Bands In Isotopes Research Articles

Structures of terminating bands in Er isotopes

The configurations of terminating bands in Er isotopes are investigated using the unpaired cranked Nilsson-Strutinsky (CNS), and the paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) models and also, new CNS(B) formalism. The calculated excitation energies of the bands have been compared with the experimental findings, and good agreements are observed. Our calculations show that the CNS(B) approach successfully is in agreement CNSB predictions and experimental results. Some systematics of terminating bands in erbium isotopes are also discussed.

The first and second crossings in low-lying rotational bands of Er isotopes: A systematic study

Essential understanding about the structure of rotating nuclei has come from the study on the band crossings which are often associated with the alignment of a pair of quasiparticles. In this work, the first and second discontinuities in the low-lying rotational bands of [Formula: see text]Er nuclei have been investigated systematically, for the first time, within the paired cranked Nilsson–Strutinsky–Bogoliubov (CNSB) framework. Our calculations show these irregularities are related to the high-j intruder [Formula: see text] neutron and [Formula: see text] proton alignment, which is consistent with the previous studies within the cranked shell model (CSM) approach. A comparison was made with the experimental data where available, and good agreement is observed.

Study of normal deformed bands in light Lutetium isotopes

The projected shell model has been employed to study the energy levels and alignment frequencies of the normally deformed bands of light lutetium isotopes. Band head spins and configurations have been reproduced for all the positive parity bands of 161−165Lu isotopes and negative parity bands of 163Lu. The theoretical aligned angular momenta reasonably reproduced the observed backbends and their corresponding rotational frequencies for all the experimentally observed normally deformed bands. Moreover, I = 7/2− state is predicted as band head spin for negative parity yrast bands of 161,165Lu. The negative parity yrast bands of 161,165Lu are predicted to have 1π1h11/2[523]7/2− configuration. Further, the calculated B(E2) values of 165Lu show reasonable agreement with the available experimental data. The dip predicted in the B(E2) values may be interpreted due to the alignment of a pair of neutrons in the neutron 1i13/2 orbital of all yrast bands of 161−165Lu.

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.

Study of Nuclear Radius and Back bending phenomenon of 20-30Mg Isotopes in sdpn Model Space

In present work, many parameters have been computed using NuShellX@ MSU code for ground state bands of 20-30Mg isotopes. These parameters were root mean square of nuclear radius, major and minor of ellipsoid axises (a and b), as well as to the different between them(ΔR) deformation parameters (β2, δ), intrinsic quadrupole moment(Q0) and back bending phenomenon. Model space(sdpn) of (0d3/2,0d5/2 and 1s1/2) for protons and neutrons orbits and cwhcdpn interaction have been used to calculate above parameters. Effective charge of Bohr - Mottelson model has been used in this work. The results showed an brilliant agree with the obtainable investigational results all isotopes in this study. Also, the back bending phenomenon was well evident in our results for all isotopes used under study. In these calculations, new values have been theoretically designated for most parameters which were previously unknown in experimental information.

Structure of the R1 and R2 Bands of Isotopes of Cr3+ Ion in a Single Crystal of Ruby at Room Temperature

Structure of the R1 and R2 Bands of Isotopes of Cr3+ Ion in a Single Crystal of Ruby at Room Temperature

Systematic study of superdeformed rotational bands in Hg isotopes

The exponential model with pairing attenuation and the nuclear softness formula have been employed to deduce the band-head spins of all the SD bands in Hg isotopes. A least-squares fitting method is performed for the γ-transition energies and the model parameters are calculated. The calculated γ-transition energies and the corresponding fitting parameters are found to depend sensitively on the established level spins. The identical band pairs in the Hg isotopes are investigated and the role of alignment is explored.

