Separable Potential Method Research Articles

High-partial-wave separable potential method for investigating Feshbach resonances of ultracold atoms

We present a high-partial-wave (non-zero partial-wave) separable potential method (SPM) for investigating magnetically induced Feshbach resonances in collisions of ultracold atoms, then derive the Lippmann–Schwinger equation for two ultracold alkali-metal atoms in an external magnetic field and calculate the generalized scattering length and weakly bound state energy. We apply this method to the 6Li system and calculate the weakly bound state energy and the scattering volume near three typical p-wave Feshbach resonances. The calculated results by using the SPM agree well with those by using the coupled channel method and with experimental measurements. The SPM is expected to simplify computation of the three-body collision Faddeev equation in the vicinity of two-body high partial-wave Feshbach resonances.

Accurate calculations of weakly bound state energy and scattering length near magnetically tuned Feshbach resonance using the separable potential method.

We present a theoretical model for investigating the magnetically tuned Feshbach resonance (MTFR) of alkali metal atoms using the separable potential method (SPM). We discuss the relationship and difference between the SPM and the asymptotic bound state model. To demonstrate the validity of the SPM, we use it to calculate the weakly bound state energy and magnetically tuned scattering length for the 6Li-40K, 7Li2, and 6Li2 systems with narrow and broad Feshbach resonances. The results of the SPM calculations are in good agreement with those of coupled channel calculations and with experimental measurements for all three systems. The SPM, by simplifying the calculation of the two-body MTFR, is expected to simplify numerical computations for three-atom collisions in a magnetic field and the Feshbach-optimized photoassociation process.

Quantum molecular dynamics of large systems beyond separable approximation: The configuration interaction classical separable potential method

A nonseparable method for time-dependent quantum simulations of large polyatomic systems is presented and applied to the dynamics of the I2Ar17 cluster, following electronic excitation of the iodine molecule. The new method is an extension of the classical separable potential (CSP) approximation, in which the evolution of each mode is governed by a time-dependent mean potential due to the other modes and the total wave packet is a product of single mode wave functions. The computational effectiveness of the CSP approach stems from the use of classical molecular dynamics (MD) trajectories, carried out at the outset of the procedure, for obtaining the effective single-mode potentials. The present method generalizes the CSP scheme by a configuration interaction (CI) treatment, in which the total wave packet is represented as a linear combination of separable terms, with coefficients determined from the time-dependent Schrodinger equation. The single mode wave functions for each configuration are propagated along effective potentials that are generated using individual classical trajectories. The classical MD simulation is also used for simplifying the dynamical equations for the CI coefficients. Thus, the selection of correlations that are included quantum mechanically is guided by classical mechanics, which is the basis for the computational efficiency of this approach. The CI wave packet for the I2Ar17 system with 51 vibrational degrees of freedom was propagated for 500 fs following I2 (B←X) excitation. About 1500 configurations proved sufficient for convergence of the CI series. The separable approximation to the wave function holds for 60 fs and begins to break down upon the first collision of the iodine atoms with argons. After the second iodine-argon collision this breakdown is almost complete, and at t=500 fs the CSP term represents less than 5% of the correlated wave packet. Both absorption and resonance Raman spectra are, however, well described by the separable CSP method, since they are determined within the first 60 fs. The CI-CSP method offers very good accuracy due to inclusion of important correlation effects between different modes, while remaining computationally feasible for systems up to 100 degrees of freedom and more.

