Transition Quadrupole Moments Research Articles

Phenomenological and analytical solution of the Bohr model for even–even and odd–even nuclei with Mie potential

In this paper, analytical solution of the Bohr model with Mie potential for even–even and odd–even nuclei are evaluated in the Bose alone symmetry [Formula: see text] and a new class of Bose–Fermi dynamical symmetry [Formula: see text], respectively. The excitation energy spectra as well as electromagnetic transition strengths, quadrupole moments and dipole moments are investigated near the critical point of shape phase transition between the spherical and deformed [Formula: see text]-unstable nuclei. To show our results are compatible with experiment, some examples are tested.

Evolution of collectivity and evidence of octupole correlations in Br73

High-spin states in the Br73 nucleus have been populated via the Cr50(Si28,αp)Br73 fusion evaporation reaction with a beam energy of 90 MeV. The deexciting gamma rays were detected using the Indian National Gamma Array (INGA). Using the γ-γ coincidence technique, two new bands and eight new interconnecting transitions have been added. The strong interconnecting E1 transitions, between positive and negative parity bands, ensure the existence of octupole correlations at low spin. Line shapes have been observed for 17 transitions, which were analyzed by the Doppler-shift attenuation method to determine the lifetime of excited states of the yrast negative parity band and its signature partner band along with the positive parity band. The deduced transitional quadrupole moments Qt for the ground state band decrease with increasing spin, with their values ranging from 2.88 to 1.00 eb. A similar trend in the quadrupole moment has also been observed for the signature partner as well as for the positive parity band. This decrease in Qt with increasing spin for these bands is interpreted in terms of the cranked Nilsson-Strutinsky model and total Routhian surface calculations, which indicate possible band termination at higher spin.

Cranked self-consistent mean-field description of the triaxially deformed rotational bands in Nd138

The survey of different configurations near Fermi surface of 138Nd results in 12 lowest configurations, at both positive- and negative-deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-minimum, which is at gamma~35, are lower than the respective configurations with negative-deformation. The general trends of the spin-versus-omega curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands `T1-T8', the calculated results using SLy4L allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data. The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in 138Nd reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-deformation. The predictions of the current calculations are complementary to that of the well-know macroscopic-microscopic calculations, both of which await future experiment to verify.

Structural investigation of neutron-deficient Pt isotopes: the case of 178Pt

Lifetime measurements with the recoil distance Doppler-shift technique have been performed to determine yrast E2 transition strengths in 178Pt. The experimental data are related to those on neighboring Pt isotopes, especially recent data on 180Pt, and compared to calculations within the interacting boson model and a Hartree-Fock Bogoliubov approach. These models predict prolate deformed ground states in Pt isotopes close to neutron midshell consistent with the experimental findings. Further, evidence was found that the prolate intruder structure observed in neutron-deficient Hg isotopes that is minimum in energy in 182Hg becomes the ground state configuration in 178Pt and neighboring 180Pt with nearly identical transition quadrupole moments. The new data on 178Pt are further discussed in the context of the systematics along the Pt isotopic chain with respect to a possible sharp shape transition towards a weakly deformed or a quasi-vibrational ground state whereas the prolate structure increases in energy in 174,176Pt and becomes an intruder configuration similar to, for example, 180,182Hg.

Electromagnetic Multipole Moments of Baryons

We calculate the charge quadrupole and magnetic octupole moments of baryons using a group theoretical approach based on broken SU(6) spin-flavor symmetry. The latter is an approximate symmetry of the QCD Lagrangian which becomes exact in the large color N_c limit. Spin-flavor symmetry breaking is induced by one-, two-, and three-quark terms in the electromagnetic current operator. Two- and three-quark currents provide the leading contributions for higher multipole moments, despite being of higher order in an 1/N_c expansion. Our formalism leads to relations between N --> N* transition multipole moments and nucleon ground state properties. We compare our results to experimental quadrupole and octupole transition moments extracted from measured helicity amplitudes.

Wobbling motion in Lu within a semi-classical framework

The results obtained for Lu with a semi-classical formalism are presented. Properties like excitation energies for the super-deformed bands TSD1, TSD2, TSD3, in 165Lu, and TSD1 and TSD2 for 167Lu, inter- and intra-band B(E2) and B(M1), the mixing ratios, transition quadrupole moments are compared either with the corresponding experimental data or with those obtained for 163Lu. Also alignments, dynamic moments of inertia, relative energy to a reference energy of a rigid symmetric rotor with an effective moment of inertia and the angle between the angular momenta of the core and odd nucleon were quantitatively studied. One concludes that the semi-classical formalism provides a realistic description of all known wobbling features in Lu.

Study of the 190Hg Nucleus: Testing the Existence of U(5) Symmetry

In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the190Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affine $$ \widehat{SU\left(1,1\right)} $$ Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.