Effects of high- j orbitals, pairing, and deformed neutron shells on upbendings of ground-state bands in the neutron-rich even-even isotopes Hf170–184

The ground-state bands (GSBs) in the even-even hafnium isotopes $^{170-184}$Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hbar\omega\approx0.5$ MeV observed (predicted) in $^{172}$Hf ($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi1i_{13/2}$ $(1/2^{+}[660])$, $\pi1h_{9/2}$ $(1/2^{-}[541])$ and orbital $\pi1h_{11/2}$ $(7/2^{-}[523])$. The first upbendings of GSBs at low frequency $\hbar\omega=0.2-0.3$ MeV in $^{170-178}$Hf, which locate below the deformed neutron shell $N=108$, attribute to the alignment of the neutron orbital $\nu1i_{13/2}$. For the heavier even-even isotopes $^{180-184}$Hf, compared to the lighter isotopes, the first band-crossing is delayed to the high frequency due to the existence of the deformed shells $N=108,116$. The upbendings of GSBs in $^{180-184}$Hf are predicted to occur at $\hbar\omega\approx0.5$MeV, which come from the sharp raise of the simultaneous alignments of both proton $\pi1i_{13/2}$, $\pi1h_{9/2}$ and neutron $\nu2g_{9/2}$ orbitals. The pairing correlation plays a very important role in the rotational properties of GSBs in even-even isotopes $^{180-184}$Hf. Its effects on upbendings and band-crossing frequencies are investigated.

O2- and N2-broadening parameters in the ν3 and 2ν3-ν3 bands of methyl chloride

In this paper, we report high-resolution measurements of oxygen and nitrogen pressure-broadening coefficients for ro-vibrational transitions in the ν3 and 2ν3-ν3 bands of methyl chloride (CH335Cl and CH337Cl). We present the first high-resolution measurement of oxygen broadening coefficients for the CH3Cl, along with an extensive determination of the nitrogen broadening coefficients in the ν3 band which complements the measurements made by diode laser spectrometer in previous works. For the 2ν3-ν3 band, the oxygen and nitrogen broadening coefficients are measured here for the first time. The results have been obtained by analyzing fourteen spectra with a mono-spectrum non-linear least squares fitting of Voigt profile using data recorded at 295 K at the AILES beamline of the SOLEIL Synchrotron facility using a Bruker IF125HR Fourier transform spectrometer. Broadening coefficients of 1793 and 1732 lines in both bands of both isotopes of CH3Cl for O2 and N2 buffer gases respectively have been retrieved. The rotational dependences of these coefficients have been modeled using an empirical model, which reproduces the measured data with a difference of about 6 %. Using the measured values of O2- and N2-broadenings, we derived the Air-broadening coefficients. Finally, comparisons with previous works are performed.

Line intensity parameters in the ν3 and 2ν3-ν3 bands of methyl chloride in the 13 µm region

We performed the systematic measurements of line intensities of ro-vibrational absorption transitions of the ν3 and 2ν3-ν3 parallel bands of 12CH335Cl and 12CH337Cl isotopes. The spectra were recorded in the spectral region between 650 and 800 cm−1 with a high-resolution Fourier transform spectrometer.A mono-spectrum fitting technique was used to fit a series of seven spectra at pressures of CH3Cl ranging from 1.02 to 10.24 mbar to retrieve line intensities of 2385 transitions of the two isotopic species. The measured line intensities are discussed in relation to rotational quantum numbers, and used to derive the square of the transition dipole moments for each line. The analysis of these moments allows us to derive a consistent set of line intensity parameters, such as vibrational transition moments, band intensities as well as Herman-Wallis coefficients for both bands. The results of the ν3 band are in satisfactory agreement with previous works and present databases, but a larger discrepancy (≈ 30%) is observed for the 2ν3-ν3 hot band.

Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.

New approach for the wobbling motion in the even-odd isotopes Lu161,163,165,167

A new interpretation for the wobbling bands in the even-odd Lu isotopes is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1), the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoI's for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space, one indicates where the points associated with the fitted parameters are located, which is the region where the transversal wobbling mode might be possible, as well as where the wobbling motion is forbidden.

