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I. Filikhin

Publications and source records attributed to I. Filikhin.

18 recordsLinked to original sources
arXiv2025

Examination of the lattice QCD-motivated strong attractive $\Omega N$ potentials in the $\Omega^- n p$ system

Within the framework of the Faddeev equations in configuration space, we examine the $\Omega^{-} np$ system, employing strongly attractive lattice HAL QCD and Yukawa-type meson exchange potentials for the $\Omega N$ interaction. Our formalism incorporates the attractive Coulomb force between the $\Omega^{-}$ and proton, treating the system as three non-identical particle pairs (the $ABC$ model). In this study, we assess the impact of the Coulomb interaction on the system and compare our results with recent $\Omega NN$ ($AAC$ model) calculations obtained using various approaches. The $ABC$ model yields low-energy characteristics for the \(\Omega NN\) system that differ from previous calculations. The Coulomb potential has a marginal perturbative effect on the $AAC$ system, shifting the three-body binding energy by the Coulomb energy of the two-body $BC$ subsystem, but only slightly deviating the spatial configuration from isosceles triangle symmetry. These effects are primarily driven by the strong \(\Omega N\) interaction. We demonstrate that the large binding energy of the $\Omega^{-} np$ system arises from the short-range behavior of the $\Omega N$ potentials.

nucl-th↗
arXiv2025

Study of light $\phi$-mesic nuclei with HAL QCD $\phi N$ interactions

We explore the possible existence of light $\phi$-mesic nuclei using HAL QCD $\phi N$ interactions for the $^2S_{1/2}$ and $^4S_{3/2}$ channels. Particularly, using the Faddeev formalism in configuration space, the $\phi NN$ system, and $^{9}_{\phi}$Be and $^{6}_{\phi\phi}$He nuclei within the framework of the three-body cluster model, are investigated. The $\phi\alpha$ effective potential, obtained through a folding procedure, involves the HAL QCD $\phi N$ interaction in the $^4S_{3/2}$ channel which does not lead to a bound state of the $\phi N$ pair while the $\phi N$ $^2S_{1/2}$ channel yields the bound state as the $^3_\phi$H nucleus. The $^4S_{3/2}$ potential ensures that the folding procedure is appropriate because there are no open channels like $\phi+N$ and $\phi +2N $ near or below the $\phi+ 4N$ threshold, and it utilizes different matter distributions of $^4$He proposed in the literature. The folding potential is approximated by the Woods-Saxon formula. The mirror systems $\phi$+$\alpha$+$\alpha$ and $\phi$+$\phi$+$\alpha$ have energy ranges from 1-11 MeV and 3-10~MeV, respectively. The predicted binding energies represent the minimal values for the hypothetical $\phi$ mesic nuclei $^{5}_{\phi}$He, $^{9}_{\phi}$Be and $^{6}_{\phi\phi}$He. The phenomenological $\alpha\alpha$ and $\phi\phi$ potentials are adopted from the literature.

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arXiv2021

Mass-Energy Equivalence in Bound Three-Nucleon Systems

The mass defect formula reflects the equivalence of mass and energy for bound nuclear systems. We study three-nucleon systems $^3$H and $^3$He, considering the neutron and proton as indistinguishable particles ($AAA$ model) or taking into account the real masses of neutrons and protons ($AAB$ model). We have focused on conceptual problems of the $AAA$ model, which is widely used for $3N$ calculations. In particular, the $AAA$ model is incompatible with the mass defect formula, which naturally corresponds to the $AAB$ model. In addition, the $AAA$ model has a cyclic permutation symmetry, which is breaking in the natural $AAB$ model. The latter problem cannot be eliminated within the perturbative $AAA$ approach, in which the mass difference effect is simulated by correcting the kinetic energy operator. Earlier it was reported that the accuracy of such $AAA$ calculations is 1~keV. An example of the $AAB$ calculation, we numerically estimate the effect of the difference between the neutron and proton masses on the energy calculated without any approximation with the accuracy of 0.1~keV. Another manifestation of the equivalence of mass $m$ and energy $E$ can be expressed by the formula $dE/dm=Const$. To show this dependence of the three-body energy on the nucleon mass, we performed realistic calculations within the $AAA$ approximation, varying the averaged nucleon mass. The mass-energy compensation effect for the three-body Hamiltonian is shown. According to this, we have determined the effective nucleon mass required to compensate for the perturbative effect of a three-body potential.

