Dipole Strength Research Articles

Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes 144,148,150,152,154Sm

A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

Spectroscopic, physicochemical characterizations and photonics applications on boron subphthalocyanine chloride as organic electronics

This work shows the structural, thermogravimetric, optical, and electrochemical properties of boron subphthalocyanine chloride (B-subPc-Cl) as organic electronic material. The Fullprof Suite program and Rietveld analysis were used to refine and index the crystal structure of B-subPc-Cl. The thermogravimetric analysis (TGA) and the differential thermogravimetric analysis (dTG) were used to study the kinetic thermogravimetric factors using the Horowitz-Metzger's and Coats-Redfern methods. The absorption spectra of B-subPc-Cl contain two strong absorption bands (Soret-like band and Q-like band). The oscillator strength and electrical dipole strength were estimated by using a Gaussian fitting of the molar absorptivity (εmolar) of the B-subPc-Cl. The HOMO-LUMO and the band gap of B-subPc-Cl were calculated by using cyclic voltammetry measurement. Details of the UV-Vis –NIR absorption spectra and optical band gap for B-subPc-Cl are also provided. Density-functional theory (DFT) method has been utilized to obtain geometrically optimized structure for the studied compound. The theoretical calculations agreed with the experimental results. The obtained results point out the prospects of B-subPc-Cl for the organic electronic applications.
 KEY WORDS: Subphthalocyanine, Optical properties, TGA, Cyclic voltammetry, DFT method
 Bull. Chem. Soc. Ethiop. 2024, 38(2), 527-538. 
 DOI: https://dx.doi.org/10.4314/bcse.v38i2.19

The Radial Interplanetary Field Strength at Sunspot Minimum as Polar Field Proxy and Solar Cycle Predictor

The minimum value of the geomagnetic aa index has served as a remarkably successful predictor of solar cycle amplitude. This value is reached near or just after sunspot minimum, when both the near-Earth solar wind speed and interplanetary magnetic field (IMF) strength fall to their lowest values. At this time, the heliospheric current sheet is flattened toward the heliographic equator and the dominant source of the IMF is the Sun’s axial dipole moment, which, in turn, has its source in the polar fields. As recognized previously, the success of aamin as solar cycle precursor provides support for dynamo models in which the sunspots of a given cycle are produced by winding up the poloidal field built up during the previous cycle. Because they are highly concentrated toward the poles by the surface meridional flow, the polar fields are difficult to measure reliably. Here we point out that the observed value of the radial IMF strength at solar minimum can be used to constrain the polar field measurements, and that this parameter, which is directly proportional to the Sun’s axial dipole strength, may be an even better solar cycle predictor than geomagnetic activity.

The effects of residual dipolar coupling on carnosine in proton muscle spectra.

Carnosine, an MR-visible dipeptide in human muscle, is well characterized by two peaks at ~8 and ~7 ppm from C2 and C4 imidazole protons. Like creatine and other metabolites, carnosine is subject to residual dipolar coupling in the anisotropic environment of muscle fibers, but the effects have not been studied extensively. Single-voxel TE 30-32 PRESS spectra from three different 3T studies were acquired from gastrocnemius medialis and soleus muscles in the human lower leg. In these studies, carnosine T2 values were measured, and spectra were obtained at three different foot angles. LCModel was used to fit the carnosine peaks with a basis set that was generated using shaped RF pulses and included a range of dipolar couplings affecting the C4 peak. A seven-parameter analytic expression was used to fit the CH2 doublets of creatine. It incorporated an optimized "effective TE" value to model the effect of shaped RF pulses. The fits confirm that the triplet C4 peak of carnosine is dipolar coupled to a pair of CH2 protons, with no need to include a contribution from a separate pool of freely rotating uncoupled carnosine. Moreover, the couplings experienced by carnosine C4 protons and creatine CH2 protons are strongly correlated (R2 = 0.88, P<0.001), exhibiting a similar 3cos2 θ - 1 dependence on the angle θ between fiber orientation and B0. T2 values for the singlet C2 peak of gastrocnemius carnosine are inversely proportional to the C4 dipolar coupling strength (R2 = 0.97, P < 0.001), which in turn is a function of foot orientation. This dependence indicates that careful positioning of the foot while acquiring lower leg muscle spectra is important to obtain reproducible carnosine concentrations. As proton magnetic resonance spectroscopy of carnosine is currently used to non-invasively estimate the muscle fiber typology, these results have important implications in sport science.

