Core Polarization Effects Research Articles

The effects of Core-polarization on the form factors of 17O,19F and 48Ca

Inelastic electron scattering for selected nuclei 17O,19F and 48Ca are investigated by considering the energies of higher configurations outside core 16O and 40Ca cores. Higher energy configurations, called core polarization effects. Bohr-Mottelson calculations were also conducted to study the form factors of the above-mentioned nuclei using Oxbash. The predicted form factors were compared to the experimental data available. The effect of higher excited configurations is found to be essential in the dynamic transfer dependence of the form factors and is remarkably well aligned with the measured data.

The Effect of Core Polarization By Means of Tassie and Bohr-mottelson Models for Some FP-Shell Nuclei

The Effect of Core Polarization By Means of Tassie and Bohr-mottelson Models for Some FP-Shell Nuclei

Current Status and Developments of the Atomic Database on Rare-Earths at Mons University (DREAM)

The main purpose of the Database on Rare Earths At Mons University (DREAM) is to provide the scientific community with updated spectroscopic parameters related to lanthanide atoms (Z = 57–71) in their lowest ionization stages. The radiative parameters (oscillator strengths and transitions probabilities) listed in the database have been obtained over the past 20 years by the Atomic Physics and Astrophysics group of Mons University, Belgium, thanks to a systematic and extensive use of the pseudo-relativistic Hartree-Fock (HFR) method modified for taking core-polarization and core-penetration effects into account. Most of these theoretical results have been validated by the good agreement obtained when comparing computed radiative lifetimes and accurate experimental values measured by the time-resolved laser-induced fluorescence technique. In the present paper, we report on the current status and developments of the database that gathers radiative parameters for more than 72,000 spectral lines in neutral, singly-, doubly-, and triply-ionized lanthanides.

Analysis of the core polarization effects in the calculated atomic parameters of Hg iii

ABSTRACT The presence of Hg iii in the stellar atmosphere in the stars HgMn χ Lupi and HR7775 was reported by Leckrone et al. and Proffitt et al. In this last work, the authors indicate that the intensities of the spectral lines of 1360.50, 1647.48, and 1738.54 Å of Hg iii are relatively strong compared to the intensities of the spectral lines of Hg ii. Although the explanation given by the authors in their conclusions should be correct, the values of the oscillator strengths used by the authors in some cases were not consistent with the experimental lifetimes obtained by Henderson et al. In addition, some of the lines studied by the authors are widely overlapped with intense lines of Hg iii of the same multiplet. In this paper, we present values of transition probabilities and line broadening by electron collision (Stark effect) of several lines of Hg iii in order to clarify the problems indicated above. Since Hg iii is a heavy element, we include the core polarization effects (using the Cowan’s code) in our calculations. Several values of polarizability, taking Fraga values for Hg iv as a starting point, have been considered in this study in order to obtain theoretical values of those parameters close to the experimental ones. The theoretical values of the lifetimes obtained in this study, close to the experimental ones, were obtained for a polarizability value of 3.5 au.

Towards a new semi-classical interpretation of the wobbling motion in 163Lu

A new interpretation for the wobbling bands in 163Lu is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I = R + j, for R = 0, 2, 4, … (TSD1), the ground band with I = R + j and R = 1, 3, 5, … (TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit j = i13/2, and the ground band of I = R + j, with R = 1, 3, 5, … and j = h9/2 (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoI’s for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space one indicates where the point associated with the fitted parameters is located and also which is the region of transversal wobbling mode as well as where the wobbling motion is forbidden.

New approach for the wobbling motion in the even-odd isotopes Lu161,163,165,167

A new interpretation for the wobbling bands in the even-odd Lu isotopes is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1), the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoI's for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space, one indicates where the points associated with the fitted parameters are located, which is the region where the transversal wobbling mode might be possible, as well as where the wobbling motion is forbidden.

