Core Polarization Effects Research Articles

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.

The effects of core polarisation on some even–even sd-shell nuclei using Michigan three-range Yukawa and modified surface delta interactions

Elastic and inelastic electron scattering from even–even \(Z=N\) sd-shell (\(^{28}\hbox {Si}, {}^{32}\hbox {S}\) and \(^{36}\hbox {Ar}\)) nuclei has been studied using the nuclear shell-model configurations. The transition rates \(B\left( {C2\uparrow } \right) \) from the ground 0\(^{+}\) state to the first excited \(2_{1}^{+}\) state, the electric quadrupole moments Q, the elastic longitudinal C0 and inelastic longitudinal C2 form factors are calculated. SDBA and USDA model spaces have been used. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (HO) and Skyrme–Hartree–Fock (SHF) potentials. The configurations higher than the core and the model space are taken into account within a microscopic theory that includes one particle–one hole excitations from the core and model space orbits to higher allowed orbits with 2\(\hbar \omega \) excitations. These effects are defined as core polarisation (CP) effects. Two-body Michigan three-range Yukawa (M3Y) effective nucleon–nucleon interaction and the modified surface delta interaction (MSDI) have been used as residual interactions for the CP matrix elements. The calculations are performed using the shell-model code Nushell@MSU, where the deduced results, including CP, are more compatible with the available experimental and theoretical results.

Inelastic longitudinal electron scattering C42 form factors in42Ti nucleus

Inelastic longitudinal electron scattering form factors for secondexcited state C42 in 42Ti nucleus have been calculated using shellmodel theory. Fp shell model space with configuration (1f7/2 2p3/21f5/2 2p1/2) has been adopted in order to distribute the valenceparticles (protons and neutrons) outside an inert core 40Ca. Modernmodel space effective interactions like FPD6 and GXPF1 have beenused to generate model space vectors and harmonic oscillator wavefunction as a single particle wave function. Discarder space (coreorbits + higher orbits) has been included in (core polarization effect)as a first order correction in microscopic theory to measure theinterested multipole form factors via the model space.Gogny and Michigan sum of three-range Yukawapotential (M3Y-p2) have been utilized as a residual interaction tocouple the (particle-hole) pair across the model space active particlesand the excitation energy of the pair is (2ħω) and four options for theused effective and residual interactions were determined for thetransitions from (+0) to (+01,2,3), (+21,2,3) and (+41,2,3).

Core-polarization effect in longitudinal electron scattering form factors of 65Cu nucleus

Inelastic longitudinal electron scattering form factors to 2+ and 4+ states in 65Cu nucleus has been calculated in the (2p3/2 1f 5/2 2p1/2) shell model space with the F5PVH effective interaction. The harmonic oscillator potential has been applied to calculate the wave functions of radial single-particle matrix elements. Two shell model codes, CP and NUSHELL are used to obtain results. The form factor of inelastic electron scattering to 1/21−, 1/22−, 3/22−, 3/23−, 5/21−, 5/22− and 7/2- states and finding the transition probabilities B (C2) (in units of e2 fm4) for these transitions and B (C4) (in units of e2 fm8) for the transition 7/2-, and comparing them with experimental data. Both the form factors and reduced transition probabilities with core-polarization effects gave a reasonable description of the experimental data.

Theoretical Study of Transition Probabilities and Stark Broadening Parameters and of Several Spectral Lines with Astrophysical Interest of Double-ionized Thallium

Abstract Leckrone et al. reported the presence of double-ionized thallium (Tl iii) in the stellar atmosphere of the chemically peculiar star, χ Lupi, in 1999. Two spectral lines at 1332.3 and 1558.6 Å were detected in its stellar spectrum. Here, we claim that there are ions and lines that need further study to make possible the LTE abundance analysis once improved atomic data is available. In this sense, Tl iii is included in the ions list that requires improved atomic data. To contribute to the solution of this problem, an analysis of the atomic parameters of the double-ionized thallium is presented here. In this work, calculations of transition probabilities were made to obtain values of the theoretical radiative lifetimes and theoretical Stark parameters for widths and shifts of 22 spectral lines of Tl iii. Relativistic Hartree–Fock calculations using Cowan’s code allowed us to obtain the required transition probabilities. In our calculations, the core polarization effects were included. Later, the Griem semiempirical approach was used to obtain the Stark parameters. Our lifetimes values for 10 levels were compared with the experimental ones. In this paper, we discuss the behavior of the Stark parameters versus the temperature of three relevant spectral lines. Stark width values of the isoelectronic sequence Tl iii–Pb iv are also displayed.

