Ground-state Band Research Articles

Ground-state bands of doubly even 166Hf Nucleus

This study was carried out to investigate the rotational structure of even-even ¹⁶⁶Hf isotopes using the phenomenological fitting, Sood’s semi-empirical formula. The rotational energies from the calculated values were compared to the experimental spectrum. The result shows that in ¹⁶⁶Hf, calculated energies fit the experimental values to a remarkable degree of accuracy.

In-beam γ -ray and electron spectroscopy of Md249,251

The odd-$Z$ $^{251}$Md nucleus was studied using combined $\gamma$-ray and conversion-electron in-beam spectroscopy. Besides the previously observed rotational band based on the $[521]1/2^-$ configuration, another rotational structure has been identified using $\gamma$-$\gamma$ coincidences. The use of electron spectroscopy allowed the rotational bands to be observed over a larger rotational frequency range. Using the transition intensities that depend on the gyromagnetic factor, a $[514]7/2^-$ single-particle configuration has been inferred for this band, i.e., the ground-state band. A physical background that dominates the electron spectrum with an intensity of $\simeq$ 60% was well reproduced by simulating a set of unresolved excited bands. Moreover, a detailed analysis of the intensity profile as a function of the angular momentum provided a method for deriving the orbital gyromagnetic factor, namely $g_K = 0.69^{+0.19}_{-0.16}$ for the ground-state band. The odd-$Z$ $^{249}$Md was studied using $\gamma$-ray in-beam spectroscopy. Evidence for octupole correlations resulting from the mixing of the $\Delta l = \Delta j = 3$ $[521]3/2^-$ and $[633]7/2^+$ Nilsson orbitals were found in both $^{249,251}$Md. A surprising similarity of the $^{251}$Md ground-state band transition energies with those of the excited band of $^{255}$Lr has been discussed in terms of identical bands. Skyrme-Hartree-Fock-Bogoliubov calculations were performed to investigate the origin of the similarities between these bands.

Possible ‘stapler’ band in 109Ag nucleus

High-spin states of 109Ag have been studied using the 7Li + 110Pd reaction at a beam energy of 46 MeV. A negative-parity band decaying to the ground-state band by several new linking transitions is established. Meanwhile, seven new E2 crossover transitions of this band are observed, thereby confirming the spin-parity assignment and ordering of the dipole transitions above the Iπ = 19/2− level. A low energy γ-ray transition of 88 keV is found and placed at the bottom of the negative-parity band, and thus the Iπ = 17/2− level is tentatively assigned as the lowest observed state of this band. Experimental excitation energies and total angular momenta of the negative-parity band are compared with the predictions of self-consistent titled axis cranking relativistic mean-field theory with a three-quasiparticle configuration of . Based on the theoretical description and the analyses of the angular momentum coupling, this negative-parity dipole band is suggested as a ‘stapler’ band. By investigating the angular momentum components, it is found that the valence nucleons in the low-j orbitals play an active role in the ‘stapler’ mechanism.

Electronic Band Structure, Density of States, Phase Transitions, Metallization and Superconducting Transition of KBr under High Pressure

The results of a full potential linear muffin-tin orbital (FP-LMTO) study on the electronic properties of ionic insulator potassium bromide (KBr) under pressure is presented. The phase transition pressure at which the compound undergoes structural phase transition from NaCl to CsCl structure is predicted from the total energy calculations. The ground state properties and band gap values are compared with the experimental results. At normal pressure KBr is a direct band gap insulator. In KBr, the metallization occurs through indirect closing of the band gap between G and H points at the reduced volume V/Vo=0.45 (CsCl structure), the corresponding metallization pressure is 1.274 Mbar. On further increase of pressure, KBr becomes superconductor, and this material comes under the class of electron-phonon-mediated high pressure superconductor. The superconducting transition temperatures (Tc) of KBr is obtained as a function of pressure for both NaCl and CsCl structures. The highest Tc estimated is 5.911 K and the corresponding pressure is 5 Mbar in the NaCl structure and 0.897 K in the CsCl structure. It is also confirmed that the metallization, structural phase transition and onset of superconductivity do not occur simultaneously in ionic compounds. DOI: http://dx.doi.org/10.17807/orbital.v12i2.1401

