Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1408.0834 · Physical Review A

Multichannel quantum defect theory for rovibrational transitions in ultracold molecule-molecule collisions

Jisha Hazra, Brandon Ruzic, N. Balakrishnan, John L. Bohn

Published Sep 10, 2014• 12 citations
arXivHTMLPDF

Abstract

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and nonresonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full close-coupling (CC) calculations when spin, hyperfine, and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for ${\mathrm{H}}_{2}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions in full dimensionality, is shown to adequately reproduce cross sections for quasiresonant rotational and vibrational transitions in the ultracold $(1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K})$ and $\ensuremath{\sim}1\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$ matrix evaluated in the ultracold regime $(1 \ensuremath{\mu}\mathrm{K})$ can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.

DOI
10.1103/physreva.90.032711

Related papers

Quantum defect theory for cold chemistry with product-quantum-state resolution

Jisha Hazra, Brandon Ruzic, John L. Bohn +1 more

We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short range with quantum defect theory at long range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for ${\mathrm{D}+\mathrm{H}}_{2}\ensuremath{\rightarrow}\mathrm{HD}+\mathrm{H}$ collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.

arXiv:1410.5873•Physical Review A•Dec 1, 2014•19 citations

Multichannel quantum defect theory for cold molecular collisions

James F. E. Croft, Alisdair O. G. Wallis, Jeremy M. Hutson +1 more

Multichannel quantum defect theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels $N$ and not to ${N}^{3}$. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy dependence and the field dependence is currently impractical.

arXiv:1105.4483•Physical Review A•Oct 6, 2011•47 citations

Cold molecular collisions : efficient methods for quantum calculations

James F. E. Croft

Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics. Multichannel quantum defect theory can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the Y matrix that encapsulates the short-range dynamics. It is shown how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test cases of Mg+NH and Li+NH, the resulting optimized Y matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000G. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels N and not to N cubed. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy and the field dependence is currently impractical.

•Jan 1, 2012•0 citations

Multichannel quantum defect theory for cold molecular collisions with a strongly anisotropic potential energy surface

James F. E. Croft, Jeremy M. Hutson

We show that multichannel quantum defect theory (MQDT) can be applied successfully as an efficient computational method for cold molecular collisions in $\text{Li}+\text{NH}$, which has a deep and strongly anisotropic interaction potential. In this strongly coupled system, closed-channel poles restrict the range over which the MQDT $\mathbit{Y}$ can be interpolated. We present an improved procedure to transform the MQDT reference functions so that the poles are removed from the energy range of interest. Effects due to very-long-range spin dipolar couplings are outside the scope of MQDT, but can be added perturbatively. This procedure makes it possible to calculate the elastic and inelastic cross sections, over the entire range of energies and fields needed to evaluate the feasibility of sympathetic cooling of NH by Li, using coupled-channel calculations at only five combinations of energy and field.

arXiv:1212.5290•Physical Review A•Mar 19, 2013•5 citations

Quantum defect theory for high-partial-wave cold collisions

Brandon Ruzic, Chris H. Greene, John L. Bohn

We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range $0--1000$ G for the scattering of ${}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}$ in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.

arXiv:1301.1370•Physical Review A•Mar 11, 2013•41 citations

Optimized multichannel quantum defect theory for cold molecular collisions

James F. E. Croft, Jeremy M. Hutson, Paul S. Julienne

Multichannel quantum defect theory (MQDT) can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the $\mathbit{Y}$ matrix that encapsulates the short-range dynamics, and there are poles in $\mathbit{Y}$ that may prevent interpolation over the range of energies of interest for cold molecular collisions. We show how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test case of Mg+NH, the resulting optimized $\mathbit{Y}$ matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000 gauss. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels $N$ and not to ${N}^{3}$.

arXiv:1206.6072•Physical Review A•Aug 20, 2012•18 citations
Multichannel quantum defect theory (MQDT) has been widely applied to resonant and nonresonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full close-coupling (CC) calculations when spin, hyperfine, and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for H2\ensuremath-H2{\mathrm{H}}_{2}\text{\ensuremath{-}}{\mathrm{H}}_{2}H2​\ensuremath-H2​ collisions in full dimensionality, is shown to adequately reproduce cross sections for quasiresonant rotational and vibrational transitions in the ultracold (1\ensuremathμK)(1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K})(1\ensuremathμK) and \ensuremath∼1\ensuremath−10K\ensuremath{\sim}1\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\mathrm{K}\ensuremath∼1\ensuremath−10K regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range KKK matrix evaluated in the ultracold regime (1\ensuremathμK)(1 \ensuremath{\mu}\mathrm{K})(1\ensuremathμK) can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.
We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short range with quantum defect theory at long range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for ${\mathrm{D}+\mathrm{H}}_{2}\ensuremath{\rightarrow}\mathrm{HD}+\mathrm{H}$ collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.
Multichannel quantum defect theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels NNN and not to N3{N}^{3}N3. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy dependence and the field dependence is currently impractical.
Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics. Multichannel quantum defect theory can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the Y matrix that encapsulates the short-range dynamics. It is shown how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test cases of Mg+NH and Li+NH, the resulting optimized Y matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000G. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels N and not to N cubed. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy and the field dependence is currently impractical.
We show that multichannel quantum defect theory (MQDT) can be applied successfully as an efficient computational method for cold molecular collisions in Li+NH\text{Li}+\text{NH}Li+NH, which has a deep and strongly anisotropic interaction potential. In this strongly coupled system, closed-channel poles restrict the range over which the MQDT $\mathbit{Y}$ can be interpolated. We present an improved procedure to transform the MQDT reference functions so that the poles are removed from the energy range of interest. Effects due to very-long-range spin dipolar couplings are outside the scope of MQDT, but can be added perturbatively. This procedure makes it possible to calculate the elastic and inelastic cross sections, over the entire range of energies and fields needed to evaluate the feasibility of sympathetic cooling of NH by Li, using coupled-channel calculations at only five combinations of energy and field.
We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers LLL. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range 0−−10000--10000−−1000 G for the scattering of 40K+87Rb{}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}40K+87Rb in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.
Multichannel quantum defect theory (MQDT) can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the $\mathbit{Y}$ matrix that encapsulates the short-range dynamics, and there are poles in $\mathbit{Y}$ that may prevent interpolation over the range of energies of interest for cold molecular collisions. We show how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test case of Mg+NH, the resulting optimized $\mathbit{Y}$ matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000 gauss. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels NNN and not to N3{N}^{3}N3.