles

The shell closure effects on α-decay half-lives with an improved formula

The shell closure effects on α-decay half-lives with an improved formula

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.

Local variations of charge radii for nuclei with even Z from 84 to 120

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even Z = 84–120 isotopic chains are first investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii appear remarkably at the neutron numbers N = 126 and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron-closed shells are naturally observed. Across the N = 184 shell closure, the abrupt increase in charge radii is still evidently emerged. In addition, the rapid raise of nuclear charge radii from the neutron numbers N = 138 to N = 144 is disclosed clearly in superheavy regions due to the enhanced shape deformation.

Nuclear structure effects on over-barrier fusion reactions investigated with a new phenomenological model

We investigate the occurrence of nuclear structure effects in the cross section of heavy-ion fusion reactions at energies above the Coulomb barrier. To this end, we initially develop a universal phenomenological model capable to reproduce, with an unprecedented accuracy, all previously published experimental fusion excitation functions with a few parameters. The new model, which foresees exclusively charge, mass, and energy of the colliding systems, shows a clear saturation of the critical angular momentum and avoids analytical non-regularities. The predictions of the newly developed model are then inspected to pin down residual discrepancies with the data, which could be ascribed to the structure of the colliding systems. In this framework, we obtain the following findings: (1) for the first time, we suggest an anomaly in the optimum value of the fusion cross section for systems having nearly-zero fusion Q-values; (2) we point out the occurrence of shell closure effects in the fusion of light systems; (3) we suggest that shell effects are washed-out at relative velocities vrel≳0.07c; (4) in the higher energy part of the fusion excitation function, the cross section for colliding systems involving fluorine or neon isotopes impinging on 2p3/2-1f5/2 nuclei is suppressed, possibly due to the occurrence of α-clustering effects enhancing α-transfer reactions.

A Hartree-Fock-Bogoliubov Study on the Pairing Correlations of the Isotopes of Cobalt

Background: The phenomena of nucleon pairing could be outlined from the Bethe-Weizäcker semi-empirical formula, from which the nuclear properties, viz. the binding energy, stability, shape etc. could be clearly sketched. Though the pairing correlation seems to be a small correction to the binding energy term, it plays a determinative role in defining the structure of nuclear systems. The addition to the binding energy in turn affects the position of the isotope on the dripline and hence increases the stability.
 Purpose: To study the effects of pairing on the ground state properties of the isotopes of Cobalt.
 Methods: We use Hartree-Fock-Bogoliubov (HFB) theory for the study. The general wave functions for the HFB approach are determined from variational principle. The eigen functions for the Hamiltonian are connected with the particle operators through the Bogoliubov transformations. The Hartree-Fock energy is obtained through the minimization of the variational parameter and the HFB equation is solved by iterative diagonalization by restoring the particle number symmetry.
 Results: The HFB analysis substantiates the effect of pairing correlation on binding energies, neutron and proton pairing energies, neutron and proton pairing gaps and one- and two-neutron separation energies of the Cobalt isotopes. The binding energies and one and two-neutron separation energies match with the experimental values and for pairing energies and pairing gaps, the regions where pairing is significant and the effects of shell closure at the vicinity of magic configuration of neutrons could be recognized.
 Conclusion: The Hartree-Fock-Bogoliubov calculations of the effects of pairing could be used as an efficient tool to study the nuclear structure. It can be ascertained that pairing plays an important role in determining the ground state properties of atomic nuclei.

Measurements of evaporation residue cross-sections for 48Ti + 140,142Ce reactions

Evaporation residue (ER) cross-sections have been measured for the 48Ti + 140,142Ce reactions to understand the influence of neutron shell closure on compound nucleus (CN) formation. The measured ER cross-sections for 48Ti + 140Ce (NT = 82) system are found to be very close to those of 48Ti + 142Ce (NT = 84) near the Coulomb barrier. The results show that the effect of shell closure in the target nucleus on fusion cross-sections is negligible for the present systems which can be attributed to the small values of the shell correction energies in the entrance channel. Statistical model calculations are performed to interpret the experimental results. Further, comparison of the present results with those from a reaction with higher mass asymmetry in the entrance channel shows no evidence of quasifission in the present systems.