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arXiv2021

3N potentials in the Faddeev coordinate space approach to Nd scattering

In the last decade, for studying 3$N$ bound states and $Nd$ scattering the Tucson-Melbourne (TM) and Urbana 3$N$ force derived from the chiral EFT have been applied. We plan to use the TM 3$N$ force for studying the $Nd$ scattering on the basis of the Faddeev equations in configuration space. In the given paper, we present our final formulas for components of the TM 3$N$ potential obtained in the coordinate space.

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arXiv2020

Three-body model for $K(1460)$ resonance

The three-body $KK\bar K$ model for the $K(1460)$ resonance is developed on the basis of the Faddeev equations in configuration space. A single-channel approach is using with taking into account the difference of masses of neutral and charged kaons. It is demonstrated that a splitting the mass of the $K(1460)$ resonance takes a place around 1460 MeV according to $K^0K^0{\bar K}^0$, $K^0K^+K^-$ and $K^+K^0{\bar K}^0$, $ K^+K^+K^-$ neutral and charged particle configurations, respectively. The calculations are performed with two sets of $KK$ and $K\bar K$ phenomenological potentials, where the latter interaction is considered the same for the isospin singlet and triplet states. The effect of repulsion of the $KK$ interaction on the mass of the $KK\bar K$ system is studied and the effect of the mass polarization is evaluated. The first time the Coulomb interaction for description of the $K(1460)$ resonance is considered. The mass splitting in the $K$(1460) resonances is evaluated to be in range of 10 MeV with taking into account the Coulomb force. The three-body model with the $K\bar K$ potential, which has the different strength of the isospin singlet and triplet parts that are related by the condition of obtaining a quasi-bound three-body state is also considered. Our results are in reasonable agreement with the experimental mass of the $K(1460)$ resonance.

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arXiv2018

On rotational-vibrational spectrum of diatomic beryllium molecule

The eigenvalue problem for second-order ordinary differential equation (SOODE) in a finite interval with the boundary conditions of the first, second and third kind is formulated. A computational scheme of the finite element method (FEM) is presented that allows the solution of the eigenvalue problem for a SOODE with the known potential function using the programs ODPEVP and KANTBP 4M that implement FEM in the Fortran and Maple, respectively. Numerical analysis of the solution using the KANTBP 4M program is performed for the SOODE exactly solvable eigenvalue problem. The discrete energy eigenvalues and eigenfunctions are analyzed for vibrational-rotational states of the diatomic beryllium molecule solving the eigenvalue problem for the SOODE numerically with the table-valued potential function approximated by interpolation Lagrange and Hermite polynomials and its asymptotic expansion for large values of the independent variable specified as Fortran function. The efficacy of the programs is demonstrated by the calculations of twelve eigenenergies of vibrational bound states with the required accuracy, in comparison with those known from literature, and the vibrational-rotational spectrum of the diatomic beryllium molecule.

physics.chem-ph↗
arXiv2017

Isospin Effect in Three-Body Kaonic Clusters

The kaonic clusters $K^{-}K^{-}p$ and $ppK^{-}$ are described based on the configuration space Faddeev equations for $AAB$ system. The $AB$ interaction is given by isospin-dependent potentials. For this isospin model, we show that the relation $\left\vert E_{3}(V_{AA}=0)\right\vert~<~2\left\vert E_{2}\right\vert$ is satisfied when $E_{2}$ is the binding energy of the $AB$ subsystem and $E_{3}(V_{AA}=0)$ is the three-body binding energy when interaction between identical particles is omitted, $V_{AA}=0$. For the $NN{\bar K}$ system, taking into account weak attraction of $NN$ interaction the relation leads to the evaluation $|E_3|\le 2|E_2|$. The "isospinless model" for the kaonic clusters based on the isospin averaged $N{\bar K}$ potential demonstrates the opposite relation $\left\vert E_{3}(V_{AA}=0)\right\vert~>~2\left\vert E_{2}\right\vert$. The isospin "given charge formalism" is presented for $NN{\bar K}$ cluster. This formalism is related to isospin model by unitary transformation of the isospin basis. An interpretation of the "particle representation" for $NN{\bar K}$ system is proposed.

