Neutron Separation Energy Research Articles

Ground state properties and bubble structure of the isotopic chains of Z = 125 and 126 using the relativistic mean-field formalism

The ground state properties of Z = 125 and 126 nuclei are investigated, taking the isotopic series from the proton to neutron drip-lines. This analysis uses the relativistic mean-field approach with NL3 and the Relativistic-Hartree–Bogoliubov model with DD-ME2 parameterization. The bulk properties under examination include the binding energy per nucleon, the neutron separation energies, the differential variation of the separation energy, the quadrupole deformation parameter β 2, and the single-particle energy. We observed the stability at N = 172 and 184 over the isotopic chain for both parameter sets. The quadrupole deformation parameter reveals a shape transition from prolate to spherical and back to prolate with mass number. No signature of a super- and/or hyper-deformed structure is found over the isotopic chain. Furthermore, the analysis is extended to examine the bubble structure, revealing a bubble/semi-bubble structure for a few neutron-rich isotopes.

Intertwined quantum phase transitions in the zirconium and niobium isotopes

Nuclei in the A ≈ 100 region exhibit intricate shape-evolution and configuration crossing signatures. Exploring both even–even and their adjacent odd-mass nuclei gives further insight on the emergence of deformation and shape-phase transitions. We employ the algebraic frameworks of the interacting boson model with configuration mixing and the new interacting boson-fermion model with configuration mixing in order to investigate the even–even zirconium with neutron number 52–70 (40Zr) and odd-mass niobium (41Nb) isotopes with 52–62. We compare between the evolution in energy levels, configuration and symmetry content of the wave functions, two neutron separation energies and E2 transition rates, alongside comparison with the experimental data. The comparisons between the two chains of isotopes denote the occurrence of two types of QPTs, a crossing of normal and intruder configurations (named Type II QPT), and a shape-evolution of the intruder configuration (named Type I QPT). The latter QPT begins from spherical shape to axially deformed rotor in the Zr isotopes and from weak to strong coupling scenario in the Nb isotopes. This occurrence, named intertwined quantum phase transitions (IQPTs), in the even–even Zr chain is thus demonstrated to persists when coupling a proton to the boson core for the odd-mass Nb chain, even as deformation increases.

Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Semi-empirical thermodynamic quantities (TQs) of 78 nuclei ranging from 43Sc to 243Pu have been systematically investigated in the temperature region below 1 MeV using the thermodynamic canonical ensemble. The latter is carried out by taking into account the experimental nuclear level density (NLD) data measured using the Oslo method for the low-excitation region below the neutron binding energy B n combining with the back-shifted Fermi gas NLD model for the excitation energy from B n to about 250 MeV. In particular, the uncertainty of the TQs propagating from the fluctuation of the experimental NLD data has been, for the first time, calculated. The results obtained indicate that the uncertainty of TQs due to the experimental NLD is incomparable with the changes caused by the nuclear structure effects. The free energy of even–even nuclei behaves differently from that of odd-A ones. The total energy in the low-temperature region below T E ≃ 0.4 − 0.6 MeV for medium-mass nuclei and T E ≃ 0.2 − 0.4 MeV for heavy-mass ones slowly varies. When temperature is from T E to 1 MeV, the total energy increases extremely faster than the increase of temperature, exhibiting the constant-temperature behavior. The entropy exhibits an abrupt change in their slope at T S ≃ 0.2 − 0.4 MeV in medium-mass nuclei and T S ≃ 0.5 − 0.6 MeV in heavy-mass ones. The existence of T E and T S has been interpreted due to the breaking of the first Cooper pair. Finally, the heat capacity shows a strongly pronounced S-shape in nuclei belonging to the rare-earth region. The temperatures defined at the center of the S − shaped heat capacities, which are known to closely relate to the critical temperature of the pairing phase transition T C, are quite close to those theoretically predicted, namely T C ≈ 0.5Δ − 0.6Δ with Δ = 12A −1/2 being the empirical pairing gap at zero temperature. The semi-empirical TQs obtained in the present work can be, therefore, a reliable data source to test and/or validate many nuclear thermodynamical models and to examine some nuclear structure properties such as pairing and deformation.

Proton Shell Gaps in N=28 Nuclei from the First Complete Spectroscopy Study with FRIB Decay Station Initiator.