Sensing cholesterol-induced rigidity in model membranes with time-resolved fluorescence spectroscopy and microscopy.

Here, we report the characterization of cholesterol levels on membrane fluidity with a twisted intramolecular charge transfer (TICT) membrane dye, namely DI-8-ANEPPS, using fluorescence lifetime techniques such as time-correlated single photon counting (TCSPC) and fluorescence lifetime imaging microscopy (FLIM). The characterized liposomes comprised a 3 : 1 ratio of POPC and POPG, respectively, 1% DI-8-ANEPPS, and increasing cholesterol levels from 0% to 50%. Fluorescence lifetime characterization revealed that increasing the cholesterol levels from 0% to 50% increases the fluorescence lifetime of DI-8-ANEPPS from 2.36 ns to 3.65 ns, a 55% increment. Such lengthening in the fluorescence lifetime is concomitant with reduced Stokes shifts and higher quantum yield, revealing that localized excitation (LE) dominates over TICT states with increased cholesterol levels. Fluorescence anisotropy measurements revealed a less isotropic environment in the membrane upon increasing cholesterol levels, suggesting a shift from liquid-disorder (Lα) to liquid-order (LO) upon adding cholesterol. Local electrostatic and dipole characterization experiments revealed that changes in the zeta-potential (ζ-potential) and transmembrane dipole potential (Ψd) induced by changes in cholesterol levels or the POPC : POPG ratio play a minimal role in the fluorescence lifetime outcome of DI-8-ANEPPS. Instead, these results indicate that the cholesterol's effect in restricting the degree of movement of DI-8-ANEPPS dominates its photophysics over the cholesterol effect on the local dipole strength. We envision that time-resolved spectroscopy and microscopy, coupled with TICT dyes, could be a convenient tool in exploring the complex interplay between membrane lipids, sterols, and proteins and provide novel insights into membrane fluidity, organization, and function.

From Feast to Famine: A Systematic Study of Accretion onto Oblique Pulsars with 3D GRMHD Simulations

Disk-fed accretion onto neutron stars can power a wide range of astrophysical sources ranging from X-ray binaries, to accretion-powered millisecond pulsars, ultraluminous X-ray sources, and gamma-ray bursts. A crucial parameter controlling the gas–magnetosphere interaction is the strength of the stellar dipole. In addition, coherent X-ray pulsations in many neutron star systems indicate that the star's dipole moment is oblique relative to its rotation axis. Therefore, it is critical to systematically explore the 2D parameter space of the star's magnetic field strength and obliquity, which is what this work does, for the first time, in the framework of 3D general-relativistic magnetohydrodynamics. If the accretion disk carries its own vertical magnetic field, this introduces an additional factor: the relative polarity of the disk and stellar magnetic fields. We find that depending on the strength of the stellar dipole and the star–disk relative polarity, the neutron star's jet power can either increase or decrease with increasing obliquity. For weak dipole strength (equivalently, high accretion rate), the parallel polarity results in a positive correlation between jet power and obliquity, whereas the antiparallel orientation displays the opposite trend. For stronger dipoles, the relative-polarity effect disappears, and jet power always decreases with increasing obliquity. The influence of the relative polarity gradually disappears as obliquity increases. Highly oblique pulsars tend to have an increased magnetospheric radius, a lower mass accretion rate, and enter the propeller regime at lower magnetic moments than aligned stars.

Vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles

In this paper, we consider the formation of vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles by numerical simulations of the Gross–Pitaevskii equation. Different dependencies of critical rotation frequency (CRF) and optical lattice height, vortex number, and rotation frequency are studied, depending on the direction of the dipole axis and dipole strength. Our results show that the CRF in z = 0 is minimum. When the optical lattice height is gradually increased, the CRF decreases gradually. Reducing of dipole strength in anisotropic dipole–dipole interaction (DDI) favours the formation of vortices, and such decline in isotropic DDI hinders the creation of vortices. The reason for this difference is that the repulsive interaction is favorable and the attractive interaction is disadvantageous for the vortex formation. In addition, we study the first-order correlation function and focus on variation of coherence. For small rotation frequency, the break of coherence occurs earlier in the case of purely repulsive interaction. With an increase in rotation frequency, the coherence concurrently disappears in layer z = 2. Moreover, we also investigate the quenched dynamics, showing that the increase of angular momentum is induced by changing the direction of dipoles and in this process the vortex number remains unchanged.

Influence of geometric structure on information entropy in spin-1 ferromagnetic dipolar Bose–Einstein condensates

In this study, we investigate the dynamics properties of spin-1 ferromagnetic Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the mean-field nonlocal Gross–Pitaevskii equation. We find that the population of the information entropy in momentum space [Formula: see text] is greatly affected by geometric structure and dipole strength. The prolate condensate is favorable to obtain bigger [Formula: see text] than oblate condensate. The density distribution verifies that the formation of magnetic domain is associated with the variation of [Formula: see text]. In addition, the kinetic energy displays that dramatical oscillation appears for strong dipolar interaction and it is larger in prolate condensate. Also, we use the order parameter to describe the order–disorder crossover. It is shown that BECs develop toward the disordered state with prolate condensate under strong DDI.

Deposition products predicted from conceptual DFT: The hydrolysis reactions of MoF6, WF6, and UF6.

Metal hexafluorides hydrolyze at ambient temperature to deposit compounds having fluorine-to-oxygen ratios that depend upon the identity of the metal. Uranium-hexafluoride hydrolysis, for example, deposits uranyl fluoride (UO2F2), whereas molybdenum hexafluoride (MoF6) and tungsten hexafluoride deposit trioxides. Here, we pursue general strategies enabling the prediction of depositing compounds resulting from multi-step gas-phase reactions. To compare among the three metal-hexafluoride hydrolyses, we first investigate the mechanism of MoF6 hydrolysis using hybrid density functional theory (DFT). Intermediates are then validated by performing anharmonic vibrational simulations and comparing with infrared spectra [McNamara et al., Phys. Chem. Chem. Phys. 25, 2990 (2023)]. Conceptual DFT, which is leveraged here to quantitatively evaluate site-specific electrophilicity and nucleophilicity metrics, is found to reliably predict qualitative deposition propensities for each intermediate. In addition to the nucleophilic potential of the oxygen ligands, several other contributing characteristics are discussed, including amphoterism, polyvalency, fluxionality, steric hindrance, dipolar strength, and solubility. To investigate the structure and composition of pre-nucleation clusters, an automated workflow is presented for the simulation of particle growth. The workflow entails a conformer search at the density functional tight-binding level, structural refinement at the hybrid DFT level, and computation of a composite free-energy profile. Such profiles can be used to estimate particle nucleation kinetics. Droplet formation is also considered, which helps to rationalize the different UO2F2 particle morphologies observed under varying levels of humidity. Development of predictive methods for simulating physical and chemical deposition processes is important for the advancement of material manufacturing involving coatings and thin films.

Deformation and destruction of north-eastward drifting dipoles

We systematically study the evolution of Larichev–Reznik dipoles in an equivalent-barotropic quasi-geostrophic beta-plane model in high-resolution numerical simulations. Our results shed light on the self-organization and rich dynamics of dipolar vortices, which are ubiquitous in geophysical flows. By varying both dipole strength and initial angle α0 of dipole tilt to the zonal direction, we discover new breakdown mechanisms of the dipole evolution. The dipoles are quickly destroyed by Rossby wave radiation, if initial tilt is too large or the dipole is too weak; otherwise, via damped oscillations, the dipoles tend to adjust themselves to different states drifting eastward. Two competing physical mechanisms that govern dipole transformations are found: (1) spontaneous dipole instability due to a growing critical linear mode and (2) meridional separation of dipole partners that accumulates over the adjustment period and prevents the above instability. Which mechanism prevails depends on the initial tilt and dipole strength, and the details of this are discussed.

Temperature-dependent solvent reorganization entropies, free energies, and transition dipole strengths for the photoexcitation of Reichardt's dye B30.

