Sn Nuclei Research Articles

Full Self-Consistent Study of Isobaric Analog Resonances

Fully self-consistent framework for isobaric-analog resonances is presented. The chains of parent neutron-rich Ca, Ni, Sn nuclei around the neutron shells at $$N=20$$ , $$28$$ , $$34$$ , $$50$$ , $$82$$ , as well as the nuclei on the neutron-deficient side of these chains are treated in the Density Functional plus Continuum Quasi particle Random Phase Approximation (DF $$+$$ CQRPA). The recently established new Fayans functional DF3-f is applied for calculations in long isotopic chains including non-magic nuclei with pairing in both neutron and proton sectors. A comparison with the relativistic QRPA and SAMi $$+$$ RPA shows a robust performance and flexibility of the DF $$+$$ CQRPA. Constraining the strength of exchange Coulomb contribution from the binding energy splitting of the doublets and triplets of the mirror nuclei allows for better description of the IAR energies.

Temperature Dependence of the Symmetry Energy Components for Finite Nuclei

We investigate the temperature dependence of the volume and surface components of the nuclear symmetry energy (NSE) and their ratio in the framework of the local density approximation. The results of these quantities for finite nuclei are obtained within the coherent density fluctuation model (CDFM). The CDFM weight function is obtained using the temperature-dependent proton and neutron densities calculated through the HFBTHO code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. We present and discuss the values of the volume and surface contributions to the NSE and their ratio obtained for the Ni, Sn, and Pb isotopic chains around double-magic 78Ni, 132Sn, and 208Pb nuclei. The results for the T-dependence of the considered quantities are compared with estimations made previously for zero temperature showing the behavior of the NSE components and their ratio, as well as with the available experimental data. The sensitivity of the results on various forms of the density dependence of the symmetry energy is studied. We confirm the existence of “kinks” of these quantities as functions of the mass number at T = 0 MeV for the double closed-shell nuclei 78Ni and 132Sn and the lack of “kinks” for the Pb isotopes, as well as the disappearance of these kinks as the temperature increases.

Shell model calculations in the A ~ 100 mass region

The properties of nuclei with 39≤Ζ≤47 and Ν=51-52 are investigated in large scale shell-model calculations. The doubly closed nucleus 100Sn is selected as the reference state and the nuclei under examination are described in terms of proton holes and one up two neutrons outside the inert core. The proton holes are distributed in a model space consisting of the orbitals g9/2, p1/2, p3/2 while f5/2 is sometimes also considerd. Similary the model space for the neutron particles in­ cludes the orbitals g7/2, d5/2, d3/2, s1/2 and in certain cases h11/2. The effective two-body interaction and the matrix elements of the effective operators were deter­ mined by introducing second-order corrections to the Sussex matrix elements. The single proton holes as well as the single-neutron energies were treated as parameters which were determined by least-squares fit to the observed levels of 39≤Ζ≤47, Ν=50 and Ν=51 respectively. The results of the calculation were found to be in satisfactory agreement with experimental data and this enable us to make predictions about the properties of some exotic nuclei in the vicinity of 100Sn.

Shell model calculations in the A=90-98 mass region. A study of the N=51. nuclei

The properties of nuclei with 39 < Ζ < 47 and N=51 are investigated in large scale shell-model calculations. The doubly closed nucleus 100Sn is selected as the reference state and the nuclei under examination are described in terms of proton holes and a single neutron outside the inert core. The proton holes are distributed in a model space consisting of the orbitals g9/2, p1/2, p3/2 while f5/2 is sometimes also considerd. Similary the model space for the single neutron includes the orbitals g7/2, d5/2, d3/2, s1/2 and in certain cases h11/2. The effective two-body interaction and the matrix elements of the effective operators were determined by introducing second-order correctios to the Sussex matrix elements. The single proton holes as well as the single-neutron energies were treated as parameters which were determined by least-squares fit to the observed levels of 39 < Ζ < 47, N=50 and Ν=51 respectively. The results of the calculation were found to be in satisfactory agreement with experimental data and this enable us to make predictions about the properties of some exotic nuclei in the vicinity of 100Sn.

