Tin Isotopes Research Articles

Experimental study of the spectroscopic factors of Sn116–125

Enriched targets of $^{116,118,120,122,124}\mathrm{SnO}_{2}$ were bombarded with proton and deuteron beams, and the angular distributions of $(p,d)$ and $(d,p)$ on tin isotopes were accurately measured using the high-precision Q3D magnetic spectrograph at the Beijing HI-13 tandem accelerator of the China Institute of Atomic Energy. Distorted-wave Born approximation calculations were performed to extract the neutron spectroscopic factors (SFs) using two different sets of systematic optical potential parameters for these neutron transfer reactions. The SFs of $^{116--125}\mathrm{Sn}$ were obtained and compared to previous values. Our results are consistent with the average of the previous data within the error range. It is worth noting that the reaction products corresponding to $^{119}\mathrm{Sn}_{\text{G.S.}}$ and $^{119}\mathrm{Sn}_{\text{0.024}}^{*}$, to $^{123}\mathrm{Sn}_{\text{G.S.}}$ and $^{123}\mathrm{Sn}_{\text{0.025}}^{*}$, and to $^{125}\mathrm{Sn}_{\text{G.S.}}$ and $^{125}\mathrm{Sn}_{\text{0.028}}^{*}$ were first distinguished by the present experiment; therefore, our results of the low lying states of $^{119,123,125}\mathrm{Sn}$ are more reliable. However, the first excited state of $^{121}\mathrm{Sn}$ is only 0.006 MeV; we failed to identify the products that correspond to the ground state and the first excited state, and the extracted SFs of $^{120}\mathrm{Sn}_{\text{G.S.}}\ensuremath{\bigotimes}n\ensuremath{\rightarrow}^{121}\mathrm{Sn}_{\text{0.006.}}$ and $^{121}\mathrm{Sn}_{\text{0.006}}\ensuremath{\bigotimes}n\ensuremath{\rightarrow}^{122}\mathrm{Sn}_{\text{G.S}}$ are not reliable. A simple linear formula was used to analyze the relationship of SFs with neutron separation energy ${S}_{n}(N)$ and the even-$A$ Sn pairing gap $\mathrm{\ensuremath{\Delta}}(N)$, and SFs are found to be positively correlated to ${S}_{n}(N)$ and $\mathrm{\ensuremath{\Delta}}(N)$.

Charge Radii of Tin Isotopes and Their Proton-Density Distributions within the Dispersive Optical Model

Proton single-particle properties of even–even tin isotopes in the mass number range between 100 and 132 were calculated on the basis of the dispersive optical model. The possibility of describing data on the charge radius $$r_{\mathrm{ch}}$$ was studied. A decrease in the rate of growth of $$r_{\mathrm{ch}}$$ with increasing $$N$$ in the region of $$N>76$$ was obtained via increasing the energy interval in the vicinity of $$E_{\mathrm{F}}$$ where the imaginary part of the potential used is close to zero. The predictive power of the dispersive optical model for the density distribution in nuclei far from the beta-stability valley was demonstrated.

Efficient separation and high-precision analyses of tin and cadmium isotopes in geological materials

A novel analytical procedure using chromatographic separation and MC-ICP-MS for high precision Sn and Cd analyses on the same sample aliquot.

Revisiting “Tin in South-eastern Europe?”

The important role of the Balkans in the origin and development of metallurgy is well established with respect to copper. In addition, Aleksandar Durman, in his 1997 paper ?Tin in South-eastern Europe??, essentially initiated studies into the role of the Balkans in Europe?s Bronze Age tin economy. He identified six geologically favourable sites for tin mineralisation and associated fluvial placer deposits in the former Yugoslavian republics, and suggested that these may have added to the tin supply of the region. The viability of two of these sites has been confirmed (Mt Cer and Bukulja, Serbia) but the exploitation potential for the other locations has remained untested. River gravels from these four sites (Motajica and Prosara in Bosnia and Herzegovina; Bujanovac in Serbia; Ograzden in North Macedonia) were obtained by stream sluicing and panning. The sites of Prosara and Bujanovac were found to be barren with respect to cassiterite (SnO2). Streams flowing from Motajica and Ograzden were both found to contain cassiterite, but in amounts several orders of magnitude less than at Mt Cer and Bukulja. Although it is possible that minor tin recovery occurred at Motajica and Ograzden, it is unlikely that they could have contributed meaningfully to regional tin trade. This is supported by the fact that the isotopic signature (?124Sn) of cassiterite from Motajica is highly enriched in light isotopes of tin compared to that associated with Late Bronze Age artefacts of the region.