Closed-shell effect in two-neutrino double- β decay for fp shell nuclei

Large scheme shell-model calculations are conducted for the two-neutrino double-$\ensuremath{\beta}$ $(2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$ decay of the $fp$ $(0{f}_{7/2},0{f}_{5/2},1{p}_{3/2},1{p}_{1/2})$ shell nuclei. 25 $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are considered, of which seven $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are either observed or candidates. The calculated half-lives, nuclear matrix elements (NMEs), strength function (SF) distributions, and phase space factors are shown. The calculated results agree with the experimental data and reveal that for the transitions involving a doubly, semimagic nucleus or only the nonmagic nuclei, the SF distributions are visibly different. This outcome indicates that the NMEs of the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are significantly influenced by the closed-shell effect.

Ground state and excited state multinucleon transfer channels in interactions of 28Si with 90,94Zr in near barrier region

Multinucleon transfer reactions were measured in interactions of 28Si with 90,94Zr at a near barrier energy using recoil mass separator, Heavy Ion Reaction Analyzer (HIRA) at Inter University Accelerator Centre (IUAC), New Delhi. The effects of shell closure, positive Q-value transfer channels on the relative strengths of ground state and excited state transfer in multinucleon transfer processes were investigated. The kinematic coincidence technique was employed to reduce the background. The m/q ambiguity was resolved by time of flight (TOF) technique. Based on the Q-value considerations, it was observed that pickup channels were predominantly of neutron transfer, whereas, stripping channels were mainly of proton transfer. A 14-element BGO array was used to extract the relative strength of excited state transfer. In interactions of 28Si with 90Zr, it was observed that the ground state and excited states competes for populating all the transfer channels. In reactions of 28Si with 94Zr, nearly similar behavior was observed except for two-neutron pickup channel, where excited state transfer was dominant and four-neutron pickup channel where ground state transfer was dominant.

Quaternary fission in Cf244–254 isotopes with two α particles as middle fragments

The quaternary fission of $^{244--254}\mathrm{Cf}$ isotope with two $\ensuremath{\alpha}$ particles as the middle fragments in collinear configuration has been studied by taking the interacting barrier as the sum of Coulomb and nuclear proximity potential. The most favorable quaternary fission path is the one that has a high Q value and a minimum driving potential with respect to the mass and charge asymmetries. The favorable fragment combinations are obtained from the cold reaction valley plot and then calculating the yield for charge minimized fragments. For $^{244,248,254}\mathrm{Cf}$ isotopes, the highest yield is predicted for the isotope of Sb as one fragment, $^{134}\mathrm{Sb}$ ($Z=51$, $N=83$), $^{130}\mathrm{Sb}$ ($Z=51$, $N=79$), $^{132}\mathrm{Sb}$ ($Z=51$, $N=81$), respectively, whereas for $^{246}\mathrm{Cf}$ isotope, fragments with isotope of I as one fragment $^{134}\mathrm{I}$ ($Z=53$, $N=81$) possesses the highest yield. For $^{250}\mathrm{Cf}$ isotope, fragments with isotope of In as one fragment, $^{132}\mathrm{In}$ ($Z=49$, $N=83$) possesses the highest yield. In the case of $^{252}\mathrm{Cf}$ isotope, the highest yield is for the fragments with Te as one fragment, $^{132}\mathrm{Te}$ ($Z=52$, $N=80$). These findings confirm the role of doubly magic or near doubly magic nucleus in quaternary fission, which supports the conclusion by Poenaru et al. [Nucl. Phys. A 747, 182 (2005)]. The deformation and orientation of fragments has also been taken into account for the two $\ensuremath{\alpha}$ accompanied quaternary fission, and it has been found that in addition to closed shell effect, ground-state deformation also plays an important role in determining the isotopic yield in the quaternary fission process. We hope that our study on isotopic yield in quaternary fission of even-even $^{244--254}\mathrm{Cf}$ isotope will be a guide for future experiments.

