Reduced Transition Probabilities Research Articles

Systematics of the ratio of electric quadrupole moments [formula omitted] to the square root of the reduced transition probabilities [formula omitted] in even–even nuclei

A survey of even–even nuclei in the nuclear chart showed regularities in the values of the ratio Q(21+)/(B(E2) for each nucleus for which independent measurements of both the electric quadrupole moment of the 21+ state, Q(21+), and the reduced transition probability B(E2;01+→21+) exist. As predicted by the rotational model, this ratio was found to be close to unity for the deformed nuclei in the rare-earth region. For non-rotational nuclei the absolute value of this ratio is almost always considerably lower. This latter observation can be interpreted within different models for different classes of nuclei as illustrated by a set of schematic IBA model calculations. A general mixing model and simple geometrical models are also suitable for collective non-rotational nuclei. Near magic nuclei a mechanism within the seniority scheme is compatible with the observed small value of RQB.

Symmetrical level schemes of the even–even Sm[formula omitted] and Yb[formula omitted] nuclei up to 10+ in the yrast bands

For the first time, we show here that three isotopes of the Sm isotopic chain almost overlay with three isotopes of the Yb isotopic chain in terms of experimental observables within the NπNν scheme. A recent systematic work by Sayğı on reduced transitional probabilities in pseudo-mirror nuclei revealed that nuclei having particle–hole symmetry tend to manifest alike experimental structures. The NπNν quantity is an indicator of the symmetry and depends on valence nucleon (or holes) number from the nearest closed shell by considering the subshell closures, which simplifies the systematics of excitation energies and related B(E2; L+→(L−2)+) values of excited states in nuclei placed in the different mass regions of nuclear chart. In the light of available data, the experimental observables in the group of 136Sm–160Yb, 134Sm–162Yb and 132Sm–164Yb nuclei have been analyzed in a vertical and horizontal perspectives and the ratio of reduced transition probabilities of the first excited states compared with existing theoretical predictions. The data brought to light that the structure of each group reflects identical yrast bands up to 10+.

Magnetic dipole response of the 169Tm nucleus

The magnetic dipole (M1) response of the 169Tm nucleus is investigated from a theoretical point of view. The theoretical tool used in this study is the Rotational Invariant Quasiparticle Phonon Nuclear Model (RI-QPNM) which gives a possibility to eliminate spurious contributions in the M1 spectrum. In the framework of this model, both the low-lying and high-lying parts of the M1 excitation spectrum of 169Tm are calculated. The result shows that the low-lying excitations have almost pure orbital character and can be interpreted as scissors mode, whereas the high-lying transitions can be read as spin-flip mode because of its spin nature. The reduced transition probability summed up in the energy range 2–4 MeV is found to be B(M1↑)=3.040μN2 which agrees with the available experimental data. The fragmentation of the low-energy M1 strength is also well reproduced. This is also the first study in which both the low-lying and high-lying M1 spectrum of the 169Tm nucleus is theoretically investigated.

Novel ΔJ=1 Sequence in ^{78}Ge: Possible Evidence for Triaxiality.

A sequence of low-energy levels in _{32}^{78}Ge_{46} has been identified with spins and parity of 2^{+}, 3^{+}, 4^{+}, 5^{+}, and 6^{+}. Decays within this band proceed strictly through ΔJ=1 transitions, unlike similar sequences in neighboring Ge and Se nuclei. Above the 2^{+} level, members of this sequence do not decay into the ground-state band. Moreover, the energy staggering of this sequence has the phase that would be expected for a γ-rigid structure. The energies and branching ratios of many of the levels are described well by shell-model calculations. However, the calculated reduced transition probabilities for the ΔJ=2 in-band transitions imply that they should have been observed, in contradiction with the experiment. Within the calculations of Davydov, Filippov, and Rostovsky for rigid-triaxial rotors with γ=30°, there are sequences of higher-spin levels connected by strong ΔJ=1 transitions which decay in the same manner as those observed experimentally, yet are calculated at too high an excitation energy.

