Rare-earth Region Research Articles

Revisiting the symmetric reactions for synthesis of super-heavy nuclei of [formula omitted

Extensive efforts have been made experimentally to reach nuclei in the super-heavy mass region of Z=110 and above with suitable choices of projectile and target nuclei. The cross sections for production of these nuclei are seen to be in the range of a few picobarn or less, and pose great experimental challenges. Theoretically, there have been extensive calculations for highly asymmetric (hot-fusion) and moderately asymmetric (cold-fusion) collisions and only a few theoretical studies are available for near-symmetric collisions to estimate the cross sections for production of super-heavy nuclei. In the present article, we revisit the symmetric heavy ion reactions with suitable combinations of projectile and target nuclei in the rare-earth region, that will lead to super-heavy nuclei of Z⩾120 with measurable fusion cross sections.

Semi-microscopic description of the proton-and neutron-induced backbending phenomena in some deformed even-even rare earth nuclei

A semi-microscopic model to study the double backbending phenomenon in some deformed even-even nuclei from the rare earth region is proposed. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states with a specific single-particle factor, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. Due to the specific construction, the wave function acquires a complex structure which allows a quantitative description of the yrast states in the region of the two backbendings.

Coupled channels optical model potential for rare earth nuclei

Inspired by the recent work by Dietrich et al., substantiating validity of the adiabatic assumption in coupled-channel calculations, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on statically deformed nuclei. The generalization consists in adding the coupling of the ground state rotational band, deforming the potential by introducing appropriate quadrupole and hexadecupole deformation and correcting the OMP radius to preserve volume integral of the spherical OMP. We choose isotopes of three rare-earth elements (W, Ho, Gd), which are known to be nearly perfect rotors, to perform a consistent test of our conjecture on integrated cross sections as well as on angular distributions for elastic and inelastic neutron scattering. When doing this we employ the well-established Koning-Delaroche global spherical potential and experimentally determined deformations without any adjustments. We observe a dramatically improved agreement with experimental data compared to spherical optical model calculations. The effect of changing the OMP radius to preserve volume integral is moderate but visibly improves agreement at lower incident energies. We find that seven collective states need to be considered for the coupled-channel calculations to converge. Our results for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkable agreement with experimental data. This result confirms that the adiabatic assumption holds and can extend applicability of the global spherical OMP to rotational nuclei in the rare-earth region, essentially without any free parameter. Thus, quite reliable coupled-channel calculations can be performed on such nuclei even when the experimental data, and consequently a specific coupled-channel potential, are not available.

Inelastic Neutron Scattering on160Gd

The nature of low-lying excitations, Kπ=0+ bands in deformed nuclei remain enigmatic in the field, especially in relationship to quadrupole vibrations. One method of characterizing these states beyond excitation energies is through measurements of absolute transition probabilities. In the rare earth region of deformation, there are five stable Gd isotopes, 154Gd, 156Gd, and 158Gd have been studied to obtain B(E2) values, a fourth, 160Gd is the focus of this work. We have examined 160Gd with the (n, n′γ) reaction and neutron energies up to 3.0 MeV to confirm known 0+ states.

Spectroscopy of excited states in234U and search for a two-phonon state in234U

Excited states of the isotope ${}^{234}$U were studied employing the one-neutron transfer reaction ${}^{235}\mathrm{U}{(d,t)}^{234}$U at a beam energy of 11 MeV. The reaction channel was selected by an identification of the outgoing tritons in a $\ensuremath{\Delta}E$-$E$ measurement. In coincidence with the tritons, $\ensuremath{\gamma}$ rays were also detected with the highly efficient MINIBALL spectrometer. Based on the analysis of $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence data, the level scheme of ${}^{234}$U was extended. The 4${}^{+}$ state at an energy of 1886.7 keV provides evidence for a possible two-phonon $\ensuremath{\gamma}\ensuremath{\gamma}$ excitation, which is based on three $\ensuremath{\gamma}$ transitions from this state to the $\ensuremath{\gamma}$ vibrational band. However, this state is populated with a high cross section via the one-neutron transfer reaction, which is not expected for a highly collective excitation. The situation is compared to other known cases from the rare-earth region and to the neighboring isotone ${}^{232}$Th, which so far is the only known case for a two-phonon excitation in the actinide region.

