Nuclear Shell Effects Research Articles

Dependence of weak interaction rates on the nuclear composition during stellar core collapse

We investigate the influences of the nuclear composition on the weak interaction rates of heavy nuclei during the core collapse of massive stars. The nuclear abundances in nuclear statistical equilibrium (NSE) are calculated by some equation of state (EOS) models including in-medium effects on nuclear masses. We systematically examine the sensitivities of electron capture and neutrino-nucleus scattering on heavy nuclei to the nuclear shell effects and the single nucleus approximation. We find that the washout of shell effects at high temperatures brings significant change to weak rates by smoothing the nuclear abundance distribution: the electron capture rate decreases by $\sim$20$\%$ in the early phase and increases by $\sim$40$\%$ in the late phase at most, while the cross section for neutrino-nucleus scattering is reduced by $\sim$15$\%$. This is because the open-shell nuclei become abundant instead of those with closed neutron shells as the shell effects disappear. We also find that the single-nucleus description based on the average values leads to underestimations of weak rates. Electron captures and neutrino coherent scattering on heavy nuclei are reduced by $\sim$80$\%$ in the early phase and by $\sim$5$\%$ in the late phase, respectively. These results indicate that NSE like EOS accounting for shell washout is indispensable for the reliable estimation of weak interaction rates in simulations of core-collapse supernovae.

Direct mass measurements of the heaviest elements with Penning traps

Penning-trap mass spectrometry (PTMS) is a mature technique to provide atomic masses with highest precision. Applied to radionuclides it enables us to investigate their nuclear structure via binding energies and derived quantities such as nucleon separation energies. Recent progress in slowing down radioactive ion beams in buffer gas cells in combination with advanced ion-manipulation techniques has opened the door to access even the elements above fermium by PTMS. Such elements are produced in complete fusion–evaporation reactions of heavy ions with lead, bismuth, and actinide targets at very low rates. Pioneering high-precision mass measurements of nobelium and lawrencium isotopes have been performed with SHIPTRAP at the GSI Darmstadt, Germany. These have illustrated that direct mass measurements provide reliable anchor points to pin down decay chains and that they allow mapping nuclear shell effects, the reason for the very existence of the heaviest elements. Thus, accurate masses contribute to our understanding of these exotic nuclei with extreme proton numbers. In this article experimental challenges in mass measurements of the heaviest elements with Penning traps are discussed. Some illustrative examples of the nuclear structure features displayed based on the presently known masses are given.

Nuclear shell effect and collinear tripartition of nuclei

A possibility of formation of the three reaction products having comparable masses at the spontaneous fission of $^{252}$Cf is theoretically explored. This work is aimed to study the mechanism leading to observation of the reaction products with masses $M_1=$136---140 and $M_2=$68---72 in coincidence by the FOBOS group in JINR. The same type of ternary fission decay has been observed in the reaction $^{235}$U(n$_{\rm th}$,fff). The potential energy surface for the ternary system forming a collinear nuclear chain is calculated for the wide range of mass and charge numbers of constituent nuclei. The results of the PES for the tripartition of $^{252}$Cf(sf,fff) shows, that we have favorable dynamical conditions for the formation of fragments with mass combinations of clusters $^{68-70}$Ni with $^{130-132}$Sn and with missing cluster $^{48-52}$Ca.

Fusion–fission dynamics studies using mass distribution as a probe

Study of quasifission reaction mechanism and shell effects in compound nuclei has important implications on the synthesis of superheavy elements (SHE). Using the major accelerator facilities available in India, quasifission reaction mechanism and shell effects in compound nuclei were studied extensively. Fission fragment mass distribution was used as a probe. Two factors, viz., nuclear orientation and direction of mass flow of the initial dinuclear system after capture were seen to determine the extent of quasifission. From the measurement of fragment mass distribution in α-induced reaction on actinide targets, it was possible to constrain the excitation energy at which nuclear shell effect washed out.

