Dipole Sum Research Articles

3D Reconstruction with Fast Dipole Sums

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination.

Competition between [formula omitted] and [formula omitted] photo-disintegration yields

A comprehensive analysis of the competition between photo-proton and photo-neutron disintegration yields is undertaken by constraining photo-absorption data with physics principles — namely, dipole sum rules, decay properties to open channels, isospin selection rules and statistical evaporation from compound nucleus formation. The trend and magnitude of disintegration yields for self-conjugate nuclei are in agreement with the evaporation model of Blatt and Weisskopf. A substantial improvement is found between the exponential trend presented in this work and that determined by Morinaga using a similar approach. This work allows for the evaluation of frequently missing or inconsistent photo-proton contributions, which impacts the photo-disintegration of light and neutron-deficient nuclei, where photo-proton contributions are relevant.

Removing center of mass effects in response function and sum rule calculations based on the harmonic oscillator basis

Response functions are at the heart of any comparison of theory with experiment in studies of the nuclear dynamics with electroweak probes. Calculations performed in the laboratory frame often suffer from center of mass contaminations that need to be removed. By confining the system in a harmonic oscillator, we derive a set of analytical formulas to subtract the center of mass effects from calculations of response functions and associated sum rules. After a general analytical derivation, we first deal specifically with the longitudinal response function appearing in electron scattering and provide expressions for the center of mass correcting functions. Next, we present a proof of principle study for the case of the electric dipole sum rules in a two-body problem with a numerical implementation of our formalism. These steps pave the way to applying the proposed method to heavier nuclei in the future.

Dipole oscillator strength distributions, sum rules, mean excitation energies, and isotropic van der Waals coefficients for benzene, pyridazine, pyrimidine, pyrazine, s-triazine, toluene, hexafluorobenzene, and nitrobenzene

Experimental, theoretical, and additive-model photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole oscillator strength density are used to construct dipole oscillator strength distributions for benzene, pyridazine (1,2-diazine), pyrimidine (1,3-diazine), pyrazine (1,4-diazine), s-triazine (1,3,5-triazine), toluene (methylbenzene), hexafluorobenzene, and nitrobenzene. The distributions are used to predict dipole sum rules S(k) for -6 ≤ k ≤ 2, mean excitation energies I(k) for -2 ≤ k ≤ 2, and isotropic van der Waals C6 coefficients. A popular combination rule for estimating C6 coefficients for unlike interactions from the C6 coefficients of the like interactions is found to be accurate to better than 1% for 606 of 628 cases (96.4%) in the test set.

Intershell correlations in endohedral atoms

We have calculated partial contributions of different endohedral and atomic subshells to the total dipole sum rule in the frame of the random phase approximation with exchange (RPAE) and found that they are essentially different from the numbers of electrons in respective subshells. This difference manifests the strength of the intershell interaction. We present concrete results of calculations for endohedrals, composed of fullerene C60 and all noble gases He, Ne, Ar, Kr, and Xe thus forming respectively He@C60, Ne@C60, Ar@C60, Kr@C60, and Xe@C60. For comparison, we obtained similar results for isolated noble gas atoms. The deviation from number of electrons in outer subshells proved to be much bigger in endohedrals than in isolated atoms thus demonstrating considerably stronger intershell correlations there.

Dipole sum rules of a hydrogen atom in a Debye-Hückel plasma

In this work, we carry out a study of the dipole oscillator strength sum rule, Sk, and the logarithmic, Lk, version, for a hydrogen atom embedded in a Debye-Huckel plasma. We solve the time-independent Schrodinger equation by means of a finite-differences approach to obtain the discrete and continuum spectrum of the atom embedded in the plasma, as a function of the screening parameter, λD. We find excellent agreement for the Sk and Lk sum rules for λD → ∞, i.e., no plasma, in comparison with exact theoretical results. For plasma interaction, we obtain the conditions for the delocalization of the hydrogen atom energy levels finding its effects on the Sk sum rules. We find that for k ≤ 0, Sk increases as the screening constant decreases until λ ~ 0.84 a.u., where the 1s ground state becomes delocalized due to the plasma weakening. For the static dipole polarizability, S−2, we find excellent agreement of our results for the discrete and continuum spectrum to available data in the literature for selected values of screening parameters. In the logarithmic counterpart, Lk, the sum rules decrease for lower values of the screening length for k ≤ 0. We observe a decrease of the mean excitation energy, I0 = eL0/S0, as the screening length decreases finding a sudden change for λD ~ 2 a.u. Furthermore, we obtain closure relations for the Sk sum rule with k = −1, 1, 2, 3 as a function of the Debye-Huckel screening and find excellent agreement with the sum over excited states for k = −1, 0, 1, and 2 and find that S3 sum rule diverges for a hydrogen atom immersed in a Debye-Huckel plasma. We conclude that the fulfillment of the closure relations requires a good description of the excitation states.