Study of nuclear structure of <SUP align=right>58,62</SUP>Ni isotopes using the F5PVH effective interaction

The nuclear structure of 58,62Ni nuclei has been calculated using F5PVH as effective interaction for 1f5/2 2p3/2 2p1/2 shell model wave functions. Skyrme-Hartree Fock (SKX), Harmonic Oscillator (HO) and Woods-Saxon (WS) potentials were used to calculate the single particle wave function. The core-polarisation effects have been adopted using the shape of Tassie model. The level schemes are compared with the experimental data up to 3.42 MeV and 4.018 MeV for 58Ni and 62Ni, respectively. In this study, very good agreements are obtained for all nuclei. Results from C2 form factor and Charge Density Distribution (CDD) calculations give good agreement with the experimental data with no adjustable parameters.

Study of nuclear structure of 58,62Ni isotopes using the F5PVH effective interaction

The nuclear structure of 58,62Ni nuclei has been calculated using F5PVH as effective interaction for 1f5/2 2p3/2 2p1/2 shell model wave functions. Skyrme-Hartree Fock (SKX), Harmonic Oscillator (HO) and Woods-Saxon (WS) potentials were used to calculate the single particle wave function. The core-polarisation effects have been adopted using the shape of Tassie model. The level schemes are compared with the experimental data up to 3.42 MeV and 4.018 MeV for 58Ni and 62Ni, respectively. In this study, very good agreements are obtained for all nuclei. Results from C2 form factor and Charge Density Distribution (CDD) calculations give good agreement with the experimental data with no adjustable parameters.

Radiative lifetime measurements and semi-empirical transition parameter calculations for high-lying levels in Ba I

Radiative lifetimes for 18 highly excited levels belonging to 5d4f, 5d6p, and 6snp (n = 10, 12, 14–19) configurations of barium were measured by time-resolved laser-induced fluorescence (TR-LIF) technique. The uncertainties of the results are less than 10%. To our best knowledge, there are 16 lifetimes of Ba I reported for the first time. Two lifetimes were measured to compare with the previous results, and good agreements were achieved. From the combination of these experimental lifetimes and theoretical branching fractions calculated using a pseudo-relativistic Hartree–Fock model including core-polarization effects, a set of semi-empirical transition probabilities and oscillator strengths was derived for 46 Ba I spectral lines in the wavelength region from 240 to 3765 nm. For about half of these transitions, the uncertainties affecting the new decay parameters were found to be equal or better than 50%.

Melting Si: Beyond Density Functional Theory

The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as nonlocal many body correlation effects of the electrons. We predict a melting temperature of about 1735 and 1640K without and with core polarization effects, respectively. Both values are within 3% of the experimental melting temperature of 1687K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200K too low, and hybrid functionals overestimate the melting point by 150K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results demonstrate that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.

The study of nuclear structure for some nuclei

An analytical form of the ground state charge density distributionsfor the low mass fp shell nuclei ( 40  A  56 ) is derived from asimple method based on the use of the single particle wave functionsof the harmonic oscillator potential and the occupation numbers ofthe states, which are determined from the comparison between theoryand experiment.For investigating the inelastic longitudinal electron scattering formfactors, an expression for the transition charge density is studiedwhere the deformation in nuclear collective modes is taken intoconsideration besides the shell model space transition density. Thecore polarization transition density is evaluated by adopting theshape of Tassie model together with the derived form of the groundstate charge density distribution. In this work, we devote ourinvestigation on 0 3 2 3 1 1   transition of Ti 50 , 0 1 2 1 1 1   transitionof Cr 50 and 0 2 2 2 1 1   of Cr 52 nuclei. It is found that the corepolarization effects, which represent the collective modes, areessential for reproducing a remarkable agreement between thecalculated inelastic longitudinal C2 form factors and those ofexperimental data.