Direct evidence of “washing out” of nuclear shell effects

Constraining excitation energy at which nuclear shell effect washes out has important implications on the production of super heavy elements and many other fields of nuclear physics research. We report the fission fragment mass distribution in alpha induced reaction on an actinide target for wide excitation range in close energy interval and show direct evidence that nuclear shell effect washes out at excitation energy ~40 MeV. Calculation shows that second peak of the fission barrier also vanishes around similar excitation energy.

Fusion – fission dynamics: fragment mass distribution studies

Using the major accelerator facilities available in India, detailed experimental studies have been made to understand the mechanism of quasi-fission and role of nuclear shell effect in heavy nuclei. Fission fragment mass distribution has been used as the probe to explore the role of entrance channel effects on fusion-fission and quasi- fission dynamics. Fission fragment mass distribution has also been demonstrated to be useful to identify the phenomenon of 'washing out' of nuclear shell effect with excitation energy.

Measurement of the Damping of the Nuclear Shell Effect in the Doubly MagicPb208Region

The damping of the nuclear shell effect with excitation energy has been measured through an analysis of the neutron spectra following the triton transfer in the (7)Li induced reaction on (205)Tl. The measured neutron spectra demonstrate the expected large shell correction energy for the nuclei in the vicinity of doubly magic (208)Pb and a small value around (184)W. A quantitative extraction of the allowed values of the damping parameter γ, along with those for the asymptotic nuclear level density parameter ã, has been made for the first time.

Advanced model for the prediction of the neutron-rich fission product yields

The consistent models for the description of the independent fission product formation cross sections in the spontaneous fission and in the neutron and proton induced fission at the energies up to 100MeV is developed. This model is a combination of new version of the two-component exciton model and a time-dependent statistical model for fusion-fission process with inclusion of dynamical effects for accurate calculations of nucleon composition and excitation energy of the fissioning nucleus at the scission point. For each member of the compound nucleus ensemble at the scission point, the primary fission fragment characteristics: kinetic and excitation energies and their yields are calculated using the scission-point fission model with inclusion of the nuclear shell and pairing effects, and multimodal approach. The charge distribution of the primary fragment isobaric chains was considered as a result of the frozen quantal fluctuations of the isovector nuclear matter density at the scission point with the finite neck radius. Model parameters were obtained from the comparison of the predicted independent product fission yields with the experimental results and with the neutron-rich fission product data measured with a Penning trap at the Accelerator Laboratory of the University of Jyvaskyla (JYFLTRAP).

The Generalized Model for the Description of Prompt Neutrons in the Low-energy Fission

Abstract The generalized model for the description of neutron emission from the spontaneous and neutron-induced fission in the energy interval up to 20 MeV is developed. For accurate calculations of nucleon composition and excitation energy of the fissioning nucleus at the scission point, the time-dependent statistical model including the pre-equilibrium neutron emission and nuclear friction effects is used. For each member of the compound nucleus ensemble at the scission point, the primary fission-fragment characteristics such as kinetic and excitation energies and yields are calculated using the scission-point fission model with nuclear shell and pairing effects, and based on the multimodal approach. The charge distribution for the primary fragment isobaric chains is considered as a result of the frozen quantal fluctuations of the isovector nuclear matter density at the finite scission neck radius. The post-scission neutron spectra are calculated as the result of the equilibrium emission from the fully accelerated fission fragments with calculated kinetic energies. The pre- scission neutron multiplicity and spectra for multi-chance fission are also calculated. The neutron and γ-ray emission during the saddle-to-scission time is also included in the consideration. This mechanism may partially explain the long standing problem of the so-called isotropic component of prompt fission neutrons.