New Data on Photoneutron Reaction Cross Sections for 76,78,80,82Se Nuclei

The problem of reliability of the cross section data obtained for partial photoneutron reactions on 76,78,80,82Se nuclei in beams of quasimonoenergetic annihilation photons by means of neutron multiplicity sorting is discussed by employing objective physical criteria. It is shown that, because of substantial systematic uncertainties, experimental data on the (γ, 1n) and (γ, 2n) cross sections are unreliable. New data satisfying the reliability criteria are obtained for the partial photoneutron reaction cross sections for 76,78,82Se nuclei by an experimental—theoretical method for evaluating such cross sections and are compared with experimental data and with data evaluated earlier for the isotope 80Se. The evaluated integrated cross sections for the total photoneutron reactions on 76,78,80,82Se nuclei are compared with the predictions of the Thomas-Reiche-Kuhn classical dipole sum rule.

Estimation of the Integral Role of Intershell Correlations in Heavy Atoms

We demonstrate that in the frame of the random phase approximation with the exchange, which preserves the validity of the precise well known dipole sum rule, the partial contributions for given subshells strongly deviates from the number of electrons in these subshells. This demonstrates strong effects of intershell interaction in atoms.

Transition sum rules in the shell model

An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energy-weighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the $sd$-shell.

Probing the Fluorescence Dipoles of Single Cubic CdSe/CdS Nanoplatelets with Vertical or Horizontal Orientations

Measuring the orientation of a single fluorescent nanoemitter and obtaining emitters with a desired orientation is of highest importance for nanophotonics, especially in plasmonics where an emitting dipole close to a metallic surface will couple efficiently to plasmonic modes only if it is deposited vertically. Control of the orientation of a nano-object remains a challenge. Achieving vertical orientation, or having an information on the dipole orientation are key steps for efficient plasmonic excitation. We consider here cubic-shaped nanoplatelets with a thin CdSe core sandwiched in a thick CdS shell. By a combination of polarization measurement and radiation pattern Fourier analysis, we show that each single platelet behaves with excellent precision as a 2D dipole (sum of 2 orthogonal incoherent dipoles) and having only two possible orientations: either they lie horizontally on the substrate or they stand vertically on the edge. The cubic shape allows some platelets to deposit vertically so that they pr...

Breaking of axial symmetry in excited heavy nuclei as identified in giant dipole resonance data

A recent theoretical prediction of a breaking of axial symmetry in quasi all heavy nuclei is confronted to a new critical analysis of photon strength functions of nuclei in the valley of stability. For the photon strength in the isovector giant dipole resonance (IVGDR) regime a parameterization of GDR shapes by the sum of three Lorentzians (TLO) is extrapolated to energies below and above the IVGDR. The impact of non-GDR modes adding to the low energy slope of photon strength is discussed including recent data on photon scattering and other radiative processes. These are shown to be concentrated in energy regions where various model calculations predict intermediate collective strength; thus they are obviously separate from the IVGDR tail. The triple Lorentzian (TLO) ansatz for giant dipole resonances is normalized in accordance to the dipole sum rule. The nuclear droplet model with surface dissipation accounts well for positions and widths without local, nuclide specific, parameters. Very few and only global parameters are needed when a breaking of axial symmetry already in the valley of stability is admitted and hence a reliable prediction for electric dipole strength functions also outside of it is expected.

Effect of broken axial symmetry on the electric dipole strength and the collective enhancement of level densities in heavy nuclei

The basic parameters for calculations of radiative neutron capture, photon strength functions and nuclear level densities near the neutron separation energy are determined based on experimental data without an ad hoc assumption about axial symmetry—at variance to previous analysis. Surprisingly few global fit parameters are needed in addition to information on nuclear deformation, taken from Hartree Fock Bogolyubov calculations with the Gogny force, and the generator coordinator method assures properly defined angular momentum. For a large number of nuclei the GDR shapes and the photon strength are described by the sum of three Lorentzians, extrapolated to low energies and normalised in accordance to the dipole sum rule. Level densities are influenced strongly by the significant collective enhancement based on the breaking of shape symmetry. The replacement of axial symmetry by the less stringent requirement of invariance against rotation by 180° leads to a novel prediction for radiative neutron capture. It compares well to recent compilations of average radiative widths and Maxwellian average cross sections for neutron capture by even target nuclei. An extension to higher spin promises a reliable prediction for various compound nuclear reactions also outside the valley of stability. Such predictions are of high importance for future nuclear energy systems and waste transmutation as well as for the understanding of the cosmic synthesis of heavy elements.

