Quadrupole Deformation Parameter Research Articles

Investigation of some nuclear structure properties of213Bi,201Tl,188Re,186Re,133Xe,131I,125I,123I,111In,94Tc,90Y,67Ga,67Cu,62Cu,61Cu,55Co, and48Vnuclei used in SPECT in axial deformation

The present work mainly purposed to investigate significant nuclear structure properties nuclei used in single photon emission computed tomography (SPECT), in addition to ground state nuclear properties such as the binding energy per particle, the root mean square (rms) charge, and proton and neutron radii. Besides, we calculated the neutron skin thicknesses (NST), the proton, neutron quadrupole moments ($Q_{P}, Q_{N})$, quadrupole deformation parameter ($\beta_{2})$, and the proton and neutron pairing energies ($P_{P}, P_{N})$ to determine shapes and deformations of SPECT nuclei including odd-odd or odd-even/even-odd nuclei in axial symmetry for Skyrme and Gogny interactions. To analyze the accuracy of the calculated results, the calculated results were compared with available experimental and the theoretical finite-range liquid-drop model (FRDM), and discussed for 12 different force interactions. Notably, the results provide thorough nuclear data to the literature for deformed nuclei of SPECT.

Effect of temperature on the volume and surface contributions in the symmetry energy of rare earth nuclei

The effect of temperature on the volume and surface contributions in the nuclear symmetry energy and their ratio in the isotopic chains of rare earth Nd, Sm, Gd, and Dy nuclei with N = 82-126 is analyzed in the framework of coherent density fluctuation model (CDFM). The weight function of nuclei, within CDFM, are calculated by using the densities from the temperature-dependent relativistic mean-field (RMF) model. Firstly, we discuss the temperature-dependence of bulk properties of nuclei, within RMF model, such as binding energy, deformation parameter, charge radius and isotopic shift along with comparison with the available experimental data at temperature T=0 MeV. Further, we discuss the thermal evolution of symmetry energy and its volume and surface components. At T=0 MeV, the persistence of a peak in the symmetry energy and components at neutron number N=100 shows the manifestation of deformed shell closure in consonance with an earlier study by one of us [L. Satpathy, S.K. Patra, J. Phys. G 30 (2004) 771; S.K. Ghorui, et al., Phys. Rev. C 85 (2012) 064327]. However, the scenario changes with rise in temperature and the magnitude of peak decreases at higher temperatures. At T=3 MeV, the peak disappears which may be due to shape change in addition to quenching of shell effects since the quadrupole deformation parameter β2 decreases with an increase in temperature and nuclei become spherical at T=3 MeV. It indicates that behavior of symmetry energy is closely related to the deformation/shape of the nuclei. We have also discussed the values of volume symmetry energy, surface symmetry energy and their ratio which are in consonance with available experimental data.

Study of angular momentum effect on the fission process by angular anisotropy method in heavy-ion-induced reactions

The study of compound nucleus characteristics through fission fragment properties is a powerful tool to understand the fission mechanism of excited nuclei formed in heavy-ion-induced reactions. In this work, angular anisotropies of fission fragments from fissioning nuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] with normal behaviors in angular anisotropy have been analyzed. In this way, the quadrupole deformation parameter of the compound nucleus is calculated by comparison between the experimental data of angular anisotropy and those predicted by the standard saddle-point statistical model. Then the rotational energy, the fission barrier height, and the effective moment of inertia of the compound nucleus are obtained through the calculated quadrupole deformation parameters. It is observed that the quadrupole deformation parameter decreases with increasing the mean square angular momentum. The obtained results illustrate that the rotational energy and the effective moment of inertia increase almost linearly with increasing the mean square angular momentum, while the fission barrier height decreases as expected. However, the calculated values of fission barrier height overestimate the rotating finite-range model predictions. Also, the calculated values of effective moment of inertia represent a nearly linear trend despite those predicted by the rotating finite-range model. In order to discuss the physical ideas underlying the effect of angular momentum on the fission properties, the interaction potential energy during the capture process is studied for the lightest and heaviest reaction systems.