Nuclear response in a finite-temperature relativistic framework

A thermal extension of the relativistic nuclear field theory is formulated for the nuclear response. The Bethe-Salpeter equation (BSE) with the time-dependent kernel for the particle-hole response is treated within the Matsubara Green's function formalism. We show that, with the help of a temperature-dependent projection operator on the subspace of the imaginary time (time blocking), it is possible to reduce the BSE for the nuclear response function to a single frequency variable equation also at finite temperature. The approach is implemented self-consistently in the framework of quantum hadrodynamics based on the meson-nucleon Lagrangian. The method is applied to the monopole, dipole and quadrupole response of $^{48}$Ca and to the dipole response of the tin isotopes $^{100,120,132}$Sn, in particular, to a study of the evolution of nuclear collective oscillations with temperature. The article is dedicated to the memory of Pier Francesco Bortignon and devoted to the developments related to his pioneering ideas.

Tin isotopes indicative of liquid–vapour equilibration and separation in the Moon-forming disk

The depletion in moderately volatile elements in the Moon relative to Earth and comparison of the isotope compositions of the Moon and Earth have placed important constraints on models of lunar formation. A liquid–vapour protolunar disk from a high-energy giant impact has been proposed to explain some of these constraints. Here we present high-precision tin isotope data for lunar rocks, measured by double-spike MC-ICP-MS (multicollector inductively coupled plasma mass spectrometry). The lunar rocks are enriched in light tin isotopes compared to the Earth (Δ124/116SnMoon–Earth = −0.48 ± 0.15‰). On the basis of our data and constraints on tin speciation, we show that this tin isotope fractionation is inconsistent with volatile loss from a lunar magma ocean. Instead, we propose a scenario with vigorous mixing between the protolunar disk and the Earth in high-energy conditions during the impact, followed by liquid–vapour equilibration and phase separation at around 2,500 K while the disk was cooling. This scenario is consistent with the depletion in moderately volatile elements and isotope composition of the Moon. Vigorous mixing between the protolunar disk and Earth followed by processes in the cooling disk may explain the enrichment in light isotopes of tin on the Moon relative to Earth, as found by analysis of lunar rocks and geochemical calculations.

Erratum: Informing direct neutron capture on tin isotopes near the N=82 shell closure [Phys. Rev. C 99 , 041302(R) (2019)

Received 2 June 2019DOI:https://doi.org/10.1103/PhysRevC.99.069901©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear astrophysicsNuclear structure & decaysTransfer reactionsUnstable nuclei induced nuclear reactionsr processProperties90 ≤ A ≤ 149Nuclear Physics

Experimental evidence for fractionation of tin chlorides by redox and vapor mechanisms

Abstract Multiple mechanisms have been proposed to induce fractionation of tin in ores and rocks. Experimental evidence to support and characterize the causes for fractionation is lacking. Here, we present laboratory vapor-induced and redox-driven experiments to resolve the directionality and relative magnitude of fractionation caused by these geologically prominent mechanisms. Vapor-induced fractionation without redox reactions at 150 °C resulted in the residual solution becoming isotopically lighter by 0.15‰ (δ124Sn with all values reported in comparison to NIST 3161A). Tin chloride solutions that were electrolytically reduced to form metal produced residual solutions that were 0.40‰ heavier (δ124Sn). The reduced metal from these experiments was lighter than the solutions and starting materials. These experiments confirm that heavier tin isotopes are favored in a stronger bonding environment associated with oxidation, and that the vapor favors heavier tin in SnCl4. Empirical confirmation of the magnitudes and directions of tin isotope fractionation determined through experimentation are evident in the comparison of the isotopic composition of cassiterite ores from contrasting mineralizing environments. Pegmatites and associated greisen ores that formed deep within the Earth, and so experienced redox reactions without vapor partitioning (Etta, South Dakota; Elsmore, New South Wales) display a variation of only 0.8‰ (δ124Sn). In contrast, cassiterite that formed from vapor-rich fluids in volcanic to subvolcanic environments, and so experienced both redox and vapor fractionation mechanisms (Taylor Creek, New Mexico, Durango, Mexico; Potosi and Oruro, Bolivia) display a much larger range of cassiterite values, of up to 2‰ (δ124Sn). It is likely that tin isotope fractionation via these mechanisms contribute to the observed variations in igneous rocks.