β and γ bands in N=88 , 90, and 92 isotones investigated with a five-dimensional collective Hamiltonian based on covariant density functional theory: Vibrations, shape coexistence, and superdeformation

A comprehensive systematic study is made for the collective β and γ bands in even-even isotopes with neutron numbers N=88 to 92 and proton numbers Z=62(Sm) to 70 (Yb). Data, including excitation energies, B(E0) and B(E2) values, and branching ratios from previously published experiments are collated with new data presented for the first time in this study. The experimental data are compared to calculations using a five-dimensional collective Hamiltonian (5DCH) based on the covariant density functional theory (CDFT). A realistic potential in the quadrupole shape parameters V(β,γ) is determined from potential energy surfaces (PES) calculated using the CDFT. The parameters of the 5DCH are fixed and contained within the CDFT. Overall, a satisfactory agreement is found between the data and the calculations. In line with the energy staggering S(I) of the levels in the 2γ+ bands, the potential energy surfaces of the CDFT calculations indicate γ-soft shapes in the N=88 nuclides, which become γ rigid for N=90 and N=92. The nature of the 02+ bands changes with atomic number. In the isotopes of Sm to Dy, they can be understood as β vibrations, but in the Er and Yb isotopes the 02+ bands have wave functions with large components in a triaxial superdeformed minimum. In the vicinity of Sm152, the present calculations predict a soft potential in the β direction but do not find two coexisting minima. This is reminiscent of Sm152 exhibiting an X(5) behavior. The model also predicts that the 03+ bands are of two-phonon nature, having an energy twice that of the 02+ band. This is in contradiction with the data and implies that other excitation modes must be invoked to explain their origin.20 MoreReceived 4 July 2018Revised 5 June 2019DOI:https://doi.org/10.1103/PhysRevC.100.044324©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsCollective modelsElectromagnetic transitionsLow & intermediate energy heavy-ion reactionsNuclear density functional theoryNuclear spin & parityNucleon induced nuclear reactionsProperties150 ≤ A ≤ 189Nuclear Physics

Systematic investigations of positive-parity doublet bands with three-quasiparticle configurations in Cs125,127,129,131

The experimental features of positive-parity doublet bands in the odd-\emph{A} cesium isotopes $^{125,127,129,131}$Cs, including angular momentum alignment, energy staggering, $B(M1)/B(E2)$ etc. are studied systematically and compared to those of the candidate chiral bands in the adjacent odd-odd Cs isotopes. The configuration assignments and the dynamics of these bands are discussed. The self-consistent tilted axis cranking relativistic mean-field calculations are performed with configuration reassigned to these bands. The experimental level schemes of four nuclei are well reproduced, and the calculations also show four nuclei have obvious triaxial deformations and thus support the candidate chiral doublet bands in $^{125,127,129,131}$Cs.

First observation of γ -soft and triaxial bands in Zr isotopes

New results obtained in this work from measurements of $\ensuremath{\gamma}$ radiation following fission of $^{248}\mathrm{Cm}$ and $^{252}\mathrm{Cf}$, performed using Eurogam2 and Gammasphere arrays, respectively, reveal excitations corresponding to $\ensuremath{\gamma}$ vibrations and triaxial deformation present in $^{100}\mathrm{Zr}$ and $^{102}\mathrm{Zr}$ nuclei. This is the first observation of nonaxial bands in Zr isotopes. Such excitations probably occur due to competing prolate and oblate configurations, identified recently in these nuclei. Evolution of $\ensuremath{\gamma}$ softness and triaxiality in Zr isotopes is observed in the function of the neutron number.

Isotope shifts and band progressions in SO2 rovibrational energy levels: using quantum theory to extract rotational constants

ABSTRACTWe report the isotope shifts of the rotational constants and vibrational band progressions of the sulfur dioxide molecule (SO), for all four stable sulfur isotopes32S,33S,34S, and36S. These are extracted from exact quantum theoretical calculations of the SO rovibrational energy levels, as reported in Chem. Phys. 450–451, 59 (2015) and Chem. Phys. 461, 34 (2015) and by fitting these levels to a J-shifting (JS)-type scheme, applied to a representative set of total angular momentum (J) values. The approach used to obtain the rotational constants is unusual in that it is derived directly from the quantum theoretical framework used for the earlier calculation, which gives rise to a flexible (i.e., vibrational- and rotational-state-dependent) but symmetric rotor description. The usual rotational quantum numbers are thus replaced with a single body-fixed azimuthal rotation quantum number, K, with various strategies introduced a posteriori to address rotor asymmetry. The new model fits the numerically computed rovibrational levels well, over a fairly broad range of vibrational (v) and rotational (J) excitations. The computed rotational constants agree well with previously reported experimental values [J. Chem. Phys. 58, 265 (1973)]. The explicitly v- and J-dependent approach used here should thus prove valuable in broader contexts—e.g., for an analysis of self-shielding in sulfur mass-independent fractionation, even though the rovibrational levels themselves exhibit mass-dependent fractionation.

