Neutron Shell Effects Research Articles

Local charge radius relations based on neutron shell effects

In this paper, we obtained the mean mass density parameter (MMDP) [Formula: see text] based on the nuclear mass AME2020 and nuclear charge radius CR2013 databases. On this basis, we study the dependence relationship between neutron number N and the two neighboring isotopes MMDP difference [Formula: see text], and then obtained the empirical formula for [Formula: see text]. By combining this empirical formula with the AME2020 and CR2013 databases, the root-mean-square deviation (RMSD) for 606 nuclear charge radii with [Formula: see text] 21 between the calculated and experimental values is 0.0046[Formula: see text]fm. Considering the odd–even staggering and isospin term correction, the study found that the RMSD is reduced to 0.0040[Formula: see text]fm. This work also uses Levenberg–Marquart (L-M) neural network approach to study the nuclear charge radius. The RMSD of nuclear charge radius is only 0.0030 fm, where the accuracy is increased by about 25%. Furthermore, the predicted values of nuclear charge radius obtained using this modified empirical formula and Neural Network model are competitive with the results of other models. These results indicate that nuclear charge radius relation and Neural Network model based on [Formula: see text] proposed in this work have a certain accuracy, simplicity and reliability.

Charge radius relations derived from the nuclear masses for two neighboring isotopes

In this paper, we get the nuclear mass-density parameter of known mass and known charge radius by using the AME2020 nuclear mass database and the CR2013 nuclear charge radius database. For the nuclei with [Formula: see text], we obtained an empirical formula of the constant parameter equal to 0 for the difference of nuclear mass-density parameter between two neighboring isotope. That is, the nuclear mass-density parameter of the two neighboring isotopes was equal. By using this empirical formula combined with AME2020 and CR2013 databases, the calculated value of 625 nuclear charge radii was obtained. The root-mean-square deviation (RMSD) of nuclear charge radius that we have successfully obtained is [Formula: see text][Formula: see text]fm. In addition, one of the corrections is the neutron factor. This correction is the key improvement which reduces the RMSD to 0.0077[Formula: see text]fm. Considering the neutron shell effect, the different shell ranges were divided into two categories for correction, and the RMSD was reduced to 0.0056[Formula: see text]fm. Based on the revised empirical formula combined with the AME2020 database, the calculated and predicted values of nuclear charge radius were obtained with high accuracy. Some of these predictions are also very consistent with experimental values measured in recent years. In addition, we use BP neural network to study the difference of nuclear mass-density parameter on the basis of two categories. The RMSDs obtained are 0.0028[Formula: see text]fm and 0.0038[Formula: see text]fm, respectively. It can be seen that such a division has a certain degree of reliability and feasibility. These results show that the new relation proposed in this paper has simplicity and reliability, which can be compared with other local nuclear charge radius relations.

Tensor force effect on the exotic structure of neutron-rich Ca isotopes * * Supported by the National Natural Science Foundation of China (U1832120, 11675265), the State Scholarship Fund of China Scholarship Council (201708130035) and the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China (A2018210146)

The structure of neutron-rich Ca isotopes is studied in the spherical Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach with SLy5, SLy5+T, and 36 sets of TIJ parametrizations. The calculated results are compared with the available experimental data for the average binding energies, two-neutron separation energies and charge radii. It is found that the SLy5+T, T31, and T32 parametrizations reproduce best the experimental properties, especially the neutron shell effects at N = 20, 28 and 32, and the recently measured two-neutron separation energy of 56Ca. The calculations with the SLy5+T and T31 parametrizations are extended to isotopes near the neutron drip line. The neutron giant halo structure in the very neutron-rich Ca isotopes is not seen with these two interactions. However, depleted neutron central densities are found in these nuclei. By analyzing the neutron mean-potential, the reason for the bubble-like structure formation is given.