Absorption spectra of the solvatochromic dye 2,6-diphenyl-4-2,4,6-triphenyl-1-pyridinophenolate (B30) were measured in seven solvents of varying polarity over temperature ranging from each solvent's freezing point to 300K. The excitation energies and their variances allowed calculations of the solvent reorganization energies, reorganization free energies and reorganization entropies as functions of temperature. The entropies of solvent packing around the chromophore are found to make major contributions to the reorganization free energies. The variances of the excitation energies depend only weakly on temperature, in disagreement with an expression that is often used for solvent reorganization free energies. Polar solvents reduce the transition dipole strength of B30's long-wavelength absorption band, probably because interactions with the solvent enhance the charge-transfer character of the transition. The dipole strength drops further at low temperatures.

Effects of the Intramolecular Group and Solvent on Vibrational Coupling Modes and Strengths of Fermi Resonances in Aryl Azides: A DFT Study of 4-Azidotoluene and 4-Azido-N-phenylmaleimide.

The high transition dipole strength of the azide asymmetric stretch makes aryl azides good candidates as vibrational probes (VPs). However, aryl azides have complex absorption profiles due to Fermi resonances (FRs). Understanding the origin and the vibrational modes involved in FRs of aryl azides is critically important toward developing them as VPs for studies of protein structures and structural changes in response to their surroundings. As such, we studied vibrational couplings in 4-azidotoluene and 4-azido-N-phenylmaleimide in two solvents, N,N-dimethylacetamide and tetrahydrofuran, to explore the origin and the effects of intramolecular group and solvent on the FRs of aryl azides using density functional theory (DFT) calculations with the B3LYP functional and seven basis sets, 6-31G(d,p), 6-31+G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311+G(d,p), 6-311++G(d,p), and 6-311++G(df,pd). Two combination bands consisting of the azide symmetric stretch and another mode form strong FRs with the azide asymmetric stretch for both molecules. The FR profile was altered by replacing the methyl group with maleimide. Solvents change the relative peak position and intensity more significantly for 4-azido-N-phenylmaleimide, which makes it a more sensitive VP. Furthermore, the DFT results indicate that a comparison among the results from different basis sets can be used as a means to predict more reliable vibrational spectra.

Hydrodynamic permeability of circular-inclusion-doped Brinkman media

Theory and computations are applied to assess the hydrodynamic permeability of cavity- doped hydrogels, central to a variety range of contemporary technological applications. Direct volume-averaging is undertaken in a two-dimensional, Brinkman-hydrodynamic context to test an ensemble-averaging methodology recently proposed for the ion permeability of such media. In two dimensions, the ensemble-averaging integral furnishes a pre-factor $2$ linking the pressure dipole strength of a single inclusion in an unbounded continuum to the effective hydrodynamic permeability of a composite with small inclusion area fraction. The factor is verified by direct computations for dilute simple-square arrays of (cylindrical) inclusions. At area fractions up to the close-packing limit, computations address the hydrodynamic interactions. The theory is shown to accurately predict the effective hydrodynamic permeability of physically relevant composites (Brinkman length of the continuous phase $\ell$ smaller than the inclusion radius $a$ ) for area fractions $\phi \lesssim {\rm \pi}/ 9 \approx 0.3$ . Computations for random ensembles demonstrate that the dilute theory may be extended to higher area fractions by drawing on Rayleigh's self-consistent approximation when the continuous-phase permeability places the continuous-phase flow well into the Darcy regime ( $a / \ell \gtrsim 10$ ). Computations also demonstrate, similarly to Rayleigh theories for scalar diffusion, that microstructural order has a very weak influence on the effective permeability when $\phi \lesssim {\rm \pi}/ 9$ with $\ell / a \lesssim 1$ (Darcy hydrodynamic interactions). Finally, a cursory examination is undertaken of the fluid velocity and its fluctuations arising from shear-viscosity heterogeneity in media with perfectly uniform permeability $\ell ^2$ .

