Tin Isotopes Research Articles

Application of reduction methodology for halo, weakly and tightly bound projectiles on tin isotopes

Application of reduction methodology for halo, weakly and tightly bound projectiles on tin isotopes

Subshell gaps and onsets of collectivity from proton and neutron pairing gap correlations

Throughout the nuclear chart, particle-hole correlations give rise to giant resonances and, together with the proton–neutron interaction, deformation and rotational bands. In order to shed light on many-body correlations in open-shell nuclei, I explore macroscopic properties that could manifest from the collective behaviour of protons and neutrons. Intuitively, the correlation of proton and neutron Cooper pairs can be inferred from the respective pairing gaps, that can precisely be extracted from the AME 2020 atomic mass evaluation through odd-even atomic mass differences. This work shows that the combination of large and close-lying proton and neutron pairing gaps is sensitive to onsets of collectivity and subshell gaps in superfluid nuclei, away from major shell closures. Trends of reduced transition probabilities or B(E2) values — which describe the collective overlap between the wave functions of initial and final nuclear states — are revealed in overall agreement with data. Specially interesting is the peak of collectivity in the tin isotopes at 110Sn, instead of at midshell, as expected by large-scale shell-model calculations; a situation that has astounded the nuclear physics community for quite some time.

Self-Consistent Calculations of Probabilities for the $${E}$$1 Transition between the Ground State and the $${[3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}}$$ Two-Phonon State in Tin Isotopes

Self-Consistent Calculations of Probabilities for the $${E}$$1 Transition between the Ground State and the $${[3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}}$$ Two-Phonon State in Tin Isotopes

Variation in the relationship between odd isotopes of tin in mass-independent fractionation induced by the magnetic isotope effect

Experimental results are presented showing the variation in the relationship between odd isotopes of tin (Sn) in mass-independent fractionation caused by the magnetic isotope effect (MIE), which has previously only been observed for mercury. These results are consistent with the trend predicted from the difference between the magnitudes of nuclear magnetic moments of odd isotopes with a nuclear spin. However, the correlation between odd isotopes in fractionation induced by the MIE for the reaction system used in this study (solvent extraction using a crown ether) was different from that reported for the photochemical reaction of methyltin. This difference between the two reaction systems is consistent with a theoretical prediction that the correlation between odd isotopes in fractionation induced by the MIE is controlled by the relationship between the spin conversion time and radical lifetime. The characteristic changes in the correlation between odd isotopes in fractionation induced by the MIE observed for Sn in this study provide a guideline for quantitatively determining fractionation patterns caused by the MIE for elements that have multiple isotopes with a nuclear spin. These results improve our understanding of the potential impact of the MIE on mass-independent fractionation observed in natural samples, such as meteorites, and analytical artifacts of high-precision isotope analysis for heavy elements.

Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory

Recent developments in nuclear many-body theory enabled the description of open-shell medium-mass nuclei from first principles by exploiting the spontaneous breaking of symmetries within correlation expansion methods. Once combined with systematically improvable inter-nucleon interactions consistently derived from chiral effective field theory, modern ab initio nuclear structure calculations provide a powerful framework to deliver first-principle predictions accompanied with theoretical uncertainties. In this Letter, controlled ab initio Bogoliubov coupled cluster (BCC) calculations are performed for the first time, targeting the ground-state of all calcium, nickel and tin isotopes up to mass A≈180. While showing good agreement with available experimental data, the shell structure evolution in neutron-rich isotopes and the location of the neutron drip-lines are predicted. The BCC approach constitutes a key development towards reliable first-principles simulations of heavy-mass open-shell nuclei.

Tin isotopes reveal changing patterns of tin trade, connectivity and consumption from Anatolia and Central Asia at Kültepe