New Energy Levels and Transitions of 5s25p2 (6d+7s) Configurations in Xe IV

Three-times ionized xenon Xe IV spectrum in the 1070–6400 Å region was analyzed using a pulsed discharge light source. A set of 163 transitions was classified for the first time, and 36 new energy levels belonging to the 5s25p26d and 5s25p27s even configurations were determined. The relativistic Hartree–Fock method, including core-polarization effects, were used. In these calculations, the electrostatic parameters were optimized by a least-square procedure in order to improve the adjustment to experimental energy levels. We also present a calculation based on a relativistic multiconfigurational Dirac–Fock approach.

Core polarization effects up to 12ℏω in 7Li and 10B nuclei

Shell model and core polarization (CP) effects have been used to calculate the transverse and longitudinal electron scattering form factors for 7Li and [Formula: see text]B nuclei. The calculations considered one particle–one hole excitation up to 12[Formula: see text][Formula: see text]. This manner seems to be essential for obtaining the best explanation for empirical results. Therefore, adding the excited states up to 12[Formula: see text][Formula: see text] gives a reasonable description for transverse and longitudinal form factors. Furthermore, with these calculations, it is possible to get a very close location of diffraction minimum, and the behavior of the momentum transfer is described properly at the high configuration for 7Li compared with 6[Formula: see text][Formula: see text] energy.

Effects of the isoscalar and isovector interaction on the ground-state magnetic moments of odd-mass 137–145Ce nuclei

A systematic study of the magnetic properties of deformed odd-neutron 137–145Ce isotopes using the microscopic quasiparticle phonon nuclear model (QPNM) has been presented. The QPNM includes residual spin–spin interaction in both isoscalar and isovector channels. The analysis shows that in the isoscalar channel contributions to the magnetic moment coming from the neutron and proton systems practically cancel out each other. On the other hand, in the isovector channel, the coherent contribution coming from the quasiparticle–phonon interactions leads to a spin polarization (core polarization), which is important for determination of the quenched spin gyromagnetic factors (gs). The quenched spin gyromagnetic factors so called [Formula: see text] have been found to range from [Formula: see text] to [Formula: see text] in the odd-mass 137–145Ce isotopic chain, which is similar to its phenomenological value ([Formula: see text] between [Formula: see text] and [Formula: see text]). By taking into consideration the core polarization effects, the available experimental data are satisfactorily reproduced with an accuracy of 0.01μN–0.1μN.

Using MSDI and M3Y Core Polarization for the Coulomb Electron Scattering for some Ground state nuclei

The analysis of Coulomb electron scattering for the ground state-nuclei Li6 , C12 , O18 , F19 and Ne 20 are performed with core polarization effects for the Modified Surface Delta Interaction (MSDI) and realistic Michigan three-range Yukawa (M3Y) interaction. The basic calculations included the Coulomb form factor, charge density, and the charge radii of the ground states. The Coulomb form factors for the M3Y interaction gave the best fit with the experimental data.

Study the Nuclear Form Factors of Low-Lying Excited States in $${}^{7}\hbox {Li}$$ Nucleus Using the Shell Model with Skyrme Effective Interaction

In the present work, the Skyrme interaction with the core polarization calculations has been used and implemented to study the inelastic electroexcitation form factor for low-lying excited states in \({}^{7}\hbox {Li}\). In particular, the \(1/2^{-}\) (0.478 MeV) and \(7/2^{-}\) (4.630 MeV) states have been analyzed within the \(0\hbar \omega \) shell model including core-polarization effect. The present results reveal that the core-polarization calculation incorporating Skyrme type interaction for the single-particle states reproduces the longitudinal electron scattering data and predicts the diffraction minimum correctly and describes the high momentum data that has not been reported before. The measured \(B(C2{\uparrow })\) value for the \(1/2^{-}\) transition is very well described. The result of the \(7/2^{-}\) transition is close to the measured value. Transverse form factors are better described by the single-particle wave functions obtained from Hartree–Fock with Skyrme type interaction, rather than by the harmonic-oscillator wave functions.