Semi-microscopic description of the double backbending in some deformed even–even rare earth nuclei

A semi-microscopic model to study the neutron- and proton-induced backbending phenomena in some deformed even–even nuclei from the rare earth region is proposed. The space of particle–core states is defined by the angular momentum projection of a quadrupole deformed product state. The backbending phenomena are described by mixing four rotational bands, defined by a set of angular momentum projected states, and a model Hamiltonian describing a set of paired particles moving in a deformed mean field and interacting with a phenomenological deformed core. The ground band corresponds to the configuration where all particles are paired, while the other rotational bands are built on one neutron or/and one proton broken pair. Four rare earth even–even nuclei which present the second anomaly in the observed moments of inertia are successfully treated within the proposed model.

Empirical rule for the pair break mechanism in three-quasiparticle rotational bands

An empirical rule on the basis of odd-even mass difference is suggested for the breaking of a proton pair or a neutron pair in odd-A nuclei to form a lower lying 3-quasiparticle state. If \Delta_p is smaller than \Delta_n, the proton pair breaks; on the other hand, if \Delta_n is smaller than \Delta_p, the neutron pair breaks down and forms a lower lying 3-quasiparticle state in an odd-A nuclide. This rule appears not only purely based on the proton paring/neutron pairing energy balancing condition but also on particular excitation energy, which is \ge 1 MeV in the case of the rare-earth region. The extension of this rule to the configuration dependent pairing energies available in the literature is discussed as well as its applications for deciding on the breaking of proton/neutron pairs at higher excitation energies.

Nuclear deformations in the region of the A=160 r-process abundance peak

In the abundance spectrum of r-process nuclei the most prominent features are the peaks that form when the r-process flow passes through the closed neutron shells. However, there are also other features in the abundance spectrum that cannot be explained by shell effects; for example, the peak in the region of the rare-earth nuclei around mass A=160. It has been argued that this peak is related to the deformation maximum of the neutron-rich isotopes. In recent years, both experimental and theoretical work has been carried out to study the deformation of neutron-rich rare-earth nuclei and to search for the point of maximum deformation. This work has focused on the nuclei around 170Dy with the aim of understanding the evolution of collectivity in the neutron shell with 82<N<126. These investigations will be discussed in terms of the Harris parameters of the variable moment of inertia model. Finally, we will discuss the possibility of reaching further into the neutron-rich rare-earth region in the future at the new experimental facilities using radioactive beams.

The isomeric structure of 132Pr

The isomeric structure of the neutron deficient nucleus 132Pr, located in the rare-earth region of the nuclear chart, has been studied with the 98Mo(40Ar,5pn)132Pr reaction at beam energies of 150, 158 and 165 MeV. The experiment was performed at the University of Jyväskylä, Finland where the 40Ar beam was accelerated onto the target by the K130 cyclotron. The JUROGAM II HPGe detector array was employed in conjunction with the RITU gas-filled recoil separator. The focal-plane chamber housed a multi wire proportional counter and a position-sensitive silicon strip detector used for the implantation and identification of recoiling nuclei. The recoil-isomer tagging technique was used to correlate the delayed decays, measured in the Planar and Clover detectors of the GREAT spectrometer, with the known prompt transitions in 132Pr. Two new delayed transitions have been observed at energies of 102 and 118 keV. The corresponding X ray peaks are consistent with Pr Kα and Kβ X rays with energies of 35.63 and 40.91 keV, respectively. The half-life of the newly established isomeric state, from which the 102 and 118-keV transitions proceed, has been measured to be 2.5(3) μs.

Influence of neutron capture rates in the rare earth region on ther-process abundance pattern

We study the sensitivity of the r-process abundance pattern to neutron capture rates along the rare earth region (A~150 to A~180). We introduce the concepts of large nuclear flow and flow saturation which determine the neutron capture rates that are influential in setting the rare earth abundances. We illustrate the value of the two concepts by considering high entropy conditions favorable for rare earth peak production and identifying important neutron capture rates among the rare earth isotopes. We also show how these rates influence nuclear flow and specific sections of the abundance pattern.