Until recently, what was known about the trade of tin in the ancient Near East was based in large part on information derived from the extensive commercial archives found at the archaeological site of Kültepe (ancient Kaneš) in Turkey dating to the Middle Bronze Age (MBA) c. 1900-1750 BC. These archives were produced by an expatriate community of traders native to the city of Assur in modern-day Iraq and document an extensive shipping of tin ingots from unnamed sources east of their hometown. Tin was carried by donkeys through northern Syria and across the Taurus Mountains to Anatolia where it was sold for silver.This paper presents the first set of tin isotope analyses of bronze objects from Kültepe to test the image provided by these ancient archives, finding that all artifacts dated to the main period of Assyrian trade excavated in the residential areas of the site indeed have high tin content and high values of δ124Sn (0.77–1.74‰) relative to the NIST 3161a standard. Such high values currently compare best with ores from Central Asia. The isotopic analysis of artifacts from the Assyrian Trading Colony Period of Kültepe is therefore consistent with the textual evidence.However, Early Bronze Age samples recovered at the site are instead characterized by lower ranges that extend to neutral δ124Sn values (0.02–1.31‰). Likewise, one artifact coming from Mound Level 7 (c. 1830-1700) at the center of the site where public buildings were concentrated, and one object dated to the Hellenistic Period (Mound Level 2), when the site saw a resurgence in political importance, likewise have lower δ124Sn compositions of 0.11 and 0.31‰, respectively. Both samples also have low to moderate tin content.The Early Bronze Age artifacts form a linear array between artifacts from low δ124Sn-low Sn wt% to high δ124Sn-high Sn wt% that suggests a mixing of two compositional groups – not simply the mixing of two isotopically distinct reservoirs of tin, but also distinct in the amount of tin present in the alloy. This would be consistent with the recycling of low tin bronze objects with local tin, together with high tin bronzes containing tin from Central Asia. The two samples from Mound Levels 7 and 2 suggest that although Central Asian tin was predominant in the MBA, Anatolian tin may have continued to be used in a separate bronze production system that remained active at shifting varying of intensity throughout antiquity.

Shape polarization in the tin isotopes near N = 60 from precision g-factor measurements on short-lived 11/2− isomers

The g factors of 11/2− isomers in semimagic 109Sn and 111Sn (isomeric lifetimes τ=2.9(3) ns and τ=14.4(7) ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses LaBr3 detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, g(11/2−;109Sn)=−0.186(8) and g(11/2−;111Sn)=−0.214(4), are significantly lower in magnitude than those of the 11/2− isomers in the heavier isotopes and depart from the value expected for a near pure neutron h11/2 configuration. Broken-symmetry density functional theory calculations applied to the sequence of 11/2− states reproduce the magnitude and location of this deviation. The g(11/2−) values are affected by shape core polarization; the odd 0h11/2 neutron couples to Jπ=2+,4+,6+... configurations in the weakly-deformed effective core, causing a decrease in the g-factor magnitudes.

Particle-Particle Collective Excitations of Sn isotopes

In this paper, energy-level schemes and reduced electric transition strengths of neutron-rich Tin isotopes 102, 110, 116, 120, 122Sn (Z=50) are studied using collective models, that is, particle-particle Tamm-Dancoff Approximation and particle-particle Random Phase Approximation. According to these models, the excited states of closed-core A+2 systems with multipolarity J and isospin T can be described as a linear combination of particle-particle pairs. In our investigation, the low-lying states of the investigated isotopes 102, 110, 116, 120, 122Sn are described by acting two-particle operators on a correlated core 100Sn, 108Sn, 114Sn, 118Sn, and 120Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2} orbits, using the matrix elements of neutron-neutron interaction and modified surface delta interaction. The calculated values are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. Our calculated results are compared to the available experimental data, and these comparisons led to reasonable agreements. Effective charges are also used to account for the core polarization effect.

Thermodynamics of pairing transition in even A tin isotopes

Thermodynamics of pairing transition in even A tin isotopes

Hole-Hole Collective Excitations in 106, 112, 130Sn Isotopes

In this paper, energy-level schemes of neutron rich and reduced electric transition strengths of Tin isotopes 106Sn, 112Sn and 130Sn were studied using collective models, i.e., hole-hole Tamm-Dancoff Approximation (hh TDA) and hole-hole Random Phase Approximation (hh RPA). According to these models, the excited states of closed core A-2 systems with multipolarity J and isospin T can be described as a linear combination of hole-hole (hh) pairs. Therefore, in our approach, the low-lying states of the investigated isotopes 106Sn, 112Sn and 130Sn are obtained by acting two-hole operators on a correlated core 108Sn, 114Sn and 132Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2} orbits, using the matrix elements of neutron-neutron (N-N) interaction and modified surface delta interaction (MSDI). The hh TDA and hh RPA are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. A comparison had been made between our theoretical predictions and the recent available experimental data. Reasonable agreements were obtained from these comparisons.