Isomer studies in the vicinity of the doubly-magic nucleus 100Sn: Observation of a new low-lying isomeric state in 97Ag

Long-lived isomeric states in 97Ag and 101−109In were investigated with the FRS Ion Catcher at GSI. In the isotope 97Ag, a long-lived (1/2−) isomeric state was discovered, and its excitation energy was determined to be 618(38) keV. This is simultaneously the first discovery of a nuclear isomeric state by multiple-reflection time-of-flight mass spectrometry. The measured excitation energies were compared to large-scale shell-model calculations, which indicated the importance of core excitation around 100Sn. Furthermore, advanced mean-field calculations for the 97Ag nucleus and relevant neighboring nuclei were performed, which have contributed to a better understanding of the repetitive appearance of certain isomeric structures in neighboring nuclei, and which have supported the discovery of the isomeric state in 97Ag in a global shell-evolution scheme.

Large-scale shell-model calculations near mass region 100-130

In this work, we have presented a microscopic shell-model description of the structure and collective behavior of intermediate-mass nuclei around doubly magic 100 Sn and 132 Sn nuclei. The Sn-isotopes lie between the two doubly magic nuclei and cover a range from exotic proton-rich N=Z nuclei to exotic neutron-rich nuclei with N/Z > 1.6. The results obtained using BIGSTICK code for the low-level excitation states and transition probabilities for the studied Sn and Ba isotopic chains have been discussed in the radiance of available experimental data. We have used 100 Sn as a core for all the studied isotopes with the same valence space (i.e. 1d 5/2 , 2s 1/2 , 1d 3/2 , 0g 7/2 , 0h 11/2 or ‘sdgh’) for both protons (Z) and neutrons (N) between 50 and 82. These calculations are performed by means of globally optimized monopole effective interaction for the sdgh-shell.

The Giant Pairing Vibration in heavy nuclei

The Giant Pairing Vibration, a two-nucleon collective mode originating from the second shell above the Fermi surface, has long been predicted and expected to be strongly populated in two-nucleon transfer reactions with cross sections similar to those of the low-lying Pairing Vibration. Recent experiments have provided evidence for this mode in 14, 15C but, despite sensitive studies, it has not been definitively identified in Sn or Pb nuclei where pairing correlations are known to play a crucial role near their ground states. In this paper we review the basic theoretical concepts of this “elusive” state and the status of experimental searches in heavy nuclei. We discuss the hindrance effects due to Q-value mismatch and the use of weakly-bound projectiles as a way to overcome the limitations of the $ (\mathrm{p},\mathrm{t})$ and $ (\mathrm{t},\mathrm{p})$ reactions. We also discuss the role of the continuum and conclude with some possible future developments.

Temperature dependence of nuclear spin-isospin response and beta decay in hot astrophysical environments

A microscopic approach to the proton-neutron nuclear response is formulated in the finite-temperature relativistic nuclear field theory framework. The approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and advances the relativistic field theory for spin-isospin response beyond the finite-temperature random phase approximation. The dynamical contribution to the in-medium proton-neutron interaction amplitude is described in a parameter-free way by the coupling between the single nucleons and strongly-correlated particle-hole excitations (phonons) within the newly developed finite-temperature formalism. In this framework we investigate temperature dependence of the Gamow-Teller and spin dipole resonances in the closed-shell nuclei 48Ca, 78Ni, and 132Sn. Broader impacts of their temperature dependence are illustrated for the associated beta decay rates and lifetimes of 78Ni and 132Sn in hot astrophysical environments. We found a remarkable sensitivity of the beta decay rates to the enhanced low-energy spin-isospin strength at finite temperature, in particular, to the contribution of the first-forbidden transitions.

