Universal description of the He3 system at low energy

Kartavtsev, O. I.

doi:10.1007/978-3-7091-6798-4_33

Cited by 10 publications

(9 citation statements)

References 16 publications

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“…With the chosen units, The numerical and analytical results will be obtained mostly by solving a system of HREs [38] where the various terms are derived analytically [26,36,37]. The HREs are written by using the center-of-mass coordinates ρ and α, which are expressed via the scaled Jacobi variables as ρ sin α = x 2 − x 3 and ρ cos α = cot ω (2x 1 − x 2 − x 3 ) given the kinematicrotation angle ω = arctan 1 + 2m/m 1 so that E th = − cos 2 ω.…”

Section: General Outline and Methodsmentioning

confidence: 99%

“…Using the method described in [26,36,37], one can derive analytical expressions for all the terms in Eq. (10),…”

Section: General Outline and Methodsmentioning

confidence: 99%

“…It is of importance that all the terms in HREs are derived analytically; the method of derivation and the analytical expressions are similar to those obtained for a number of problems with zero-range interactions [26,36,37]. To describe the dependence on the mass ratio and interaction-strength ratio for the threebody binding energies and the (2 + 1)-scattering length, the two limiting cases λ 1 = 0 and λ 1 → ∞ are considered and the precise critical values of m/m 1 for which the threebody bound states arise and the (2 + 1)-scattering length becomes zero are determined.…”

Section: Introductionmentioning

confidence: 91%

“…In the low-energy limit, the contact potential is a good approximation for any short-range interaction and its usage provides a universal, i. e., independent of the potential form, description of the dynamics [23,26,34,35,36,37]. More specifically, it is assumed that one particle interacts with the other two via an attractive contact interac-tion of strength λ < 0 while the sign of the interaction strength λ 1 for the identical particles is arbitrary.…”

Section: Introductionmentioning

confidence: 99%

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

Kartavtsev

Malykh

Sofianos

2009

J. Exp. Theor. Phys.

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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 → ∞ and λ 1 → −∞ 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.

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Section: General Outline and Methodsmentioning

confidence: 99%

“…Using the method described in [26,36,37], one can derive analytical expressions for all the terms in Eq. (10),…”

Section: General Outline and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Kartavtsev

Malykh

Sofianos

2009

J. Exp. Theor. Phys.

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“…Techniques to efficiently compute eigenvalues at small distances are readily available but become inefficient and error prone when employed at large interparticle separations [2,21]. In this case, however, analytic expressions for the asymptotic wavefunctions, energy eigenvalues and coupling matrix elements are known [5,22] in the ZRP limit for states with J = 0 [16,18]. The methods of [16] also apply to J = 0.…”

Section: Introductionmentioning

confidence: 99%

Hyperspherical adiabatic eigenvalues for zero-range potentials

Gasaneo

Macek

2002

J. Phys. B: At. Mol. Opt. Phys.

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The scattering length a associated with two-body interactions is the relevant parameter for near threshold processes in cold atom-atom collisions. For this reason zero-range potentials are traditionally used to model collective behaviour of dilute collections of bosons. The model is also used to compute three-body recombination rates, where it gives an a 4 law. In this paper we examine the applicability of the zero-range model to real physical systems. Hyperspherical adiabatic potentials obtained from the zero-range model are compared with published potentials based on realistic two-body interactions. From these comparisons it is possible to determine the regions where the model applies.

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Low-energy three-body dynamics in binary quantum gases

Kartavtsev¹,

Malykh²

2007

J. Phys. B: At. Mol. Opt. Phys.

130

253

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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 ≥ λ 1 ≈ 8.17260 and m/m 1 ≥ λ 2 ≈ 12.91743, respectively. For m/m 1 λ 1 and m/m 1 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.

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Universal description of the He3 system at low energy

Cited by 10 publications

References 16 publications

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

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

Hyperspherical adiabatic eigenvalues for zero-range potentials

Low-energy three-body dynamics in binary quantum gases

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