THE RARE EARTH PEAK: AN OVERLOOKEDr-PROCESS DIAGNOSTIC

The astrophysical site or sites responsible for the r-process of nucleosynthesis still remains an enigma. Since the rare earth region is formed in the latter stages of the r-process it provides a unique probe of the astrophysical conditions during which the r-process takes place. We use features of a successful rare earth region in the context of a high entropy r-process (S>100k_B) and discuss the types of astrophysical conditions that produce abundance patterns that best match meteoritic and observational data. Despite uncertainties in nuclear physics input, this method effectively constrains astrophysical conditions.

Measurement of the entry-spin distribution imparted to the high excitation continuum region of gadolinium nuclei via (p,d) and (p,t) reactions

Over the last several years, the surrogate reaction technique has been successfully employed to extract ($n,\phantom{\rule{-0.16em}{0ex}}f$) and ($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$) cross sections in the actinide region to a precision of $\ensuremath{\sim}$5$%$ and $\ensuremath{\sim}$20$%$, respectively. However, attempts to apply the technique in the rare earth region have shown large (factors of 2--3) discrepancies between the directly measured ($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$) and extracted surrogate cross sections. One possible origin of this discrepancy lies in differences between the initial spin-parity population distribution in the neutron induced and surrogate reactions. To address this issue, the angular momentum transfer to the high excitation energy quasicontinuum region in Gd nuclei has been investigated. The ($p,\phantom{\rule{-0.16em}{0ex}}d$) and ($p,\phantom{\rule{-0.16em}{0ex}}t$) reactions on ${}^{154,158}$Gd at a beam energy of 25 MeV were utilized. Assuming a single dominant angular momentum transfer component, the measured angular distribution for the ($p,\phantom{\rule{-0.16em}{0ex}}d$) reactions is well reproduced by distorted-wave Born approximation (DWBA) calculations for $\ensuremath{\Delta}L=4$ $\ensuremath{\hbar}$ transfer, whereas the ($p,\phantom{\rule{-0.16em}{0ex}}t$) reactions are better characterized by $\ensuremath{\Delta}L=5$ $\ensuremath{\hbar}$. A linear combination of DWBA calculations, weighted according to a distribution of $L$ transfers (peaking around $\ensuremath{\Delta}L=4$--5 $\ensuremath{\hbar}$), is in excellent agreement with the experimental angular distributions.

Consistent description of nuclear charge radii and electric monopole transitions

A systematic study of energy spectra throughout the rare-earth region (even-even nuclei from ${}_{58}$Ce to ${}_{74}$W) is carried out in the framework of the interacting boson model (IBM), leading to an accurate description of the spherical-to-deformed shape transition in the different isotopic chains. The resulting IBM Hamiltonians are then used for the calculation of nuclear charge radii (including isotope and isomer shifts) and electric monopole transitions with consistent operators for the two observables. The main conclusion of this study is that an IBM description of charge radii and electric monopole transitions is possible for most of the nuclei considered but that it breaks down in the tungsten isotopes. It is suggested that this failure is related to hexadecapole deformation.

Design of mid-infrared amplifiers based on fiber taper coupling to erbium-doped microspherical resonator

A dedicated 3D numerical model based on coupled mode theory and solving the rate equations has been developed to analyse, design and optimize an optical amplifier obtained by using a tapered fiber and a Er³⁺-doped chalcogenide microsphere. The simulation model takes into account the main transitions among the erbium energy levels, the amplified spontaneous emission and the most important secondary transitions pertaining to the ion-ion interactions. The taper angle of the optical fiber and the fiber-microsphere gap have been designed to efficiently inject into the microsphere both the pump and the signal beams and to improve their spatial overlapping with the rare earth doped region. In order to reduce the computational time, a detailed investigation of the amplifier performance has been carried out by changing the number of sectors in which the doped area is partitioned. The simulation results highlight that this scheme could be useful to develop high efficiency and compact mid-infrared amplifiers.