Study of Deformation Parameters (β2, δ) For 18,20,22,24,26,28Ne isotopes in sdpf shell

The quadrupole deformation is basic to study the shape transitions; it is possible to predict many important properties of even-even nuclei as a function of the deformation parameter. The deformations of nuclei are important for understanding their shapes prolate or oblate. The quadrupole deformation parameters were calculated by the transition probability B (E2) for 18, 20, 22, 24, 26,28Ne isotopes, were adopted different interactions three. The calculations are performed with the Bohr-Mottelson (B-M) effective charges, which represent the effect of the core-polarizations. Also, the deformation parameters were calculated for different nuclei and adopted two methods of calculation: from reduced the transition probability (B2) and from the intrinsic quadrupole moment. In calculations, the Shell model is adopted.

Electron spectrometer for electric monopole (E0) transition studies in nuclei

The study of electric monopole (E0) transitions between two 0+ states is important because the monopole strength carries vital information about the nuclear structure due to its direct link with the mean squared charge radius r2 and quadrupole deformation parameter β. Therefore, the measurement of internal conversion electrons (ICE) or internal pair formation (IPF) is crucial for E0 transition studies. Transitions between 0+ states do not change angular momentum. Hence, single-photon emission is forbidden, but can decay by conversion electrons or pair formation and two-photon emission which is mostly negligible. In order to implement E0 studies at iThemba LABS, an electron spectrometer that uses a solenoidal magnetic field acting as a lens and a Si(Li) detector has been refurbished and characterized using calibration sources of ICE. Figures of merit have been extracted and compared with simulations. The spectrometer coupled with an array of LaBr3:Ce detectors and Low Energy Photon Spectrometers (LEPS) was successfully implemented for in-beam experiments. Measurements of internal conversion coefficients (ICC) and monopole strengths extracted from in-beam measurements of 72As, 72Ge, and 72Se are presented.

Giant dipole resonance and shape evolution in Nd isotopes within TDHF method

The isovector giant dipole resonance (IVGDR) in even–even Nd isotopes from A = 124 to A = 160 is studied in the framework of time-dependent Hartree–Fock (TDHF) with Skyrme forces SkI3, SVbas, SLy5 and SLy6. The dipole strength is calculated and compared with the experimental data on photon absorption cross section σγ. An overall agreement between them is obtained. The dipole strengths in 124–140Nd and 152–160Nd are predicted. In addition, the correlation between the quadrupole deformation parameter β2 and the splitting of the giant dipole resonance (GDR) spectra is studied. The results confirm that is proportional to β2. Shape phase transition in Nd isotopes is also investigated in the light of IVGDR.

Investigation of the existence of new nuclear magic number in even-even O isotopes using shell model and Hartree–Fock Bogoliubov method

In the present work, the features of some excited states in some even–even 14-26O isotopes have been investigated. The aim is to predict the evaluated existence of magic numbers in these isotopes using shell model and Hartree-Fock Bogoliubov method based on SLy4, SkC, SkD Skyrme parameterizations. In particular, root mean square radius, binding energies, one and two neutron separation energies, pairing gaps, transition probabilities, excitation energies, energy levels, transition densities and quadrupole deformation parameters have been investigated. The results are compared with the available experimental data.