Morphological, optical and electrochemical properties of tin(II) 2,3-naphthalocyanine for organic electronic applications

Herein, tin(II) 2,3-naphthalocyanine (SnNC) organic dye was successfully thermally deposited onto different optical transparent substrates such as glass, quartz, ITO, and FTO. FE-SEM technique reveals that SnNC film shows a uniform and symmetrical spherical-shaped with an average diameter of ∼50 nm. Annealing up to 473 K for 4 h increases the crystallite size of SnNC thin film. SnNC thin film shows absorption bands centered at 858 nm, 313 nm, and 249 nm with two shoulders at 775 nm and 350 nm. We present the absorbance, specular transmittance, specular reflectance and fluorescence properties of SnNc deposited on the different transparent substrates. The oscillator strengths (f) and the electric dipole strength (q2) of SnNC thin film were estimated from the molar absorptivity () spectra. According to the Tauc model, two optical gap transitions were estimated as 1.03 eV and 3.48 eV. Annealing up to 473 K for 4 h slightly increases them to 1.15 eV and 3.59 eV, respectively. At excitation wavelength = 360 nm, two emission bands were observed at around 403 nm and 674 nm. Upon annealing at 373 K and 473 K, the real part of the refractive index of SnNC thin film decreases, which is correlated with a decrease in mass density. Electrochemical HOMO—LUMO band gaps of SnNC estimated from the cyclic voltammetry (CV) measurements () agree well with the observed optical energy gap estimated from the optical measurements. The wide range absorption, emission, good thermal stability, suitable optical band gap, and electrochemical properties, prove an effective example of organic dye suitable for organic electronic applications.

Stimulation of peroneal nerves reveals maintained somatosensory representation in transtibial amputees.

Several studies have found changes in the organization of the primary somatosensory cortex (SI) after amputation. This SI reorganization was mainly investigated by stimulating neighboring areas to amputation. Unexpectedly, the somatosensory representation of the deafferented limb has rarely been directly tested. We stimulated the truncated peroneal nerve in 24 unilateral transtibial amputees and 15 healthy controls. The stimulation intensity was adjusted to make the elicited percept comparable between both stimulation sides. Neural sources of the somatosensory-evoked magnetic fields (SEFs) to peroneal stimulation were localized in the contralateral foot/leg areas of SI in 19 patients and 14 healthy controls. We demonstrated the activation of functionally preserved cortical representations of amputated lower limbs. None of the patients reported evoked phantom limb pain (PLP) during stimulation. Stimulation that evoked perceptions in the foot required stronger intensities on the amputated side than on the intact side. In addition to this, stronger stimulation intensities were required for amputees than for healthy controls. Exploratorily, PLP intensity was neither associated with stimulation intensity nor dipole strength nor with differences in Euclidean distances (between SEF sources of the healthy peroneus and mirrored SEF sources of the truncated peroneus). Our results provide hope that the truncated nerve may be used to establish both motor control and somatosensory feedback via the nerve trunk when a permanently functional connection between the nerve trunk and the prosthesis becomes available.

Investigating the strength of the scissors mode in 151Sm

Change in nuclei deformation leads to changes in statistical properties such as the nuclear level density (NLD) and γ-ray strength function (γSF). The NLD and γSF of 151Sm were extracted using the Oslo method. The strength of the scissors resonance (SR) and its centroid energy for 151Sm were found to be 2.13 ± 0.60 and 2.48 ± 0.25 MeV, respectively. These results were used to place the SR of 151Sm and its magnetic dipole strength B(M1)SR into the context of previously measured Sm isotopes.

The structure of low-lying 1− states in 90,94Zr from (α,α′γ) and (p,p′γ) reactions

The low-lying dipole strength was investigated in 90,94 Zr via the (p,p′γ) reaction at 80 MeV and via the (α,α′γ) reaction at 130 MeV. These experiments were performed at the Research Center for Nuclear Physics (Osaka University) and made combined use of the high-resolution magnetic spectrometer Grand Raiden and the CAGRA HPGe gamma array. The comparison of our results with existing (γ,γ′) reaction data shows differences in the excitation patterns. In the present experimental conditions, in fact, both α and p probes are exciting the investigated 1− states mainly through the short-range nuclear force, expected to favour the population of surface excitations. Distorted Wave Born Approximation (DWBA) calculations were made using form factors built assuming specific transition densities, characterized by a strong neutron component at the nuclear surface and based on Random Phase Approximation (RPA). A combined analysis of the (α,α′γ) and (p,p′γ) data was performed to investigate the isoscalar character of the 1− states in 90,94Zr. Although an overall general consistency was obtained in the studied energy intervals, not all (p,p′γ) cross sections were well reproduced using the isoscalar strength deduced from (α,α′γ) data. This might suggest that the mixing of isoscalar and isovector components and the degree of collectivity are not the same for all the 1− states studied.