The first complete measurement of the β-decay strength distribution of _{17}^{45}Cl_{28} was performed at the Facility for Rare Isotope Beams (FRIB) with the FRIB Decay Station Initiator during the second FRIB experiment. The measurement involved the detection of neutrons and γ rays in two focal planes of the FRIB Decay Station Initiator in a single experiment for the first time. This enabled an analytical consistency in extracting the β-decay strength distribution over the large range of excitation energies, including neutron unbound states. We observe a rapid increase in the β-decay strength distribution above the neutron separation energy in _{18}^{45}Ar_{27}. This was interpreted to be caused by the transitioning of neutrons into protons excited across the Z=20 shell gap. The SDPF-MU interaction with reduced shell gap best reproduced the data. The measurement demonstrates a new approach that is sensitive to the proton shell gap in neutron rich nuclei according to SDPF-MU calculations.

High quality microscopic nuclear masses of superheavy nuclei

To synthesize new superheavy elements, the accurate prediction of nuclear masses of superheavy nuclei is essential for calculations of reaction Q values, neutron separation energies and α-decay energies, which are important for estimating beam energies, survival probabilities and also for identifications. In this work, we include existing α-decay energies of superheavy nuclei in the fitting procedure of extended Skyrme density functionals as corresponding nuclear masses are not available. Systematic α-decay energies are well reproduced with a standard deviation of 0.24 MeV. The high quality α-decay energies make it feasible for direct identification of new elements and new isotopes. The resulting binding energies in the heaviest region are surprisingly close to the inferences by AME2020. Our work should be useful for guiding experimental synthesis of new elements 119 and 120.

Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes 144,148,150,152,154Sm

A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

Correlation between the shape coexistence and stability in Mo and Ru isotopes

In a rapidly changing shape phase region, the presence of shape coexistence and its possible impact on the decay modes and half-lives, has been explored in astrophysically interesting Mo and Ru isotopes, in an extensive study within the microscopic theoretical framework using Nilsson Strutinsky Method and Relativistic Mean Field Model. The isotopic chains of Mo and Ru exhibit rapid shape phase transitions, triaxial γ softness, shape instability along with many coexisting states mostly with oblate and triaxial shapes. Proton and neutron separation energies have been calculated and compared with the available data. Results obtained from both the formalisms are in good agreement with each other as well as the available experimental data. Our computed β-decay half-lives and separation energy for nuclei exhibiting shape coexistence were examined for the decay mode from second minima state of the parent nuclei to the ground or excited state of the daughter nuclei. The second minima state of the coexisting shapes in Mo and Ru isotopes, were seen to impact the structural properties, β-decay half-lives, separation energy and hence the stability of the nuclei.

Theoretical estimation of synthesizing superheavy nuclei using neutron rich targets

The next double magic nucleus after the double magic nucleus lead (208Pb) proton number Z=82 and neutron number N=126 is predicted to be flerovium 298Fl, Z=114 and N=184, and “Island of Stability” around this nucleus is predicted in the nuclear chart. In the synthesis of new elements, it was assumed that the projectile and target nuclei used in the experiments would be stable nuclei. In particular, it was experimentally impossible to use unstable nuclei as target nuclei. Therefore, it was considered difficult to synthesize nuclei on Island of Stability because of the insufficient number of neutrons when it came to fusion between stable nuclei. To approaching Island of Stability, it is necessary to use unstable nuclei with an excess of neutrons. However, until now there has been no method to achieve this. Recently, a new method of colliding unstable nuclei has been planned. It has also been reported that neutron-rich nuclei in the superheavy mass region have lower neutron binding energy than stable nuclei and lower temperature due to neutron emission more quickly, resulting in a high survival probability even at medium and high excitation energies. The goal of this study is to create and analyze neutron emission and mass distribution of fission fragments in the superheavy mass region using the statistical and the dynamical model. In addition, we present the results of calculations using neutron-rich nuclei.

Status of experimental knowledge on the unbound nucleus 13Be

The structure of the unbound nucleus 13Be is important for understanding the Borromean, two-neutron halo nucleus 14Be. The experimental studies conducted over the last four decades are reviewed in the context of the beryllium chain of isotopes and some significant theoretical studies. The focus of this paper is the comparison of new data from a 12Be(d,p) reaction in inverse kinematics, which was analyzed using Geant4 simulations and a Bayesian fitting procedure, with previous measurements. Two possible scenarios to explain the strength below 1 MeV above the neutron separation energy were proposed in that study: a single p-wave resonance or a mixture of an s-wave virtual state with a weaker p- or d-wave resonance. Comparisons of recent invariant mass and the (d,p) experiments show good agreement between the transfer measurement and the two most recent high-energy nucleon removal measurements.

