Electric Quadrupole Transition Probabilities Research Articles

Mapping low-lying states and [formula omitted] in even-even nuclei with machine learning

A machine-learning algorithm, Light Gradient Boosting Machine, was applied for the first time to investigate the fundamental experimental observables in even-even nuclei over the Segrè chart. Specifically, we focused on the excitation energies of the 21+ and 41+ states, and the reduced electric quadrupole transition probability B(E2;01+→21+). Present obtained results well reproduced experimental data within an accuracy of 1.07, 1.05, and 1.14 times for the 21+ and 41+ states as well as B(E2;01+→21+), respectively, being significantly precise than the results from any state-of-the-art nuclear models and from any machine-learning-based approaches. The predictive capability of our machine learning methodology was further validated using 17 newly measured data points which were not used in the training set. Taking O, Ca, Sn, and Pb isotopes as examples, it has been found that our methodology precisely captures both the isotopic trend and absolute values, surpassing all theoretical models hitherto. Our findings reveal the double-magic nature of 100Sn and the disappearance of the N=20 shell in 28O.

Study of Octupole Transitions in Xe, Ba, Ce and Nd Nuclei within Interacting Boson Model

For nuclei with 54≤Z≤60 and 86≤N≤94, the results regarding the excitation spectra at low energies, both in positive and negative parity, as well as the transition probabilities for electric dipole (B(E1)), quadrupole (B(E2)), and octupole transitions (B(E(3)), indicate the emergence of significant octupole behavior. These observations have been made using the Interacting Boson Model-1 (IBM-1). The study examines the onset of octupole deformation and its impact on the spectroscopic characteristics in even-even neutron-rich lanthanide isotopes, specifically in the Ba and Nd nuclei. The investigation compares the results obtained from the Interacting Boson Model-1 (IBM-1) with the existing experimental data. The focus is on understanding how the addition of neutrons influences the development of octupole deformation and its manifestation in the observed spectroscopic features. The onset of strong octupolarity for Z≈ 56 and N ≈ 88 nuclei is indicated by the results obtained for the electric dipole, quadrupole, and octupole transition probabilities, as well as the low-energy positive and negative-parity excitation spectra. Conversely, discrepancies between the spectroscopic data and the IBM results suggest that the mapping quality needs to be evaluated in order to determine if the mapped boson Hamiltonian or the fermionic calculations are the source of the issues.

Nuclear Shape-Phase Transition From Spherical U(5) to Deformed gamma-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

The shape transition from spherical vibrator U(5) to gamma-unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter beta and by using the catastrophe theory in terms of the two essential parameters (r_1, r_2). By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at gamma =0. For the studied isotopic chains, the chi ^2-test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that ^{100}Ru, ^{102}Pd and ^{130}Xe nuclei are good candidates for the E(5) critical point symmetry.

New pattern in regular nuclei based on their experimental quadrupole transition rates and some new candidates

In this paper, we tried to get a new signature of regular nuclei based on their quadrupole transition rates. We have analyzed the experimental electric quadrupole transition probabilities of well-known "regular nuclei". The results indicate finding specific repetition patterns for E2 transition rates, similar to what has been reported for the energy levels of these nuclei. We also tested the existence of this observed repetition scheme for all known isotopes whose experimental transition rates are available and introduced several new candidates as regular nuclei. Then, the energy spectra (Experimental) of these new suggested "regular nuclei" are investigated in the framework of the Interacting Boson Model, in which the parameters of Hamiltonian confirm the placement of these nuclei in the "Alhassid-Whelan arc of regularity" region. In order to further study the statistical distribution of experimental energy levels related to the electromagnetic transitions we are considering, we studied using the random matrix theory. The results confirmed their regularity.

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

Investigation of the statistical fluctuations of the electric quadrupole transition rates of spherical nuclei by kernel density estimation method‎

In this study, the statistical correlation of the electric quadrupole transition probabilities in the spherical nuclei is investigated. To this aim, the spherical even-even nuclei in the 100 < A < 126 mass region are selected and the electric quadrupole transition rates of different levels in the ground band are determined by the interacting boson model in the U(5) dynamical limit. A non-parametric kernel density estimation method is used in the framework of nearest neighbor spacing distribution of random matrix theory to consider the statistical correlation of these quadrupole transition rates. Also, the Kullback-Leibler divergence is used to describe the regular or chaotic behavior of the considered sequences. The results show the correlation of the electric quadrupole transition probabilities between different levels of the ground band. Also, the correlation increased for such transitions that the angular momentum of the initial state of quadrupole transitions increased.