Nuclear structure of even-even Ytterbium isotopes 166−176Yb

A nuclear phenomenological study of the even-even Ytterbium Isotopes Yb166−176 was carried out, in the framework of the interacting Boson model-1 (IBM-1) and modified soft rotor formula (MSRF). The energy levels for ground-state, γ- and β-rotational bands were calculated. Also, electric transition probability B (E2) for these isotopes was calculated. Furthermore, the intrinsic coherent state was used to find the potential energy surfaces. The staggering effect of a γ-band, which is a function of spin, was analyzed. The results obtained by applying the IBM-1 and the MSRF are in good agreement with the corresponding experimental data for most of the nuclear states.

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.

Analysis of the 18Fg,m(d,p)F19 reactions in the rotational model

Spectroscopic strengths for the ${}^{18}{\mathrm{F}}^{g,m}(d,p)\phantom{\rule{0.16em}{0ex}}^{19}\mathrm{F}$ reactions to members of the ground-state band in $^{19}\mathrm{F}$ are interpreted in the rotational model. The analysis considers two different coupling schemes, namely, the strong and decoupled limits of the particle rotor model to describe the ground and isomeric states of $^{18}\mathrm{F}$, as well as the transitions to the ground-state band in $^{19}\mathrm{F}$. Our results, obtained using Nilsson amplitudes for the neutron levels $\frac{1}{2}[220], \frac{3}{2}[211]$, and $\frac{5}{2}[202]$ calculated at a deformation ${\ensuremath{\epsilon}}_{2}=0.32$ are in agreement with the measurements and USDB shell-model calculations.

Exploring the Magnetic Properties of the Largest Single-Molecule Magnets.

The giant {Mn70} and {Mn84} wheels are the largest nuclearity single-molecule magnets synthesized to date, and understanding their magnetic properties poses a challenge to theory. Starting from first-principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled {Mn7} subunits carrying an effective S = 2 spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest-energy excitations arising from Heisenberg-ring-like excitations of the {Mn7} subunits around the wheel. We further describe how weak longer-range couplings can select the precise spin ground-state of the Mn wheels out of the nearly degenerate ground-state band.

Shape evolution of neutron-rich Mo106,108,110 isotopes in the triaxial degree of freedom

Background: Neutron-rich nuclei with mass number between 100 and 110 attract much attention, since several kinds of shapes, such as spherical, prolate, oblate, and triaxial shapes, are predicted. In particular, for neutron-rich Mo isotopes, different models predict different magnitudes and rigidity of triaxial deformation. Previous interpretations of experimental results based solely on low-lying 22+ states are insufficient to distinguish between the rigid triaxial shape, γ vibration, or γ-soft rotor. Purpose: The shape evolution of Mo106, Mo108, and Mo110 is investigated through their 21+-state lifetimes, decay-branching ratios of the 22+ state, and energies of the low-lying collective excited states with Kπ=0+,2+, and 4+. Method: β-delayed γ-ray spectroscopy was employed for neutron-rich Nb and Zr isotopes produced at the RIKEN RI Beam Factory to populate excited states in Mo106, Mo108, and Mo110. The EUroball-RIKEN Cluster Array was used for high-resolution γ-ray detection and lifetimes of the 21+ states were determined using the UK fast-timing array of LaBr3(Ce) detectors. Results: New γ-ray transitions and levels are reported, including newly assigned 02+ states in Mo108,110. Quadrupole deformations were obtained for Mo106,108,110 from their 21+ energies and lifetimes. The β-delayed neutron-emission probabilities of Nb108 and Nb110 were determined by examining the γ rays of their respective daughter decays. Conclusions: The even-odd energy staggering in the 22+ band was compared with typical patterns of the γ-vibrational band, rigid triaxial rotor, and γ-soft rotor. The very small even-odd staggering of Mo106, Mo108, and Mo110 favors a γ-vibrational band assignment. The kinematic moment of inertia for the 22+ band showed a trend similar to the ground-state band, which is as expected for the γ-vibrational band. Beyond-mean-field calculations employing the constrained Hartree-Fock-Bogoliubov and local quasiparticle-random-phase approximation method using the SLy5+T interaction reproduced the ground and 22+ bands in Mo106 and Mo108. The collective wave functions are consistent with the interpretation of the 22+ band as the γ-vibrational band of the prolate shape. However, the staggering pattern observed in Mo110 differs from the one suggested in the calculations which predict a γ-soft rotor. There was no experimental indication of the oblate shape or the γ-soft rotor predicted in these Mo isotopes.10 MoreReceived 28 August 2019Revised 19 December 2019Accepted 17 January 2020DOI:https://doi.org/10.1103/PhysRevC.101.044311©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeta decayCollective levelsNuclear structure & decaysNucleon distributionProperties90 ≤ A ≤ 149Nuclear Physics