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arXiv2017

Spin-flip doublets of $^9$Be spectrum within a cluster model

The structure of the $^9$Be low-lying spectrum is studied within the cluster model $\alpha+\alpha+n$. In the model the total orbital momentum is fixed for each energy level. Thus each level is determined as a member of the spin-flip doublet corresponding to the total orbital momentum ($L^\pi=0^+, 2^+,4^+, 1^-, 2^-,3^-, 4^-$) of the system. The Ali-Bodmer potential (model E) is applied for the $\alpha\alpha$ interaction. We employ a local $\alpha n$ potential which was constructed to reproduce the $\alpha-n$ scattering data. The Pauli blocking is simulated by the repulsive core of the $s$-wave components of these potentials. Configuration space Faddeev equations are used to calculate the energy of the bound state ($E_{cal.}$=-1.493 MeV v.s. $E_{exp.}$=-1.5735 MeV) and resonances. A variant of the method of analytical continuation in the coupling constant is applied to calculate the energies of low-lying levels. Available $^9$Be spectral data are satisfactorily reproduced by the proposed model.

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arXiv2017

On mass polarization effect in three-body systems

We evaluate the mass polarization term of the kinetic-energy operator for different three-body nuclear $AAB$ systems by employing the method of Faddeev equations in configuration space. For a three-boson system this term is determined by the difference of the doubled binding energy of the $AB$ subsystem $2E_{2}$ and the three-body binding energy $E_{3}(V_{AA}=0)$ when the interaction between the identical particles is omitted. In this case: $\left\vert E_{3}(V_{AA}=0)\right\vert >2\left\vert E_{2}\right\vert$. In the case of a system complicated by isospins(spins), such as the kaonic clusters $ K^{-}K^{-}p$ and $ppK^{-}$, the similar evaluation impossible. For these systems it is found that $\left\vert E_{3}(V_{AA}=0)\right\vert <2\left\vert E_{2}\right\vert$. A model with an $AB$ potential averaged over spin(isospin) variables transforms the later case to the first one. The mass polarization effect calculated within this model is essential for the kaonic clusters. Besides we have obtained the relation $|E_3|\le |2E_2|$ for the binding energy of the kaonic clusters.

nucl-th↗
arXiv2014

Modeling of $^6_Λ$He hypernucleus within configuration space Faddeev approach

The cluster $^4\rm He+Λ+\rm n$ model is applied to describe the $^6_Λ$He hypernucleus. The consideration is based on the configuration space Faddeev equations for a system of non-identical particles. A set of the pair potentials includes the OBE simulating (NSC97f) model for the $Λ\rm n$ interaction and the phenomenological potentials for the $αΛ$ and $α\rm n$ interactions. We calculated energies of spin (1$^-$,2$^-$) doublet. For the 2$^-$ excitation energy, the obtained value is 0.18 MeV. The hyperon binding energy of the bound 1$^-$ state is less than the experimental value, which may be an evidence for violation of the exact three-body cluster structure.

