Pauli Correlations Research Articles

Testing the ϕ-nuclear potential in pion-induced ϕ meson production on nuclei near threshold

The near-threshold pion-induced ϕ production off nuclei has been studied in the kinematical conditions of the HADES experiment using a collision model based on the nuclear spectral function. Starting from the elementary reaction π−p→ϕn, absolute differential and integral cross sections for the production of ϕ mesons off a light carbon and a heavy tungsten target have been calculated and compared to the recently reported experimental cross sections. The absolute cross section values are shown to be sensitive to the effective nuclear scalar ϕ and neutron potentials while the transparency ratio is governed by the ϕN absorption cross section. The experimental data are found to be consistent with an attractive ϕ-nucleus potential of ≈ -(50–100) MeV at normal nuclear matter density ρ0 and an effective ϕN absorption cross section of ≈ 12–25 mb. The extracted ϕ-nucleus potential is deeper than previous theoretical and experimental findings as well as those obtained in the present work within the (tρ) approximation with accounting for Pauli correlations from the spin-averaged ϕ-p scattering length reported in a recent ALICE experiment.

First application of a microscopic K−NN absorption model in calculations of kaonic atoms

Strong interaction energy shifts and widths in kaonic atoms are calculated for the first time using microscopic $K^- N$ + $K^- NN$ potentials derived from $K^- N$ scattering amplitudes constructed within SU(3) chiral coupled-channels models of meson-baryon interactions. The in-medium modifications of the free-space amplitudes due to the Pauli correlations are taken into account. The $K^-N+K^-NN$ potentials evaluated for 23 nuclear species are confronted with kaonic atoms data. The description of the data significantly improves when the $K^-NN$ absorption is included. To get $\chi^2$ as low as for the $K^-N+$phenomenological multi-nucleon potential an additional phenomenological term, accounting for $K^{-}-3N(4N)$ processes, is still needed. However, density dependence of this phenomenological term points out some deficiencies in the microscopic potentials and further improvements of the applied model are thus desirable. The calculated branching ratios for $K^-N$ and $K^-NN$ absorption channels in the $^{12}$C$+K^-$ atom are in reasonable agreement with the old bubble chamber data, as well as with the latest data from the AMADEUS Collaboration.

Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper's quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.

The 'Quantal Newtonian' First Law: A Complementary Perspective to the Stationary-state Quantum Theory of Electrons.

A complementary perspective to the Göttingen-Copenhagen interpretation of stationary-state quantum theory of electrons in an electromagnetic field is described. The perspective, derived from Schrödinger-Pauli theory, is that of the individual electron via its equation of motion or 'Quantal Newtonian' First Law. The Law is in terms of 'classical' fields experienced by each electron: the sum of the external and internal fields vanishes. The external field is a sum of the electrostatic and Lorentz fields. The internal field is a sum of fields' representative of Pauli and Coulomb correlations; kinetic effects; electron density; and internal magnetic component. The energy is obtained from these fields. The sources of the fields are expectation values of Hermitian operators. The perspective is elucidated by application to quantum dots in a magnetic field in a ground, excited singlet and triplet states. The relationship of the perspective to Quantal and traditional density functional theories is briefly explained.

Single- and two-nucleon antikaon absorption in nuclear matter with chiral meson-baryon interactions

We developed a microscopic model for antikaon absorption on two nucleons in nuclear matter. The absorption is described within a meson-exchange picture and the primary $K^-N$ interaction strength is derived from state-of-the-art chiral coupled channel meson-baryon interaction models. We took into account the medium modification of the $K^-N$ scattering amplitudes due to the Pauli correlations. We derived the $K^-NN$ as well as $K^-N$ optical potentials as functions of nuclear matter density including the real part of the $K^-NN$ potential. We calculated the $K^-$ single- and two-nucleon absorption fractions and branching ratios for various mesonic and non-mesonic channels. We confirmed the crucial role of in-medium effects in our calculations. Our results are in very good agreement with available experimental data from old bubble chamber experiments as well as with the latest results from the AMADEUS collaboration.