Direct Mapping of Nuclear Shell Effects in the Heaviest Elements

Quantum-mechanical shell effects are expected to strongly enhance nuclear binding on an "island of stability" of superheavy elements. The predicted center at proton number Z = 114, 120, or 126 and neutron number N = 184 has been substantiated by the recent synthesis of new elements up to Z = 118. However, the location of the center and the extension of the island of stability remain vague. High-precision mass spectrometry allows the direct measurement of nuclear binding energies and thus the determination of the strength of shell effects. Here, we present such measurements for nobelium and lawrencium isotopes, which also pin down the deformed shell gap at N = 152.

The impact of the properties of the heaviest elements on the chemical and physical sciences

Abstract The unique role of the heaviest elements in chemical and physical sciences is discussed. With the actinide series (Z = 90-103) and the superactinide series (Z = 122-155), the heaviest elements have significantly shaped the architecture of the Periodic Table of the elements. Relativistic effects in the electron shells of the heaviest elements change the chemical properties in a given group in a non-linear fashion. Relativistically stabilized sub-shell closures give rise to a new category of elements in the Periodic Table: volatile metals. The prototype for this property is element 114 which, due to the relativistic stabilization of its 7s2 7p2 1/2 electron configuration, is volatile in its elementary state, but, in contrast to a noble gas, exhibits a marked metalmetal interaction with a gold surface at room temperature. Nuclear shell effects dominate the physical properties of the transuranium elements. These give rise to superdeformed shape isomers (fission isomers) in the actinides (U-Bk). Superheavy elements (Z ≥ 104) owe their existence solely to nuclear shell effects at N = 152, 162, and 184. At this time, a building lot is the location of the next spherical proton shell closure as there is evidence that the center of the “island of stability” is not at Z = 114. This needs urgently further theoretical and experimental efforts. The cross sections for the syntheses of elements 119 and 120 will give us important information on the “upper end of the Periodic Table of the elements”.

Role of 208Pb daughter nucleus and nuclear shell effects in trans‐lead cluster radioactivity by emission of neon clusters from 218–236U isotopes

AbstractIn the present work, the cluster radioactivity of even A uranium isotopes (218–236U) with the emission of both alpha‐like and non‐alpha‐like neon clusters (20,22,24,26,28Ne) was studied. The decimal logarithm of half‐lives (expressed in seconds) were calculated by three different approaches based on (i) the single line of Universal curve (UNIV) for alpha and cluster radioactive decay, (ii) the Universal Decay law (UDL) and (iii) by considering a fission‐like model in which the interacting nuclear potential barrier was taken to be the sum of Coulomb and proximity potentials (CPPM) respectively. Based on the half‐lives calculated by using the three different approaches mentioned above, significance of the role of 208Pb nucleus (doubly magic nucleus) and nuclear shell effects in trans‐lead cluster radioactivity were investigated. The calculated half‐lives have also been compared with available experimental results. It was observed that cluster decay modes leading to the formation of 208Pb daughter nucleus have the lowest half‐lives. This implies that there is a shell closure at proton number (Z) = 82 and neutron number (N) = 126. Hence, it confirms the existence of nuclear shell effect and stresses the significance of role of 208Pb daughter nucleus in the trans‐lead cluster radioactivity. It can be noticed that the calculated half‐lives for several cluster decay modes are well within the present experimental upper limit for measurements (T1/2 < 1030S). These results may be useful for future experiments.

Deep crustal heating in a multicomponent accreted neutron star crust

A quasistatistical equilibrium model is constructed to simulate the multicomponent composition of the crust of an accreting neutron star. The ashes of rp-process nucleosynthesis are driven by accretion through a series of electron captures, neutron emissions, and pycnonuclear fusions up to densities near the transition between the neutron star crust and core. A liquid droplet model which includes nuclear shell effects is used to provide nuclear masses far from stability. Reaction pathways are determined consistently with the nuclear mass model. The nuclear symmetry energy is an important uncertainty in the masses of the exotic nuclei in the inner crust and varying the symmetry energy changes the amount of deep crustal heating by as much as a factor of two.