Neutron-induced cross sections of short-lived nuclei via the surrogate reaction method

The measurement of neutron-induced cross sections of short-lived nuclei is extremely difficult due to the radioactivity of the samples. The surrogate reaction method is an indirect way of determining cross sections for nuclear reactions that proceed through a compound nucleus. This method presents the advantage that the target material can be stable or less radioactive than the material required for a neutron-induced measurement. We have successfully used the surrogate reaction method to extract neutron-induced fission cross sections of various short-lived actinides. In this work, we investigate whether this technique can be used to determine neutron-induced capture cross sections in the rare-earth region.

Nuclear Level Density of161Dy in the Shell Model Monte Carlo Method

We extend the shell-model Monte Carlo applications to the rare-earth region to include the odd-even nucleus ${}^{161}$Dy. The projection on an odd number of particles leads to a sign problem at low temperatures making it impractical to extract the ground-state energy in direct calculations. We use level counting data at low energies and neutron resonance data to extract the shell model ground-state energy to good precision. We then calculate the level density of ${}^{161}$Dy and find it in very good agreement with the level density extracted from experimental data.

Deformed one-quasiparticle states in covariant density functional theory

Systematic investigation of the accuracy of the description of the energies of deformed one-quasiparticle states has been performed in covariant density functional theory in actinide and rare-earth mass regions. The sources of the discrepancies between theory and experiment are analyzed. Although some improvements in the description of ground state configurations and one-quasiparticle spectra can be achieved by better parametrization of the relativistic mean field Lagrangian, the analysis suggests that spectroscopic quality of their description can be achieved only in theoretical framework which takes into account particle–vibration coupling.

Properties of the 3/2−[521] band in the odd-N rare-earth nuclei

High-spin states in 161Er have been studied experimentally via the 150Nd(16O, 5n) reaction at a beam energy of 86 MeV. Three rotational bands built on the 5/2+[642], 3/2−[521], and 11/2−[505] configurations have been extended up to high-spin states, and particularly, the α = −1/2 branch of the ground state 3/2−[521] band has been revised significantly. It is found that signature inversion occurs in the 3/2−[521] band after the band crossing in 161Er. The systematics of the signature inversion associated with the 3/2−[521] configuration in the rare-earth region is discussed. The band properties are analyzed within the framework of a triaxial particle-rotor model, and a triaxial deformation is proposed to the 3/2−[521] band.

Scissors modes: The first overtone

Scissors modes were predicted in the framework of the Two-Rotor Model. This model has an intrinsic harmonic spectrum, so that the level above the Scissors Mode, the first overtone, has excitation energy twice that of the Scissors Mode. Since the latter is of the order of 3 MeV in the rare earth region, the energy of the overtone is below threshold for nucleon emission, and its width should remain small enough for the overtone to be observable. We find that $B(E2)\uparrow_{overtone} = {3 /over 64 \theta_0^{2}}B(E2)\uparrow_{scissors}$, where $\theta_0$ is the zero-point oscillation amplitude, which in the rare earth region is of order $ 10^{-1}$.

Mass measurements on stable nuclides in the rare-earth region with the Penning-trap mass spectrometer TRIGA-TRAP

The masses of 15 stable nuclides in the rare-earth region have been measured with the Penning-trap mass spectrometer TRIGA-TRAP. This is the first series of absolute mass measurements linking these nuclides to the atomic-mass standard $^{12}\mathrm{C}$. Previously, nuclear reaction studies almost exclusively determined the literature values of these masses in the Atomic-Mass Evaluation. The TRIGA-TRAP results show deviations on the order of 3--4 standard deviations from the latest published values of the Atomic-Mass Evaluation 2003 for some cases. However, the binding-energy differences that are important for nuclear structure studies have been confirmed and improved. The new masses are discussed in the context of valence proton-neutron interactions using double differences of binding energies, $\ensuremath{\delta}{V}_{\mathit{pn}}(Z,N)$.