Nuclear structure properties and decay rates of molybdenum isotopes

Electron capture and $\beta ^{-}$ decay are the dominant decay processes during late phases of evolution of heavy stars. Previous simulation results show that weak rates on isotopes of Molybdenum (Mo) have a meaningful contribution during the development of phases of stars before they go supernova. The relative abundance coupled with the stellar weak rates on Mo isotopes may change the lepton-to-baryon content of the core material. Here we report on the calculation of nuclear structure properties of 82−138Mo isotopes employing the RMF model. Later we calculate the weak decay rates of these isotopes. We use the pn-QRPA model to compute these rates. In the first step, the ground-state nuclear properties of Mo isotopes such as binding energy per nucleon, neutron and proton separation energies, charge radii, total electric quadrupole moments and deformation parameter of electric quadrupole moments have been calculated using density dependent version of RMF model with DD-PC1 and DD-ME2 functionals. The calculated electric quadrupole deformation parameters have been used in a deformed pn-QRPA calculation in the second phase of this work to calculate half-lives and weak decay rates for these Mo isotopes in stellar matter. We calculate the electron capture and $\beta $-decay rates over an extensive range of temperature ($0.01\times 10^{9}$ K to $30\times 10^{9}$ K) and density (10 to $10^{11}$) g/cm3. Our study can prove useful for simulation of presupernova evolution processes of stars.

Physics of even-even superheavy nuclei with 96<Z<110 in the quark-meson-coupling model

The Quark-Meson-Coupling (QMC) model has been applied to the study of the properties of even-even super-heavy nuclei with 96 < Z < 110, over a wide range of neutron numbers. The aim is to identify the deformed shell gaps at N = 152 and N = 162 predicted in macroscopic-microscopic (macro-micro) models, in a model based on the mean-field Hartree-Fock+BCS approximation. The predictive power of the model has been tested on proton and neutron spherical shell gaps in light doubly closed (sub)shell nuclei. In the super-heavy region, the ground state binding energies of 98 < Z < 110 and 146 < N < 160 differ, in the majority of cases, from the measured values by less than 2.5 MeV, with the deviation decreasing with increasing Z and N. The axial quadrupole deformation parameter, calculated over the range of neutron numbers 138 < N < 184, revealed a prolate-oblate coexistence and shape transition around N = 168, followed by an oblate-spherical transition towards the expected N = 184 shell closure in Cm, Cf, Fm and No. The closure is not predicted in Rf, Sg, Hs and Ds as another shape transition to a highly deformed shape in Sg, Hs and Ds for N > 178 appears, while 288Rf (N = 184) remains oblate. The bulk properties predicted by QMC are found to have a limited sensitivity to the deformed shell gaps at N = 152 and 162. However, the evolution of the neutron single-particle spectra with 0 < beta2 < 0.55 gives unambiguous evidence for the location and size of the N = 152 and 162 gaps as a function of Z and N. In addition, the neutron number dependence of neutron pairing energies provides supporting evidence for existence of the energy gaps.

Analysis of the reaction cross-sections of 22−36Na+12C and 19−27F+12C at 240MeV/u

The nucleus–nucleus reaction cross-sections of [Formula: see text]C and [Formula: see text]C at 240[Formula: see text]MeV/u are calculated using the optical limit of the Glauber model. The deformation and radii of a deformed Fermi density are calculated from the relativistic mean field (RMF). The results are compared with the recent experimental data. It is found that the Fermi density whose quadrupole deformation parameters and radii are derived from RMF, using TMA effective interaction in the RMF Lagrangian, provide a satisfactory explanation of the experimental data of Na isotopes, except for [Formula: see text]Na, which are expected to be strongly deformed. For F isotopes, the deformed Fermi density adjusted to the radii derived from RMF, using TMA interaction, presents a lower reaction cross-section. The Lagrangian parameters set NL3* gives a good description of the data which is better than that predicted by TMA. On the other hand, the two forces cannot describe the reaction cross-section of [Formula: see text]F since it is expected to have a deformed halo structure. The radius deduced from the data is found to be of the order 3.5[Formula: see text]fm.

