Nuclear Attraction Research Articles

Overlapping photo-ionized doubly excited resonance series for Li+ ion

Based on two different approaches, the B-spline-based K-matrix method and the eigenchannel R-matrix method, we present a detailed theoretical study on the photoionization from the ground and bound excited and states of an Li+ ion to continua between the N = 2 and N = 3 thresholds, dominated by overlapping doubly excited resonance series embedded in multiple singly ionized channels. The nearly identical theoretical spectra from these two different calculations, together with the excellent agreement between the length and velocity results, suggests that our study has successfully led to a reliable estimate of the Li+ photoionization spectra. In addition to identifying all overlapping doubly excited autoionization series, our calculated spectrum is in good agreement with the only observed data for two broad resonances. Our study has also shown that the strong interaction between neighboring resonances from different resonance series, which is responsible for the level crossing for in the He atom, is substantially smaller due to a stronger nuclear attraction to atomic electrons for the two-electron ions.

Self-friction power series and their use for evaluation of atomic nuclear attraction integrals with noninteger indices of Slater orbitals and Coulomb–Yukawa-like potentials

Using complete orthogonal [Formula: see text]-Self-Friction Polynomials ([Formula: see text]-SFPs) introduced by one of the authors, the analytical and power series formulas for SF atomic nuclear attraction integrals over [Formula: see text]-noninteger Slater type orbitals ([Formula: see text]-NISTOs) and [Formula: see text]-noninteger Coulomb–Yukawa-like potentials ([Formula: see text]-NICYPs) are presented, where [Formula: see text] are the integer ([Formula: see text] or noninteger ([Formula: see text] SF quantum numbers and [Formula: see text]. As an application, the computer calculations for dependence of the atomic nuclear attraction integrals over [Formula: see text]-NISTOs and [Formula: see text]-NICYPs functions are presented.

Evaluation of Self-Friction Three-Center Nuclear Attraction Integrals with Integer and Noninteger Principal Quantum Numbers n over Slater Type Orbitals

We have proposed a new approach to evaluate self-friction (SF) three-center nuclear attraction integrals over integer and noninteger Slater type orbitals (STOs) by using Guseinov one-range addition theorem in standard convention. A complete orthonormal set of Guseinov ψα exponential type orbitals (ψα-ETOs, α=2,1,0,-1,-2,…) has been used to obtain the analytical expressions. The overlap integrals with noninteger quantum numbers occurring in SF three-center nuclear attraction integrals have been evaluated using Qnsq auxiliary functions. The accuracy of obtained formulas is satisfactory for arbitrary integer and noninteger principal quantum numbers.

The response electron–electron repulsion energy and energy component analysis in CC/MBPT methods

Molecular properties are computed as responses to perturbations (energy derivatives) in coupled-cluster (CC)/many-body perturbation theory (MBPT) models. Here, the CC/MBPT energy derivative with respect to a general two-electron (2-e) perturbation is assembled from gradient theory for 2-e property evaluation, including the electron repulsion energy. The correlation energy (∆E) is shown to be the sum of response kinetic (∆T), electron–nuclear attraction (∆V), and electron repulsion (∆V ee ) energies. Thus, evaluation of total V ee for energy component analysis is simple: For total energy (E), total 1-e responses T and V, and nuclear–nuclear repulsion energy (V NN ), V ee = E − V NN − T − V is the true 2-e response value. Component energy analysis is illustrated in an assessment of steric repulsion in ethane’s rotational barrier. Earlier SCF-based results (Bader et al. in J Am Chem Soc 112:6530, 1990) are corroborated: The higher-energy eclipsed geometry is favored versus staggered in the two repulsion energies (V NN and V ee ), while decisively disfavored in electron–nuclear attraction energy (V). Our best quality calculations (CCSD/cc-pVQZ) attain practical Virial Theorem compliance (i.e., agreement among the kinetic energy, potential energy, and total energy representations) in assigning 2.70 ± 0.06 to the barrier height; −195.80 kcal/mol is assigned to the drop in “steric” repulsion upon going to the eclipsed geometry. Steric repulsion is not responsible for any fraction of the ~3 kcal/mol barrier.