Microscopic description of triaxiality in Ru isotopes with covariant energy density functional theory

The triaxiality in nuclear low-lying states has attracted great interests for many years. Recently, the reduced transition probabilities for levels near the ground state in $^{110}$Ru have been measured and provided strong evidences for a triaxial shape of this nucleus. The aim of this work is to provide a microscopic study of low-lying states for the Ru isotopes with $A\sim100$ and to examine in detail the role of triaxiality, and the evolution of quadrupole shapes with the isospin and spin degrees of freedom. The low-lying excitation spectra and transition probabilities of even-even Ru isotopes are described at the beyond mean-field level by solving a five-dimensional collective Hamiltonian with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1. The calculated energy surfaces, low-energy spectra, intraband and interband transition rates, as well as some characteristic collective observables, such as $E(4_{\rm g.s.}^+)/E(2^+_{\rm g.s.})$, $E(2^+_\gamma)/E(4^+_{\rm g.s.})$, $B(E2; 2^+_{\rm g.s.}\to 0^+_{\rm g.s.})$, and $\gamma$ band staggerings are in a good agreement with the available experimental data. The main features of the experimental low-lying excitation spectra and electric transition rates are well reproduced, and thus strongly support the onset of triaxiality in the low-lying excited states of the Ru isotopes around $^{110}$Ru.

Determine the 134–140Nd isotopes identity using IBM and NEF

The property of 134−140Neodymium nuclei have been studied in framework Interacting Boson Model (IBM) and a new method called New Empirical Formula (NEF). The energy positive parity bands of 134−140Nd have been calculated using (IBM) and (NEF) while the negative parity bands of 134−140Nd have been calculated using (NEF) only. The E-GOS curve (Eγ/I) as a function of the spin (I) has been drawn to determine the property of the positive parity yrast band. The parameters of the best fit to the measured data are determined. The reduced transition probabilities B(E2) of these nuclei was calculated. The critical point has been determined for 140Nd isotope. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic coherent state.

Excited negative parity bands in 160Yb

Negative parity rotational bands in Yb nucleus have been studied. They were populated in the 148Sm(16O, 4n)160Yb reaction at 90 MeV. The gamma-coincidence data have been collected using Indian National Gamma Array composed of twenty Compton suppressed clover germanium (Ge) detectors. Double gating on triple gamma coincidence data were selectively used to develop the decay scheme for these negative parity bands by identifying and taking care of the multiplet transitions. The even- and odd-spin negative parity bands in 160Yb have been studied by comparing the reduced transition probability ratios with the similar bands in neighbouring even–even rare earth nuclei. It is concluded that the concerned odd-spin and even-spin bands are not signature partners and that their structures are compatible with those of the ‘pear-shape’ and ‘pyramid-shape’ oscillations, respectively, the octupole shapes superposed with the quadrupole shape of the ground-state.

Theoretical description of the deformation properties for 154–164Gd isotopes

The 154–164Gd isotopes in SU(3) region were investigated. For these nuclei, the positive ground-state band of 154–164Gd has been calculated using Bohr–Mottelson Model, Interacting Vector Boson Model and Interacting Boson Model, while the negative-parity band of 154–164Gd has been calculated using Bohr–Mottelson Model and Interacting Vector Boson Model only. To determine the property of the ground-state band, the ratio (r(I+2)/I) and E-GOS curve (Eγ/I) as a function of the spin (I) have been drawn. The reduced transition probabilities B(E2) of these nuclei were calculated. The results were compared with the experimental data and the previous calculations. It is shown that there is a good agreement between the results found and especially with the experimental ones. The potential energy surface (PES) has been calculated within the framework using interacting boson model (IBM-1). The contour plot of the potential energy surfaces shows that the interested nuclei are deformed and have rotational characters.

Probing the structure of the stable Xe isotopes with inelastic neutron scattering

The stable isotopes of xenon, which have attracted interest for a number of reasons, span a transitional region that evolves from γ-soft structures for the lighter mass isotopes to nearly spherical 136Xe with a closed neutron shell. The nature of this transition, which is gradual, is not well understood. To provide detailed spectroscopic information on the Xe isotopes, we have studied 130,132,134,136Xe at the University of Kentucky Accelerator Laboratory using inelastic neutron scattering and γ-ray detection. These measurements yielded γ-ray angular distributions, branching ratios, multipole mixing ratios, and level lifetimes (from the Doppler-shift attenuation method), which allowed the determination of reduced transition probabilities and provided insight into the structure of these nuclei.