Third minima in thorium and uranium isotopes in a self-consistent theory

Background: Well-developed third minima, corresponding to strongly elongated and reflection-asymmetric shapes associated with dimolecular configurations, have been predicted in some non-self-consistent models to impact fission pathways of thorium and uranium isotopes. These predictions have guided the interpretation of resonances seen experimentally. On the other hand, self-consistent calculations consistently predict very shallow potential-energy surfaces in the third minimum region.Purpose: We investigate the interpretation of third-minimum configurations in terms of dimolecular (cluster) states. We study the isentropic potential-energy surfaces of selected even-even thorium and uranium isotopes at several excitation energies. In order to understand the driving effects behind the presence of third minima, we study the interplay between pairing and shell effects.Methods: We use the finite-temperature superfluid nuclear density functional theory. We consider two Skyrme energy density functionals: a traditional functional SkM${}^{*}$ and a recent functional UNEDF1 optimized for fission studies.Results: We predict very shallow or no third minima in the potential-energy surfaces of ${}^{232}$Th and ${}^{232}$U. In the lighter Th and U isotopes with $N=136$ and 138, the third minima are better developed. We show that the reflection-asymmetric configurations around the third minimum can be associated with dimolecular states involving the spherical doubly magic ${}^{132}$Sn and a lighter deformed Zr or Mo fragment. The potential-energy surfaces for ${}^{228,232}$Th and ${}^{232}$U at several excitation energies are presented. We also study isotopic chains to demonstrate the evolution of the depth of the third minimum with neutron number.Conclusions: We show that the neutron shell effect that governs the existence of the dimolecular states around the third minimum is consistent with the spherical-to-deformed shape transition in the Zr and Mo isotopes around $N=58$. We demonstrate that the depth of the third minimum is sensitive to the excitation energy of the nucleus. In particular, the thermal reduction of pairing, and related enhancement of shell effects, at small excitation energies help to develop deeper third minima. At large excitation energies, shell effects are washed out and third minima disappear altogether.

Canonical-basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations

We present simple equations for a canonical-basis (Cb) formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the Cb. The Cb formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasiparticle random-phase approximation with Skyrme functionals. We show systematic studies of $E1$ strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, which include the neutron excess, the separation energy, the neutron-shell effects, the deformation, and the pairing.

Energy dependence of the level density parameter

Combinatorial level densities are calculated using a fixed level scheme for several nuclei to study the energy dependence of the level density parameter when the nucleus is either doubly magic, nearly magic or non-magic. It is shown that variations of the level density parameter can be described from a general point of view only by an analytic expression which accounts separately for proton and neutron shell effects.

Semiempirical formula for describing neutron shell effects in the resonance-level density for s-wave resonances

A simple formula for the resonance-level density for s-wave resonances is found by fitting the assumed function of the number of neutrons to numerous experimental data. To describe shell effects, demonstrated as strong decreases in experimental data at the magic numbers of neutrons, the dependence of the assumed function on the “complexity” of a compound nucleus is introduced. The resulting function describes quite well the character of changes in the resonance-level density with the number of neutrons, including the regions of the magic numbers.

Investigation of neutron shell effects and fission channels in the spontaneous fission of the PU-isotopes

The fission fragment energy and mass distributions of the spontaneously fissioning 236, 238, 240, 242, 244pu isotopes have been studied. These characteristics are an ideal data set for the investigation of shell effects and fission channels under identical conditions, i.e. constant Z, I π = 0 + and zero excitation energy. The important variations observed in the distributions are discussed in terms of the scission point model (Wilkins et al.) as well as in terms of the fission channel model with random neck-rupture (Brosa et al.).

A systematic study of (n, 2n) cross sections at 14 MeV

Abstract The experimental (n,2n) cross sections around 14 MeV have been collected, analyzed, and evaluated. Data were taken from 124 nuclei for A=19–209 up to the end of 1983. Relation between σn, 2n and (N-Z)/A has been studied. No neutron shell effect is found. The cross sections for some nuclei have been calculated by using a statistical theory. The good agreement with the experimental σn, 2n at 14 MeV has been obtained in terms of a single set of fitting parameters.

The RMS radii of the charge distribution in nuclei

A semi-empirical formula for calculating the RMS radii of the charge distribution in stable nuclei and nuclei close to stability with Z, N>or=5 is presented. The results of calculations of the RMS radii for a spherical distribution of charge in deformed and diffused nuclei under rotation, which is assumed to be the Fermi distribution, are also presented. In both calculations the neutron shell effect is observed in addition to the nuclear deformation effect.

The elastic scattering of 25MeV α-particles and neutron shell effects in the A = 50 TO A = 93 mass region

Experimental elastic scattering angular distributions of 25 MeV α-particles scattered from 28 nuclei ranging from 50Cr to 93Nb have been measured and then analysed in terms of a regular optical model with standard Woods-Saxon geometries for both the real and imaginary potentials. The experimental distributions are well fitted over the whole angular range from 5° to 175° c.m. by the predictions, provided that a smaller than normal diffuseness is used for the imaginary potentials. The usual families of potentials with volume integrals differing by approximately 100 MeV · fm 3 are found. The family with volume integral ranging from 540 to 420 MeV· fm 3 over the nuclei studied has been chosen as the most appropriate, corresponding to the single family found for α-particle elastic scattering at above 100 MeV. When plotted as functions of the back-angle enhancement parameter γ(θ), the derived parameter at the strong absorption radius, v sar, shows clear grouping into nuclei with similar neutron shell configurations. The derived optical model rms radii also show an abrupt change at the N = 40 neutron sub-shell closure. These effects are shown to be consistent with a contribution to the α-nucleus potential from the neutron pairing interaction.