Importance of Deformations in Dynamical Evolution of Proton-halo Nuclei

Based on the cluster–core model, we have extended our recent study on neutron-halo structure of light nuclei to investigate the effects of deformations and orientations on the observed and proposed cases of proton-rich light nuclei. The relevance of “hot compact” over “cold elongated” configurations due to orientations is explored along with the possible role of angular momentum effects. The cases of both 1pand 2p-halo nuclei are analyzed in terms of potential energy surfaces calculated as a sum of binding energies, Coulomb repulsion, nuclear proximity attraction and the centrifugal potential for all the possible cluster+core configurations of a nucleus. The halo structures of N and S nuclei are of special interest as they exhibit strong influence of deformations and angular momentum effects.

Benchmark values for molecular three-center integrals arising in the Dirac equation.

Previous papers by the authors report that they obtained compact, arbitrarily accurate expressions for two-center, one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In the present study, accuracy limits of expressions given are examined for three-center nuclear attraction integrals, which are one-electron, three-center integrals with no analytically closed-form expression. In this work new molecular auxiliary functions are used. They are obtained via Neumann expansion of the Coulomb interaction. The numerical global adaptive method is used to evaluate these integrals for arbitrary values of orbital parameters and quantum numbers. Several methods, such as Laplace expansion of Coulomb interaction, single-center expansion, and the Fourier transformation method, have previously been used to evaluate these integrals considering the values of principal quantum numbers in the set of positive integer numbers. This study of three-center integrals places no restrictions on quantum numbers in all ranges of orbital parameters.

Libcint: An efficient general integral library for Gaussian basis functions.

An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library is able to evaluate arbitrary integral expressions on top of p, r and σ operators with one-electron overlap and nuclear attraction, two-electron Coulomb and Gaunt operators for segmented contracted and/or generated contracted basis in Cartesian, spherical or spinor form. Using a symbolic algebra tool, new integrals are derived and translated to C code programmatically. The generated integrals can be used in various types of molecular properties. To demonstrate the capability of the integral library, we computed the analytical gradients and NMR shielding constants at both nonrelativistic and 4-component relativistic Hartree-Fock level in this work. Due to the use of kinetically balanced basis and gauge including atomic orbitals, the relativistic analytical gradients and shielding constants requires the integral library to handle the fifth-order electron repulsion integral derivatives. The generality of the integral library is achieved without losing efficiency. On the modern multi-CPU platform, Libcint can easily reach the overall throughput being many times of the I/O bandwidth. On a 20-core node, we are able to achieve an average output 8.3 GB/s for C60 molecule with cc-pVTZ basis.

Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

Background: Exotic non-spherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short range nuclear attraction and long range Coulomb repulsion. Purpose: We explore the impact of nuclear pasta on nucleosynthesis, during neutron star mergers, as cold dense nuclear matter is ejected and decompressed. Methods: We perform classical molecular dynamics simulations with 51200 and 409600 nucleons, that are run on GPUs. We expand our simulation region to decompress systems from an initial density of 0.080 fm^{-3} down to 0.00125 fm^{-3}. We study proton fractions of Y_P=0.05, 0.10, 0.20, 0.30, and 0.40 at T =0.5, 0.75, and 1.0 MeV. We calculate the composition of the resulting systems using a cluster algorithm. Results: We find final compositions that are in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than Y_P=0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

Use of Modified Self-Frictional Laguerre Power Series for Study of Atomic Nuclear Attraction Integrals of Noninteger Slater-Type Orbitals and Coulomb–Yukawa-Like Potentials

Abstract Using complete orthonormal L(α*)-modified self-frictional Laguerre polynomials (L(α*)-MSFLPs) in standard convention introduced by the author, the expressions for transformation of χ-noninteger Slater type orbitals (χ-NISTOs) and V-noninteger Coulomb–Yukawa-like potentials (V-NICYPs) to the MSF Laguerre power series are suggested, where α* are the integer (α* = α, −∞ < α ≤ 2) or noninteger (α* ≠ α, −∞ < α* < 3) SF quantum numbers. By the use of these power series, the atomic nuclear attraction integrals of χ-NISTOs and V-NICYPs are evaluated. The convergence and accuracy of obtained MSF Laguerre power series are tested by calculating concrete cases.