Investigating the pygmy dipole resonance in 96Mo using the (p,d) reaction

The pygmy dipole resonance (PDR) thus far has been described microscopically as a cluster of 1− states around the neutron separation energy (S n ). This study is an attempt to probe the nature of the PDR, specifically the single-particle or collective character of these states. One-step transfer reactions represents a good probe for this study due to their selectivity in exciting single-particle states. The 97Mo(p,d) 96Mo and 95Mo(d,p)96Mo reactions, were used to populate the nucleus of interest. The experiment was conducted at the INFN-LNS facility in Catania, Italy. The ejectiles were momentum-analysed by the MAGNEX spectrometer and detected by its focal-plane detector. In this paper, preliminary results for the 97Mo(p, d) 96Mo reaction will be presented.

Missed prediction of the neutron halo in 37Mg

Halo phenomena have long been an important frontier in both experimental and theoretical nuclear physics. 37Mg was identified as a halo nucleus in 2014 and remains the heaviest nuclear halo system to date. While the halo phenomenon in 37Mg was not predicted before the discovery, its description has been still challenging afterwards. In this Letter, we report a microscopic and self-consistent description of the neutron halo in 37Mg using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) that was developed in 2010. The experimental neutron separation energies and empirical matter radii of neutron-rich magnesium isotopes as well as the deformed p-wave halo characteristics of 37Mg are well reproduced without any free parameters. In particular, the orbital occupied by the halo neutron in 37Mg, exhibiting p-wave components comparable to those suggested in experiments, remains consistent across various employed density functionals including PC-F1, PC-PK1, NL3*, and PK1. The DRHBc theory investigated only even-even magnesium isotopes in previous works and for that reason missed predicting 37Mg as a halo nucleus before 2014. Although the core and the halo of 37Mg are both prolate, higher-order shape decoupling on the hexadecapole and hexacontatetrapole levels is predicted.

Correlation between the nuclear structure and reaction dynamics of Ar-isotopes as projectile using the relativistic mean-field approach

This theoretical study is devoted to bridging the gap between the nuclear structure and reaction dynamics and unravelling their impact on each other, considering the neutron-rich light mass 30−60Ar isotopes. Using the relativistic mean-field with the NL3⁎ parameter set, several bulk properties such as binding energies, charge radii, quadrupole deformation parameter, two neutron separation energy, and differential two neutron separation energy with the shell closure parameter are probed for the mentioned isotopic chain. For validation, the RMF (NL3⁎) results are compared with those obtained from the finite range droplet model (FRDM), Weizsäcker-Skyrme model with WS3, WS⁎ parameters, and the available experimental data. Most of the participating isotopes are found to be prolate in structure, and neutron shell closures are conspicuously revealed at N=14,20,40 but weakly shown at N=24,28,34. From our analysis, a central depletion in the nucleonic density is identified in 32 Ar and 42−58 Ar, indicating that they are possible candidates for a semi-bubble-like structure. Interestingly, these results are consistent with recent theoretical and experimentally measured data. Furthermore, using the Glauber model, the reaction cross-sections are determined by taking 26−48Ar as projectiles and stable targets such as 12C, 16O, 40Ca, 90Zr, 124,132Sn, 208Pb and 304120. Although there is no experimental evidence for the stability of 304120, it was predicted by Bhuyan and Patra (2012) [115] as a stable nucleus. A relatively higher cross-section value is noticed between 30 Ar and 32 Ar, which infers that 32Ar is the most stable isotope among the considered chain. Moreover, we noticed that the profile of the differential cross-sections and scattering angle are highly influenced by the mass of the target nuclei and the magnitude of the incident energy of the projectile nucleus.

Experimental evidence of large collective enhancement of nuclear level density and its significance in radiative neutron capture

The collective enhancement of nuclear level density and its fade out with excitation in the deformed 171Yb nucleus has been inferred through an exclusive measurement of neutron spectra. The statistical model analysis of neutron spectra demonstrated a large collective enhancement factor of 40±3, a value consistent with recent microscopic model predictions but is an anomalous result compared with the measurements in the nearby deformed nuclei. The complete picture of the energy dependent collective enhancement has been obtained by combining the present results with those obtained with the Oslo method below neutron binding energy. The signature of a large collective enhancement in radiative neutron capture cross section of astrophysical interest is highlighted.

Comparison and estimation of photoneutron dose produce between 10 MV flattened and unflattened beam in Elekta Versa HD™ medical linac.