Tin Anomaly in Coulomb Energies and Analog Resonances of Neutron-Rich Tin Isotopes

Tin Anomaly in Coulomb Energies and Analog Resonances of Neutron-Rich Tin Isotopes

Asymmetry correlation of neutron skin thickness using relativistic density-dependent hadronic formalism

The neutron skin thickness is calculated for spherically symmetric even–even lead and tin isotopes, and [Formula: see text] and [Formula: see text] isotones, with known experimental masses. A relation correlating the neutron skin thickness with the asymmetry parameter is determined, which may be used to constrain the nuclear equation of state.

Offline commissioning of a new gas cell for the MARA Low-Energy Branch

Results of offline commissioning tests for a new dedicated gas cell for the Mass Analysing Recoil Apparatus (MARA) Low-Energy Branch are reported. Evacuation time, ion survival and transport efficiency in helium buffer gas were characterized with a radioactive 223Raα-recoil source. Suppression of the ion signal, originating from non-neutralized species in the gas cell, was explored with 219Rn ions, the daughter recoil of 223Ra, as a function of voltage applied to one of the ion-collector electrodes. Two-step laser resonance ionization of stable tin isotopes produced inside the gas cell from a heated bronze filament was demonstrated, and broadening of the atomic resonances in argon buffer gas was studied. These tests indicate the suitability of the new gas cell for future in-gas laser spectroscopy studies of exotic nuclei at the Accelerator Laboratory of the University of Jyväskylä.

High-resolution laser system for the S[formula omitted]-Low Energy Branch

In this paper we present the first high-resolution laser spectroscopy results obtained at the GISELE laser laboratory of the GANIL-SPIRAL2 facility, in preparation for the first experiments with the S3-Low Energy Branch. Studies of neutron-deficient radioactive isotopes of erbium and tin represent the first physics cases to be studied at S3. The measured isotope-shift and hyperfine structure data are presented for stable isotopes of these elements. The erbium isotopes were studied using the 4f126s23H6→4f12(3H)6s6pJ= 5 atomic transition (415 nm) and the tin isotopes were studied by the 5s25p2(3P0)→5s25p6s(3P1) atomic transition (286.4 nm), and are used as a benchmark of the laser setup. Additionally, the tin isotopes were studied by the 5s25p6s(3P1)→5s25p6p(3P2) atomic transition (811.6 nm), for which new isotope-shift data was obtained and the corresponding field-shift F812 and mass-shift M812 factors are presented.

Dynamical Correlations in the Ground State: Transitions between One-Phonon Nuclear States

The probabilities of the E1 transition between the first {{2}^{ + }} and {{3}^{ - }} excited levels in nuclei with pairing have been calculated within the self-consistent many-body nuclear theory and Green’s function method. Calculations for a long chain of even–even tin isotopes have been performed for the first time. The known Fayans energy density functional has been used to calculate the characteristics of phonons and E1 transitions between excited states. A good description has been achieved for existing experimental data for the reduced probabilities of E1 transitions between the first one-phonon states for the 116–124Sn isotopes but not for the 112Sn and 114Sn isotopes. Possible reasons for this discrepancy have been discussed; the most probable reason is the deformation in the ground or excited states. It has been shown that new dynamical three-quasiparticle correlations in the ground state should be taken into account to explain the experimental data for 116–124Sn.

Neutron 3s1/2 occupation change across the stable tin isotopes investigated using isotopic analysis of proton scattering at 295 MeV