Study of the Electric Quadrupole Moments for some Scandium Isotopes Using Shell Model Calculations with Different Interactions

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the experimental data. The theoretical results of the quadrupole moments for some scandium isotopes performed with FPD6 interaction and Bohr-Mottelson effective charge agree with experimental values.

Theoretical Study of Density Distributions and Size Radii of 8B and 17Ne

The proton, neutron and matter density distributions, the corresponding size radii and elastic electron scattering form factors of one-proton 8 B and two-proton 17 Ne halo nuclei are calculated. The theoretical technique used to fulfill calculations is by assuming that both nuclei under study are composed of two main parts; the first is the compact core and the second is the unstable halo part. The single-particle radial wavefunctions of harmonic-oscillator (HO) and Woods-Saxon (WS) potentials are used to study core and halo parts, respectively. And other approach is studied by using HO potential for both core and halo parts, but using two HO size parameters for both supposed parts. The long tail behavior which is the main characteristic of halo nuclei are well produced for both 8 B and 17 Ne. The calculated size radii are in general in good agreement with the available experimental data. The electron scattering form factors of the C0+C2 and C0 components are also calculated for 8 B and 17 Ne, respectively and compared with corresponding stable 10 B and 20 Ne nuclei. For 8 B calculations, the core-polarization (CP) effects are taken into account by using Tassie and Bohr-Mottelson models. The contribution from model-space (MS) part C2 component is taken through pwt interaction. The results of the calculated charge form factors are left for the planned electron-radioactive ion beam colliders where the study of skin or halo on the charge form factors are going to be studied.

Core polarization effects: Oscillator strengths, transition probabilities and radiative lifetimes of levels in Bi IV

In this work a systematic analysis of Bi IV atomic properties is presented. Ab initio relativistic Hartree–Fock calculations in an intermediate coupling (IC) formalism and taking into account Core Polarization Effects (CPE) are used. We use for the IC calculations the standard method of least square fitting of experimental energy levels by means of computer codes from Cowan which was modified in order to include CPE. Our calculations have been made from 17 configurations of Bi IV: 5d106s2, 5d106p2, 5d106sns (n= 7–10) and 5d106snd (n= 6–9) for even parity and 5d106snp (n=6,7), 5d106snf (n=5,6), 5d96s26p and 5d96s2nf (n=5,6) for odd parity. Transition probabilities and oscillator strengths for 100 lines and some radiative lifetimes of Bi IV have been calculated. Besides a comparison of our results with the scarce experimental values available in the bibliography are presented. The presence of spectral lines of bismuth in stellar atmospheres has been reported in different stars. This is the motivation by this work can be very interest in astrophysical area. Recently the Bi IV is taking importance because it is considered as the main dopant in the prospective used for the design and synthesis of new scintillators.

Polarization effects in above-threshold ionization with a mid-infrared strong laser field

Using a semiclassical approach, we theoretically study the above-threshold ionization of magnesium by intense, mid-infrared laser pulses. The formation of low-energy structures in the photoelectron spectrum is found to be enhanced by comparing with a calculation based on the single-active electron approximation. By performing electron trajectory and recollision-time distribution analysis, we demonstrate that this phenomenon is due to the laser-induced ionic core polarization effects on the recolliding electrons. We also show that the polarization effects should be experimentally detectable. Our finding provides new insight into ultrafast control of strong-field photoionization and imaging of polar molecules.

Excitation energy shift and size difference of low-energy levels in p -shell Λ hypernuclei

We investigated structures of low-lying $0s$-orbit $\Lambda$ states in $p$-shell $\Lambda$ hypernuclei ($^A_\Lambda Z$) by applying microscopic cluster models for nuclear structure and a single-channel folding potential model for a $\Lambda$ particle. For $A>10$ systems, the size reduction of core nuclei is small, and the core polarization effect is regarded as a higher-order perturbation in the $\Lambda$ binding. The present calculation qualitatively describes the systematic trend of experimental data for excitation energy change from $^{A-1} Z$ to $^A_\Lambda Z$, in $A>10$ systems. The energy change shows a clear correlation with the nuclear size difference between the ground and excited states. In $^7_\Lambda \textrm{Li}$ and $^9_\Lambda \textrm{Be}$, the significant shrinkage of cluster structures occurs consistently with the prediction of other calculations.