Trends in nuclear radii from the energy density method

A systematic comparison between experimental charge radii rc and values obtained by using the energy density method shows that the model reproduces the average behaviour of rc with particle number. On the other hand, the calculations failed to reproduce observed neutron-shell effects in the charge radii, although calculated neutron radii exhibit significant neutron-shell effects. This calls for the inclusion of a polarising interaction between the valence neutrons and the proton distribution. The calculated proton and neutron radii rp and rn are summarised in graphical form, which gives an idea of the general trends of rp and rn against N and Z. On the grounds of the calculated densities, a simple parametrisation, which goes beyond the A1/3 law, is suggested.

Isotopic mass dispersion discontinuity in various fission processes and its interpretation as a neutron shell effect

The isotopic dispersions have been calculated for fission processes listed in the Introduction below by using recommended fission yield data. Those dispersions in which the neutron numbers of isotopes lying in the vicinity of the most probable mass fit a strong shell have been found to be pronouncedly discontinuous; the discontinuity is proved to occur exactly at the most probable mass. The influence of neutron shells on mass dispersion with special reference to discontinuity is discussed on the basis of shell correction vs deformation and neutron number reported by Wilkins, Steinberg, and Chasman. In discontinuous dispersions on the narrower branch lie the isotopes fitting the strong spherical and deformed neutron shells. Apart from recommended data, the relative isotopic fragment yields predicted by the Wilkins-Steinberg model for the complementary pairs $z=50\ensuremath{-}42, 51\ensuremath{-}41, 54\ensuremath{-}38, \mathrm{and} 56\ensuremath{-}36$, in thermal-neutron fission of $^{235}\mathrm{U}$ have also been used to calculate the corresponding dispersions. These have been found to be in good agreement with those calculated from recommended data, and discontinuities were observed, in general, wherever expected.NUCLEAR REACTIONS, FISSION $^{232}\mathrm{Th}$, $^{233}\mathrm{U}$, $^{235}\mathrm{U}$, $^{238}\mathrm{U}$, $^{239}\mathrm{Pu}$, $^{252}\mathrm{Cf}$; calculated isotopic mass dispersions from recommended yields and Wilkins-Steinberg model. Discontinuity as neutron-shell effect.

Yields of tin and antimony isotopes in the vicinity of the closed shell N = 82 from reactor neutron induced fission of 232Th

The independent yields of the isotopes 131,132Sn and 131–133Sb from the reactor neutron induced fission of 232Th were measured. Tin and antimony were chemically separated as hydrides and the decay or the growth and decay of their γ-ray spectra were followed. The independent yields of 131,132Sn and 132,133Sb were obtained by a direct measurement, while the yield of 131Sb was derived from the corresponding measured isobaric yield and the respective chain yield. An enhancement of yield of ∼70% was found for the closed neutron shell nucleus ( 132Sn) while the other measured nuclei showed either an enhancement or a decrease, i.e. a proton odd-even effect of ∼30%. The contribution of the data to the fission yields system of Z = 90–98 is discussed. The odd-even systematics is discussed according to previous studies, while the neutron shell effect is examined with regard to the primary mass split and the neutron emission probabilities.

Independent yields of fast-neutron fission ofTh232: Observation of proton odd-even effect and neutron shell effect on the yields

Elemental yields in the fission of $^{232}\mathrm{Th}$ induced by reactor neutrons were measured and found to disclose a pronounced odd-even effect. Independent and cumulative yields of isotopes of Kr, Xe, Sn, and Sb were measured and the independent yields of isotopes of Rb, Cs, and Sb were subsequently derived. A comparison of the yield values obtained with the calculated "normal" yields reveals a constant enhancement of products with an even number of protons, relative to those with an odd number. An average amplitude of 30(\ifmmode\pm\else\textpm\fi{}12)% in the fluctuation of proton pairing was established for all isotopes measured, except for the doubly magic $^{132}\mathrm{Sn}$, which shows an extreme effect, apparently due to its closed neutron shell. The odd-even effect is discussed in connection with the mass distribution, excitation, and total kinetic energies. The neutron shell effect on the yields is discussed with regard to the primary mass split and the neutron emission probabilities.[NUCLEAR REACTIONS, FISSION Fission yields $^{232}\mathrm{Th}(n,f)$, calculated proton odd-even effect, calculated neutron closed shell effect.]

