arXiv subjects

A. V. Malykh

Publications and source records attributed to A. V. Malykh.

13 recordsLinked to original sources

arXiv2022

Mass-ratio condition for non-binding of three two-component particles with contact interactions

Binding of two heavy fermions interacting with a light particle via the contact interaction is possible only for sufficiently large heavy-light mass ratio. In this work, the two-variable inequality is derived to determine a specific value $ μ^* $ providing that there are no three-body bound states for the mass ratio smaller than $ μ^* $. The value $ μ^* = 5.26 $ is obtained by analyzing this inequality for a total angular momentum and parity $ L^P = 1^- $. For other $ L^P $ sectors, the specific mass-ratio values providing an absence of the three-body bound states are found in a similar way. For generality, the method is extended to determine corresponding mass-ratio values for the system consisting of two identical bosons and a distinct particle for different $ L^P $ ($ L > 0 $) sectors.

cond-mat.quant-gas↗

arXiv2022

Minlos-Faddeev regularization of zero-range interactions in the three-body problem

To regularize the three-body problem, Minlos and Faddeev suggested a modification of zero-range model, which diminishes interaction at the triple-collision point. The analysis reveals that this regularization results in four alternatives depending on the regularization parameter $ σ$. Explicitly, Efimov or Thomas effects remain for $ σ< σ_c $, the additional boundary conditions of two types should be imposed at the triple-collision point for $ σ_c \le σ< σ_e $ and $ σ_e < σ< σ_r $, and the problem is regularized for $ σ\ge σ_r $. Critical values $ σ_c < σ_e < σ_r $ separating different alternatives are determined both for a two-component three-body system and for three identical bosons.

physics.atom-ph↗

arXiv2019

Three two-component fermions with contact interactions: correct formulation and energy spectrum

Properties of two identical particles of mass $m$ and a distinct particle of mass $m_1$ in the universal low-energy limit of zero-range two-body interaction are studied in different sectors of total angular momentum $L$ and parity $P$. For the unambiguous formulation of the problem in the interval $μ_r(L^P) < m/m_1 \le μ_c(L^P)$ ($μ_r(1^-) \approx 8.619$ and $μ_c(1^-) \approx 13.607$, $μ_r(2^+) \approx 32.948$ and $μ_c(2^+) \approx 38.630$,~etc.) in each $L^P$ sector an additional parameter $b$ determining the wave function near the triple-collision point is introduced; thus, a one-parameter family of self-adjoint Hamiltonians is defined. Within the framework of this formulation, dependence of the bound-state energies on $m/m_1$ and $b$ in the sector of angular momentum and parity $L^P$ is calculated for $L \le 5$ and analysed with the aid of a simple model. A number of the bound states for each $L^P$ sector is analysed and presented in the form of `phase diagrams' in the plane of two parameters $m/m_1$ and $b$.

cond-mat.quant-gas↗

arXiv2016

Universal description of three two-component fermions

A quantum mechanical three-body problem for two identical fermions of mass $m$ and a distinct particle of mass $m_1$ in the universal limit of zero-range two-body interaction is studied. For the unambiguous formulation of the problem in the interval $μ_r < m/m_1 \le μ_c$ ($μ_r \approx 8.619$ and $μ_c \approx 13.607$) an additional parameter $b$ determining the wave function near the triple-collision point is introduced; thus, a one-parameter family of self-adjoint Hamiltonians is defined. The dependence of the bound-state energies on $m/m_1$ and $b$ in the sector of angular momentum and parity $L^P = 1^-$ is calculated and analysed with the aid of a simple model.

cond-mat.quant-gas↗

arXiv2013

Recent advances in description of few two-component fermions

Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$: it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.

physics.atom-ph↗

arXiv2010

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9.

nucl-th↗

arXiv2008

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a different one of mass $m_1$, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio $m/m_1$, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength $λ_1$ of the identical particles. A number of exact results are enlisted and asymptotic dependences both for $m/m_1 \to \infty$ and $λ_1 \to -\infty$ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.

physics.atom-ph↗

arXiv2007

Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass $m$ and the third particle of the mass $m_1$ in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio $m/m_1$ and the total angular momentum $L$. If the two-body scattering length is positive, a number of vibrational states is finite for $L_c(m/m_1) \le L \le L_b(m/m_1)$, zero for $L>L_b(m/m_1)$, and infinite for $L 2$ and only slightly deviates from those for $L = 1, 2$. The universal description implies that the critical values $L_c(m/m_1)$ and $L_b(m/m_1)$ increase as $0.401 \sqrt{m/m_1}$ and $0.563 \sqrt{m/m_1}$, respectively, while a number of vibrational states for $L \ge L_c(m/m_1)$ is within the range $N \le N_{max} \approx 1.1 \sqrt{L(L+1)}+1/2$.

physics.atom-ph↗

arXiv2006

Low-energy three-body dynamics in binary quantum gases

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio $m/m_1$ for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at $m/m_1 \ge λ_1 \approx 8.17260$ and $m/m_1 \ge λ_2 \approx 12.91743$, respectively. For $m/m_1 \alt λ_1$ and $m/m_1 \alt λ_2$, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.

physics.atom-ph↗

arXiv2006

Universal low-energy properties of three two-dimensional particles

Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere and the system of hyper-radial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyper-radial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyper-radius $ρ$ is studied and the universal logarithmic dependence $\sim \ln^3 ρ$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2 + 1$ scattering length are calculated.

physics.atom-ph↗

arXiv2005

Effective three-body interactions in the alpha-cluster model for the ^{12}C nucleus

Properties of the lowest $0^{+}$ states of $^{12}\mathrm{C}$ are calculated to study the role of three-body interactions in the $α$-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the $α$-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited $0_2^+$ state and the monopole $0_2^+ \to 0_1^+ $ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the $0_2^+$ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.

nucl-th↗

arXiv2004

Three-alpha-cluster structure of the 0^+ states in ^{12}C and the effective alpha-alpha interactions

The $0^{+}$ states of $^{12}\mathrm{C}$ are considered within the framework of the microscopic three-$α$-cluster model. The main attention is paid to accurate calculation of the width of the extremely narrow near-threshold $0^+_2$ state which plays a key role in stellar nucleosynthesis. It is shown that the $0^{+}_2$-state decays by means of the sequential mechanism ${^{12}\mathrm{C}} \to α+{^8\mathrm{Be}} \to 3α$. Calculations are performed for a number of effective $α- α$ potentials which are chosen to reproduce both energy and width of $^8\mathrm{Be}$. The parameters of the additional three-body potential are chosen to fix both the ground and excited state energies at the experimental values. The dependence of the width on the parameters of the effective $α- α$ potential is studied in order to impose restrictions on the potentials.

nucl-th↗

arXiv2004

Effect of dtμquasi-nucleus structure on energy levels of the (dtμ)Xee exotic molecule

Precise energies of rovibrational states of the exotic hydrogen-like molecule $(dtμ)Xee$ are of importance for $dtμ$ resonant formation, which is a key process in the muon-catalyzed fusion cycle. The effect of the internal structure and motion of the $dtμ$ quasi-nucleus on energy levels is studied using the three-body description of the $(dtμ)Xee$ molecule based on the hierarchy of scales and corresponding energies of its constituent subsystems. For a number of rovibrational states of $(dtμ)dee$ and $(dtμ)tee$, the shifts and splittings of energy levels are calculated in the second order of the perturbation theory.

physics.atom-ph↗