Re-measurement of Reduced Transition Probabilities in $^{132}$Ba

Re-measurement of Reduced Transition Probabilities in $^{132}$Ba

Investigation of Energy Levels and Electromagnetic Transitions for Yb–Pt Nuclei with N=108 Using IBM, IVBM, and BMM

The interacting boson and vector boson models, as well as the Bohr–Mottelson one, are employed to describe the energy levels and electromagnetic transitions of the 178Yb–186Pt (N = 108) nuclei. For the purpose of determining the evolution of the ground state, both r((I + 2)/I) and E-GOS ratios have been calculated as functions of the spin I. Based on the interacting vector boson model and Bohr–Mottelson model, the negative-parity and GSB bands have been calculated, while the interacting boson model is only employed to calculate GSB, y, and b. The interacting boson model is also used to calculate the reduced transition probabilities B(E2). The obtained findings show a very well agreement with experimentally obtained results elsewhere. We also used the intrinsic coherent state to obtain the potential energy surfaces. These results indicate that these nuclei have a rotational property SU(3), while 186Pt has property O(6).

Spin-dependent evolution of collectivity in Te112

The evolution of collectivity with spin along the yrast line in the neutron-deficient nucleus $^{112}\mathrm{Te}$ has been studied by measuring the reduced transition probability of excited states in the yrast band. In particular, the lifetimes of the ${4}^{+}$ and ${6}^{+}$ excited states have been determined by using the recoil distance Doppler-shift method. The results are discussed using both large-scale shell-model and total Routhian surface calculations.

No evidence of reduced collectivity in Coulomb-excited Sn isotopes

In a series of Coulomb excitation experiments the first excited ${2}^{+}$ states in semimagic $^{112,116,118,120,122,124}\mathrm{Sn}$ isotopes were excited using a $^{58}\mathrm{Ni}$ beam at safe Coulomb energy. The $B(E2$; ${0}^{+}\ensuremath{\rightarrow}{2}^{+})$ values were determined with high precision $(\ensuremath{\sim}3%)$ relative to $^{58}\mathrm{Ni}$ projectile excitation. These results disagree with previously reported $B(E2\ensuremath{\uparrow})$ values [A. Jungclaus et al., Phys. Lett. B 695, 110 (2011).] extracted from Doppler-shift attenuation lifetime measurements, whereas the reported mass dependence of $B(E2\ensuremath{\uparrow})$ values is very similar to a recent Coulomb excitation study [J. M. Allmond et al., Phys. Rev. C 92, 041303(R) (2015)]. The stable Sn isotopes, key nuclei in nuclear structure, show no evidence of reduced collectivity and we, thus, reconfirm the nonsymmetric behavior of reduced transition probabilities with respect to the midshell $A=116$.

Projected Shell Model Description of Positive Parity Band of 130Pr Nucleus

Theoretical investigation of positive parity yrast band of odd-odd 130Pr nucleus is performed by applying the projected shell model. The present study is undertaken to investigate and verify the very recently observed side band in 130Pr theoretically in terms of quasi-particle (qp) configuration. From the analysis of band diagram, the yrast as well as side band are found to arise from two-qp configuration πh 11/2 ⊗ νh 11/2. The present calculations are viewed to have qualitatively reproduced the known experimental data for yrast states, transition energies, and B(M1) / B(E2) ratios of this nucleus. The recently observed positive parity side band is also reproduced by the present calculations. The energy states of the side band are predicted up to spin 25+, which is far above the known experimental spin of 18+ and this could serve as a motivational factor for future experiments. In addition, the reduced transition probability B(E2) for interband transitions has also been calculated for the first time in projected shell model, which would serve as an encouragement for other research groups in the future.

Level lifetimes and the structure of Xe134 from inelastic neutron scattering

The level structure of $^{134}\mathrm{Xe}$ was studied with the inelastic neutron scattering reaction followed by $\ensuremath{\gamma}$-ray detection. A number of level lifetimes were determined for the first time with the Doppler-shift attenuation method and the low-lying excited states were characterized. From this new spectroscopic information, the third excited state, a ${0}^{+}$ level which had only been observed in a previous inelastic neutron scattering study, was verified. Reduced transition probabilities were calculated; comparisons were drawn with a vibrational description of the nucleus and found lacking. The ${3}^{\ensuremath{-}}$ octupole phonon has been confirmed, and the complete negative-parity multiplet resulting from the $\ensuremath{\nu}(1{h}_{11/2}2{d}_{3/2})$ configuration has also been tentatively identified for the first time in the $N=80$ isotones.