Order-degree-modulated ferroic response and an unconventional electrocaloric effect in B-site complex systems: a case study in Pb[(Yb1/2Nb1/2)0.84(Mg1/3Nb2/3)0.16]O3 ceramic

The order-degree-modulated ferroic response and electrocaloric effect (ECE) in Pb(B1,B2)O3-type B-site complex antiferroelectrics (AFEs) are explored in this work. The results show that local/phase structure and dielectric/ferroic properties are strikingly dependent on the degree of order (high, intermediate and low for samples S1, S2 and S3, respectively). A decrease in the content of the AFE orthorhombic phase and an increase in the weakly polar disorder phase is observed from S1 to S3, accompanied by an enhanced relaxation behavior with a smearing of the AFE-to-paraelectric phase transition. Ferroic and EC responses in the three samples present distinct features. Antiferroelectricity wakes-up significantly in sample S1, which boosts the ECE to ∼0.95 K and is almost three times that of S3 (∼0.23 K). An abnormal ECE [negative ECE with a hop–hop character and asymmetrical electrocaloric (EC) response] is unexpectedly found in sample S1. The underlying mechanism is unveiled by dipolar relaxation and phenomenology analysis, which states that the AFE coupling strength dominates the EC performance in this AFE. This work not only presents a refreshing method for order-degree regulation of the ECE in B-site complex AFEs, but also clarifies the possibility that AFEs with robust dipolar coupling strength have an unconventional ECE.

Annealing effect on the morphology, linear and non-linear optical properties of squaraine derivative thin films for optoelectronics applications

Squaraine is a class of organic compounds that possess unique optical properties, including strong absorption of light, high fluorescence quantum yields, etc. Here, we explore the structural and spectroscopic investigations of 2,4-Bis[4-(N,N-dibenzylamino)-2,6 dihydroxyphenyl] squaraine dye (SQ) under different conditions of thermal effects. The molar absorptivity (εmolar) spectra were used to describe the electric dipole strength (q2) and the oscillator strengths (f) of SQ dye. The Surface morphology of SQ dye was investigated by AFM and the average roughness shows dependence on the annealing effect. A slight change in the optical energy gap (⁓ 0.3 eV) after annealing up to 473 K reflects the optical stability of our investigated thin films. The optical band transitions and photoluminescence (PL) emission spectra were described before and after annealing at 423 & 473 K. As the temperature annealing film increased to 473 K, the nonlinear parameters such as χ(3) and n2 decreased by about 44% and 36%, respectively. The good thermal stability, suitable optical band gap, and refractive index offer potential applications as active photonic materials in photonic/optoelectronic applications.

Number of virtual photons in the Coulomb dipole excitation

In this study, the number of virtual photons obtained through general, relativistic, nonrelativistic, and intermediate methods was investigated, which is an important factor in obtaining the Coulomb dipole strength distribution. The number of virtual photons was studied according to the incident energy ${E}_{\text{lab}}$ using five methods. The general method, which has two different forms (integral and differential), is valid for all energy regions, whereas the relativistic method is effective for regions with high $\ensuremath{\beta}$ values. In addition, the validity of the nonrelativistic approximation was tested by comparing it with the general method in the low-incident-energy region, and the intermediate method was shown to be not effective in the high-excitation-energy region. Further, an investigation was conducted on the dependence of the number of virtual photons on the charges of the projectile and target nuclei. Using the same $R$ value, target nuclei, and incident energy, it was found that the number of virtual photons does not depend on the charge number of the projectile in the relativistic method. With the same $R$ value, projectile, and incident energy, in contrast it can be seen that the number of virtual photon depends on the square of the charge number of target nuclei.