Signatures of shape phase transitions in krypton isotopes based on relativistic energy density functionals

Spectroscopic properties that characterize the shape phase transitions in krypton isotopes with the mass $A\approx80$ region are investigated within the framework of the nuclear density functional theory. Triaxial quadrupole constrained self-consistent mean-field calculations that employ relativistic energy density functionals and a pairing interaction are carried out for the even-even nuclei $^{76-86}$Kr. The spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with the ingredients, i.e., the deformation-dependent moments of inertia and mass parameters, and the collective potential, determined by using the SCMF solutions as microscopic inputs. Systematic behaviors of the SCMF potential energy surfaces, the corresponding low-energy spectra, electric quadrupole and monopole transition probabilities, and the fluctuations in the triaxial quadrupole deformations indicate evolution of the underlying nuclear structure as functions of the neutron number, that is characterized by a considerable degree of shape mixing. A special attention is paid to the transitional nucleus $^{82}$Kr, which has been recently identified experimentally as an empirical realization of the E(5) critical-point symmetry.

Energy Levels and B(E2) Calculation for 50Fe Isotope Using F754 and F7mbz Interactions

In this work was calculated energy levels and reduced electric quadrupole transition probability B(E2) for 50Fe isotope using OXBASH code within the 1f7/2 shell and using the F754 and F7mbz effective interaction. 50Fe isotope contain 6 proton and 4 neutron out side 40Ca core in shell. In general, an acceptable agreement was obtained for a number of energy levels, and the total angular momentum and ground state parity were matched for all these isotopes, also new energy levels were obtained that have no practical values so far.

Systematic Projected Shell Model Study of Even-Even Dysprosium Isotopes

Back-bending phenomenon is one of the important phenomena usually seen at high spin states of even - even heavy nuclei. As a result, any changes in the behavior of nuclear rotation, such as increase in moment of inertia versus rotational frequency can be shown in the usual back-bending plots which have been studied in many papers before. In this paper we show for the first time that these changes can be seen in the ratio of electromagnetic reduced transition probabilities B (E2) and B (M1) in even - even 152-164 Dy isotopes using the Projected Shell Model (PSM) theory. The electric quadrupole transition probability B (E2) and the magnetic dipole transition probability B (M1) moments are sensitive to nuclear shape deformation and nuclear charge distribution, respectively. Our findings confirm the well-known back-bending previously seen and are in good agreement with experimental results. While intrinsic quadrupole moments are constant for each Dy isotope, the new findings show that spectroscopic quadrupole moments are increasing with spin. 15.00 Normal 0 false false false EN-US X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";}

Description of the energy levels and electric quadrupole transitions of the 92Nb and 92Mo nuclei using nuclear shell model

In current study ,92Nb and 92Mo isotopes have been determined for calculating energy levels and electric quadrupole transition probabilities. Two interaction have been applied in this study are surface delta and modified surface delta interactions. The calculations have been achieved by using appropriate effective charges for proton and neutron as well as parameter length of harmonic potential. Computed results have been compared with the experimental values. After this comparison, energy and the transition probability values have a good agreement with the experimental values, also there are values of the total angular momentum and parity are determined and confirmed for some of the experimental energies, undetermined and unconfirmed experimentally. Theoretically, new values of quadrupole electric transition probabilities have been explored which have not been known in the experimental data.

Positive parity low-spin states of even–odd 129−133Ba isotopes

The positive parity low-spin states of even-odd 129−133Ba isotopes were studied in this study using the Interacting Boson–Fermion Model (IBFM-1). The single fermion is predicted to be in one of three single-particle orbits: 2d5/2, 2d3/2, and 3s1/2. The Interacting Boson Model (IBM-1) was used to investigate the energy levels, electric quadrupole transition probabilities, and potential energy surface of even-even Barium isotopes (a core for even-odd nuclei).The measured positive parity low-state energy spectra and predicted energy levels, as well as the B(E2) transition probabilities, are reasonably consistent with the experimental data and previous research for Ba isotopes. The potential energy surface contour plot reveals that all interesting nuclei are deformed and have γ-unstable-like properties.