A Study on the Emission of 1, 2 Proton Halo Nuclei from Parent with Z = 121–128 in the Superheavy Nuclei via Cluster Radioactivity

Probabilities for the emission of various one proton and two proton halo nuclei from parent superheavy (SH) isotopes with Z = 121–128 are studied with the Coulomb and proximity potential model (CPPM) as the interacting barrier. The half-lives and other characteristics for the emission of one proton halo nuclei, 8B, 11,12N, 17F, 23Al, 27,28P, and two proton halo nuclei, 9C, 17,18Ne, 20Mg, 29S from the SH parent isotopes are determined and plotted it as a function of neutron number of daughter nuclei. The shell closure effects of parent and daughter nuclei are evident from the plot of computed half-lives. The peaks in the plot of half-life show the shell closure of parent and dips in the half-life show the shell closure of daughter nuclei. In the SH region with Z = 121–128 and N = 147–194, we observed that neutron shell closure of parent occurs at N~184 and neutron shell closure of daughter nuclei at N~174–184. Moreover, the most probable proton halo nuclei emissions are also evident from the computed half-life values. We have also studied the Geiger-Nuttall plots of log10 (T1/2) vs. Q−1/2 and log10 (T1/2) vs. −ln(P) for all the selected proton halo nuclei emitting from the SH parent isotopes with Z = 121–128 and are found to be linear. From the linearity of these plots, we found that GN law is valid for the proton halo decay also.

Studies on the Existence of Various 1p, 2p Halo Isotopes via Cluster Decay of Nuclei in Superheavy Region

The 1p and 2p halo structures of various halo candidates are identified from the separation energy calculations and driving potential curves. 11N, 23Al, and 26,27,28P are belonging to the 1p halo structure with low S(p) than S(2p) but 27,28,29S shows 2p halo structure. The decay possibilities of the 1p halo nuclei 8B, 11,12N, 17F, 23Al, and 26,27,28P and 2p halo nuclei 9C, 17,18Ne, 20Mg, and 28,29S from the superheavy parent isotopes with Z = 103 to 114 are studied within the Coulomb and Proximity Potential Model by evaluating the decay half-lives. Plots connecting the half-life for the emission of proton halos with the neutron number of daughter nuclei give the evidence for the possibility for the existence of the selected halo nuclei. It is evident from the computed half-lives that the emission of 1p halo nuclei such as 8B, 12N, and 17F and 2p halo nucleus 18Ne from various superheavy isotopes is probable. The plot connecting computed half-lives versus neuron number of the daughter nuclei indicates the nuclear shell closure effect of parent and daughter nuclei at N=126, 132, and 138

Measurement of fusion evaporation residue cross sections in the Ti48+Ba138 reaction

Evaporation residue cross sections are measured for the reaction $^{48}\mathrm{Ti}+^{138}\mathrm{Ba}$ which forms the compound nucleus ${}^{186}{\mathrm{Pt}}^{*}$. The cross sections are measured at beam energies in the range of 189.3--234.4 MeV. The experimental evaporation residue cross sections are compared with the dynamical model which employs one-dimensional Langevin dynamical calculations. The dissipation strength of the Langevin equation is calculated using both chaos weighted wall formula and a constant reduced dissipation function. The measured ER cross sections are found to be much less than the theoretical predictions. Further, the measured ER cross sections for the system $^{48}\mathrm{Ti}+^{138}\mathrm{Ba}$ are compared with those of $^{32}\mathrm{S}+^{154}\mathrm{Sm}$ forming the same compound nucleus. The suppression in the evaporation residue cross sections of the former reaction may be attributed to the increasing competition from quasifission. The quasifission reaction is found to have superseded any effect of neutron shell closure $(N=82)$ of the target in the present study.

Analysis of competing ground state channels observed in decay of Cm isotopes

The possible decay modes of even [Formula: see text] [Formula: see text]Cm parents have been analyzed to explore the relative emergence of various ground state emission mechanisms using the collective clusterization approach. Based on the collective availability of [Formula: see text], cluster and spontaneous fission (SF) experimental half-life data, we limit our study to isotopes of Cm. In view of this, the most probable decaying fragments from [Formula: see text]Cm are identified in different mass regions and a comprehensive analysis of the shell closure effect of the decay fragments corresponding to different mass domains is carried out within the methodology of Preformed Cluster Model (PCM). The isotopic analysis of the mass distributions and the related barrier characteristic quantities are investigated in view of ground state decay of [Formula: see text]Cm isotopes. The PCM calculated [Formula: see text] and SF half-lives compare nicely with the experimental data and the predictions are made on cluster and heavy-cluster decay of Cm isotopes, where experimental data is not available. It will of further interest to validate these predictions by performing corresponding experiments.