Electron correlations in an excited state of a quantum dot in a uniform magnetic field

Electron correlations in a two-electron two-dimensional ‘artificial atom’ or quantum dot (with harmonic confining potential) in the presence of a uniform magnetic field in an excited singlet state are studied via quantal density functional theory (QDFT). QDFT allows for the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, as well as the determination of the contribution of these correlations to the kinetic energy. The QDFT mapping is from the excited state of the quantum dot to one of noninteracting fermions in their ground state possessing the same basic variables of the density and physical current density, and the same orbital and spin angular momentum. A detailed analysis of these correlations in terms of their quantal sources, the corresponding ‘classical’ fields, and resulting potentials and energies is presented. The key conclusions are that as in natural atoms, the contributions of the Pauli and Coulomb correlations relative to the total energy for the excited state, are less than but of the same order of magnitude as those for the ground state of a quantum dot. However, in contrast, the correlation-kinetic contributions are an order of magnitude greater than those for a quantum dot in its ground state. These correlations constitute nearly 75% of the kinetic and 25% of the total energy. This result is consistent with prior work on low electron density Wigner systems in three-dimensions in which correlation-kinetic effects too play a significant role. The significance of these correlations to traditional excited state density functional theory is noted.

Electron Correlations in Local Effective Potential Theory

Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.

K+-nucleus potentials from K+-nucleon amplitudes

Optical potentials for K+-nucleus interactions are constructed from K+-nucleon amplitudes using recently developed algorithm based on K+-N kinematics in the nuclear medium. With the deep penetration of K+ mesons into the nucleus at momenta below 800 MeV/c it is possible to test this approach with greater sensitivity than hitherto done with K− and pions. The energy-dependence of experimental reaction and total cross sections on nuclei is better reproduced with this approach compared to fixed-energy amplitudes. The inclusion of Pauli correlations in the medium also improves the agreement between calculation and experiment. The absolute scale of the cross sections is reproduced very well for 6Li but for C, Si and Ca calculated cross sections are (23±4)% smaller than experiment, in agreement with earlier analyses. Two phenomenological models that produce such missing strength suggest that the imaginary part of the potential needs about 40% enhancement.

Asymptotic Structure in the Classically Forbidden Region of the Hooke's Atoms

The two-electron Hooke's atom — a quantum mechanical system with two electrons bound in a harmonic potential — is well known for its exact analytical properties at certain oscillator strengths. The Hooke's atoms with more than two electrons offer more scope for valuable practical applications. In this work, we study the asymptotic structure of these Hooke's atoms in the classically forbidden region. The leading-order term of the long-range expression for the KS exchange-correlation potential vxc(r) is shown to be −1/r. The second and third higher order terms are also exactly obtained. Various components of vxc(r) are also studied. It is shown that the leading term of O(1/r) in vxc(r) is due to the pure Pauli correlation, while the leading contribution of the Coulomb correlation is of O(1/r3). Neither of them makes contribution to the term of O(1/r2), which is shown to be solely due to the kinetic correlation effect. Results for the two-electron Hooke's atom were obtained before in the literature. Our results reduce to those of the two-electron Hooke's atom as a special case.

Kaonic atoms and in-medium amplitudes II: Interplay between theory and phenomenology

A microscopic kaonic-atom optical potential V K − ( 1 ) is constructed, using the Ikeda–Hyodo–Weise NLO chiral K − N subthreshold scattering amplitudes constrained by the kaonic hydrogen SIDDHARTA measurement, and incorporating Pauli correlations within the Waas–Rho–Weise generalization of the Ericson–Ericson multiple-scattering approach. Good fits to kaonic atom data over the entire periodic table require additionally sizable K − N N -motivated absorptive and dispersive phenomenological terms, in agreement with our former analysis based on a post-SIDDHARTA in-medium chirally-inspired NLO separable model by Cieplý and Smejkal. Such terms are included by introducing a phenomenological potential V K − ( 2 ) and coupling it self-consistently to V K − ( 1 ) . Properties of resulting kaonic atom potentials are discussed with special attention paid to the role of K − -nuclear absorption and to the extraction of density-dependent amplitudes representing K − multi-nucleon processes.

Treatment of carrier scattering in quantum dots beyond the Boltzmann equation

As quantum dots (QD) can confine a small number of carriers in localized states with discrete energies, it is questionable to neglect correlations between the carriers when describing their dynamics. We analyze the influence of carrier correlations in a single QD on Coulomb scattering processes, which are due to the contact with a quasicontinuum of wetting-layer (WL) states. Results obtained from a Boltzmann equation are compared with the fully correlated dynamics governed by a von Neumann--Lindblad equation. In a first step, we take into account correlations generated by the exact treatment of Pauli blocking due to the contributing QD carrier configurations. Subsequently, we include correlations generated by energy renormalizations due to Coulomb interaction between the QD carriers. It is shown that at low WL carrier densities, neither Pauli correlations nor Coulomb correlations can be safely neglected, if the dynamics of single-particle states in the QD are to be predicted qualitatively and quantitatively. In the high-density regime, both types of correlations play a lesser role and thus a description of carrier dynamics by a Boltzmann equation becomes reliable. Furthermore, the efficiency of WL-assisted scattering processes as well as scattering-induced dephasing rates depending on the WL carrier density are discussed.