Evolution of octupole deformation and collectivity in neutron-rich lanthanides

The onset of octupole deformation and its impact on related spectroscopic properties is studied in even-even neutron-rich lanthanide isotopes Xe, Ba, Ce, and Nd with neutron number $86\leqslant N\leqslant 94$. Microscopic input comes from the Hartree-Fock-Bogoliubov approximation with constrains on the axially symmetric quadrupole and octupole operators using the Gogny-D1M interaction. At the mean-field level, reflection asymmetric ground states are predicted for isotopes with neutron number around $N=88$. Spectroscopic properties are studied by diagonalizing the interacting boson model Hamiltonian, with the parameters obtained via the mapping of the mean-field potential energy surface onto the expectation value of the Hamiltonian in the $s$, $d$, and $f$ boson condensate state. The results obtained for low-energy positive- and negative-parity excitation spectra as well as the electric dipole, quadrupole, and octupole transition probabilities indicate the onset of pronounced octupolarity for $Z\approx 56$ and $N\approx 88$ nuclei.

Extended analytical solutions of the Bohr Hamiltonian with the sextic oscillator

Low-lying collective quadrupole states in even–even nuclei are studied for the particular case of a γ-unstable potential within the Bohr Hamiltonian. In particular, the quasi-exactly solvable β-sextic potential is extended to cover the most relevant part of the low-lying spectra in nuclei. In previous papers (2004 Phys. Rev. C 69 014304, 2010 Phys Rev. C 81 044304), the same situation was solved for β-wavefunctions with up to one node (M = 0, 1), which are relevant for the first few low-lying states. Here, the model space is enlarged by including β-wavefunctions also with two nodes (M = 2), which generate many more states, in order to make it useful for actual fittings and more detailed checking of shape phase transitions between spherical and γ-unstable β-deformed shapes in nuclei. In addition to the energy eigenvalues and wavefunctions, closed analytical formulas are obtained for electric quadrupole and monopole transition probabilities too. The model is applied to the chains of even Ru and Pd isotopes to illustrate the transition between the spherical and deformed γ-unstable phases. These applications indicate that the optional extension of the model with a phenomenologic rotational term L ⋅ L is consistent with the experimental data.

Octupole correlations in 127I

In-beam [Formula: see text]-ray spectroscopy of [Formula: see text]I was carried out following [Formula: see text]Sn(7Li, 4n[Formula: see text]) fusion-evaporation reaction at a beam energy of 33 MeV. Ratio of the electric dipole (E1) and electric quadrupole (E2) transition probabilities [B(E1)/B(E2)] for the transitions depopulating from the [Formula: see text] states have been extracted from this study. Existence of enhanced E1 transition rates between the opposite parity bands, associated dominantly with [Formula: see text] and [Formula: see text] configurations, provides an indication of octupole correlations in this nucleus

Investigation of transition symmetry shapes of 160-168Yb nuclei using IBM

The interacting boson models, and were used to perform a complete study of even –even 160-168Yb isotopes .The low –lying positive parity states, dynamic symmetries, reduced electric quadrupole transition probability , quadruple momentum , and potential energy surface for 160-168Yb were investigated. Energy level sequences and energy ratios showed the gradual transition of the properties of these nuclei from the γ-unstable features to the rotational features . Adding the pairing parameter to Hamiltonian had a very slight effect on this feature, but it raised the β band, since it represents symmetry breaking such as in γ-unstable features . This applies to the experimental decay scheme of 160-168Yb isotopes. In , proton and neutron quadruple deformation parameters and showed values equal to -1.24 and approximately 0.7, respectively, which supports the same idea in the interacting boson model . A contour plot of the potential energy surface for 160-168Yb isotopes showed that the minimum potential occurs at approximately .