Study of the Electric Quadrupole Moments for some Scandium Isotopes Using Shell Model Calculations with Different Interactions

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the experimental data. The theoretical results of the quadrupole moments for some scandium isotopes performed with FPD6 interaction and Bohr-Mottelson effective charge agree with experimental values.

Long-range behavior of the transition dipole moments of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) based on ab initio calculations.

The ab initio electronic transition dipole moments (ETDMs) of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) were calculated between the ground and excited states converging to the lowest three dissociation limits. The spin-allowed ETDMs were evaluated in a wide range of interatomic distances, R, by means of the quasi-relativistic electronic wave functions obtained by the multi-reference configuration interaction method. The inner-shell electrons (2 electrons for Li and Na atoms, and 10 and 28 for K and Rb, respectively) were described using the non-empirical shape-consistent effective core potentials. The l-independent core polarization potentials of each atom were used to take core-polarization and core-valence correlation effects into account. The long-range behavior of both singlet-singlet X1Σ+-(2,3)1Σ+;(1,2)1Π and triplet-triplet a3Σ+-(2,3)3Σ+;(1,2)3Π transition moments is perfectly fitted at large R-distance by the asymptotic formula of X. Chu and A. Dalgarno, Phys. Rev. A: At., Mol., Opt. Phys., 2002, 66, 024701: , where the coefficient β is equal to 2 and -1 for the Σ-Σ and Σ-Π transitions, respectively. The n2S-n2P transition moments, dA, and dynamic polarizabilites, αB, of the alkali atoms in the n2S state extracted from the present molecular calculations coincide with their empirical and ab initio counterparts to within a few percent.

Lifetime calculations in energy levels of Kr vii

Calculations of the lifetimes for all experimentally known energy levels of the spectrum of the six times-ionized krypton (Kr vii) are presented. The relativistic Hartree–Fock method including core-polarization effects were used. The energy matrix was calculated using energy parameters adjusted to the experimental energy levels. We also present a calculation based on a relativistic multiconfigurational Dirac–Fock approach. For some energy levels, a comparison of these results with the bibliography data was made.

Radiative Decay Rates for Electric Dipole, Magnetic Dipole and Electric Quadrupole Transitions in Triply Ionized Thulium (Tm IV)

A new set of radiative decay parameters (oscillator strengths, transition probabilities) for spectral lines in triply ionized thulium (Tm IV) has been obtained within the framework of the pseudo-relativistic Hartree-Fock (HFR) approach. The effects of configuration interaction and core-polarization have been investigated in detail and the quality of the results has been assessed through a comparison between different HFR physical models. The spectroscopic data listed in the present paper cover electric dipole as well as magnetic dipole and electric quadrupole transitions in a wide range of wavelengths from extreme ultraviolet to near infrared.

Lifetime measurements and oscillator strengths in singly ionized scandium and the solar abundance of scandium

The lifetimes of 17 even-parity levels (3d5s, 3d4d, 3d6s and 4p2) in the region 57 743–77 837 cm−1 of singly ionized scandium (Sc ii) were measured by two-step time-resolved laser induced fluorescence spectroscopy. Oscillator strengths of 57 lines from these highly excited upper levels were derived using a hollow cathode discharge lamp and a Fourier transform spectrometer. In addition, Hartree–Fock calculations where both the main relativistic and core-polarization effects were taken into account were carried out for both low- and high-excitation levels. There is a good agreement for most of the lines between our calculated branching fractions and the measurements of Lawler & Dakin in the region 9000–45 000 cm−1 for low excitation levels and with our measurements for high excitation levels in the region 23 500–63 100 cm−1. This, in turn, allowed us to combine the calculated branching fractions with the available experimental lifetimes to determine semi-empirical oscillator strengths for a set of 380 E1 transitions in Sc ii. These oscillator strengths include the weak lines that were used previously to derive the solar abundance of scandium. The solar abundance of scandium is now estimated to loge⊙ = 3.04 ± 0.13 using these semi-empirical oscillator strengths to shift the values determined by Scott et al. The new estimated abundance value is in agreement with the meteoritic value (logemet = 3.05 ± 0.02) of Lodders, Palme & Gail. (Less)