The semiclassical helium atom

Wintgen, Dieter; Richter, Klaus; Tanner, Gregor

doi:10.1063/1.165920

Cited by 168 publications

(139 citation statements)

References 50 publications

Supporting

Mentioning

135

Contrasting

Unclassified

Order By: Relevance

“…In the early 20th century the failure of finding a stable solution for the classical helium atom (2 electrons and a nucleus) heralded the demise of Niels Bohr's program of semiclassical atomic physics (1). Quantum mechanics then added yet another surprising twist to the three-body problem when in 1970 Vitaly Efimov predicted the appearance of an infinite series of stable three-body states of enormous spatial extents (2).…”

mentioning

confidence: 99%

Observation of the Efimov state of the helium trimer

Kunitski

Zeller

Voigtsberger

et al. 2015

Science

226

219

View full text Add to dashboard Cite

Quantum theory dictates that upon weakening the two-body interaction in a three-body system, an infinite number of three-body bound states of a huge spatial extent emerge just before these three-body states become unbound. Three helium atoms have been predicted to form a molecular system that manifests this peculiarity under natural conditions without artificial tuning of the attraction between particles by an external field. Here we report experimental observation of this long predicted but experimentally elusive Efimov state of 4 He3 by means of Coulomb explosion imaging. We show spatial images of an Efimov state, confirming the predicted size and a typical structure where two atoms are close to each other while the third is far away. One Sentence Summary:We report experimental discovery of a gigantic molecule that consists of three helium atoms and is bound solely by a universal feature of quantum mechanics called "Efimov effect".Ever since the early days of celestial mechanics, the three-body problem posed a major challenge to physicists. In the early 20th century the failure of finding a stable solution for the classical helium atom (2 electrons and a nucleus) heralded the demise of Niels Bohr's program of semiclassical atomic physics (1). Quantum mechanics then added yet another surprising twist to the three-body problem when in 1970 Vitaly Efimov predicted the appearance of an infinite series of stable three-body states of enormous spatial extents (2). These Efimov states are predicted to exist for short-range interactions like the van der Waals force between atoms or the strong force between nucleons. When the potential becomes so shallow that the last two-body bound state is at the verge of becoming unbound or is unbound, then three particles stick together to form Efimov states. Intriguingly, this three-body behavior does not depend on the details of the underlying two-body interactions. This makes the Efimov effect a universal phenomenon, with important applications in particle, nuclear (3, 4), atomic (4), condensed matter (5) and biological physics (6).Figure 1 summarizes two facets of Efimov's prediction, namely the energy spectrum and the structure of an Efimov state. Figure 1A shows how the two-and three-body binding energies (the binding energy of an atomic cluster is defined as the energy needed to separate all constituents of the cluster to infinite distances) change as the depth of the two-body potential is increased. As 2 indicated by the arrow above Figure 1A, the depth of the two-body potential increases along the horizontal axis. As the depth increases, the s-wave scattering length a changes from negative values to infinitely large values to positive values. Negative a values correspond to the domain where shallow two-body bound states do not exist. For positive a, a shallow two-body bound state, the dimer (see the blue solid line), exists. Bound three-body states (called trimers) exist in the green-shaded area. The extremely weakly-bound three-body states close to threshold (see...

show abstract

mentioning

confidence: 99%

Observation of the Efimov state of the helium trimer

Kunitski

Zeller

Voigtsberger

et al. 2015

Science

226

219

View full text Add to dashboard Cite

show abstract

“…The first modern semiclassical calculations to properly account for the chaotic dynamics in helium appeared in the early 1990's. [6,7] These and subsequent works have enabled the quantization of a large number of bound and resonance states of the atom. [1,6,7,8,9] Although other restricted-configuration coplanar studies have been carried out, [10] most recent semiclassical treatments are based on a collinear model for the classical motion of the electrons, with corrections added for stable motion in the remaining degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical initial value calculations of the collinear helium atom

Harabati

Kay

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

Semiclassical calculations using the Herman-Kluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the eZe configuration (where the classical motion is fully chaotic) and the Zee configuration (where the classical dynamics is nearly integrable) are treated. The classical motion is regularized to remove singularities that occur when the electrons collide with the nucleus. Very good agreement is obtained with quantum energies for bound and resonance states calculated by the complex rotation method.

show abstract

“…in the Wigner limit, where the uncertainty of the (cm) vector X is small compared with the mean electron-electron distance, we can neglect X in the denominator of the interaction term in Eq. (5). By omitting of the center of mass term, the Hamiltonian…”

Section: Unitary Transformation and Numerical Calculationmentioning

confidence: 99%

“…A large class of three-body problems appear in various branches of physics either in classical or quantum annals from moon-earth-sun system [1] to the helium-like atoms [2][3][4][5][6][7]. On the other hand, the study of a few body system might lead to a better and deeper understanding of a more testable many-body problem.…”

Section: Introductionmentioning

confidence: 99%

A Unitary Transformation and Spectrum of a Three-Electron Quantum Dot

2011

View full text Add to dashboard Cite

We consider the Hamiltonian of a three-electron quantum dot composed of parabolic confinement plus the Coulomb terms. Instead of using the Jacobi coordinates, we apply a unitary transformation to this system. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schrödinger equation in terms of the Wigner parameter.

show abstract

The semiclassical helium atom

Cited by 168 publications

References 50 publications

Observation of the Efimov state of the helium trimer

Observation of the Efimov state of the helium trimer

Semiclassical initial value calculations of the collinear helium atom

A Unitary Transformation and Spectrum of a Three-Electron Quantum Dot

Contact Info

Product

Resources

About