Identification of high-spin proton configurations in Ba136 and Ba137

The high-spin structures of 136Ba and 137Ba are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. 136Ba is populated in a 136Xe+238U MNT 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 two 9Be + 130Te fusion-evaporation reactions using the High-efficiency Observatory for -Ray Unique Spectroscopy (HORUS) at the FN tandem accelerator of the University of Cologne, Germany. Furthermore, both isotopes are populated in an elusive reaction channel in the 11B+130Te fusion-evaporation reaction utilizing the HORUS -ray array. The level scheme above the J� = 10+ isomer in 136Ba is revised and extended up to an excitation energy of approx. 5.5 MeV. From the results of angular-correlation measurements, the Ex = 3707- and Ex = 4920-keV states are identified as the bandheads of positive- and negative-parity cascades. While the high-spin regimes of both 132Te and 134Xe are characterized by high-energy 12+ ! 10+ transitions, the 136Ba E2 ground-state band is interrupted by negativeparity states only a few hundred keV above the J� = 10+ isomer. Furthermore, spins are established for several hitherto unassigned high-spin states in 137Ba. The new results close a gap along the highspin structure of N < 82 Ba isotopes. Experimental results are compared to large-scale shell-model calculations employing the GCN50:82, Realistic SM, PQM130 and SN100PN interactions. The calculations suggest that the bandheads of the positive-parity bands in both isotopes are predominantly of proton character.

Spins and moment of inertia of superdeformed bands in the Pb isotopes

A variable moment of inertia (VMI) inspired interacting boson model (IBM) is used to deduce the band-head spins of the SD bands in the odd-A Pb isotopes in the $A \sim 190$ mass region. We find that the calculated transition energies and band-head moment of inertia (MoI) explicitly depend upon the assigned band-head spin. The experimental and calculated transition energies and the band-head MoI of signature partners SD bands matches extremely well whenever an accurate spin is assigned to the SD band. The dynamic MoI is also deduced for the flat SD bands in the odd-A Pb isotopes, and its variation with the rotational frequency is explored. We observe that a competition between the pairing and anti-pairing effect is responsible for the flatness in the dynamic moment of inertia. Also, the role of the perturbation holding the $SO_{sdg}(5)$ (or $SU_{sdg}(5)$) symmetry on the dynamic MoI in the flat SD band is explored.

Normal-deformed structures in hafnium isotopes

The structures of yrast normal-deformed (ND) bands in Hf isotopes have been investigated using the unpaired cranked Nilsson-Strutinsky (CNS), and the paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) models. New optimized Nilsson parameters have been derived and used in the models to interpret the experimental data in $^{168--175}\mathrm{Hf}$ isotopes. The calculated kinematic moments of inertia, as well as the excitation energies of the yrast bands, have been compared with the experimental findings, and good agreements are observed. Configuration changes along the yrast lines have been traced by the aid of the CNS calculations. The calculated single-particle excitations shed more light on the nature of the crossings and successfully explain some features of the observed rotational bands which had not been clear before.

Deformed band structures in neutron-rich Pm152–158 isotopes

High spin band structures of neutron-rich $^{152-158}$Pm isotopes have been obtained from the measurement of prompt $\gamma$-rays of isotopically identified fragments produced in fission of $^{238}$U+$^{9}$Be and detected using the VAMOS++ magnetic spectrometer and EXOGAM segmented Clover array at GANIL and also from the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ data from the spontaneous fission of $^{252}$Cf using Gammasphere. The excited states in $^{157}$Pm and those above the isomers in even-A Pm isotopes $^{152,154,156,158}$Pm have been identified for the first time. The spectroscopic information on the rotational band structures in odd-A Pm isotopes has been extended considerably to higher spins and the possibility of the presence of reflection asymmetric shapes is explored. The configuration assignments are based on the results of Cranked Relativistic Hartree-Bogoliubov calculations. From the systematics of bands in odd-A Pm isotopes and weak population of opposite parity bands, octupole deformed shapes in neutron rich Pm isotopes beyond $N=90$ seem unlikely to be present.