A study of charge radii and neutron skin thickness near nuclear drip lines

We studied the charge radius, rms radius and neutron skin thickness Δrnp in even-even isotopes of Si, S, Ar and Ca and isotones of N = 20, 28, 50 and 82. The Δrnp in doubly-magic 48Ca, 68Ni, 120,132Sn and 208Pb nuclei has also been calculated. Theoretical calculations are done with the Hartree-Fock-Bogoliubov theory with the effective Skyrme interactions. Calculated theoretical estimates are in good agreement with the recently available experimental data. The charge radii for Si, S, Ar and Ca isotopes is observed to be minimum at neutron number N = 14. The theoretically computed results with UNEDF0 model parameterization of functional are reasonably reproducing the experimental data for Δrnp in 48Ca, 68Ni and 120,132Sn. The energy density functional of UNEDF1 model provides much improved result of Δrnp for 208Pb.

Determination of the density region of the symmetry energy probed by the ratio

The nuclear symmetry energy around or below saturation density has been extensively studied and roughly pinned down, while its behavior at suprasaturation densities is rather uncertain. Related experimental studies are being carried out or planned at facilities that offer radioactive beams worldwide. Towards the physical goal of probing the nuclear symmetry energy at high densities, π measurements in the medium nuclei 132Sn + 124Sn collisions at 300 or 200 MeV/nucleon incident beam energies are ongoing at the Radioactive Isotope Beam Facility at RIKEN in Japan. However, our studies show that the observable π−/π+ ratio in the 132Sn + 124Sn reactions at 300 or 200 MeV/nucleon incident beam energies mainly probes the symmetry energy around the saturation density. Only the π−/π+ ratio in the heavy reaction system and at relatively high incident beam energies may mainly probe the symmetry energy at suprasaturation densities.

Improved Value for the Gamow-Teller Strength of the ^{100}Sn Beta Decay.

A record number of ^{100}Sn nuclei was detected and new isotopic species toward the proton dripline were discovered at the RIKEN Nishina Center. Decay spectroscopy was performed with the high-efficiency detector arrays WAS3ABi and EURICA. Both the half-life and the β-decay end point energy of ^{100}Sn were measured more precisely than the literature values. The value and the uncertainty of the resulting strength for the pure 0^{+}→1^{+} Gamow-Teller decay was improved to B_{GT}=4.4_{-0.7}^{+0.9}. A discrimination between different model calculations was possible for the first time, and the level scheme of ^{100}In is investigated further.

Scission point model for the mass distribution of ternary fission

A modified scission point model is adopted to study the mass distribution of thermal neutron induced binary and ternary fission of 235U. The scission configuration and the most favourable fragment deformation is identified through an energy balance criterion where the macroscopic part due to liquid drop and the microscopic part due to shell correction together with the deformation dependent interaction potential are used. The available energy for each channel together with fragment deformation is used to evaluate nuclear level densities in the Fermi gas model. Since the model is found to give the expected double humped mass distribution for binary fission of 236U, this is then applied for the ternary fission of the same nuclei with fixed third fragment. Two different third fragments with two cases of collinear arrangement were studied with the model. The obtained ternary mass distribution was then compared with the calculated binary mass distribution. In all the cases, the influence of shell effects is found to be prominent with one of the fragments associated with the Sn nucleus. The closed shell nuclei possess maximum yield in both binary and ternary mass distribution.

New isomers in 125Pd79 and 127Pd81: Competing proton and neutron excitations in neutron-rich palladium nuclides towards the N = 82 shell closure

The neutron-rich isotopes of palladium have attracted considerable interest in terms of the evolution of the N=82 neutron shell closure and its influence on the r-process nucleosynthesis. In this Letter, we present the first spectroscopic information on the excited states in 125Pd79 and 127Pd81 studied using the EURICA γ-ray spectrometer, following production via in-flight fission of a high-intensity 238U beam at the RIBF facility. New isomeric states with half-lives of 144(4) ns and 39(6) μs have been assigned spins and parities of (23/2+) and (19/2+) in 125Pd and 127Pd, respectively. The observed level properties are compared to a shell-model calculation, suggesting the competition between proton excitations and neutron excitations in the proton-hole and neutron-hole systems in the vicinity of the doubly magic nucleus 132Sn.