Quantal density-functional theory of the density amplitude: Application to atoms

Local effective potential theory of electronic structure is the mapping from a system of electrons in an external field to one of noninteracting fermions or bosons with the same electronic density. The energy and ionization potential are also thereby determined. The mappings may be achieved via either quantal density-functional theory (QDFT) or Hohenberg-Kohn-Sham density-functional theory (HKS-DFT). The wave function for the model fermionic system is a Slater determinant of spin orbitals, whereas that for the model bosons is the density amplitude. In the QDFT mappings, the contributions of the electron correlations due to the Pauli exclusion principle, Coulomb repulsion and correlation-kinetic effects are separately delineated. It has been proved via QDFT that the contribution of Pauli and Coulomb correlations to these model systems is the same; the difference lies solely in their correlation-kinetic component. In this paper, we apply the QDFT of the density amplitude to study the mapping to the bosonic model. The application is to atoms and performed at the Hartree-Fock theory level of electron correlations. A principal conclusion is that correlation-kinetic effects play a significant role in the mapping to the bosonic model, whereas they are negligible in the mapping to the model fermions. For the bosonic model, this contribution increases with electron number, becoming nearly as significant as those due to the corresponding electron-interaction (the sum of the Hartree and Pauli) term. The significance of the correlation-kinetic effects will be further enhanced on the inclusion of Coulomb correlations and the corresponding correlation-kinetic contributions. The consequences of these conclusions for the HKS-DFT of the density amplitude are discussed, as are directions for future work.

Spin-lattice relaxation study of the methyl proton dynamics in solid 9,10-dimethyltriptycene (DMT)

Proton spin-lattice relaxation studies are performed for powder samples of 9,10-dimethyltriptycene (DMT) and its isotopomer DMT- d 12 in which all the non-methyl protons in the molecule are replaced by deuterons. The relaxation data are interpreted in terms of the conventional relaxation theory based on the random jump model in which the Pauli correlations between the relevant spin and torsional states are discarded. The Arrhenius activation energies, obtained from the relaxation data, 25.3 and 24.8 kJ mol −1 for DMT and DMT- d 12, respectively, are very high as for the methyl groups. The validity of the jump model in the present case is considered from the perspective of Haupt theory in which the Pauli principle is explicitly invoked. To this purpose, the dynamic quantities entering the Haupt model are reinterpreted in the spirit of the damped quantum rotation (DQR) approach introduced recently for the purpose of NMR lineshape studies of hindered molecular rotators. Theoretical modelling of the relevant methyl group dynamics, based on the DQR theory, was performed. From these calculations it is inferred that direct assessments of the torsional barrier heights, based on the Arrhenius activation energies extracted from relaxation data, should be treated with caution.

Chiral [formula omitted] dynamics and antikaon-nuclear quasibound states

Recent developments are summarised concerning low-energy K¯N interactions as they relate to the possible existence of antikaon-nuclear quasibound states. An exploratory study of antikaons bound to finite nuclei is performed, with emphasis on the evolution of such states from light to heavy nuclei (A=16–208). The energy dependent, driving attractive K¯N interactions are constructed using the s-wave coupled-channel amplitudes involving the Λ(1405) and resulting from chiral SU(3) dynamics, plus p-wave amplitudes dominated by the Σ(1385). Effects of Pauli and short-range correlations are discussed. The decay width induced by K−NN two-body absorption is estimated and found to be substantial. It is concluded that K¯-nuclear quasibound states can possibly exist with binding energies ranging from 60 to 100 MeV, but with short life times corresponding to decay widths of similar magnitudes.

The many-particle scattering system He++ on He: Experiment and a complete unified description

Highly differential experimental results of the scattering system He++ on He at 30 keV are presented as well as a complete unified theoretical description where excitation, transfer and ionization are treated simultaneously on an ab initio level. The agreement even for highly differential cross sections is nearly complete although no explicit correlation besides Pauli correlation is included in the calculations.

Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential ${v}_{ee}(\mathbf{r})$. In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is ${v}_{ee}(r)={v}_{ee}(0)+\ensuremath{\beta}r+O({r}^{2})$, with ${v}_{ee}(0)$ being finite. By assuming that the Schr\odinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange ${v}_{x}(\mathbf{r})$ and correlation ${v}_{c}(\mathbf{r})$ potentials. These functions also approach the nucleus linearly with the linear term of ${v}_{x}(\mathbf{r})$ being solely due to the lowest-order correlation kinetic effects, and the linear term of ${v}_{c}(\mathbf{r})$ being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.

Generation of photocurrent in quantum dot infrared photodetectors: Role of Pauli correlations

We report on our study of the role of the Pauli exclusion principle in the generation of photocurrent in quantum dot infrared photodetectors. The properties of photodetectors are determined by the balance between relaxation and photogeneration rates. Due to the Pauli principle, the relaxation rate depends on the number of available states in the quantum dots. This dependence is strong for small quantum dots with few levels in each dot and weak for large quantum dots or quantum wells. We study both the $I\text{\ensuremath{-}}V$ characteristics of the system and low-frequency current noise. In $I\text{\ensuremath{-}}V$ dependence, the Pauli principle enhances the photocurrent at a given bias voltage. The current noise has more complicated dependence. At low bias voltage, the Pauli principle enhances the noise, while at high voltage, the exclusion principle suppresses the noise of the current. With increasing intensity of illumination, the effects of the Pauli principle are suppressed due to depletion of the dot levels.

Comparative analysis of sequential and coherent tunneling models in resonant diodes

We compare the sequential and coherent tunneling models for the current voltage $(I\text{\ensuremath{-}}V)$ characteristic and shot noise suppression in double-barrier resonant diodes. The results confirm that the $I\text{\ensuremath{-}}V$ characteristic remains the same for the two models, while at increasing voltage the shot noise power at zero frequency shows significant differences. In sequential tunneling, shot noise exhibits in general two regions of suppression due to Pauli and Coulomb correlations, respectively, and with the associated Fano factor never dropping below the value of 0.5. By contrast, in coherent tunneling shot noise exhibits a single region of suppression with the associated Fano factor having the possibility of dropping below the value of 0.5 at voltages near to the current peak. We also investigate the current spectral density and the Fano factor as a function of frequency up to values below that corresponding to the energy difference between the first and the second resonant electron states. At all frequencies the Fano factor for sequential tunneling never drops below the value of 0.5. By contrast, for coherent tunneling, at high frequencies the Fano factor is found to become suppressed systematically below the value of 0.5 to a minimum value of 0.25 which is independent of frequency. These results confirm that coherent tunneling can lead to shot noise suppression below the value of 0.5 contrary to the case of sequential tunneling.

DEFORMED OPTICAL POTENTIAL ANALYSES FOR P+12C

The high energy single folding optical potential approximation is studied to calculate the differential cross-section for proton elastic scattering of 12 C at 156 MeV and 1440 MeV and 12 C for state 2+ (4.44 MeV) at 1440 MeV. A Gaussian nuclear density distribution was used for the proton and Gaussian and Brink nuclear density distributions for the 12 C target. We used the following three effects to derive twelve different methods for the central optical potential: (i) Love and Franey and the Gaussian amplitudes, with the Brink and one-term Gaussian nuclear density distributions, (ii) Pauli correlation in the Gaussian amplitude with these densities, (iii) coupling channels on the differential cross-sections in proton elastic scattering of 12 C at 1440 MeV with single channel calculations using these amplitudes, nuclear density distributions and Pauli correlation in the Gaussian amplitude. A new numerical technique was performed to solve the deformed optical potential equations using computational programs.

Nucleus-Nucleus Elastic Scattering with Pauli Correlation Effect

The elastic scattering of nucleus-nucleus collisions is described in terms of the optical model scattering theory. Two forms of the optical-model have been applied to the description of the elastic nucleus-nucleus collisions in the framework of the double-folding model. The first prescription consists in adding to the effective nucleon-nucleon interaction a pseudo-potential with weak energy dependence, while the second one is obtained as a folding of the effective nucleon-nucleon interaction potential with a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both cases. A phenomenological imaginary part of the Woods-Saxon optical potential is added to the real potential. The angular distributions of the nucleus-nucleus elastic scattering are calculated for various systems at different bombarding energies. It is found that using the effective nucleon-nucleon interaction with Pauli correlation function gives agreement with the experimental data similar or better than that using the effective nucleon-nucleon interaction with a pseudo-potential.