Binding energies of polyatomic 4He-molecules

Schmid, Erich W.; Schwager, J.; Tang, Y.C.; Herndon, R.C.

doi:10.1016/0031-8914(65)90159-x

Cited by 32 publications

(10 citation statements)

References 15 publications

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“…Both the radii of gyration and the interparticle distance go through a minimum at He 7 . This minimum has been already observed in the little known very early variational Monte Carlo study of Schmid et al 23 which used a simple Lennard-Jones 6/12 potential model. The special structure of He 7 discussed in Ref.…”

Section: Resultsmentioning

confidence: 60%

“…22 Actually one of the earliest applications of such techniques on vibrational dynamics were studies of small helium clusters regarded as models of nuclear matter. 12,[23][24][25] This analogy is nicely discussed in a recent review. 26 The idea of the diffusion quantum Monte Carlo ͑DMC͒ method [27][28][29][30] is based on the isomorphism between the time dependent many body Schrödinger equation and a multidimensional reaction diffusion equation with anisotropic diffusion coefficients.…”

Section: Methodsmentioning

confidence: 89%

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Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential

Lewerenz¹

1997

The Journal of Chemical Physics

134

176

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We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.

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Section: Resultsmentioning

confidence: 60%

Section: Methodsmentioning

confidence: 89%

Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential

Lewerenz¹

1997

The Journal of Chemical Physics

134

176

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“…The first term (K, if)=(0, 0) gives an equal probability for all shapes of the three-atom triangle, and we can understand that an expansion with this term alone would not give a bound state because of the effect from the repulsive part of the potential. The figure shows contours of the functions (4, 0), (8, 0) and (6,3). The functions (~, 0) all give greatest probability for an equilateral triangle whereas a function such as (6, 3) favours a linear configuration.…”

Section: The Bound State For the H% Potentialmentioning

confidence: 98%

“…For m=6 our lowest energy is -0.235 • 10 ~4 eV which is lower than that deduced by Beck [11] for the same potential ( -0.207 x 10 -4 eV). 3. CALCULATIONS ON HE s USING THE PARTIAL WAVE EXPANSION OF SIMONOV [12] One set of coordinates (relative to the centre of mass) for the three-body problem which has been used in 3-nucleon calculations is the following :…”

Section: The Bound State For the H% Potentialmentioning

confidence: 99%

“…An upper bound to the energy of 4He 3 was calculated by Schmid and coworkers [3] using a Lennard-Jones 6-12 potential with depth 10.22 K and minimum 2-87 A~. A variational calculation based upon a product of twoparticle functions gave an upper bound of -0.067 K. Kruger [4] calculated the binding energy of 4He 3 using a two-body Morse potential and the method of Faddeev [5], and obtained an energy of 0.4 K, which is closer to the estimated lower bounds given above.…”

Section: Introductionmentioning

confidence: 99%

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Variational calculation on the possible existence of a bound state of He₃

Bosanac

Murrell

1973

Molecular Physics

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A variational calculation has confirmed earlier suggestions that 4He3 has a bound state. The partial wave expansion of Simonov was found to be slowly convergent and by this method no bound state was obtained although there was clear evidence that He3 would be closer to a stable bound state than He2. A variational wave function based directly on interparticle separations and the use of Morse-potential eigenfunctions was rapidly convergent and gave a lower limit to the binding energy of 0"63 K.

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