Nuclear structure in the neutron-deficient Sn nuclei TKEL effects on lifetime measurements

The presence of seniority-like isomers along the Z = 50 isotopic chain have been an experimental limitation to the investigation of the electromagnetic properties of the low-lying states in the light Sn nuclei. Combining a multi-nucleon transfer reaction with the Recoil-Distance Doppler-Shift technique, the lifetimes of the 21+ and 41+ excited states have been directly measured in the neutron-deficient 106, 108Sn isotopes for the very first time. The emitted γ rays were detected by the AGATA array, while the reactionproducts were uniquely identified by the VAMOS++ magnetic spectrometer. The control of the direct feeding of the statesby gating on the Total Kinetic Energy Loss, together with the unique capabilities of the two spectrometers, was crucial for the measurementin 108Sn.

Impact of pear-shaped fission fragments on mass-asymmetric fission in actinides.

Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass splits1. Without quantum shell effects, which can give extra binding energy to their mass-asymmetric shapes, these nuclei would fission symmetrically. The strongest shell effects appear in spherical nuclei, such as the spherical 'doubly magic' (that is, both its atomic and neutron numbers are 'magic' numbers) nucleus 132Sn, which contains 50 protons and 82 neutrons. However, a systematic study of fission2 has shown that heavy fission fragments have atomic numbers distributed around Z=52 to Z=56, indicating that the strong shell effects in 132Sn are not the only factor affecting actinide fission. Reconciling the strong spherical shell effects at Z=50 with the different Z values of fission fragments observed in nature has been a longstanding puzzle3. Here we show that the final mass asymmetry of the fragments is also determined by the extra stability provided by octupole (pear-shaped) deformations, which have been recently confirmed experimentally around 144Ba (Z=56)4,5, one of very few nuclei with shell-stabilized octupole deformation6. Using a quantum many-body model of superfluid fission dynamics7, we find that heavy fission fragments are produced predominantly with 52 to 56 protons, which is associated with substantial octupole deformation acquired on the way to fission. These octupole shapes, which favour asymmetric fission, are induced by deformed shells at Z=52 and Z=56. By contrast, spherical magic nuclei are very resistant to octupole deformation, which hinders their production as fission fragments. These findings may explain surprising observations of asymmetric fission in nuclei lighter than lead8.

Millisecond 23/2+ isomers in the N=79 isotones Xe133 and Ba135

Detailed information on isomeric states in A ≈ 135 nuclei is exploited to benchmark shell-model calculations in the region northwest of doubly-magic nucleus 132Sn. The N = 79 isotones 133Xe and 135Ba are studied after multinucleon transfer (MNT) in the 136Xe + 208Pb reaction employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy and in a pulsed-beam experiment at the FN tandem accelerator of the University of Cologne, Germany utilizing a 9Be+130Te fusion-evaporation reaction at a beam energy of 40 MeV. Isomeric states are identified via delayed γ-ray spectroscopy. Hitherto tentative excitation energy, spin, and parity assignments of the 2107-keV Jπ = 23/2+ isomer in 133Xe are confirmed and a half-life of T1/2 = 8.64(13) ms is measured. The 2388-keV state in 135Ba is identified as a Jπ = 23/2+ isomer with a half-life of 1.06(4) ms. The new results show a smooth onset of isomeric Jπ = 23/2+ states along the N = 79 isotones and close a gap in the high-spin systematics towards the recently investigated Jπ = 23/2+ isomer in 139Nd. The resulting systematics of M2 reduced transition probabilities is discussed within the framework of the nuclear shell model. Latest large-scale shell-model calculations employing the SN100PN, GCN50:82, SN100-KTH, and a realistic effective interaction reproduce the experimental findings generally well and give insight into the structure of the isomers.

