Global-Vector Representation of the Angular Motion of Few-Particle Systems

Varga, K.; Suzuki, Yasunobu; Usukura, J.

doi:10.1007/s006010050077

Cited by 38 publications

(39 citation statements)

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“…Note the k-dependence of Y k LM ; this is included since there are many ways to couple the individual angular momenta, l j , to achieve the desired total angular momentum L and it may be necessary to include several sets of the l j 's in order to obtain a realistic description of the wave function. Varga and Suzuki 55,56 have recently proposed representing the angular dependence of the wave function using a single solid harmonic whose argument contains additional variational parameters, u ¼ (U 1 ,U 2 ,Á Á Á,U n ):…”

Section: Diatomic Non-born-oppenheimer Calculationsmentioning

confidence: 99%

Non-Born–Oppenheimer calculations of atoms and molecules

Cafiero

Bubin

Adamowicz

2003

Phys. Chem. Chem. Phys.

146

144

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We review a recent development in high-accuracy non-Born-Oppenheimer calculations of atomic and molecular systems in a basis of explicitly correlated Gaussian functions. Much of the recent progress in this area is due to the derivation and implementation of analytical gradients of the energy functional with respect to variational linear and non-linear parameters of the basis functions. This method has been used to obtain atomic and molecular ground and excited state energies and the corresponding wave functions with accuracy that exceeds previous calculations. Further, we have performed the first calculations of non-linear electrical properties of molecules without the Born-Oppenheimer approximation for systems with more than one electron. The results for the dipole moments of such systems as HD and LiH agree very well with experiment. After reviewing our non-Born-Oppenheimer results we will discuss ways this method can be extended to deal with larger molecular systems with and without an external perturbation.

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Section: Diatomic Non-born-oppenheimer Calculationsmentioning

confidence: 99%

Non-Born–Oppenheimer calculations of atoms and molecules

Cafiero

Bubin

Adamowicz

2003

Phys. Chem. Chem. Phys.

146

144

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“…Its accuracy was confirmed in ref. [11] by comparing with the partial-wave expansion (PWE) for 3 H and α-particle interacting with central and tensor forces. In these studies only a single GV is used, and its application is thus restricted to natural parity states.…”

Section: Introductionmentioning

confidence: 99%

Global-vector representation of the angular motion of few-particle systems II

et al. 2008

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Abstract. The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three-and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0 − 1 state of 4 He. Twoparticle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.

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“…rel |ψ k , and the matrix element for the confining [32][33][34][35][36][37]. Here, it is understood that the integration is performed over all 3n − 3 Jacobi coordinates and that ψ k is characterized by A k , u 1k and u 2k while ψ k ′ is characterized by A k ′ , u 1k ′ and u 2k ′ .…”

Section: System Under Study and Stochastic Variational Approachmentioning

confidence: 99%

“…Following Refs. [32][33][34][35][36][37][38], we write the basis functions ψ k as a product of a correlated Gaussian [second line of Eq. (5)] and a "prefactor" [first line of Eq.…”

Section: System Under Study and Stochastic Variational Approachmentioning

confidence: 99%

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Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

2012

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Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large s-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2, 2) and (3, 1) systems at unitarity as a function of the range r0 of the underlying two-body potential and extrapolate to the r0 → 0 limit. Our calculations include all states with vanishing and finite angular momentum L (and natural and unnatural parity Π) with relative energy up to 10.5 Ω, where Ω denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2, 2) and (3, 1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3, 2) and (4, 1) systems at unitarity.

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Global-Vector Representation of the Angular Motion of Few-Particle Systems

Cited by 38 publications

References 0 publications

Non-Born–Oppenheimer calculations of atoms and molecules

Non-Born–Oppenheimer calculations of atoms and molecules

Global-vector representation of the angular motion of few-particle systems II

Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

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