Two-Photon Absorption and Two-Photon Circular Dichroism of a Hexahelicene Derivative with a Terminal Donor-Phenyl-Acceptor Motif.

Herein, we report on the theoretical-experimental analysis of the two photon absorption and circular dichroism spectra of 1-(2-pyridyl)-4-methoxy-carbo[6]helicene derivative (P6). The primary outcomes of our investigation on this particular helicene derivative with a donor-acceptor motif on one end led to two important conclusions: (1) the lengthening of the π-electron delocalization within the helical core of P6 predominantly increases the contribution of the magnetic dipole transition moment to the two-photon circular dichroism (TPCD) signal; and (2) the electric quadrupole transition moment contribution to the TPCD signal is enhanced by the intramolecular charge transfer (ICT) produced by the donor-acceptor combination on one end of the molecule. To corroborate our results, we performed a comparative theoretical analysis of the effect of the energy gap and ICT on TPCD on a series of P6-like helicenes with different donor-acceptor combinations. Two-photon absorption and TPCD spectra were obtained using the double L-scan technique over a broad spectral range (400-900 nm) using 90 fs pulses at a low repetition rate (2-50 Hz) produced by an amplified femtosecond system. The theoretical simulations were calculated using time dependent density functional theory at the CAM-B3LYP/6-311++G(d,p) level of theory.

Optical orbital angular momentum: twisted light and chirality.

The question of how the orbital angular momentum of structured light might engage with chiral matter is a topic of resurgent interest. By taking account of electric quadrupole transition moments, it is shown that the handedness of the beam can indeed be exhibited in local chiral effects, being dependent on the sign of the topological charge. In the specific case of absorption, a significant interplay of wavefront structure and polarization is resolved, and clear differences in behavior are identified for systems possessing a degree of orientational order and for those that are randomly oriented.

Lifetime measurements with improved precision in S30,32 and possible influence of large-scale clustering on the appearance of strongly deformed states

The formation of large size clusters and/or their relative motion as possible excitation mode are suggested to be closely related to the origin of deformation in specific cases. In $^{32}\mathrm{S}$, the consideration of some excitations in this nucleus as based on the existence of two doubly magic $^{16}\mathrm{O}$ clusters offers a possible solution to the long-standing problem of missing quadrupole collectivity in shell-model calculations aiming to describe electromagnetic $E2$ transition strengths and quadrupole moments. To experimentally check again this collectivity, lifetime measurements were performed on $^{30}\mathrm{S}$ and $^{32}\mathrm{S}$. In $^{32}\mathrm{S}$, at least, the reproduction of a number of observables supports the cluster scenario. Additionally, the superdeformed yrast band in $^{80}\mathrm{Zr}$ could find an explanation as based on the relative motion of two $^{40}\mathrm{Ca}$ clusters. Simultaneously, a necessity arises to revise experimentally some lifetimes derived in the past within the Blaugrund approximation when using the Doppler-shift attenuation method.

Study of rotational bands and electromagnetic properties of odd mass 153−159Eu

Some positive and negative parity energy bands of odd-A isotopes of Europium [Formula: see text] have been studied within the Projected Shell Model (PSM) framework. Calculated excitation energy spectra, transition energies, E2 and M1 transition probabilities, quadrupole and magnetic moments are compared with experimental data wherever available. Reasonably good agreement is obtained with the observed data.

Lifetime measurement of neutron-rich even-even molybdenum isotopes

Background: In the neutron-rich $A\ensuremath{\approx}100$ mass region, rapid shape changes as a function of nucleon number as well as coexistence of prolate, oblate, and triaxial shapes are predicted by various theoretical models. Lifetime measurements of excited levels in the molybdenum isotopes allow the determination of transitional quadrupole moments, which in turn provides structural information regarding the predicted shape change.Purpose: The present paper reports on the experimental setup, the method that allowed one to measure the lifetimes of excited states in even-even molybdenum isotopes from mass $A=100$ up to mass $A=108$, and the results that were obtained.Method: The isotopes of interest were populated by secondary knock-out reaction of neutron-rich nuclei separated and identified by the GSI fragment separator at relativistic beam energies and detected by the sensitive PreSPEC-AGATA experimental setup. The latter included the Lund-York-Cologne calorimeter for identification, tracking, and velocity measurement of ejectiles, and AGATA, an array of position sensitive segmented HPGe detectors, used to determine the interaction positions of the $\ensuremath{\gamma}$ ray enabling a precise Doppler correction. The lifetimes were determined with a relativistic version of the Doppler-shift-attenuation method using the systematic shift of the energy after Doppler correction of a $\ensuremath{\gamma}$-ray transition with a known energy. This relativistic Doppler-shift-attenuation method allowed the determination of mean lifetimes from 2 to 250 ps.Results: Even-even molybdenum isotopes from mass $A=100$ to $A=108$ were studied. The decays of the low-lying states in the ground-state band were observed. In particular, two mean lifetimes were measured for the first time: $\ensuremath{\tau}=29.{7}_{\ensuremath{-}9.1}^{+11.3}$ ps for the ${4}^{+}$ state of $^{108}\mathrm{Mo}$ and $\ensuremath{\tau}=3.{2}_{\ensuremath{-}0.7}^{+0.7}$ ps for the ${6}^{+}$ state of $^{102}\mathrm{Mo}$.Conclusions: The reduced transition strengths $B(E2)$, calculated from lifetimes measured in this experiment, compared to beyond-mean-field calculations, indicate a gradual shape transition in the chain of molybdenum isotopes when going from $A=100$ to $A=108$ with a maximum reached at $N=64$. The transition probabilities decrease for $^{108}\mathrm{Mo}$ which may be related to its well-pronounced triaxial shape indicated by the calculations.