In a high-energy medical linear accelerator (linac), if the interaction of photon energy is higher than the neutron binding energy of high atomic material, it emits a neutron field through photonuclear (γ, n) reaction. The current study, evaluates the photoneutron dose equivalent (PNDE) produced between the 10 MV flattened and unflattened beams as a function of field sizes in the Elekta Versa HD™ linac. The PNDE produced from Versa linac was recorded along the patient plane using the bubble detector personal neutron dosimeter and from the measured PNDE values, the theoretical PNDE values were simulated for various field sizes using nonlinear least-squares curve-fitting as a function of a polynomial. The percentage of deviation (PoD) and Chi-square (χ2) tests were performed between the measured and simulated PNDE values to study the reliability and validity. The results show that the mean PoD between the measured and simulated PNDE values for respective positions of a field size of FF beam was found to be -1.99% for 0.3×0.3, -4.39% for 5×5, -3.868% for 10×10, 0.590% for 15×15, 9.18% for 20×20, -4.133% for 25×25, and 0.467% for 30×30 cm2. Similarly, the mean PoD between the measured and simulated PNDE values for flattening filter-free (FFF) beam was found to be 1.36% for 0.3×0.3, -1.39% for 5×5, -5.38% for 10×10, 4.41% for 15×15, 3.84% for 20×20, 5.69% for 25×25, and -1.75% for 30×30 cm2. The maximum deviation between the measured and simulated PNDE values lies within the range ± 5%. From the study, it is observed that the FFF beam produces lesser neutron contamination than the FF beam.

Low-lying structure of 15C: Information on the N=8 shell gap

The low-lying structure of 15C has been investigated via the neutron-removal d(16C, t) reaction. The experiment was performed at GANIL using a secondary 16C beam produced by fragmentation in the LISE spectrometer at 17.2 MeV/nucleon with an intensity of 5 × 104 pps and 100% purity. The angle and energy of the light ejectile were detected by three MUST2 telescopes. The missing mass technique was used to reconstruct the excitation energy of 15C. In this spectrum, two bound states were observed (gs and the first excited state) and two unbound resonant states above the neutron separation threshold (S n = 1.218 MeV). From the differential cross sections, information on the angular momentum of the transferred nucleon and spectroscopic factors were deduced. The excitation energies and the deduced spectroscopic factors of the negative parity states placed above the neutron separation energy are an important measurement of the 2p-1h configurations in 15C. Our results show good agreement with shell-model calculations with the YSOX interaction and show a sensitivity to the N=8 shell gap.

Nuclear structure data obtained by the (nth,2γ) reaction

The determination of nuclear structure parameters such as gamma transitions, level scheme, nuclear level density and radiative strength functions is one of the most important tasks in low-energy nuclear physics. The two-step gamma cascades method based on detection of gamma coincidences following neutron capture, ie. the (n,2γ) reaction has been proven to give spectroscopic data and data concerning level density and radiative strength function. This method allows for the study of the dynamics of interaction and inter-transition between Fermi-and Bose-states of the nucleus near the neutron binding energy. There is an essential difference between these intranuclear processes from those in classical and high-temperature superfluidity, which is determined by a shape of the investigated nucleus, the nucleon parity in it, existence of nucleons of different types (protons and neutrons) etc. Two-step gamma cascades technique has so far been successfully applied for 45 nuclei in the mass region 28<A<200. Brief description of the method will be included here with examples from the recent research

New Capabilities of the RPI γ-Multiplicity Detector to Measure γ-Production

Accurate modeling of γ-production in neutron capture reactions is critical for many applications including on-proliferation, safeguards and modeling nuclear reactors. To improve this work, the Rensselaer Polytechnic Institute (RPI) 16-segment γ-multiplicity NaI(Tl) detector at the Gaerttner Linear Accelerator (LINAC) Center has been upgraded by implementing a digital data acquisition system. The new digitized system records the γ-energy deposition distribution in each individual detector, and γ-multiplicity values as a function of neutron time-of-flight (TOF). With the new capabilities, high precision capture (and fission) yield measurements can be made, and the accuracy of simulation tools used to predict capture γ-cascades can be tested. To validate the updated system, an experiment was performed using a natural Ta sample to measure 181Ta and 180mTa resonance capture yield by detecting prompt γ-rays emitted from neutron capture interactions as a function of both neutron energy and measured γ-multiplicity of each capture event. The results confirm earlier measurements and agree with theoretical yield in the low energy resonance region from 1 to 20 eV. A 238U(n, γ) measurement was also performed to generate γ-spectra. For capture γ-cascades where the total γ-energy deposition is close to the neutron binding energy, γ-spectra were measured for individual resonance energies and observed γ-multiplicities. The results are comparable in shape to a recent measurement done using the Detector for Advanced Neutron Capture Experiments (DANCE) array at Los Alamos Neutron Science Center (LANSCE); however, differences need to be compared to Monte-Carlo n-particle simulations.