Microscopic study of evolution of shape change across even-even mass chain of tellurium isotopes using relativistic Hartree-Bogoliubov model

The density dependent point coupling and meson exchange effective interactions are employed in the relativistic Hartree-Bogoliubov (RHB) model to study the development of ground state deformation and occurrence of shape transitions with change of neutron number in 104−144Te isotopes. Besides this, the systematics of other nuclear structure properties with increasing neutron number are also obtained. The RHB model reproduces well the available experimental data on binding energies, quadrupole deformation parameters, two neutron separation energies and root mean square charge radii. The results of three-dimensional potential energy surfaces predict prolate ground state minima for proton rich and neutron rich tellurium isotopes, oblate minima for 114−124Te, triaxial minima for 126,128Te and spherical minima for 130−134Te. Besides, oblate prolate shape coexistence is predicted in 116−120Te isotopes.

Change in the Shape of Nuclei in the Chains of Krypton, Strontium, Zirconium, Molybdenum, and Ruthenium Isotopes in the Relativistic-Mean-Field Approximation

Changes in the shape of nuclei in the chains of even—even crypton, strontium, zirconium, molybdenum, and ruthenium isotopes are studied on the basis of the relativistic Hartree—Bogolyubov method implemented with the DD-PC1 and DD-ME2 Lagrangian models. Nucleon pairing is described in terms of separable two-body interaction. The dependence of the calculated nuclear features on the choice of pairing strength is investigated. The respective calculations show that, in the vicinity of N = 60, large jumps of the mean squares of charge radii and quadrupole-deformation parameters are observed for some strontium, zirconium, and molybdenum isotopes in response to variations in the pairing-strength parameters.

Ground-state shape evolution in Er and Yb isotopes

The ground-state shape (phase) evolution in Er and Yb isotopes is manifested in the axially deformed Nilsson mean-field plus extended pairing model. The energy ratio R02+/21+, the odd-even mass differences, the ground-state occupation probabilities of valence nucleon pairs with different angular momenta and the information entropy are calculated. It is shown from these quantities as functions of the quadrupole deformation parameter and the overall pairing interaction strength that the ground-state shape (phase) evolution is mainly driven by the pairing interaction and less affected by the quadrupole deformation, which thus provides a possible origin of the ground-state shape (phase) evolution of these isotopes.

Observation of excited states in Mg20 sheds light on nuclear forces and shell evolution

The exotic Borromean nucleus $^{20}$Mg with $N$ = 8, located at the proton drip-line provides a unique testing ground for nuclear forces and the evolution of shell structure in the neutron-deficient region. We report on the first observation of proton unbound resonances together with bound states in $^{20}$Mg from the $^{20}$Mg($d$,$d'$) reaction performed at TRIUMF. Phenomenological shell-model calculations offer a reasonable description. However, our experimental results present a challenge for current first-principles nuclear structure approaches and point to the need for improved chiral forces and {\it ab initio} calculations. Furthermore, the differential cross section of the first excited state is compared with distorted-wave Born approximation calculations to deduce a neutron quadrupole deformation parameter of $\beta_n$=0.46$\pm$0.21. This provides the first indication of a possible weakening of the $N$ = 8 shell closure at the proton drip-line.

Calculations of Quadrupole Deformation Parameters for Nuclei in fp shell

The quadrupole transition rates and intrinsic quadrupole moment are calculated for some fp shell nucleus. For fp-shell nuclei with neutron number N > 20 and with proton number p > 20, fp shell model space and fpd6 effective interaction are used. The calculations are performed using effective charges obtained from Bohr – Mottelson model and also the standard proton and neutron effective charges, and the results are compared with the available experimental values. The results of the quadrupole deformation parameter calculated from transition probabilities are better from the intrinsic quadrupole moment with ST effective charges.

Quadrupole Moment & Deformation Parameter for Even-Even 38Sr (A=76-102) Nuclide

In this work, the electric quadrupole moment (Qo) and deformation parameter (β2) have been studied for 38Sr isotopes which has neutron magic number (N=50).The aim of this work is to study the effect of electric quadrupole moment (charge distribution) on the deformation of the nucleus by calculating the deformation parameter depending on the value of electric quadrupole moment.Also electric quadrupole moment (Qo) and deformation parameter (β2) have been plotted as a function to neutron number to study the effect of neutron magic number (N=50) on them.The results show that the shapes of nuclei approach to spherical shape due to its charge distribution when the nuclei be closer to the neutrons magic number.

