Helium bound state

The energies of the selective adsorption resonances are very sensitive to the details of the physisorption potential. Accurate measurement allied to computation of bound state energies can be used to obtain a very accurate quantitative fonn for the physisorption potential, as has been demonstrated for helium atom scattering. For molecules, we have... 

Until recently there was no firm theoretical evidence that a positron could bind to any atom other than positronium it had been rigorously proved by Armour (1978, 1982) that it cannot bind to atomic hydrogen, and the evidence that it cannot bind to helium is overwhelming. The most likely candidates were the highly polarizable alkali atoms, and states of the positron-atom system below the positron-atom scattering threshold do indeed exist. However, they were all believed to lie above the threshold for positronium scattering by the corresponding positive ion, and were therefore not true bound states. 

A number of data are available for Is and 2s hfs intervals in hydrogen, deuterium and the helium-3 ion. The potential of this difference for the hfs intervals in the helium-3 ion [21] with respect to testing bound state QED is compatible with the ground state hfs in muonium both values are sensitive to fourth-order perturbative contributions. The difference of the Lamb shift plays an important role in the evaluation of optical data on the hydrogen and deuterium spectrum [22]-... 

The fine structure constant a can be determined with the help of several methods. The most accurate test of QED involves the anomalous magnetic moment of the electron [40] and provides the most accurate way to determine a value for the fine structure constant. Recent progress in calculations of the helium fine structure has allowed one to expect that the comparison of experiment [23,24] and ongoing theoretical prediction [23] will provide us with a precise value of a. Since the values of the fundamental constants and, in particular, of the fine structure constant, can be reached in a number of different ways it is necessary to compare them. Some experiments can be correlated and the comparison is not trivial. A procedure to find the most precise value is called the adjustment of fundamental constants [39]. A more important target of the adjustment is to check the consistency of different precision experiments and to check if e.g. the bound state QED agrees with the electrical standards and solid state physics. 

Helium and helium-like ions are the prototypical many-electron system. All the bound-state QED physics of one-electron atoms is still present, of course, but with considerable added complication due to the electron-electron interaction. 

Namely, the circular orbit (l = n — 1), which is a rotating state with a nodeless radial wavefunction, corresponds to a vibrational quantum number v = 0, and the next-to-circular single-node state (l = n — 2) corresponds to v = 1,.... This theoretical possibility of large-/ circular orbits behaving like bound states in a Morse potential seems to have no other natural manifestation than in the present case of metastable exotic helium. This situation is presented in Fig. 2, where the potential as well as the wavefunctions are shown. 

Following the discovery of metastable bound states of antiprotons in helium gas [29] the use of this product as an intermediate step towards antihydrogen formation has been discussed ... 

Precision studies of the g factor of a bound electron in simple atoms were started with experiments on hydrogen [11] and its comparison with deuterium [12,13,14] and tritium [15], as well as on the helium ion [16]. In particular in case of low Z the result for the non-trivial bound-state term... 

The theoretical conclusion of Isenburg (17) that H should ionize to H+ in metals applies, under the assumptions used, only to dilute and undistended solid solutions of hydrogen. This conclusion may also mean that the field of the proton under these conditions is completely screened by the conduction electrons. Additional work is needed to show that this condition indeed implies lack of a bound state rather than what amounts to a o- orbital or helium-like distribution of electrons around the proton in an actual hydride. 

Systems in the collinear eZe configuration which have tori would be the antiproton-proton-antiproton (p-p-p) system, the positronium negative ion (Pr- e-e-e)), which corresponds to the case of Z= 1, = 1, and If these systems have bound states, we can see the effect of our finding in the Fourier transform of the density of states for the spectrum. For a positronium negative ion, the EBK quantization was done [34]. Stable antisymmetric orbits were obtained and were quantized to explain some part of the energy spectrum. As hyperbolic systems, H and He have been already analyzed in Refs. 11 and 17, respectively. Thus, Li+ is the next candidate. We might see the effect of the intermittency for this system in quantum defect as shown for helium [14]. 

The nuclear charge in Fig. 10.2 is not specified in order to be able to describe any other member of the two-electron iso-electronic family, such as H , Li" ", etc. For helium, Z — 2. Even when focussing on a specific two-electron atom or ion we would like to keep the nuclear charge Z variable in order to study the sensitivity of bound states and resonances to small changes of Z. This topic is covered in Section 10.5.2. 

Saville, G.F., Goodkind, J.M. and Platzman, P.M. (1993). Single-electron tunneling from bound states on the surface of liquid helium, Phys. Rev. Lett. 70, 1517-1520. 

T. J. Greytak, R. Woerner, J. Yan, and R. Benjamin. Experimental evidence for a two-phonon bound state in superfluid helium. Phys. Rev. Lett., 25 1547-1550 (1970). 

The collinear model (Eq. (15)) has been successfully used in the semiclassical description of many bound and resonant states in the quantum mechanical spectrum of real helium [49-52] and plays an important role for the study of states of real helium in which both electrons are close to the continuum threshold [53, 54]. The quantum mechanical version of the spherical or s-wave model (Eq. (16)) describes the Isns bound states of real helium quite well [55]. The energy dependence of experimental total cross sections for electron impact ionization is reproduced qualitatively in the classical version of the s-wave model [56] and surprisingly well quantitatively in a quantum mechanical calculation [57]. The s-wave model is less realistic close to the break-up threshold = 0, where motion along the Wannier ridge, = T2, is important. 

For the H ion, Hill [108] proved that there is only one bound state with natural parity. This result, along with Kato s proof [109] that the Helium atom has an infinite number of bound states, seems to suggest that the critical point for the excited natural states is X = 1 [87]. 

Using the finite-size scaling method, study of the analytical behavior of the energy near the critical point shows that the open-shell system, such as the lithium-like atoms, is completely different from that of a closed-shell system, such as the helium-like atoms. The transition in the closed-shell systems from a bound state to a continuum resemble a first-order phase transition, while for the open-shell system the transition of the valence electron to the continuum is a continuous phase transition [9]. 

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