2009
DOI: 10.1088/0953-4075/42/18/185202
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Optimization of generalized multichannel quantum defect reference functions for Feshbach resonance characterization

Abstract: This work stresses the importance of the choice of the set of reference functions in the Generalized Multichannel Quantum Defect Theory to analyze the location and the width of Feshbach resonance occurring in collisional cross-sections. This is illustrated on the photoassociation of cold rubidium atom pairs, which is also modeled using the Mapped Fourier Grid Hamiltonian method combined with an optical potential. The specificity of the present example lies in a high density of quasi-bound states (closed channe… Show more

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Cited by 7 publications
(10 citation statements)
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“…Adjusting θ i at each energy such that Y ii = 0 was shown to produce a weak energy dependence of off-diagonal Y matrix elements across thresholds [31]. However, this approach required propagating the full multichannel wave function many times at different energies, which is precisely what the present work tries to avoid.…”
Section: Resultsmentioning
confidence: 94%
See 1 more Smart Citation
“…Adjusting θ i at each energy such that Y ii = 0 was shown to produce a weak energy dependence of off-diagonal Y matrix elements across thresholds [31]. However, this approach required propagating the full multichannel wave function many times at different energies, which is precisely what the present work tries to avoid.…”
Section: Resultsmentioning
confidence: 94%
“…Rotated reference functions have previously been used to transform Y matrices in the study of atomic spectra [26][27][28][29][30] and atomic collisions [31]. Adjusting θ i at each energy such that Y ii = 0 was shown to produce a weak energy dependence of off-diagonal Y matrix elements across thresholds [31].…”
Section: Resultsmentioning
confidence: 99%
“…5. We then combine this approach with a reference-function rotation to obtain any particular set of reference functions [50,57,58]. In our case this corresponds to choosing them such that ξ = δ bg as discussed earlier.…”
Section: G Computationsmentioning
confidence: 99%
“…( 27). These QDT parameters are then rotated [50,57,58] such that ξ = δ bg following the procedure in Appendix B 3. We note that because φ is defined at short range (where both the collision energy and the centrifugal term are small compared to the depth of the potential) a single energy independent φ will reproduce the energy dependent δ bg over the entire range of energies we are interested in here.…”
Section: G Computationsmentioning
confidence: 99%
“…The phase-amplitude approach for Schrödinger's radial (or one-dimensional) equation was pioneered by Milne [1], and has since been used extensively in atomic and molecular physics [2][3][4][5][6][7][8][9][10][11][12][13][14], in chemical physics [15][16][17], and in other areas of physics [18][19][20][21][22][23][24][25][26][27][28]. Although it was originally intended for tackling bound states, the phase-amplitude method is also applicable for scattering problems; indeed, Milne's approach is especially suitable in the framework of many-channel quantum defect theory [29][30][31][32] because it makes it possible to construct optimal reference functions in each scattering channel.…”
Section: Introductionmentioning
confidence: 99%