The relationship of Nuclear Decay Methods (alpha and beta) Particles with the Nuclear Deformation for Nuclei inUranium-238 and Thorium -232 Series

In this work, a study of the relationship of the decay mode (alpha and beta) emission and the deformed shape of even-even nuclei in uranium -238 and thorium -232 series is presented. To achieve our purpose the quadrupole deformation parameter (β2) (which refers to the shape of nuclei) and eccentricity (e) (represented the radioactivity) have been compute for each nuclei which decay by (alpha or beta) particles emission in each series. The results of deformation parameter show that the deformation on the shape of nuclei (near from spherical shape) for nuclei which decay by beta particles emission is lower than the deformation on the shape of the nuclei which decay by alpha particles emission for two series. In addition, we shows that the effected of deformation parameter greeter than the effected of eccentricity by the type of decay (alpha & beta) emission. Finally, an empirical equation has been extracted from plotting deformation parameter as a function to eccentricity, which can be used to calculate the defamation parameter for any nuclei has eccentricity value.

Scattering of α-particles by 11B nuclei at an energy of 40MeV and role of the exchange mechanism with transfer of 7Li

The elastic and inelastic scatterings of [Formula: see text]-particles were investigated at an energy of 40[Formula: see text]MeV with excitation of low-lying states of the [Formula: see text]B nucleus [0.0 (3/2[Formula: see text]), 4.445 (5/2[Formula: see text]), 6.74 (7/2[Formula: see text]), 2.125 (1/2[Formula: see text]) and 5.02[Formula: see text]MeV (3/2[Formula: see text])]. The analysis of the experimental angular distributions was carried out via the coupled channels method within the framework of the collective model. The value of the quadrupole deformation parameter [Formula: see text] was extracted. Calculations indicate a preference for a negative sign for deformation. It is shown that the exchange mechanism with the transfer of the heavy 7Li cluster does not play an important role in the scattering of [Formula: see text]-particles on [Formula: see text]B nuclei at an energy of 40[Formula: see text]MeV.

Study of the nuclear deformation of some even–even isotopes using Hartree–Fock–Bogoliubov method (effect of the collective motion)

In the present research, the nuclear deformation of the Ne, Mg, Si, S, Ar, and Kr even–even isotopes has been investigated within the framework of Hartree–Fock–Bogoliubov method and SLy4 Skyrme parameterization. In particular, the deform shapes of the effect of nucleons collective motion by coupling between the single-particle motion and the potential surface have been studied. Furthermore, binding energy, the single-particle nuclear density distributions, the corresponding nuclear radii, and quadrupole deformation parameter have been also calculated and compared with the available experimental data. From the outcome of our investigation, it is possible to conclude that the deforming effects cannot be neglected in a characterization of the structure of the neutron-rich nuclei. The relation between the single-particle motion and the potential surface leads to note that the change in the interactions between the nucleons causes the evolution of nuclear surface and leads to variation in the potential shape.

Nuclear structure and decay properties of Nd isotopes

Using the Hartree–Fock–Bogoliubov mean-field theory, the ground-state structural and decay properties of Nd isotopes are investigated from the proton-rich side up to the neutron drip-line. Quantities such as binding energies per nucleon, one and two-neutron separation energies, rms charge radii, and quadrupole deformation parameters have been calculated. Compared with the relativistic mean-field results, the present calculations are in better agreement with the available experimental data. The results show clearly the signature of a shape transition at [Formula: see text] and an abrupt increase in the deformation near the neutron drip-line. Further, the possible decay modes like alpha, cluster and [Formula: see text]-decay are analyzed in a unified fission model and phenomenological formulas. Overall, a good agreement is achieved between the calculated and experimental [Formula: see text]-values and half-lives wherever available. The most likely decay modes are thus identified throughout the isotopic chain.