Search for stabilizing effects of the Z=82 shell closure against fission

Presence of closed proton and/or neutron shells causes deviation from macroscopic properties of nuclei which are understood in terms of the liquid drop model. It is important to investigate experimentally the stabilizing effects of shell closure, if any, against fission. This work aims to investigate probable effects of proton shell ($Z = 82$) closure in the compound nucleus, in enhancing survival probability of the evaporation residues formed in heavy ion-induced fusion-fission reactions. Evaporation residue cross sections have been measured for the reactions $^{19}$F+$^{180}$Hf, $^{19}$F+$^{181}$Ta and $^{19}$F+$^{182}$W from $\simeq9\%$ below to $\simeq42\%$ above the Coulomb barrier, leading to formation of compound nuclei with same number of neutrons ($N = 118$) but different number of protons across $Z = 82$. Measured excitation functions have been compared with statistical model calculation, in which reduced dissipation coefficient is the only adjustable parameter. Evaporation residue cross section, normalized by capture cross section, is found to decrease gradually with increasing fissility of the compound nucleus. Measured evaporation residue cross sections require inclusion of nuclear viscosity in the model calculations. Reduced dissipation coefficient in the range of 1\textendash3 $\times$ $10^{21}$ s$^{-1}$ reproduces the data quite well. No abrupt enhancement of evaporation residue cross sections has been observed in the reaction forming compound nucleus with $Z = 82$. Thus, this work does not find enhanced stabilizing effects of $Z = 82$ shell closure against fission in the compound nucleus. One may attempt to measure cross sections of individual exit channels for further confirmation of our observation.

Shell closure effects on spectral statistics of calcium neutron-rich isotopes

The knowledge of nuclear energy-levels in the atomic nucleus as a many-body system is necessary for understanding various reactions and nuclear structure. The calcium chain is an ideal test bench for the study of nuclear structure. Energy-levels are derived from the shell-model calculations for Ca isotopes. In this paper, the study on the fluctuation of energy-levels in Ca isotopes is carried out based on the quantum chaos theory. The shell structure of the isotopes is determined by statistical analysis of their energy levels. These analyses show that isotopes with strongly double shell closures that are called doubly magic isotopes show behavior close to the chaotic region.

Evaporation residue cross-section measurements for Ti48 -induced reactions

Background: A significant research effort is currently aimed at understanding the synthesis of heavy elements. For this purpose, heavy ion induced fusion reactions are used and various experimental observations have indicated the influence of shell and deformation effects in the compound nucleus (CN) formation. There is a need to understand these two effects.Purpose: To investigate the effect of proton shell closure and deformation through the comparison of evaporation residue (ER) cross sections for the systems involving heavy compound nuclei around the ${Z}_{\mathrm{CN}}=82$ region.Methods: A systematic study of ER cross-section measurements was carried out for the $^{48}\mathrm{Ti}+^{142,150}\mathrm{Nd}, ^{144}\mathrm{Sm}$ systems in the energy range of $140--205\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. The measurement has been performed using the gas-filled mode of the hybrid recoil mass analyzer present at the Inter University Accelerator Centre (IUAC), New Delhi. Theoretical calculations based on a statistical model were carried out incorporating an adjustable barrier scaling factor to fit the experimental ER cross section. Coupled-channel calculations were also performed using the ccfull code to obtain the spin distribution of the CN, which was used as an input in the calculations.Results: Experimental ER cross sections for $^{48}\mathrm{Ti}+^{142,150}\mathrm{Nd}$ were found to be considerably smaller than the statistical model predictions whereas experimental and statistical model predictions for $^{48}\mathrm{Ti}+^{144}\mathrm{Sm}$ were of comparable magnitudes.Conclusion: Though comparison of experimental ER cross sections with statistical model predictions indicate considerable non-compound-nuclear processes for $^{48}\mathrm{Ti}+^{142,150}\mathrm{Nd}$ reactions, no such evidence is found for the $^{48}\mathrm{Ti}+^{144}\mathrm{Sm}$ system. Further investigations are required to understand the difference in fusion probabilities of $^{48}\mathrm{Ti}+^{142}\mathrm{Nd}$ and $^{48}\mathrm{Ti}+^{144}\mathrm{Sm}$ systems.