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arXiv2012

Electron tunneling in chaotic InAs/GaAs quantum ring

Two dimensional InAs/GaAs quantum ring (QR) is considered using the effective potential approach. The symmetry of QR shape is violated as it is in the well-known Bohigas annular billiard. We calculate energy spectrum and studied the spatial localization of a single electron in such QR. For weak violation of the QR shape symmetry, the spectrum is presented as a set of quasi-doublets. Tunneling between quasi-doublet states is studied by the dependence on energy of the states. The dependence is changed with variation of the QR geometry that is related to the eccentricity of the QR. An interpretation of the experimental result obtained in [1] is proposed. We show that the "chaos-assisted tunneling" effect found in this paper can be explained by inter-band interactions occurred by anti-crossing of the levels with different "radial" quantum numbers.

cond-mat.mes-hall↗
arXiv2012

Quantum Mechanics of Semiconductor Quantum Dots and Rings

We consider the several phenomena which are taking place in Quantum Dots (QD) and Quantum Rings (QR): The connection of the Quantum Chaos (QC) with the reflection symmetry of the QD, Disappearance of the QC in the tunnel coupled chaotic QD, electron localization and transition between Double Concentric QR in the transverse magnetic field, transition of electron from QR to the QD located in the center of QR. Basis of this consideration is the effective Schrödinger equation for the corresponding systems.

cond-mat.mes-hall↗
arXiv2011

Electron localizations in double concentric quantum ring

We investigate the electron localization in double concentric quantum rings (DCQRs) when a perpendicular magnetic field is applied. In weakly coupled DCQRs, the situation can occur when the single electron energy levels associated with different rings may be crossed. To avoid degeneracy, the anti-crossing of these levels has a place. We show that in this DCQR the electron spatial transition between the rings occurs due to the electron level anti-crossing. The anti-crossing of the levels with different radial quantum numbers provides the conditions for electron tunneling between rings. To study electronic structure of the semiconductor DCQR, the single sub-band effective mass approach with energy dependence was used. Results of numerical simulation for the electron transition are presented for DCQRs of geometry related to one fabricated in experiment.

quant-ph↗
arXiv2011

Electron Transfer between Weakly Coupled Concentric Quantum Rings

The electronic structure of the semiconductor double concentric quantum nano-ring (DCQR) is studied under the single sub-band effective mass approach. We show that in the weakly coupled DCQR, that has been placed in transverse magnetic field, the electron spatial transition between the rings can occur due to electron level anti-crossing. The anti-crossing of the levels with different radial quantum numbers provides the conditions when the electron tunneling between rings becomes possible. Results of numerical simulation for the electron transition are presented for DCQRs of different geometry. In particularly, the system of a QR with a QD located at center of this QR is considered.

cond-mat.mes-hall↗
arXiv2009

Electronic and Level Statistics Properties of Si/SiO2 Quantum Dots

Spherical shaped Si quantum dots (QDs) embedded into the SiO2 substrate are considered in the single sub-band effective mass approach. Nonparabolicity of the Si conduction band is described by the energy dependence of electron effective mass. Calculations of low-lying single electron and hole energy levels are performed. For small sizes QD (diameter D<6nm) there is a strong confinement regime when the number of energy levels is restricted to several levels. The first order of the perturbation theory is used to calculate neutral exciton recombination energy taking into account the Coulomb force between electron and heavy hole. The PL exciton data are reproduced well by our model calculations. For weak confinement regime (size D>10 nm), when the number of confinement levels is limited by several hundred, we considered the statistical properties of the electron confinement. Distribution function for the electron energy levels is calculated and results are discussed.

cond-mat.mes-hall↗
arXiv2004

Cluster models of Lambda-Lambda-6He and Lambda-9Be hypernuclei

Configuration space Faddeev calculations are performed for the binding energy of Lambda-Lambda-6He and Lambda-9Be bound states, here considered as alpha-Lambda-Lambda and alpha-alpha-Lambda clusters respectively, in order to study the dependence of the calculated binding energy on the alpha-Lambda potential input. For Lambda-Lambda-6He, using realistic interactions, the uncertainty in extracting the Lambda-Lambda S=L=0 interaction strength does not exceed 0.1 MeV, which is a fraction of the order of magnitude derived for other theoretical uncertainties. For Lambda-9Be, the dependence of the calculated binding energy on the alpha-Lambda potential is considerably larger, of order 1 MeV. Our results for Lambda-9Be suggest that the odd-state alpha-Lambda interaction is substantially reduced with respect to the even-state component.

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