Core-polarization effects and effective charges in O and Ni isotopes from chiral interactions

Most nuclear structure calculations, even for full configuration interaction approaches, are performed within truncated model spaces. These require consistent transformations of the Hamiltonian and operators to account for the missing physics beyond the active space, so that several recent efforts have been devoted to find compatible derivations of the effective operators. The effective charges employed in the shell-model calculations, and fitted to reproduce experimental data, can be seen as the phenomenological counterpart of such renormalization for electromagnetic operators. Here, we make a first step to lay the bases for their microscopic derivation in the context of the Self-Consistent Green's Function approach. We compute electric quadrupole (E2) effective charges from microscopic theory by coupling the single-nucleon propagators to core-polarization phonons, derived consistently from a realistic nuclear interaction. The polarization effects are included by evaluating the Feynman diagrams that couple the internal multi-nucleon configurations to the single-particle transitions induced by the electromagnetic operator. The effective charges for E2 static moments and transitions are computed for selected isotopes in the Oxygen ($^{14}\text{O}$, $^{16}$O, $^{22}$O and $^{24}$O) and Nickel ($^{48}$Ni, $^{56}$Ni, $^{68}$Ni and $^{78}$Ni) chains. The values found are orbital dependent especially for the neutron effective charges, which show also a characteristic decreasing trend along each isotopic chain. In general, the values are compatible with the phenomenological ones commonly used for shell-model studies in the $0p\, 1s\, 0d$ and $1p\,0f\,0g_{\frac{9}{2}}$ valence spaces.The phenomenological shell-model effective charges can be explained through \textit{ab initio} approaches, where the sole experimental input comes from the fitting of the realistic nuclear interaction.

Auger decay of the 2p vacancy in chlorine

We calculate the spectra of electrons emitted upon Auger decay of the $2p$ vacancy in chlorine. The vacant atomic and ionic states are populated by a single-photon absorption from the ground state of the chlorine atom and are tested by comparing the calculated photoabsorption spectrum with the existing theoretical and experimental photoionization data. The agreement is reasonably good, although the calculated Auger decay rates and oscillator strengths of the low-lying states are overestimated due to neglect of the core polarization effects. In the absence of any published experimental result, the nonresonant $L\ensuremath{-}{M}_{23}^{2}$ Auger spectrum of Cl at 220 eV photon energy is compared with the Cl $L\ensuremath{-}{V}^{2}$ Auger spectrum of HCl, measured at 235 eV photon energy. The calculated spectator and participator resonant Auger spectra of some strongly photoexcited Cl $2{p}^{\ensuremath{-}1}$ states are presented for future reference.

Spectral Analysis and New Visible and Ultraviolet Lines of Ar v

Abstract A capillary discharge tube was used to record the Ar spectrum in the region of 330–4400 Å. We analyzed a set of 109 lines of Ar v, with 10 of them being classified for the first time. Part of these newly identified lines (six in total) corresponds to electric dipole transitions in the visible and ultraviolet regions of the spectrum. We calculated weighted transition rates (gA) for all experimentally observed lines and the corresponding lifetimes using a relativistic Hartree–Fock method with configuration interaction. The equations were modified to consider core polarization (CP) effects. A study on the Si isoelectronic sequence found that considering CP effects is essential for the correct description of the Ar v structure.

Energy Levels, Wavelengths, and Transition Probabilities of Intercombination Lines in the Spectra of Gе-Like I, Cs, and La Ions

Energy levels, wavelengths, transition probabilities, and line strengths are calculated for the allowed electric dipole 4s24p2–4s4p3 and 4s24p2–4s24p4d transitions of Ge-like ions with Z = 53, 55 and 57, I XXII, Cs XXIV, and La XXVI. By employing active-space techniques to expand the confi guration list, we also include the Breit interaction and quantum electrodynamical (QED) effects to correct the atomic state wave functions and the corresponding energies. Both valence correlation and core polarization effects are included. The results are compared with the available experimental and other theoretical results.