Role of e–e repulsion interaction in nonsequential double ionization of Xe by linearly and elliptically polarized laser pulses

We investigated the nonsequential double ionization (NSDI) of Xe by linearly polarized (LP) and elliptically polarized (EP) laser pulses using the classical ensemble model. For the two cases, the ensemble from NSDI was separated into two kinds of subensemble according to the relative momentum along the y-axis [Formula: see text], respectively. The results show only for the case of relatively small [Formula: see text], the momentum distribution along the x-axis can show a V-like shape obviously, which is according with the experiment [Phys. Rev. Lett.99, 263003 (2007)]. What is important is that we firstly examine the role of the repulsion interaction between two electrons for the two kinds of subensemble, and find that the process of NSDI for the case of relatively small [Formula: see text] exits a strong repulsion interaction which contributes significantly to the V-like shape. However, for the case of relatively big [Formula: see text], the repulsion interaction between two electrons is relatively weak, and both the nuclear Coulomb attraction and electric field force dominate the process of NSDI.

Fission dynamics of240Cf*formed in34,36S induced reactions

We have studied the entrance channel effects in the decay of Compound nucleus 240 Cf * formed in 34 S+ 206 Pb and 36 S+ 204 Pb reactions by using energy density dependent nuclear proximity potential in the framework of dynamical cluster-decay model (DCM). At different excitation energies, the fragmentation potential and preformation probability of decaying fragments are almost identical for both the entrance channels, which seem to suggest that decay is independent of its formation and entrance channel excitation energy. It is also observed that, with inclusion of deformation effects upto quadrupole within the optimum orientation approach, the fragmentation path governing potential energy surfaces gets modified significantly. Beside this, the fission mass distribution of Cf* isotopes is also investigated. The calculated fission cross-sections using SIII force for both the channels find nice agreement with the available experimental data for deformed choice of fragments, except at higher energies. In addition to this, the comparative analysis with Blocki based nuclear attraction is also worked out. It is observed that Blocki proximity potential accounts well for the CN decay at all energies whereas the use of EDF based nuclear potential suggests the presence of some non-compound nucleus process (such as quasi-fission (qf)) at higher energies.

Studies of quantum self-frictional atomic potentials and nuclear attraction forces in standard convention

This paper is devoted to examine a physical nature of quantum self-frictional atomic potentials and nuclear attraction forces. Using analytical formulas for the L(pl∗)-generalized Laguerre polynomials (L(pl∗)-GLPs) and ψ(pl∗)-generalized exponential type orbitals (ψ(pl∗)-GETOs) in standard convention, the self-frictional atomic potentials and nuclear attraction forces are investigated, where pl∗=2l+2-α∗ and α∗ is the integer (α∗=α, -∞<α⩽2) or noninteger (α∗≠α, −∞<α∗<3) self-frictional quantum number. We notice that the L(pl∗)-GLPs, the origin of which is the quantum self-frictional fields, are the radial parts of the ψ(pl∗)-GETOs. The dependence of the quantum self-frictional potentials and nuclear attraction forces as a function of the distance from nucleus is analyzed. The relationships presented are valid for the arbitrary values of quantum numbers and scaling parameters.

Transmembrane voltage potential of somatic cells controls oncogene-mediated tumorigenesis at long-range.

The microenvironment is increasingly recognized as a crucial aspect of cancer. In contrast and complement to the field's focus on biochemical factors and extracellular matrix, we characterize a novel aspect of host:tumor interaction - endogenous bioelectric signals among non-excitable somatic cells. Extending prior work focused on the bioelectric state of cancer cells themselves, we show for the first time that the resting potentials of distant cells are critical for oncogene-dependent tumorigenesis. In the Xenopus laevis tadpole model, we used human oncogenes such as mutant KRAS to drive formation of tumor-like structures that exhibited overproliferation, increased nuclear size, hypoxia, acidity, and leukocyte attraction. Remarkably, misexpression of hyperpolarizing ion channels at distant sites within the tadpole significantly reduced the incidence of these tumors. The suppression of tumorigenesis could also be achieved by hyperpolarization using native CLIC1 chloride channels, suggesting a treatment modality not requiring gene therapy. Using a dominant negative approach, we implicate HDAC1 as the mechanism by which resting potential changes affect downstream cell behaviors. Based on published data on the voltage-mediated changes of butyrate flux through the SLC5A8 transporter, we present a model linking resting potentials of host cells to the ability of oncogenes to initiate tumorigenesis. Antibiotic data suggest that the relevant butyrate is generated by a native bacterial species, identifying a novel link between the microbiome and cancer that is mediated by alterations in bioelectric signaling.