Nuclear structure study of some tin isotopes using the self-consistent mean field method

Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

MC‐ICP‐MS analyses of tin isotopes in Roman‐era bronze coins reveal temporal and spatial variation

Tin's small mass fractionation and the lack of accepted reference standards have hindered Sn isotopy in archaeology and conservation science. Because of ore field variation and potential fractionation during ore reduction, attempts to determine artefacts’ ore sources have been limited. After norming the fractionations to NIST 3161a (Lot #070330), significant differences in Sn isotope mass fractionation in Judaean bronze ‘Biblical’ coins minted by different rulers during the first centuries bce and ce were discovered. These variations and those in δ 65Cu and 206Pb/204Pb are connected to historical events in the Levant.

Isoscalar giant resonance in 100,116,132Sn isotopes using Skyrme HF-RPA

Fully self-consistent spherical Hartree–Fock HF based random-phase approximation RPA calculations were performed for tin isotopes 100,116,132Sn using five type of Skyrme interaction: QMC2, LNS5, BsK21, NRAPR and MSKA. Isoscalar E0, E1, E2 and E3 transition strength distribution, centroid energy and transition density distribution have been investigated and compared with the available experimental data. Relations between the parameters and properties of the investigated Skyrme force, with the calculated properties of nuclei are analyzed.

Isotopic Dependence of Fragment Production Cross Sections in the Reactions of Deuterons on Enriched Lead and Tin Isotopes

The isoscaling behavior of the fragment production cross section was studied for reactions with deuterons on enriched lead targets (204Pb, 206Pb, 207Pb, 208Pb). The information about the reaction mechanism as well as the origin of the residues in the mass range 20 ≤ A ≤ 100 were obtained. During the analysis it was found the same behavior of the reactionmechanism as in the reactions with deuteron on enriched tin isotopes (112Sn, 118Sn, 120Sn, 124Sn). In the present article the estimation of the temperature and the symmetry energy coefficient of composite systems was done.

GDR Isospin Splitting and Photoproton Reactions on Isotopes of Tin

Photonuclear reactions on a natural mixture of tin isotopes are studied by means of gamma activation. The experiment is performed using the bremsstrahlung γ-beam of an RTM55 racetrack microtron with a maximum electron energy of 55.6 MeV. The measured yields of photoproton and photoneutron reactions are compared to results from other experimental studies, and to calculations using the TALYS code and the combined model of photonucleon reactions (CMPR).

Structure of the Lightest Tin Isotopes.

We link the structure of nuclei around ^{100}Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers (N=Z=50), to nucleon-nucleon (NN) and three-nucleon (NNN) forces constrained by data of few-nucleon systems. Our results indicate that ^{100}Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of ^{101}Sn based on three-particle-two-hole excitations of ^{100}Sn, and we find that one interaction accurately reproduces the small splitting between the lowest J^{π}=7/2^{+} and 5/2^{+} states.

Charge-exchange Resonances of Tin Isotopes in Sn(3He,t)Sb Reaction

Charge-exchange resonances: the giant Gamow–Teller, analog and the so-called “pygmy” resonances have been studied in the self-consistent theory of finite Fermi systems. Microscopic and semi-classical calculations are presented for nine tin isotopes with known experimental data 112,114,116,117,118,119,120,122,124Sn. These data is from Sn(3He,t)Sb charge-exchange reaction at the energy (3He) = 200 MeV. The average standard deviation for GTR and AR energies is δE ≤ 0.30 MeV that is close to the experimental E

Tin isotope fractionation during experimental cassiterite smelting and its implication for tracing the tin sources of prehistoric metal artefacts