The isotopic systematics of Sn isotopes in the range A=116--124 were investigated by combining the nuclear structure and reaction calculations for the analysis of Sn(p,p) reactions at 295 MeV. The Sn(p,p) reactions were calculated employing relativistic impulse approximation (RIA) with theoretical densities obtained for the Sn isotopes from relativistic Hartree-Bogoliubov (RHB) calculations with the DD-ME2 interaction and nonrelativistic Skyrme Hartree-Fock-Bogoliubov (SHFB) calculations with the SKM* interaction. Calculation using the DD-ME2 density reproduced the experimental data for $^{122}$Sn(p,p) but overestimated the $^{116}$Sn(p,p) and $^{118}$Sn(p,p) cross sections at backward angles. In the isotopic analysis of the cross section ratio $R(\sigma)$ of $^{122}$Sn to $^{116}$Sn, a calculation using the SKM* density reproduced the peak amplitudes of $R(\sigma)$ obtained from the experimental cross sections, whereas a calculation using the DD-ME2 density did not. The ratio $R(\sigma)$ was found to be sensitive to the isotopic change of the neutron $3s_{1/2}$ occupation through the isotopic difference of the surface neutron density around r=4--5 fm. Isotopic analysis indicated that a rapid increase of the $3s_{1/2}$ occupation from $^{116}$Sn to $^{122}$Sn obtained by the DD-ME2 calculation is unlikely. This result derived from the 295 MeV Sn(p,p) cross section data is consistent with the direct measurement of the neutron occupations in Sn isotopes by neutron transfer and pick-up reactions.

β2 corrections to spherical energy-density functional calculations for root-mean-square charge radii

Root-mean-square charge radii are discussed in terms of spherical Energy Density Functional (EDF) models corrected for quadrupole deformations. Comparisons between experiment and theory are made for the absolute radii of all even-even nuclei, for the isotonic shift between cadmium and tin isotopes, the isotopic shifts of the calcium isotopes and the isotonic shift for nuclei with $ N=28 $. We conclude that the data are well described in this approach, except for the sharp rise just after the neutron magic numbers.

An Application of Interacting Boson Model-2 (IBM-2) Configuration Mixing in Tin Nuclei

Using IBM-2 configuration mixing calculations, the normal and intruder 2p-2h bands in even-even tin isotopes are examined. The states of the normal and intruder bands were computed separately and then mixed using a basic band-mixing Hamiltonian. The experimental data for energy levels and electronic transition probability from current and past investigations are compared.

Self-Consistent Calculations of Probabilities for Transitions between $${3}_{1}^{{-}}$$ and $${2}_{1}^{{+}}$$ One-Phonon States in Tin Isotopes

Self-Consistent Calculations of Probabilities for Transitions between $${3}_{1}^{{-}}$$ and $${2}_{1}^{{+}}$$ One-Phonon States in Tin Isotopes

The Salcombe metal cargoes: New light on the provenance and circulation of tin and copper in Later Bronze Age Europe provided by trace elements and isotopes

Since the mid-1970s a Bronze Age assemblage of metal objects has been recovered from the seabed off the south Devon coast at Salcombe, southwest England. The assemblage spans two suspected shipwreck events and comprises nearly 400 pieces of raw materials and finished artefacts, primarily in copper, tin, bronze and gold. Among these are 280 copper and 40 tin ingots, by far the largest discovery of Bronze Age ingots in either metal from northwestern Europe. Research in recent years revealed the microstructural and chemical nature of the ingots and enabled some preliminary conclusions on the metals trade in Europe in the Later Bronze Age. The present study aims to extend this knowledge by determining the tin, copper and lead isotopic compositions of the ingots using HR-MC-ICP-MS. In addition, bronze artefacts (swords, rapiers, palstaves and weights) from the Salcombe site are included in the multi-proxy approach in order to investigate their history and the possible relationships between finished products and ingots. In combination with the available chemical data of previous studies, the current results of the tin metal show that most likely two tin sources in southwest Britain supplied the ore for their production. This also sheds light on Late Bronze Age tin ingots from Israel that share the same geochemical characteristics with one group of the finds from Salcombe. Although the tin in the bronzes is similar to the tin in the ingots, it is not certain that the latter were used to make the bronzes. Correlations of copper and tin isotopes and trace elements of the bronzes point to a mixing or even recycling of copper-tin alloys rather than the alloying of individual components of copper and tin. However, the copper ingots from the assemblage could have been an additional component in the mixing process given their impurity pattern and isotopic composition. At the same time, a close relationship between swords of the Rosnoën type and palstaves from the cargo is disclosed. Lead isotope ratios for their part suggest Sardinian and/or south Spanish copper ores as a source for both the copper ingots and the copper of the bronzes. This would mean long-distance metal trade in the Later Bronze Age in both cases and would provide new insights into the interpretation of the prehistoric networks in Europe.