Energies, transition probabilities, predissociation rates, and lifetimes of the , HD, and state

Transition probabilities of H2, HD, and D2 − electric dipole, − discrete-continuum magnetic dipole, and electric quadrupole transitions have been calculated using accurate energies and ro-vibrational wave functions obtained from precise ab initio potential energy curves. The predissociation rates of the () levels by direct and indirect spin–spin and spin–orbit coupling between − fine structure levels, have been also determined. The present investigation achieved good agreement with measured lifetimes of the fine structure levels without adjustment. A comparison of the calculated and observed lifetimes of metastable H2, HD, and D2 suggests that the − magnetic dipole and electric quadrupole transition moments underestimate the spontaneous emission rate of the metastable levels by ∼370 s−1. The measured and calculated lifetimes of H2, HD, and D2 fine structure levels are in very good agreement after the adjustment of 370 s−1 to the spontaneous decay rate of the − transition. The calculated energies, transition probabilities, and predissociation rates obtained in the present work, along with the state excitation function, are sufficient to determine the state emission cross section, the kinetic energy distribution of H(1s) atoms, and the energy deposition rate of the − excitation. In a previous investigation by Berg and Ottinger (1994 J. Chem. Phys. 100 8746), the authors were forced to insert a large scale factor into the predissociation rate in order to reconcile with measured lifetimes. Errors introduced in the approximations made in the previous investigations are discussed in the text. The H2 state has the second largest triplet state excitation cross section. Predissociation and spontaneous emission of the state plays an important role in the energy deposition of H2-dominated atmospheres.

Nuclear structure of low-lying states in 60,62,64,66Zn — A shell model description

Shell model calculation has been performed for even–even [Formula: see text]Zn using NuShellX code in [Formula: see text] model space with two different effective Hamiltonians, viz. JUN45 and jj44b. The low-lying structure is studied up to angular momentum, [Formula: see text] = 10[Formula: see text] by calculating level energies, reduced transition probabilities, occupation numbers, lifetimes, and quadrupole moments. The results of the calculations are compared with the available experimental data. It is observed that the inclusion of 1[Formula: see text] orbital in the model space is essential to understand nuclear structure in these isotopes. Shell model calculation with an improved set of effective Hamiltonian parameters and inclusion of [Formula: see text] orbital in the model space are necessary in order to produce finer agreement with the experimental observations.

Deformation and shape changes inW167

Lifetime measurements of yrast levels in $^{167}\mathrm{W}$ were measured using the recoil-distance Doppler-shift method. The differential decay-curve method was applied for a lifetime determination. Excited states of the nucleus $^{167}\mathrm{W}$ were populated by the reaction $^{142}\mathrm{Nd}$ ($^{28}\mathrm{Si}, 3n$) at a beam energy of 144 MeV. The energy spectra and measured transition quadrupole moments inferred from the lifetimes of $^{167}\mathrm{W}$ are compared with the predictions of the cranked Nilsson-Strutinsky-Bogoliubov calculations. The changes of deformations and shapes with increasing spin due to the $\ensuremath{\gamma}$-polarization effect of aligned particles are discussed. The signature inversion visible in the negative parity yrast band is explained to be related to the triaxial shapes.