Microscopic study of ground state bands in N = 45 and 46 isotones in mass region A ∼ 70–80

Using the angular-momentum projected quasiparticle states and a simple quadrupole–quadrupole + monopole–pairing + quadrupole-pairing type Hamiltonian, Projected Shell Model calculations have been performed to study the nuclear structure properties of some N = 45, 46 isotones in the mass region A = 70–80. The results are obtained for the yrast energy spectrum, rotational alignments, back-bending and reduced transition probabilities [B(M1) and B(E2)]. Results of our calculations exhibit satisfactory agreement with experimental data. Signature splitting and signature inversion which are the characteristics of this mass region have also been reproduced and discussed for these nuclei.

Effect of fluoro-substituted acceptor-based ancillary ligands on the photocurrent and photovoltage in dye-sensitized solar cells

Herein, we report four novel heteroleptic ruthenium (II) complexes, namely SD-7 to SD-10, containing fluoro- and trifluoro- methyl antennas as substituents on the ancillary ligands for dye-sensitized solar cells, and were compared to the benchmark dye N719. Photosensitizers (dyes) SD-7 to SD-10 were synthesized according to a typical one-pot three-step procedure with the corresponding ancillary ligands (LS-7 to LS-10). All the dyes were characterized by ATR-FTIR, 1H NMR and mass spectrometry. Furthermore, the photophysical, electrochemical and photovoltaic performances were compared with N719. The band gaps, ground and excited state oxidation potentials were measured. The photovoltaic performance of the dyes showed that SD-7 with five fluorine atoms and SD-8 with CF3 at the –ortho position of the phenyl moiety outperformed the benchmark dye N719 with the efficiencies of 8.03% and 8.17%, respectively, with current density of 19.57 and 19.46 mA∙cm−2, respectively, and open-circuit voltages of 0.65 V and 0.69 V, respectively, under optimized conditions. The fabricated solar devices at lab-scale showed a systematic trend of decreasing JSC when the fluoro-substituted dyes were sensitized on TiO2: SD-7 (with five –F) > SD-8 (with one CF3 at ortho position) > SD-9 (with one CF3 at para position) > SD-10 (with two CF3, one at ortho and one at para position). This can be attributed to the greater number of fluorine atoms directly attached to sp2 hybridized carbon atoms, which greatly enhanced the dipole moment and intimate electronic coupling of SD-7 with TiO2 nanoparticles leading to better photocurrent density.

W(5): Wobbling Mode in the Framework of the X(5) Model

Using in the Bohr Hamiltonian the approximations leading to the Bohr and Mot- telson description of wobbling motion in even nuclei, a W(5) model for wobbling bands, coexisting with a X(5) ground state band, is obtained. Separation of vari­ ables is achieved by assuming that the relevant potential has a sharp minimum at 70, which is the only parameter entering in the spectra and B(E2) transition rates (up to overall scale factors). B(E2) transition rates exhibit the features expected in the wobbling case.

Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

Identical bands in doubly even nuclei in framework of variable moment of inertia (VMI) and interacting boson models

The variable moment of inertia (VMI) model and the interacting boson model (IBM) are applied to study the identical bands (IB's) for doubly even normally deformed nuclei in rare earth mass region 158 ≤ A ≤ 170. The VMI used to calculate the energy levels of the positive parity state bands before the band crossing. One important feature of the IBM is its ability to describe the nuclear shapes by using the consistent Q-formalism and intrinsic coherent state, which allow generating the potential energy surface (PES). The PES′s, which describe all deformation effects, are systematically analyzed. For most of our considered nuclei the plot of PES against the deformation parameter shows two wells, one on the prolate and one on the oblate side, which indicate that the considered nuclei are deformed and have rotational character.The IB's parameters are extracted it is observed that the nuclei having similar NpN/nΔ values exhibit identical excitation energies where, Np and Nn are the valence proton and neutron numbers and Δ is the average-pairing gap. Pairs of conjugate nuclei with the same F-spin and ±F0 projections have identical NpNn value. The nuclear kinematic and dynamic moments of inertia for the ground state bands for our proposed nuclei are calculated and systematically analyzed. For each nucleus, the best parameters for both VMI and IBM models are obtained by using a fitting procedure of the theoretical results with experimental data for the positive parity excitation energies by using the computer code PHINT and a simulated search program.

BAND STRUCTURE, METALLIZATION AND STRUCTURAL PHASE TRANSITION OF NABR UNDER HIGHPRESSURE

The metallization and the phase transition of the alkali bromide sodium bromide (NaBr) is investigated through its band structure. The equilibrium lattice constant, bulk modulus, pressure derivative of bulk modulus and the phase transition pressure at which the compound undergo structural phase transition from NaCl (B1) to the CsCl (B2) structure is predicted from the total energy calculations. The ground state properties and band gap values are compared with the experimental and other theoretical results. At normal pressure NaBr is a direct band gap insulator. When the pressure is increased there is enhanced overlapping between the wave functions of the neighboring atoms. As a result the widths of the valence and empty conduction bands increase. These changes lead to the narrowing and indirect closing of band gap in NaBr (metallization). It is also confirmed that the metallization and structural phase transition do not occur simultaneously in ionic compounds.

Evidence for octupole collectivity in ^{172}{mathrm {Pt}}

Excited states in the extremely neutron-deficient nucleus ^{172}{mathrm {Pt}} were populated via ^{96}mathrm {Ru}(^{78}mathrm {Kr},2p) and ^{92}mathrm {Mo}(^{83}mathrm {Kr},3n) reactions. The level scheme has been extended up to an excitation energy of approx 5~hbox {MeV} and tentative spin-parity assignments up to I^pi = 18^+. Linear polarization and angular distribution measurements were used to determine the electromagnetic E1 character of the dipole transitions connecting the positive-parity ground-state band with an excited side-band, firmly establishing it as a negative-parity band. The lowest member of this negative-parity structure was firmly assigned spin-parity 3^-. In addition, we observed an E3 transition from this 3^- state to the ground state, providing direct evidence for octupole collectivity in ^{172}{mathrm {Pt}}. Large-scale shell model (LSSM) and total Routhian surface (TRS) calculations have been performed, supporting the interpretation of the 3^- state as a collective octupole-vibrational state.

High-K multi-particle bands and pairing reduction in 254No * * Supported by the National Natural Science Foundation of China (11775112, 11535004, 11875027, 11761161001) and the Priority Academic Program Development of Jiangsu Higher Education Institutions

The multi-particle states and rotational properties of the two-particle bands in are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method. The rotational bands on top of the two-particle and states and the pairing reduction are studied theoretically in for the first time. The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations. Better agreement with the data is achieved by including the high-order deformation , which leads to enlarged and deformed shell gaps. An increase of in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.