Microscopic study of shape variation across even–even mass chain of cadmium isotopes

The ground state shapes and properties of even–even [Formula: see text]Cd isotopes have been studied in the framework of relativistic Hartree–Bogoliubov model with two effective interactions that are density-dependent meson exchange and point coupling. The theoretical results on the binding energies, charge radii and two neutron separation energies are presented in this paper in comparison to experimental data and a reasonable agreement is found between the two. Both the interactions predict spherical to axially prolate, prolate to triaxial, triaxial to prolate and prolate to spherical transitions in cadmium isotopic mass chain. In addition, the present calculations confirm the existence of shape coexistence observed in [Formula: see text]Cd. The comparison of calculated ground state properties with the results based on PC-PK1 functional shows that PC-PK1 employed in the deformed relativistic Hartree–Bogoliubov theory in continuum has the lowest root mean square deviation for average binding energies and two neutron separation energies.

Measurement of fusion-evaporation cross sections for reactions of Ca44 with Gd154,156,157,160 targets

Background: Previously reported fusion-evaporation cross sections of residues in $^{45}\mathrm{Sc}$-induced reactions with lanthanide targets are much smaller than $^{48}\mathrm{Ca}$-induced reactions on the same targets. $^{44}\mathrm{Ca}$ is one proton removed from $^{45}\mathrm{Sc}$ and could be used to produce nuclei with a relative neutron content between those produced in the $^{45}\text{Sc-}$ and $^{48}\mathrm{Ca}$-induced reactions.Purpose: Several experiments worldwide have attempted to discover elements beyond the currently heaviest known element, oganesson ($Z=118$). Due to a lack of appropriate targets, these efforts focused on projectiles other than $^{48}\mathrm{Ca}$, which has been widely used for a number of successful element discovery experiments. The present study continues our previous work to understand the influence of various projectiles on the compound nucleus in fusion-evaporation reactions, and addresses the influence of target neutron number on fusion-evaporation cross sections.Methods: In experiments performed at the Cyclotron Institute at Texas A University, a beam of $^{44}\mathrm{Ca}^{6+}$ with an energy of $\ensuremath{\approx}5\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/u$ was delivered by the K500 superconducting cyclotron to the Momentum Achromat Recoil Spectrometer (MARS). The $^{44}\mathrm{Ca}$ projectiles bombarded various isotopically enriched Gd targets in the MARS target chamber to create evaporation residues, which were spatially separated from unreacted projectiles by MARS and identified via their characteristic $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{decay}$ energies. Excitation functions for the reactions of $^{44}\mathrm{Ca}$ with $^{154,156,157,160}\mathrm{Gd}$ were measured at several projectile energies each.Results: The maximum $4n$ cross sections in the $^{44}\mathrm{Ca}{+}^{154,156,157,160}\mathrm{Gd}$ reactions were $0.038\ifmmode\pm\else\textpm\fi{}0.008, 0.83\ifmmode\pm\else\textpm\fi{}0.08, 3.8\ifmmode\pm\else\textpm\fi{}0.2$, and $3.0\ifmmode\pm\else\textpm\fi{}0.5$ mb, respectively. Production cross sections for the more neutron-rich targets were surprisingly constant even given the substantial changes in the difference in neutron binding energy and fission barrier of the compound nuclei.Conclusions: Collective enhancements to level density caused a reduction in compound nucleus survivability for all targets. While this effect was required to obtain good agreement between theoretical calculations and experimental data, it was not sufficient to explain the cross sections for the reaction with the most neutron-deficient target studied $(^{154}\mathrm{Gd})$. Instead, it appears that the difference in the fission barrier and neutron binding energy is the dominant factor affecting the survival of the compound nucleus in this case.

Quenching of Single-Particle Strength in A=15 Nuclei.

Absolute cross sections for the addition of s- and d-wave neutrons to ^{14}C and ^{14}N have been determined simultaneously via the (d,p) reaction at 10 MeV/u. The difference between the neutron and proton separation energies, ΔS, is around -20 MeV for the ^{14}C+n system and +8 MeV for ^{14}N+n. The population of the 1s_{1/2} and 0d_{5/2} orbitals for both systems is reduced by a factor of approximately 0.5 compared with the independent single-particle model, or about 0.6 when compared with the shell model. This finding strongly contrasts with results deduced from intermediate-energy knockout reactions between similar nuclei on targets of ^{9}Be and ^{12}C. The simultaneous technique used removes many systematic uncertainties.