Single-particle and collective excitations inNi62

{\bf Background:} Level sequences of rotational character have been observed in several nuclei in the $A=60$ mass region. The importance of the deformation-driving $\pi f_{7/2}$ and $\nu g_{9/2}$ orbitals on the onset of nuclear deformation is stressed.\\ {\bf Purpose:} A measurement was performed in order to identify collective rotational structures in the relatively neutron-rich $^{62}$Ni isotope. \\ {\bf Method:} The $^{26}$Mg($^{48}$Ca,2$\alpha$4$n\gamma$)$^{62}$Ni complex reaction at beam energies between 275 and 320~MeV was utilized. Reaction products were identified in mass ($A$) and charge ($Z$) with the Fragment Mass Analyzer (FMA) and $\gamma$ rays were detected with the Gammasphere array. \\ {\bf Results:} Two collective bands, built upon states of single-particle character, were identified and sizable deformation was assigned to both sequences based on the measured transitional quadrupole moments, herewith quantifying the deformation at high spin. \\ {\bf Conclusions:} Based on Cranked Nilsson-Strutinsky calculations and comparisons with deformed bands in the $A=60$ mass region, the two rotational bands are understood as being associated with configurations involving multiple $f_{7/2}$ protons and $g_{9/2}$ neutrons, driving the nucleus to sizable prolate deformation.

Band structure inSn113

The structure of collective bands in $^{113}\mathrm{Sn}$, populated in the reaction $^{100}\mathrm{Mo}(^{19}\mathrm{F},\phantom{\rule{0.16em}{0ex}}p5n)$ at a beam energy of 105 MeV, has been studied. A new positive-parity sequence of eight states extending up to 7764.9 keV and spin $(39/{2}^{+})$ has been observed. The band is explained as arising from the coupling of the odd valence neutron in the ${g}_{7/2}$ or the ${d}_{5/2}$ orbital to the deformed 2p-2h proton configuration of the neighboring even-$A$ Sn isotope. Lifetimes of six states up to an excitation energy of 9934.9 keV and spin $47/{2}^{\ensuremath{-}}\mathrm{belonging}$ to a $\mathrm{\ensuremath{\Delta}}I=2$ intruder band have been measured for the first time, including an upper limit for the last state, from Doppler-shift-attenuation data. A moderate average quadrupole deformation ${\ensuremath{\beta}}_{2}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ is deduced from these results for the five states up to spin $43/{2}^{\ensuremath{-}}$. The transition quadrupole moments decrease with increase in rotational frequency, indicating a reduction of collectivity with spin, a feature common for terminating bands. The behavior of the kinematic and dynamic moments of inertia as a function of rotational frequency has been studied and total Routhian surface calculations have been performed in an attempt to obtain an insight into the nature of the states near termination.

From superdeformation to extreme deformation and clusterization in theN≈Znuclei of theA≈40mass region

A systematic search for extremely deformed structures in the N~Z nuclei of the A~40 mass region has been performed for the first time in the framework of covariant density functional theory. At spin zero such structures are located at high excitation energies which prevents their experimental observation. The rotation acts as a tool to bring these exotic shapes to the yrast line or its vicinity so that their observation could become possible with future generation of $\gamma-$tracking (or similar) detectors such as GRETA and AGATA. The major physical observables of such structures (such as transition quadrupole moments as well as kinematic and dynamic moments of inertia), the underlying single-particle structure and the spins at which they become yrast or near yrast are defined. The search for the fingerprints of clusterization and molecular structures is performed and the configurations with such features are discussed. The best candidates for observation of extremely deformed structures are identified. For several nuclei in this study (such as $^{36}$Ar), the addition of several spin units above currently measured maximum spin of $16\hbar$ will inevitably trigger the transition to hyper- and megadeformed nuclear shapes.

Lifetime measurements in the yrast band of the gamma-soft nuclei 131Ce and 133Pr

Lifetimes of excited states in the yrast band of the gamma-soft nuclei 131Ce and 133Pr have been measured using the recoil distance Doppler shift and Doppler shift attenuation methods. The yrast bands in 131Ce and 133Pr are based on odd decoupled neutron νh 11/2 high Ω and proton π h 11/2 low Ω orbitals, respectively. The triaxiality parameter extracted from the experimentally deduced values of transition quadrupole moments, within the framework of cranked Hartree–Fock–Bogoliubov (CHFB) and total Routhian surface (TRS) calculatons, is γ ∼ −80∘ for the band in 131Ce at high spins, while for the band in 133Pr, the value of γ is close to 0∘. This agrees well with the γ shape polarization property of high and low Ωh 11/2 orbitals in these gamma-soft nuclei.

Analysis methods of safe Coulomb-excitation experiments with radioactive ion beams using the GOSIA code

With the recent advances in radioactive ion beam technology, Coulomb excitation at safe energies becomes an important experimental tool in nuclear-structure physics. The usefulness of the technique to extract key information on the electromagnetic properties of nuclei has been demonstrated since the 1960's with stable beam and target combinations. New challenges present themselves when studying exotic nuclei with this technique, including dealing with low statistics or number of data points, absolute and relative normalisation of the measured cross sections and a lack of complimentary experimental data, such as excited-state lifetimes and branching ratios. This paper addresses some of these common issues and presents analysis techniques to extract transition strengths and quadrupole moments utilising the least-squares fit code, {\rmfamily \textsc{gosia}}.