Nuclear structure study of [22,24]Ne and [24]Mg nuclei

Shell model calculations based on large basis has been conducted to study the nuclear structure of $^{20}Ne$, $^{22}Ne$ and $^{24}Mg$ nuclei. The energy levels, inelastic electron scattering form factors and transition probabilities are discussed by considering the contribution of configurations with high-energy beyond the model space of sd-shell model space which is denoted as the core polarization (CP) effects.~The Core polarization is considered by taking the excitations of nucleus from the $1s$ and $1p$ core orbits and also from the valence $2s$ $1d$ shell orbit in to higher shells with $4\hbar\omega$. The effective interactions $USDA$ and $USDB$ are employed with $sd$ shell model space to perform the calculation and the core polarization are calculated with $MSDI$ as residual interaction.~The calculated energy level schemes, form factors and transition probabilities were compared with the corresponding experimental data. The effect of core polarization is found very important for the calculation of $B(C2)$, $B(C4)$ and form factors, and gives excellent results in comparison with the experimental data without including any adjustable parameters.

Theoretical investigation of the fully differential cross sections for single ionization of He in collisions with 75-keV protons

We present a theoretical investigation of the single ionization of He in collisions with ${\mathrm{H}}^{+}$ projectile ions at 75-keV impact energy. Using the frameworks of the independent-electron model and the impact parameter picture, fully differential cross sections (FDCS) are evaluated in the continuum distorted-wave with eikonal initial-state approximation (CDW-EIS). Comparisons are made to the recent measurements of Schulz et al. [Phys. Rev. A 73, 062704 (2006)] and Arthanayaka et al. [J. Phys. B: At. Mol. Opt. Phys. 49, 13LT02 (2016)]. Strong influence of the internuclear interaction and effects of target core polarization due to the presence of the projectile ion are observed. Comparing the present results to experimental data and other theoretical predictions, it has been found that the CDW-EIS method qualitatively reproduces structures in the FDCS. Projectile coherence effects are investigated by representing the projectile beam as a Gaussian wave packet. Evidence of interference effects due to projectile-electron and projectile-target core interactions are discussed and the need for further theoretical investigations is proposed.

Microscopic calculations of the electric Quadrupole transition strengths of Be isotopes (9, 10, 12, 14)

Electric Quadrupole transitions are calculated for beryllium isotopes (9, 10, 12 and 14). Calculations with configuration mixing shell model usually under estimate the measured E2 transition strength. Although the consideration of a large basis no core shell model with 2ℏtruncations for 9,10,12 and14 where all major shells s, p, sd are used, fail to describe the measured reduced transition strength without normalizing the matrix elements with effective charges to compensate for the discarded space. Instead of using constant effective charges, excitations out of major shell space are taken into account through a microscopic theory which allows particle–hole excitations from the core and model space orbits to all higher orbits with 2ℏw excitations which are called core-polarization effects. The two body Michigan sum of three ranges Yukawa potential (M3Y) is used for the core-polarization matrix element. The simple harmonic oscillator potential is used to generate the single particle matrix elements of all isotopes considered in this work. The b value of each isotope is adjusted to reproduce the experimental matter radius, These size parameters of the harmonic oscillator almost reproduce all the root mean square (rms) matter radii for 9,10,12,14Be isotopes within the experimental errors. Almost same effective charges are obtained for the neutron- rich Be isotopes which are smaller than the standard values. The major contribution to the transition strength comes from the core polarization effects. The present calculations of the neutron-rich 12,14Beisotopes show a deviation from the general trends in accordance with experimental and other theoretical studies. The configurations arises from the shell model calculations with core-polarization effects reproduce the experimental B(E2) values.

Quadrupole moments of exotic carbon isotopes (9C, 11C, 17C and 19C) including core polarization effect

Quadrupole Q moments and effective charges are calculated for 9C, 11C, 17C and 19C exotic nuclei using shell model calculations. Excitations out of major shell space are taken into account through a microscopic theory which are called core-polarization effects. The simple harmonic oscillator potential is used to generate the single particle matrix elements of 9,11,17,19C. The present calculations with core-polarization effects reproduced the experimental and theoretical data very well.

Inelastic electron scattering form factors involving the second excited 2+ level in the isotopes 50,54,52Cr

An expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimental data.