New perspective of the nuclear structure of $$^{96}$$Ru–$$^{114}$$Ru isotopes

The angular momentum induced rigid tri-axiality observed at higher spins in $$^{110}$$Ru–$$^{114}$$Ru, a unique phenomenon, is studied. It is different from the tri-axiality observed in W, Os and Pt isotopes and in the neutron deficient Xe and Ba isotopes, occurring near shell closures. In Ru isotopes, it is enhanced at the middle of the deformed region at $$N=66$$. To understand this, the increasing collectivity in the ground state bands and in the $$\gamma $$-bands, in the full chain of $$^{96}$$Ru–$$^{106}$$Ru and the saturation at $$^{108}$$Ru–$$^{114}$$Ru are studied. The varying odd–even spin staggering displayed in the $$\gamma $$-bands of $$^{108}$$Ru–$$^{112}$$Ru and the formation of odd–even spin doublets and the wobbling motion displayed in $$^{112}$$Ru are illustrated. Microscopic basis of this is also pointed out. Relation with neighboring odd-A isotopes is studied. Comparison is made with the predictions of the Interacting Boson Model-1, as well as of the rigid tri-axial rotor (RTR) model. Distinguishing features of the anharmonic vibrator or U(5), and the $$\gamma $$-soft rotor or O(6) symmetry are illustrated. The different roles of the asymmetry parameter $$\gamma $$ for a $$\gamma $$-rigid nucleus and spherical anharmonic vibrator are explicitly demonstrated from the study of the $$\gamma $$-$$\hbox {g }B(E2)$$ ratios in Ru, for the first time. Limitation of the RTR model for transitions from the higher spin level is illustrated.

The Deformation Dependent Mass Davidson Model

The Deformation Dependent Mass Davidson Model is an extension of the well known Bohr-Mottelson Hamiltonian for the atomic nuclei. It primarily refers to the mass dependence on the deformation and secondary to the Davidson behavior for the potential of the Ø-vibration. This article will be devoted solely in the solution of the radial equation. Fitting results for the 162Dy and 238U ground state, β1 and γ1 bands are also presented.

联三吡啶铂(Ⅱ)配合物的非线性吸收和光限幅（特邀）

The reported work in 2003-2019 on the reverse saturable absorption (RSA) or two-photon absorption (TPA) and/or optical limiting (OPL) of platinum(II) terpyridine complexes was summarized in this minireview. Photophysical properties, including the ground-state absorption (GSA), excited-state absorption (ESA), excited-state lifetimes, and the quantum yields of triplet excited-state formation, RSA/OPL at 532 nm for ns laser pulses, TPA characteristics in the near-IR spectral regions, and the structure-property correlations were reviewed. This paper is composed of four sections. First, the current status of OPL materials and devices, the general requirements for reverse saturable absorbers and two-photon absorbing materials, and the different types and characteristics of square-planar platinum(II) complexes were briefly introduced. Then the photophysics and RSA/OPL of six series of Pt(Ⅱ) terpyridine-analogous complexes and the structure-property correlations were discussed. Following it the TPA of five series of Pt(Ⅱ) terpyridine complexes and the impacts of structural variations on the TPA cross sections (σ2) were reviewed. Finally, brief conclusions were drawn based on the reported studies. A general trend discovered was that the charge transfer absorption band(s) and the ESA can be readily tuned by substituents on the acetylide or the terpyridine ligand. Introducing electron-donating substituent to the acetylide or terpyridine ligand or improving the coplanarity between the aromatic substituent and the terpyridine ligand red-shifted the ground-state charge-transfer absorption band(s) at the price of decreasing/quenching the triplet ESA, which consequently reduced the RSA/OPL at 532 nm. Extending the π-conjugation of the terpyridine ligand dramatically improved the σ2 values of the Pt(Ⅱ) terpyridine complexes. Incorporation of electron-withdrawing π-conjugated aromatic substituent restrained the GSA to < 500 nm while keeping a long-lived triplet excited state with broadband ESA in the visible spectral regions and moderately strong TPA in the NIR regions. This approach could provide a solution for developing broadband OPL materials.