Nitrogen Discharged from the Earth’s Interior Regions

The abundant nitrogen in the Earth’s atmosphere can be interpreted as the result of endothermic nuclear transmutation of carbon and oxygen atom pairs in (Ca, D) CO3 or CaCO3 aragonite lattice of Earth’s crust from the Archean era to the present time, by physical catalytic help of excited electrons e* generated by stick sliding due to plate tectonics and geoneutrinos ν by the radioactive decay of elements such as uranium and thorium in Earth’s mantle: through a nuclear attraction effect that is due to deuteron catalysis of nitrogen formation. The relationship between the critical temperature T and the critical pressure P for the nuclear transmutation is expressed as 7253 × e-0.014P, and the formation of nitrogen in the mantle is possible at temperatures ≥ 2510 K and pressure ≥ 58 GPa.

On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions

Using one-range addition theorems, the three-center nuclear attraction integrals are expressed through the overlap integrals containing χ - and χα -Slater-type orbitals (χ -STOs and χα -STOs), where - ∞ < α ⩽ 2 and . For the fast calculation, the partial summation is utilized for some indices of series expansion relations which correspond to progressively increasing upper limits. The binomial coefficients are stored in the memory of the computer. The convergence and accuracy of series are tested by calculating concrete cases. The best values are obtained for α = 0 .

Spontaneous fission modes and lifetimes of superheavy elements in the nuclear density functional theory

Background: The reactions with the neutron-rich ${}^{48}\mathrm{Ca}$ beam and actinide targets resulted in the detection of new superheavy (SH) nuclides with $Z=104--118$. The unambiguous identification of the new isotopes, however, still poses a problem because their $\ensuremath{\alpha}$-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between $\ensuremath{\alpha}$-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and to assess its extent.Purpose: We perform self-consistent calculations of the competing decay modes of even-even SH isotopes with $108\ensuremath{\le}Z\ensuremath{\le}126$ and $148\ensuremath{\le}N\ensuremath{\le}188$.Methods: We use the state-of-the-art computational framework based on self-consistent symmetry-unrestricted nuclear density functional theory capable of describing the competition between nuclear attraction and electrostatic repulsion. We apply the SkM* Skyrme energy density functional. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (HFB) approach. This paper constitutes a systematic self-consistent study of spontaneous fission in the SH region, carried out at a full HFB level, that simultaneously takes into account both triaxiality and reflection asymmetry.Results: Breaking axial symmetry and parity turns out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases. We predict two competing SF modes: reflection symmetric modes and reflection asymmetric modes.Conclusions: The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by ${}^{280}\mathrm{Hs}$, ${}^{284}\mathrm{Fl}$, and ${}_{118}^{284}\mathrm{Uuo}$ that separates the regions of SH nuclei synthesized in ``cold-fusion'' and ``hot-fusion'' reactions. The region of long-lived SH nuclei is expected to be centered on ${}^{294}\mathrm{Ds}$ with a total half-life of $\ensuremath{\sim}1.5\phantom{\rule{0.28em}{0ex}}\mathrm{days}$. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

Accurate and Fast Evaluation of Three-Center Nuclear Attraction Integrals of Coulomb–Yukawa Like Correlated Interaction Potentials and Slater Type Orbitals

Abstract With the use of one-range addition theorems of Slater type orbitals (STOs) introduced by one of the authors, three-center nuclear attraction integrals containing Coulomb–Yukawa like correlated interaction potentials (C-CIPs and Y-CIPs) appearing in the Hartree–Fock–Roothaan (HFR) equations for molecules are evaluated. These integrals are expressed through the overlap integrals which depend on the frictional quantum number α, where −∞ &amp;lt; α ≤ 2. The convergence of the series is tested by calculating three-center nuclear attraction integrals of C-CIPs, Y-CIPs, and STOs for the arbitrary values of potential parameters and locations of orbitals. For rapid calculations of these integrals, we use the partial summations of some indices corresponding to progressively increasing upper limits appearing in the series expansion relations. Additionally, the binomial coefficients arising in the series are stored in the memory of the computer using their recurrence relation. The fast and accurate computation approach suggested in this work is demonstrated.