Constrained dipole oscillator strength distributions, sum rules, and dispersion coefficients for Br2 and BrCN

Dipole oscillator strength distributions for Br2 and BrCN are constructed from photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density and molar refractivity data when available. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C6 coefficients. Coupled-cluster calculations of the static dipole polarizabilities of Br2 and BrCN are reported for comparison with the values of S(-2) extracted from the distributions.

Breaking of axial symmetry in excited nuclei as identified in experimental data

A phenomenological prediction for radiative neutron capture is presented and compared to recent compilations of Maxwellian averaged cross sections and average radiative widths. Photon strength functions and nuclear level densities near the neutron separation energy are extracted from data without the assumption of axial symmetry – at variance to common usage. A satisfactory description is reached with a small number of global parameters when theoretical predictions on triaxiality (from constrained HFB calculations with the Gogny D1S interaction) are inserted into conventional calculations of radiative neutron capture. The photon strength is parametrized using the sum of three Lorentzians (TLO) in accordance to the dipole sum rule. The positions and widths are accounted for by the droplet model with surface dissipation without locally adjusted parameters. Level densities are influenced strongly by the significant collective enhancement based on the breaking of axial symmetry. With the less stringent requirement of invariance against rotation by 180∘ a global set of parameters which allows to describe the photon strength function and the level densities in the nuclear mass range from mass number 50 < A < 250 is found.

Effective restoration of dipole sum rules within the renormalized random-phase approximation

The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in $^{48, 52, 58}$Ca and $^{90, 96, 110}$Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, causing the violation of the corresponding energy-weight sum rules (EWSR). It is shown that this sum rule violation can be eliminated by taking into account the contribution of the particle-particle and hole-hole excitations together with the particle-hole ones in a simple and perturbative way. Consequently, the ratio of the energy-weighted sum of strengths of the pygmy dipole resonance to that of the giant dipole resonance increases.

Constrained Dipole Oscillator Strength Distributions for CF4, CClF3, CCl2F2, CCl3F, CHF3, CH3F, CH3Cl, CH3Br, CH3I, C2F6, and CCl3CF3

Abstract Dipole oscillator strength distributions are constructed for CF4, CClF3, CCl2F2, CCl3F, CHF3, CH3F, CH3Cl, CH3Br, CH3I, C2F6, and CCl3CF3 from experimental and theoretical photoabsorption cross-sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density, and either molar refractivity data or static dipole polarizabilities depending upon the availability of refractivities. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C 6 coefficients. Pseudospectral representations of the DOSDs are reported.

Dipole properties of PH3, PF3, PF5, PCl3, SiCl4, GeCl4, and SnCl4

ABSTRACTExperimental and theoretical photoabsorption cross sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule, the high-energy behaviour of the dipole oscillator strength density, static dipole polarisabilities, and molar refractivity data when available are used to construct dipole oscillator strength distributions for PH3, PF3, PF5, PCl3, SiCl4, GeCl4, and SnCl4. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C6 coefficients.

On the dipole polarisability and dipole sum rules of ozone

Ab initio calculations of the dipole polarisability and other Cauchy moments of the dipole oscillator strength distribution (DOSD) of ozone are reported to help resolve discrepancies between theory and experiment. A number of coupled-cluster methods based on a Hartree–Fock reference function, multiconfiguration-reference configuration interaction methods, and perturbatively corrected, complete-active-space self-consistent field methods are used. The C DOSD of Kumar and Thakkar is probably preferable to their B1 distribution. Our best estimate of the mean polarisability is atomic units.

Efficient method for evaluating energy-dependent sum rules

Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the energy. More complicated weight functions are also encountered, e.g., in nuclear polarization corrections of atomic spectra. Using the Lorentz integral transform method and the Lanczos algorithm, we derive a computationally efficient technique for evaluating such sum rules that avoids the explicit calculation of both the continuum states and the response function itself. Our numerical results for electric dipole sum rules of the $^{4}\mathrm{He}$ nucleus with various energy-dependent weights show rapid convergence with respect to the number of Lanczos steps. This demonstrates the usefulness of the method in a variety of electroweak reactions.

The Bertlmann–Martin Inequality and Spin Degrees of Freedom

The Bertlmann–Martin inequality based on the dipole sum rule is revisited taking into account the spin degrees of freedom. We consider 1 and 2 particles of spin 1/2 in a mean field, adding a spin dependent interaction. The derivation of the inequality relies on the closure relation. We discuss the effect of the Pauli principle, and the restrictions it imposes on the use of the closure relation. The problem is exemplified by a simple model based on harmonic forces. Moreover, in the 2 particle case, the model we use is separable in the relative and centre of mass coordinates. In this case, we show that for operators connecting only singlet states, their sum rule can be calculated in the usual way, i.e. via the double commutator of this operator with the Hamiltonian. An upper bound can also be obtained by using the Bertlmann–Martin technique. This is not possible for operators involving a transition between singlet and triplet states.