The effect of shell closure on the thermodynamic properties of 207Pb and 89Y

Nuclear level densities of [Formula: see text]Pb and [Formula: see text]Y are calculated using the Lipkin–Nogami (LN) method and Bradeen–Cooper–Schrieffer (BCS) model. It is revealed that the calculated nuclear level densities are highly matched with the experimental data of Oslo group. The excitation energy and entropy are calculated for mentioned nuclei. In the case of two studied nuclei the characteristic of being magic for the number of neutrons or protons causes the decrease of the excitation energy and entropy contribution of magic system at low temperatures.

Probable Heavy Particle Decays from 306–339128 Superheavy Nuclei

The heavy particle decays that are probable from the isotopes of Z = 128 superheavy nuclei within the range A = 306–339 have been analyzed within the Coulomb and proximity potential model (CPPM). The study includes the evaluation of heavy particle decay half-lives of 24 clusters, including both odd and even clusters that are supposed to be emitted from the Z = 128 superheavy nuclei. The predicted values in comparison with the models Universal curve (UNIV), Universal decay law (UDL), and scaling law of Horoi et al. are observed to follow the same trend, and almost all the values lie well within the experimental limit (T 1/2 <1030s). The interesting point of the study is the confirmation of the importance of neutron magicity in the superheavy region, noticed from the plots of log10(T 1/2) vs. neutron number of the daughter nuclei. The minimum observed corresponds to the daughter nucleus with N = 184, which strongly supports the possibility of N = 184 to be a shell closure number. Also, the abrupt increase in the half-lives at A = 330 of the parent nuclei is the signature of neutron magicity at N = 202 associated with the parent nuclei. In addition, in the emission of odd mass clusters, the odd–even staggering (OES) effect is found which is more prominent in the case of heavy odd mass clusters. Importantly, the different slopes and intercepts obtained from the Geiger–Nuttall plots of log10(T 1/2) vs. Q −1/2 confirming the presence of shell closure effect and the plot of universal curve of log10(T 1/2) vs.−lnP revealed the reliability of the model CPPM.

Fusion measurements for the O+ reaction and search for neutron shell closure effects

Evaporation residue (ER) and fission cross sections were measured for the reaction O+ forming the compound nucleus 212Rn. Fission fragment angular distributions and anisotropies are consistent with the saddle point model predictions. Measured ER cross sections were fitted with statistical model calculations assuming shell-corrected free energy fission barrier height. The non-zero dissipation strength required to fit the ER cross section supports the dissipative nature of fission dynamics in heavy ion fusion. In the present study shell closure effects are not observed in the dissipation strength.

α-accompanied cold ternary fission ofPu238–244isotopes in equatorial and collinear configuration

The cold ternary fission of $^{238}$Pu, $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, with $^{4}$He as light charged particle, in equatorial and collinear configuration has been studied within the Unified ternary fission model (UTFM). The fragment combination $^{100}$Zr+$^{4}$He+$^{134}$Te possessing the near doubly magic nuclei $^{134}$Te (N=82, Z=52) gives the highest yield in the alpha accompanied ternary fission of $^{238}$Pu. For the alpha accompanied ternary fission of $^{240}$Pu, $^{242}$Pu and $^{244}$Pu isotopes, the highest yield was found for the fragment combination with doubly magic nuclei $^{132}$Sn (N=82, Z=50) as the heavier fragment. The deformation and orientation of fragments have also been taken into account for the alpha accompanied ternary fission of $^{238-244}$Pu isotopes, and it has been found that in addition to closed shell effect, ground state deformation also plays an important role in determining the isotopic yield in the ternary fission process. The emission probability and kinetic energy of long range alpha particles have been calculated and are found to be in good agreement with the experimental data.