Provenance studies of metal artefacts are well-established in the interdisciplinary field of science-based archaeology primarily using the chemical and isotopic composition. In the last decades, tin isotopes became gradually more important as a fingerprinting tool for the provenance of tin, but many questions especially regarding the behaviour of tin isotopes during pyrometallurgical processes are still not satisfactorily answered. This paper is a contribution to the understanding of tin isotope fractionation on tin ore smelting under prehistoric conditions and discusses the consequences for tin provenance studies. It presents the results of smelting experiments that were carried out with cassiterite in the laboratory and in the field, respectively. Besides chemical characterisation with XRF, SEM-EDX and Q-ICP-MS, tin isotope composition of tin ores and smelting products (tin metal, tin vapour, slag) were determined using solution MC-ICP-MS.Although tin recovery on smelting in the field was low (20–30%) due to tin losses to fuming and slag formation, the results indicate that the tin isotope composition is less affected than anticipated from theoretical considerations (Rayleigh fractionation). If cassiterite is completely reduced during the smelting reaction the tin metal becomes enriched in heavy tin isotopes with a fractionation of Δ124Sn = 0.09–0.18‰ (0.02–0.05‰ u−1) relative to the original cassiterite. An estimate of the provenance of the original cassiterite and the potential ore source would still be possible because the variability of tin isotope ratios in tin ore provinces is much larger. If the cassiterite becomes incompletely reduced, however, then fractionation increases significantly up to Δ124Sn = 0.88‰ (0.22‰ u−1) and conclusions on tin sources are limited. Similarly, condensed tin vapours (Δ124Sn = 1.13‰ (0.28‰ u−1)) and slags (Δ124Sn = 0.42–1.32‰ (0.11–0.33‰ u−1)) that are by-products of the smelting process show large fractionation with respect to the original tin ore as well, which makes them unsuitable for provenance studies.

Self-consistent description of the SHFB equations for 112Sn

Abstract The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

Systematics of the electric dipole response in stable tin isotopes

The electric dipole is an important property of heavy nuclei. Precise information on the electric dipole response provides information on the electric dipole polarisability which in turn allows to extract important constraints on neutron-skin thickness in heavy nuclei and parameters of the symmetry energy. The tin isotope chain is particularly suited for a systematic study of the dependence of the electric dipole response on neutron excess as it provides a wide mass range of accessible isotopes with little change of the underlying structure. Recently an inelastic proton scattering experiment under forward angles including 0º on 112,116,124Sn was performed at the Research Centre for Nuclear Physics (RCNP), Japan with a focus on the low-energy dipole strength and the polarisability. First results are presented here. Using data from an earlier proton scattering experiment on 120Sn the gamma strength function and level density are determined for this nucleus.

Nuclear structure study for the neutron-rich nuclei beyond 132Sn: In-beam gamma-ray spectroscopy of 136Sn and 132Cd

The neutron-rich nuclei 136Sn and 132Cd have been studied in the purpose of nuclear structure for the nuclei beyond the doubly-magic nucleus 132Sn. The 2+1 → 0+ gs transitions were identified for these two nuclei using in-beam γ-ray spectroscopy in coincidence with one- and two-proton removal reactions, respectively, at the RIKEN Radioactive Isotope Beam Factory. The 2+ 1 state in 136Sn is found to be similar to that for 134Sn indicating the seniority scheme may also hold for the heavy tin isotopes beyond N = 82. For 132Cd, the 2+ 1 state provides the first spectroscopic information in the even-even nuclei locating in the region “southeast” of 132Sn and the result is discussed in terms of proton-neutron configuration mixing. In both these two nuclei, it was found that the valence neutrons play an essential role in their low-lying excitations.

Investigation of (n, p), (n, 2n) reaction cross sections for Sn isotopes for fusion reactor applications

The compound Nb3Sn possess superconductivity at suitable temperatures, therefore, it is best suited to be used in the toroidal coils of superconducting magnets which holds the fusion plasma and confine it inside the reactor core. The neutron induced reaction cross-sections are required from threshold to 20MeV for different isotopes of Tin (Sn). Since limited data is available for the reactions with the Sn isotopes. Therefore, we have optimized the (n, p) and (n, 2n) reaction cross-sections for all possible Sn isotopes from threshold to 20MeV with modified input parameters in the nuclear reaction modular codes EMPIRE-3.2.2 and TALYS-1.8. These codes account for the major nuclear reaction mechanisms, including direct, pre-equilibrium, and compound nucleus contributions. The present results from 116Sn(n,p)116mIn, 117Sn(n,p)117In, 117Sn(n,p)117mIn, 118Sn(n,2n)117mSn,120Sn(n,2n)119mSn and 124Sn(n,2n)123mSn reactions calculated with nuclear modular codes: TALYS – 1.8, EMPIRE – 3.2.2 were compared with EXFOR data, systematics proposed by several authors and with the existing evaluated nuclear data library ENDF/B-VII.1, as well. The results from the present study can be used for the future development of ITER devices as well as to upgrade the nuclear model codes.