Explicit and implicit multi‐center integrations

AbstractWe present truncated expansions of multicenter one‐electron nuclear attraction and two‐electron repulsion integrals over localized basis functions in terms of one‐ and two‐center integrals of “Coulomb,” “exchange,” and “hybrid” type. Two variants are discussed: the “Explicit Multi‐center Integrations” and the “Implicit Multi‐Center Integrations” (abbreviated as “EMCI” and “IMCI”, respectively). While EMCI also deals with individual integrals, the IMCI option is the more appealing one: it enables us to evaluate the entire matrix elements of “Restricted Hartree–Fock”‐type in a very effective and chemically meaningful way. Due to the diatomic nature of our expansions, integrations over “Slater‐Type Orbitals” become well‐feasible, too. © 2012 Wiley Periodicals, Inc.

The analysis of polarization effects on the interelectronic separations in the atoms and molecules of the G1 test set

AbstractWe have calculated the differences between kinetic, nuclear attraction, and two‐electron energies as well as the position intracules, P(u), for 56 molecules and 17 atoms contained in the G1 test set, using basis sets differing in their degree of polarization. The calculations were performed using an unrestricted Hartree–Fock wave function that was expanded using the 6‐31G, 6‐31G(d,p), 6‐31G(3d,3p), 6‐31G(3df,3pd), 6‐311G, 6‐311G(d,p), 6‐311G(3d,3p), 6‐311G(3df,3pd), 6‐311++G, 6‐311++G(d,p), 6‐311++G(3d,3p), and 6‐311++G(3df,3pd) basis sets. In addition to these Pople basis sets, the Dunning's cc‐pVDZ and cc‐pVTZ bases as well as the non‐polarized portions of these basis sets were used. We observe a consistent contraction of electron pairs (as measured by the distribution in P(u)) as the number of polarization functions is increased beyond zero in molecular systems. This contraction is related to an increase in the electron density in the internuclear bonding regions of molecules as the wave functions are polarized. We note that the increased flexibility in the polarized basis set allows for a more accurate description of the chemical bond and is energetically favorable due to an increased level of attraction to the nuclei (despite the obvious increase in electronic repulsion energy). Because of the increase in electron density in internal regions of the molecule (at the expense of electron density depletions in outer regions), the probability of observing electrons closer together (i.e., at smaller u) increases due to the relationship between P(u) and its Coulomb component, J(u). © 2012 Wiley Periodicals, Inc.

Relativistic explicit correlation: Coalescence conditions and practical suggestions

To set up the general framework for relativistic explicitly correlated wave function methods, the electron-electron coalescence conditions are derived for the wave functions of the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), Dirac-Coulomb-Breit (DCB), modified Dirac-Coulomb (MDC), and zeroth-order regularly approximated (ZORA) Hamiltonians. The manipulations make full use of the internal symmetries of the reduced two-electron Hamiltonians such that the asymptotic behaviors of the wave functions emerge naturally. The results show that, at the coalescence point of two electrons, the wave functions of the DCG Hamiltonian are regular, while those of the DC and DCB Hamiltonians have weak singularities of the type r(12)(ν) with ν being negative and of O(α(2)). The behaviors of the MDC wave functions are related to the original ones in a simple manner, while the spin-free counterparts are somewhat different due to the complicated electron-electron interaction. The behaviors of the ZORA wave functions depend on the chosen potential in the kinetic energy operator. In the case of the nuclear attraction, the behaviors of the ZORA wave functions are very similar to those of the nonrelativistic ones, just with an additional correction of O(α(2)) to the nonrelativistic cusp condition. However, if the Coulomb interaction is also included, the ZORA wave functions become close to the large-large components of the DC wave functions. Note that such asymptotic expansions of the relativistic wave functions are only valid within an extremely small convergence radius R(c) of O(α(2)). Beyond this radius, the behaviors of the relativistic wave functions are still dominated by the nonrelativistic limit, as can be seen in terms of direct perturbation theory (DPT) of relativity. However, as the two limits α → 0 and r(12) → 0 do not commute, DPT is doomed to fail due to incorrect descriptions of the small-small component Ψ(SS) of the DC wave function for r(12) < R(c). Another deduction from the possible divergence of Ψ(SS) at r(12) = R(c) is that the DC Hamiltonian has no bound electronic states, although the last word cannot be said. These findings enrich our understandings of relativistic wave functions. On the practical side, it is shown that, under the no-pair approximation, relativistic explicitly correlated wave function methods can be made completely parallel to the nonrelativistic counterparts, as demonstrated explicitly for MP2-F12. Yet, this can only be achieved by using an extended no-pair projector.