Athermal recrystallization behavior of (Sn) solid-solution at an intermetallic-free Cu/Sn interface induced by room temperature electromigration

The present study, for the first time, revealed the athermal recrystallization behavior at a heterogeneous metallic interface using room temperature electromigration. The athermal recrystallization occurred within the meta-stable amorphous Cu-Sn interphase, which was formed during the early stage electromigration, for stress relaxation after further electromigration. The nano-scale polycrystalline (Sn) interphase was favorably recrystallized at the intermetallic-free Cu/Sn interface where the current crowding effect occurred. Athermal electromigration force facilitated the nucleation of Sn nuclei through the kinetic energy provided by the electron momentum transfer. The formation of the recrystallized (Sn) interphase is believed to be an intermediate material interaction product prior to further intermetallic nucleation under room temperature electromigration.

Decay modes of highly excited nuclei

The deexcitation of single excited $$^{112}$$ Sn nuclei at T = 1–30 MeV is simulated using the isospin-dependent quantum molecular dynamics (IQMD) model and GEMINI model. The fragmentation mechanism, critical behavior, and kinematic characteristics are investigated within these two models. The results show that the IQMD model can be applied to the analysis of fragmentation processes, critical points, and slope temperature extraction. The results of IQMD are generally consistent with experimental $$\langle M_{\text {IMF}}\rangle - Z_{\text {bound}}$$ data. However, GEMINI can reproduce the experimental data better than IQMD for isotopic distributions.

Spectroscopy of Pionic Atoms in ^{122}Sn(d,^{3}He) Reaction and Angular Dependence of the Formation Cross Sections.

We observed the atomic 1s and 2p states of π^{-} bound to ^{121}Sn nuclei as distinct peak structures in the missing mass spectra of the ^{122}Sn(d,^{3}He) nuclear reaction. A very intense deuteron beam and a spectrometer with a large angular acceptance let us achieve a potential of discovery, which includes the capability of determining the angle-dependent cross sections with high statistics. The 2p state in a Sn nucleus was observed for the first time. The binding energies and widths of the pionic states are determined and found to be consistent with previous experimental results of other Sn isotopes. The spectrum is measured at finite reaction angles for the first time. The formation cross sections at the reaction angles between 0° and 2° are determined. The observed reaction-angle dependence of each state is reproduced by theoretical calculations. However, the quantitative comparison with our high-precision data reveals a significant discrepancy between the measured and calculated formation cross sections of the pionic 1s state.

Interplay of quasiparticle-vibration coupling and pairing correlations on β-decay half-lives

The nuclear β-decay half-lives of Ni and Sn isotopes, around the closed shell nuclei 78Ni and 132Sn, are investigated by computing the distribution of the Gamow–Teller strength using the Quasiparticle Random Phase Approximation (QRPA) with quasiparticle-vibration coupling (QPVC), based on ground-state properties obtained by Hartree–Fock–Bogoliubov (HFB) calculations. We employ the effective interaction SkM⁎ and a zero-range effective pairing force. The half-lives are strongly reduced by including the QPVC. We study in detail the effects of isovector (IV) and isoscalar (IS) pairing. Increasing the IV strength tends to increase the lifetime for nuclei in the proximity of, but lighter than, the closed-shell ones in QRPA calculations, while the effect is significantly reduced by taking into account the QPVC. On the contrary, the IS pairing mainly plays a role for nuclei after the shell closure. Increasing its strength decreases the half-lives, and the effect at QRPA and QRPA+QPVC level is comparable. The effect of IS pairing is particularly pronounced in the case of the Sn isotopes, where it turns out to be instrumental to obtain good agreement with experimental data.