NEW EQUATIONS OF STATE IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison shows that the model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison to the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows to determine the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.

Nuclear masses, deformations and shell effects

We show that the Liquid Drop Model is best suited to describe the masses of prolate deformed nuclei than of spherical nuclei. To this end three Liquid Drop Mass formulas are employed to describe nuclear masses of eight sets of nuclei with similar quadrupole deformations. It is shown that they are able to fit the measured masses of prolate deformed nuclei with an RMS smaller than 750 keV, while for the spherical nuclei the RMS is, in the three cases, larger than 2000 keV. The RMS of the best fit of the masses of semi-magic nuclei is also larger than 2000 keV. The parameters of the three models are studied, showing that the surface symmetry term is the one which varies the most from one group of nuclei to another. In one model, isospin dependent terms are also found to exhibit strong changes. The inclusion of shell effects allows for better fits, which continue to be better in the prolate deformed nuclei region.

Systematic study of survival probability of excited superheavy nuclei

The stability of excited superheavy nuclei (SHN) with $100 \leq Z \leq 134$ against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. In present calculations the neutron separation energies and shell correction energies are consistently taken from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z=115 and N=179. It turns out that this island of stability persists for excited SHN in the sense that the calculated survival probabilities in the 1n-channel of excited SHN at the optimal excitation energy are maximized around Z=115 and N=179. This indicates that the survival probability in the 1n-channel is mainly determined by the nuclear shell effects.

DYNAMICAL SHELL EFFECT IN THE FUSION REACTIONS

Dynamical nuclear shell effect is introduced to the improved quantum molecular dynamics model in interaction potential energy in the process of fusion reactions. The dynamical shell correction energy of the system is calculated and applied to dynamical process of fusion reactions with a switch function employed to connect the shell correction energy of the projectile and target with that of the compound nucleus. It is found that the shell effect enhances the fusion barrier and the calculated fusion (capture) cross-sections decrease for subbarrier fusion reactions which both projectile and target are doubly magic nuclei. The experimental data of the fusion cross-sections for four systems 40 Ca + 48 Ca , 48 Ca + 48 Ca , 16 O + 208 Pb and 48 Ca + 208 Pb can be reproduced better with the shell effect being considered by using the ImQMD model.

Quantum size effects in the inner crust of neutron stars

It is generally accepted that the inner crust of neutron stars is formed by a Coulomb lattice of nuclei immersed in a gas of quasi-free neutrons. We discuss the implications of the inhomogeneity of the crust and of nuclear shell effects on the linear response and on the superfluid properties of the system, as well as on the structure of vortices.

NUCLEAR POINT-GROUP SYMMETRIES AND NEW IDEAS ABOUT NUCLEAR STABILITY: AN OVERVIEW

The nuclear mean-field theory and the group representation theory can be used to optimise the search for strong nuclear shell effects. The two theories allow to correlate the symmetry aspects with the presence of large gaps in the single-particle spectra, facilitate in this way the conditions of search for strong nucleonic- and nuclear-binding and thus for an increased nuclear stability. In this article we give a short overview of the related on-going research, focussing on the results of the TetraNuc Collaboration.

Exotic decay in proton-rich Nd isotopes

Exotic decay of various Nd isotopes emitting4He, 8Be, 12C, 20Ne, 24Mg, 28Si and 32S was studied taking the potential barrier as the sum of Coulomb and proximity potentials. The predicted half-lives are well within the present upper limit for measurements (T1/2< 1030 s). It is found that 16O and 20Ne emissions from 120Nd are the most favourable for measurements with T1/2 ≈ 1010 s. The predicted lowest half-life time for 20Ne emission from 120Nd, stresses the role of the doubly magic 100Sn daughter in the exotic decay process. The nuclear structure effect and shell effect are evident from the Geiger–Nuttall plots for different clusters. It is found that the presence of neutron excess in the parent nuclei slows down the exotic decay process.