Study of odd mass 115−125Sb isotopes with the projected shell model calculations

The projected shell model (PSM) with the deformed single-particle states, generated by the standard Nilsson potential, is applied to study the negative-parity high spin states of [Formula: see text] nuclei. The nuclear structure quantities like band structure and back-bending in moment of inertia have been calculated with PSM method and are compared with the available experimental data. In addition, the reduced transition probabilities, i.e., B[Formula: see text] and B[Formula: see text], are also obtained for the yrast band of these isotopes for the first time by using PSM wave function. A multi-quasiparticle structure has been predicted for [Formula: see text] isotopes by the present PSM calculations.

Collectivity in 196,198Pb isotopes probed in Coulomb-excitation experiments at REX-ISOLDE

The neutron-deficient Pb isotopes have been studied in Coulomb-excitation experiments employing the Miniball γ-ray spectrometer and radioactive ion beams from the REX-ISOLDE post-accelerator at CERN. The reduced transition probabilities of the first excited 2+ states in 196Pb and 198Pb nuclei have been measured for the first time. Values of W.u. and W.u., were obtained, respectively. The experiment sheds light on the development of collectivity when moving from the regime governed by the generalised seniority scheme to a region, where intruding structures, associated with different deformed shapes, start to come down in energy and approach the spherical ground state.

Collective quadrupole behavior in Pd106

Excited states in $^{106}\mathrm{Pd}$ were studied with the $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction, and comprehensive information for excitations with spin $\ensuremath{\le}6\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}$ was obtained. The data include level lifetimes in the femtosecond regime, spins and parities, transition multipolarities, and multipole mixing ratios, which allow the determination of reduced transition probabilities. The $E2$ decay strength to the low-lying states is mapped up to $\ensuremath{\approx}2.4$ MeV in excitation energy. The structures associated with quadrupole collectivity are elucidated and organized into bands.

Lifetimes in Te124 : Examining critical-point symmetry in the Te nuclei

The Doppler-shift attenuation method following inelastic neutron scattering was used to determine the lifetimes of nuclear levels to 3.3-MeV excitation in $\phantom{\rule{0.16em}{0ex}}^{124}\mathrm{Te}$. Level energies and spins, $\ensuremath{\gamma}$-ray energies and branching ratios, and multipole-mixing ratios were deduced from measured $\ensuremath{\gamma}$-ray angular distributions at incident neutron energies of 2.40 and 3.30 MeV, $\ensuremath{\gamma}$-ray excitation functions, and $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidence measurements. The newly obtained reduced transition probabilities and level energies for $\phantom{\rule{0.16em}{0ex}}^{124}\mathrm{Te}$ were compared to critical-point symmetry model predictions. The $E(5)$ and ${\ensuremath{\beta}}^{4}$ potential critical-point symmetries were also investigated in $\phantom{\rule{0.16em}{0ex}}^{122}\mathrm{Te}$ and $\phantom{\rule{0.16em}{0ex}}^{126}\mathrm{Te}$.

Microscopic description of the even-even 140-148Ba isotopes using BM, IBM and IVBM

A description of the even-even Ba isotopes for A = 140 to 148 in framework of Bohr-Mottelson model, interacting boson model and interacting vector boson model are carried out. The E-GOS curve (E $\gamma$ /I and the ratio between the energies of the (I + 2) and (I) states (r(I + 2)/I) as a function of the spin (I have been drawn to determine the property of the ground-state band. The positive ground-state band of 140-148Ba has been calculated using Bohr-Mottelson model, interacting boson model and interacting vector boson model, while the negative-parity band of 140-148Ba has been calculated using Bohr-Mottelson model and interacting vector boson model only. The reduced transition probabilities B(E2) of these nuclei were calculated. The parameters of the best fit to the measured data are determined. The potential energy surfaces (PESs) to the IBM Hamiltonian have been obtained using the intrinsic coherent state.