arXiv:physics/9802016 · Physical Review A

Ultralow energy scattering of a He atom off a He dimer

Elena A. Kolganova, Alexander Konstantinovich Motovilov, S. A. Sofianos

Published Sep 1, 1997• 18 citations

Abstract

We present a mathematically rigorous method suitable for bound-state and scattering process calculations for various three-atomic or molecular systems where the underlying forces are of a hard-core nature. We employed this method to calculate the binding energies and the ultra-low-energy scattering phase shifts below as well as above the breakup threshold for the three-He-atom system. The method has proved to be highly successful and suitable for solving the three-body bound-state and scattering problem in configuration space and thus it paves the way to study various three-atomic systems, and to calculate important quantities such as the cross sections, recombination rates, etc.

DOI: 10.1103/physreva.56.r1686

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arXiv:physics/9802016 · Physical Review A

Ultralow energy scattering of a He atom off a He dimer

Elena A. Kolganova, Alexander Konstantinovich Motovilov, S. A. Sofianos

Published Sep 1, 1997• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.56.r1686

Related papers

Three-body configuration space calculations with hard-core potentials

Elena A. Kolganova, Alexander Konstantinovich Motovilov, S. A. Sofianos

We present a mathematically rigorous method suitable for solving three-body bound-state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the boundary condition model and it has been employed to calculate the binding energies for a system consisting of three atoms. Two realistic He-He interactions of Aziz and collaborators have been used for this purpose. The results obtained compare favourably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultralow-energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.We present a mathematically rigorous method suitable for solving three-body bound-state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the boundary condition model and it has been employed to calculate the binding energies for a system consisting of three atoms. Two realistic He-He interactions of Aziz and collaborators have been used for this purpose. The results obtained compare favourably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultralow-energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.

arXiv:physics/9612012Journal of Physics B Atomic Molecular and Optical PhysicsMar 28, 199849 citations

Four-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scatteringFour-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scattering

Deltuva, A.

The strong short-range repulsion, characteristic to realistic interatomic potentials, complicates the description of weakly-bound few-body systems such as those of \He atoms. The present work proposes an approach for solving this problem and applies it to a realistic system of four ${}^4\mathrm{He}$ atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the ${}^4\mathrm{He}$ tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.The strong short-range repulsion, characteristic to realistic interatomic potentials, complicates the description of weakly-bound few-body systems such as those of \He atoms. The present work proposes an approach for solving this problem and applies it to a realistic system of four ${}^4\mathrm{He}$ atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the ${}^4\mathrm{He}$ tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.

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Calculations of recombination rates for cold He4 atoms from atom-dimer phase shifts and determination of universal scaling functions

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Three-body recombination rates for cold $^{4}\mathrm{He}$ are calculated with a method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the $S$ -matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for $^{4}\mathrm{He}$ are governed by ``Efimov physics,'' they depend on universal functions of a scaling variable. The computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions.Three-body recombination rates for cold $^{4}\mathrm{He}$ are calculated with a method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the $S$-matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for $^{4}\mathrm{He}$ are governed by ``Efimov physics,'' they depend on universal functions of a scaling variable. The computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions.

arXiv:cond-mat/0702290Physical Review AJun 27, 200722 citations

Universality in the three-body problem for 4He atoms

Eric Braaten, H.‐W. Hammer

The two-body scattering length a for ${}^{4}\mathrm{He}$ atoms is much larger than their effective range ${r}_{s}.$ As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by ${r}_{s}/a,$ all low-energy three-body observables are determined by a and a three-body parameter ${\ensuremath{\Lambda}}_{*}.$ We give simple expressions in terms of a and ${\ensuremath{\Lambda}}_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\ensuremath{\Lambda}}_{*}$ for several ${}^{4}\mathrm{He}$ potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.The two-body scattering length a for ${}^{4}\mathrm{He}$ atoms is much larger than their effective range ${r}_{s}.$ As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by ${r}_{s}/a,$ all low-energy three-body observables are determined by a and a three-body parameter ${\ensuremath{\Lambda}}_{*}.$ We give simple expressions in terms of a and ${\ensuremath{\Lambda}}_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\ensuremath{\Lambda}}_{*}$ for several ${}^{4}\mathrm{He}$ potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.

arXiv:cond-mat/0203421Physical Review AApr 11, 200370 citations

Universal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold

Alejandro Kievsky, M. Gattobigio

We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\mathrm{cot}\ensuremath{\delta}$. Using the He-He system as a reference, we solve the Schr\"odinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $ak\mathrm{cot}\ensuremath{\delta}={c}_{1}(ka)+{c}_{2}(ka)\mathrm{cot}[{s}_{0}\mathrm{ln}({\ensuremath{\kappa}}_{*}a)+\ensuremath{\phi}(ka)]$, for selected values of the three-body parameter ${\ensuremath{\kappa}}_{*}$. Using the parametrization of the universal functions ${c}_{1},{c}_{2},\ensuremath{\phi}$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\ensuremath{\kappa}}_{*}$.We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\mathrm{cot}\ensuremath{\delta}$. Using the He-He system as a reference, we solve the Schr\"odinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $ak\mathrm{cot}\ensuremath{\delta}={c}_{1}(ka)+{c}_{2}(ka)\mathrm{cot}[{s}_{0}\mathrm{ln}({\ensuremath{\kappa}}_{*}a)+\ensuremath{\phi}(ka)]$, for selected values of the three-body parameter ${\ensuremath{\kappa}}_{*}$. Using the parametrization of the universal functions ${c}_{1},{c}_{2},\ensuremath{\phi}$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\ensuremath{\kappa}}_{*}$.

arXiv:1212.3457Physical Review AMay 31, 201340 citations

Ultra-low energy elastic scattering in a system of three He atoms

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. 1Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. 1

Jan 1, 20020 citations

Four-body system of

{}^4\mathrm{He}

atoms: Dimer-dimer scattering

{}^4\mathrm{He}

atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the

{}^4\mathrm{He}

tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.

Three-body recombination rates for cold

^{4}\mathrm{He}

are calculated with a method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the

S

-matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for

^{4}\mathrm{He}

are governed by ``Efimov physics,'' they depend on universal functions of a scaling variable. The computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions.

The two-body scattering length a for

{}^{4}\mathrm{He}

atoms is much larger than their effective range

{r}_{s}.

As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by

{r}_{s}/a,

all low-energy three-body observables are determined by a and a three-body parameter ${\ensuremath{\Lambda}}_{*}.$ We give simple expressions in terms of a and ${\ensuremath{\Lambda}}_{*}$ for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine ${\ensuremath{\Lambda}}_{*}$ for several

{}^{4}\mathrm{He}

potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.

a

and we compare our results to the universal zero-range form deduced by Efimov, $ak\mathrm{cot}\ensuremath{\delta}={c}_{1}(ka)+{c}_{2}(ka)\mathrm{cot}[{s}_{0}\mathrm{ln}({\ensuremath{\kappa}}_{*}a)+\ensuremath{\phi}(ka)]$, for selected values of the three-body parameter ${\ensuremath{\kappa}}_{*}$. Using the parametrization of the universal functions ${c}_{1},{c}_{2},\ensuremath{\phi}$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\ensuremath{\kappa}}_{*}$.