Establishment of Neutron Shell Effects in (n, 2n) Cross-Sections at 14 MeV

The existence of shell effects in ( n , 2 n ) cross-sections at 14 MeV neutron energy has been controversial for more than a decade. In the present work, recently available systematised data on ( n , 2 n ) cross-sections at 14.7 MeV has been reinvestigated critically in the vicinity of closed shells. These plots of σ( n , 2 n ) versus N and ( N - Z )/ A show definite shell effects at N =20,28 and 50 which have never been revealed so distinctly by earlier investigations. The disappearance of shell effect in heavy nuclei N =82 has been explained. It has been demonstrated that shell closure effect is perceptible clearly only in comparison to neighbouring nuclei of same N - Z and pairing effects. The distinct sharp rise of σ ( n , 2 n ) with ( N - Z )/ A >∼0.1, has been noted to be a characteristic of closed shell or sub-shell isotones only. An empirical relation for σ( n , 2 n ) is devised, for A ≧110.

Activation cross sections, isomeric cross-section ratios and systematics of (n, 2n) reactions at 14–15 MeV

Total cross sections for eighteen (n, 2n) reactions at 14.7 ± 0.3 MeV in the medium- and heavymass regions have been measured by the activation technique using Ge(Li) detector γ-ray spectroscopy. Isomeric (n, 2n) cross-section ratios were determined for 54Fe, 92Mo, 191Ir, 198Pt and 198Hg. A comparison of the experimental cross-section values with theoretical estimates based on the statistical model confirms that this reaction at 14–15 MeV proceeds mainly via compound nucleus formation. The dependence of the cross-section values on the relative neutron excess of the target nucleides and the systematic trends in these values are discussed in the light of the latest experimental data. No significant closed proton or neutron shell effects were discernible.

Lack of evidence for shell effects in the (n, 2n) cross sections

According to Bormann there exist strong neutron shell effects in the (n, 2n) cross sections at 14 MeV neutron energy. There seems to be no contradiction to this statement in the literature up to now. Using the same experimental values for the cross sections as Bormann did, a strong dependence of the (n, 2n) cross sections on the asymmetry factor ( N− Z)/ A is demonstrated, to which shell effects could represent only second-order corrections. While the quality of the experimental cross sections is too poor to exclude definitely small shell effects, there is certainly no clear evidence of any such effect.

14.5-MeV Neutron Activation Cross Section for Some of the Rare-Earth Nuclides and Their Relation to the Nuclear Shell Structure

The 14.5-MeV neutron cross sections for the production of $^{139m}\mathrm{Ce}$, $^{140}\mathrm{Pr}$, $^{141m}\mathrm{Nd}$, $^{143m}\mathrm{Sm}$, $^{143g}\mathrm{Sm}$, and $^{149}\mathrm{Nd}$ nuclides have been measured using thick-target samples. The ($n,2n$) cross sections for the target nuclides, some of which were calculated from previously reported isomeric yield ratios, have been plotted as functions of mass number and of the separation energies of the last neutron from the target nuclides. The results are discussed in the light of previously observed neutron shell effects in the systematics of ($n,2n$) cross sections. The importance of the cross-section measurements to the 14-MeV neutron activation analysis of these rare-earth elements is also pointed out.

Neutron shell effects in the (n, 2n) cross-sections at 14 MeV

The systematics of the available total (n, 2n) reaction cross-sections for 14 MeV neutrons have been investigated for even-neutron target nuclei. The existence of neutron shell effects is found and discussed on the background of the statistical theory. Minima in the (n, 2n) cross-sections at the magic neutron numbers N=28 and 50 for even and N=20 for odd-proton target nuclei can be accounted for by similar trends in the Q values. Cross-section maxima at the closed neutron shells N=82 and 126 for even and N = 28, 50, 82 and 126 for odd-proton target nuclei can be understood as an effect of shell closure on the nuclear level density, the relative decrease of which on passing across a closed shell is larger for higher excitation energies. The (n, n′γ) reaction is the principal one competing with the (n, 2n) process at 14 MeV in the medium and heavy mass regions. Since for the (n, n′γ) reaction the residual excitation energies lies in the region up to 12 MeV, whereas for the (n, 2n) reaction, it does not exceed 4 MeV, and since the relative change in the level density is greater at the higher excitation energies, the competition between (n, n′γ) and (n, 2n) reactions favours the latter in the region of closed neutron shells and thus accounts for the observed maxima in the (n, 2n) cross-section systematics.