Quantum dynamics simulations of nonadiabatic processes in many-atom systems: Photoexcited Ba(Ar)10 and Ba(Ar)20 clusters

Quantum simulations are reported for the dynamics following the photoexcitation Ba(1S)→Ba(1P) in Ba(Ar)10 and Ba(Ar)20 clusters. The evolution in time is studied in a framework that treats quantum-mechanically all the coupled degrees of freedom. The focus is on the role of nonadiabatic transitions between the three adiabatic surfaces corresponding to the P states of the Ba atom. The time scales of electronic relaxation and of electronic depolarization (orbital reorientation) are computed, and the competition between adiabatic and nonadiabatic effects is assessed. The calculations are carried out by a new scheme that extends the recent classically based separable potential method. Semiclassical surface-hopping simulations are used to produce effective single-mode potentials on which nuclear ‘‘orbitals’’ are then generated. The full wave packet is constructed from the electronic states involved, and from these nuclear wave functions. Among the main results we find that nonadiabatic transitions become appreciable around 1 ps after photoexcitation, and they are stronger in the smaller cluster. Comparing Tully’s semiclassical method with the quantum simulations, good qualitative agreement is found. Quantitatively, the semiclassical predictions for the electronic states branching rations deviate from the quantum results roughly by a factor of 2 after 1 ps. In the smaller cluster direct dissociation of the Ba atom dominates over energy redistribution within the cluster, the opposite being true for the large system. This example demonstrates the feasibility of quantum simulations of nonadiabatic processes in large systems with the new method.

Quantum dynamics of large polyatomic systems using a classically based separable potential method

A new method for approximate solution of the time-dependent vibrational Schrödinger equation, applicable to extended molecular systems, is presented. The new method is essentially an approximate time-dependent quantization of classical dynamics. A molecular dynamics simulation is used to obtain a separable, effective time-dependent potential for each mode, that implicitly includes also the effects of all the other modes on this degree of freedom. A time-dependent wave packet is then propagated separately for each mode, using the corresponding effective potential. The new approximation is valid for short time scale processes only, but it is easily applicable to large realistic systems. Test calculations against exact quantum and time-dependent self-consistent field (TDSCF) results are carried out for two examples; photodissociation of HI in the collinear Xe...HI cluster, and electron photodetachment from the collinear Ar...I−...Ar cluster. For illustration, the new scheme is also applied to photodetachment from large linear clusters Arn...I−...Arn (n=2–8) and the results are discussed. For the test systems, the results of the new method are virtually identical to those following from the computationally much more demanding TDSCF approach, and they are in excellent agreement with the exact results.

The Separable Potential Method and Its Connection with the Embedded‐Atom Method

AbstractA detailed comparison of the separable potential method (SPM), recently proposed by one of us, with the embedded‐atom method (EAM) allows a characterization of the embedding function F through a nonlinear differential equation. The complete solutions of the nonlinear differential equation are given, and as a demonstration of the applicability of the method, one of the solutions is employed to calculate various physical quantities for some f. c. c. metals. The applicability of the unified approach discussed here, goes beyond f. c. c. metals. We illustrate this important point by comparing some of our results obtained for b. c. c. metallic vanadium with similar results obtained recently by Adam and Foiles in 1990.

Analytic nearest-neighbour model for fcc metals

A recently proposed analytic nearest-neighbour model for fcc metals is criticised and two alternative nearest-neighbour models derived from the separable potential method (SPM) are recommended. Results for copper and aluminium illustrate the utility of the recommended models.

The Separable Potential Method A Unified Approach to Various Lattice Models

AbstractThis work proposes the separable potential method (SPM) as a unified treatment of a class of lattice models. The richness in structure of the unified approach is demonstrated through contact with some of the most important lattice models in the literature, the embedded‐atom method (EAM) being one of such models. As a practical application of SPM some fairly extensive results for f.c.c. metallic copper are reported.

Comparison of methods of scattering from two potentials

Several approximations to multiple scattering are compared with an exact calculation. The model chosen for comparison is scattering from two Gaussian potentials of range 0.5 fm and depth 16 ${\mathrm{fm}}^{\ensuremath{-}2}$. Particular attention is paid to the case of overlapping potentials. It is shown that, of all approximations considered, only the separable potential method is capable of giving good agreement in this region. It is demonstrated that a separable potential can always be chosen to give the exact answer for multiple scattering in the case in which the (spherically symmetric) interaction regions are nonoverlapping as well as when the interaction regions are concentric.