Theoretical Study of Isospin Mixing States with T&gt; 0 in sd Even-Even N=Z Nuclei Using Shell Model

Nuclear excited states with T &gt; 0 in sd even-even N=Z nuclei have been studied by using shell model. The calculations have employed the USDB Hamiltonian in order to predict the energy levels, the reduced electric quadrupole transition probabilities and reduced magnetic dipole transition probabilities. The study also include the average number of nucleons in each sd- active orbitals. The results compared with available experimental data. The comparison showed a good agreement between theoretical and experimental energy sates for most of the states studied in this work. On the other hand there was a difference between theoretical and experimental values of transition probabilities, but it can be said that it remained within the acceptable range of the difference.

Influence of triaxial deformation on wobbling motion in even–even nuclei

The influence of triaxial deformation γ on the purely collective form of wobbling motion in even–even nuclei is discussed based on the triaxial rotor model. It is found that the harmonic approximation is realized well when the value γ = 30° is adopted for the properties of energy spectra and electric quadrupole transition probabilities, while this approximation gets worse when γ gradually deviates from 30°. Recent data from a Coulomb excitation experiment, namely and for 110Ru, are studied and might be suggested as the bandhead of the wobbling bands. In addition, two types of angular momentum geometries for wobbling motion, stemming from different γ values, are exhibited by the azimuthal plots.

Electric Monopole Transitions in Nd Nuclei within IBM-2

The monopole transitions of 144-154Nd isotopes have been investigated in this work within the interacting boson model-2 (IBM-2) framework. The low-lying energy levels, electric quadrupole transition probability rates B(E2), electric quadrupole moments for first excited states monopole transition matrix elements and the intensity ratio were calculated in this work. The results of IBM-2 have been compared with the available experimental data; we have obtained a reasonable agreement. Unfortunately, the experimental data available on E0 transitions are very rare.The electric transition probability rates of beta and gamma bands to ground state band were calculated are fairly good agreement with available experimental values. Concerning the electric transition rates properties in IBM-2, we find that all calculations trends is reproduced well reasonably. The effective charges for neutron bosons and proton bosons calculated within IBM-2 are depending on the IBM-2 symmetries, we get suitable values for which is a constant for all 144-154Nd isotopes because the number of proton bosons is constant. The effective charge for neutron bosons varies from isotope to another

Calculation of Energy Levels and Reduced Electric Quadrupole Transition Probability for &lt;sup&gt;22&lt;/sup&gt;F Isotope Using Oxbash Code

A study on the calculation of energy levels and reduced electric quadrupole transition probability for fluorine-22 isotope using Oxbash Code has been carried out. The shell model and OXBASH was used to calculate the energy levels and probability of quadratic transition B(E2) of the 22 F isotope in the SD region through PW, CWH active interactions. A comparison was made between the calculation results and the experimental data. The comparison shows considerable consistency with the experimental results. The total angular momentum of the ground level 4 + 1 was confirmed when comparing with the experimental values. A significant consistency was obtained for the calculated energy values MeV (1.734, 2.387, 2.946) with the available experimental values of the same angular momentum (1 + 1 ,12+,4 + 2 ). It can be concluded that the reduced transition probabilities B(E2) can be calculated using the PW, CWH reactions and OXBASH code.

Study of excitation energies and transmission potential of the reduced quadruple B (E2) for the 70Zn isotope by applying the nuclear shell model

In this paper, the excited energy levels and reduced electric quadrupole transition probabilities (BE2 ↓) in both pure and mixed configuration s of 70Zn nucleus have been calculated by applying the nuclear shell model. In the present study, the surface delta and modified surface delta interactions within the model space (1p3/2,0f5/2, 1p1/2 and 0g9/2) have been used for two protons outside the closed nuclear core represented by the 68Ni nucleus. The equations are programmed for the above two interactions and the reduced electric quadrupole transition probabilities (BE2 ↓) equations using the Fortran version 95. Through the used Fortran version 95 program code, the elements of the matrix have been calculated for two particles which are necessary to calculate the eigenvalues, the eigenvectors and then the final energies of the nucleus that has been used in the current study. Through the calculations, theoretical results that have well agreement with the available practical values have been obtained. The total angular momentum and parity of some uncertain and unspecified energy levels have been confirmed and determined by the total angular momentum and the practical parity. Also, new values have been identified for both the excited energy levels and the reduced electric quadrupole transition probabilities (BE2 ↓), these values are considered as a suggestion that increases theoretical knowledge of each of the energy levels and the expected transition probabilities during this study.