Helium doubly excited states

Table 5.3 The total binding energy ( ) and autoionization half width (T/2) for the helium doubly excited states of odd parity below He+(n = 2)...

Notwithstanding, after hydrogen, helium is also the simplest naturally available atomic species, which, in contrast to one electron atoms, exhibits the additional electron-electron interaction, as a source of electronic correlations. Hence, helium is one of the simplest systems where electronic correlations can be studied. Direct manifestations of electronic correlations have been found, e.g., in doubly excited states of helium localized along highly asymmetric, though very stable, frozen planet configurations (FPC) (K. Richter et.al., 1990), or scarred by... 

Another well-defined configuration of the classical three body Coulomb problem with unambiguous quantum correspondence is the collinear antisymmetric stretch configuration, where the electrons are located on opposite sides of the nucleus. In contrast to the frozen planet orbit, the antisymmetric stretch is unstable in the axial direction (G.S. Ezra et.al., 1991 P. Schlagheck et.al., 2003), with the two electrons colliding with the nucleus in a perfectly alternating way (Fig. 3 (left)). Hence, already the one dimensional treatment accounts for the dominant classical decay channel of this configuration. As for the frozen planet, there are doubly excited states of helium associated to the periodic orbit of the ASC as illustrated in Fig. 3 (left). 

It is clear that a core-hole represents a very interesting example of an unstable state in the continuum. It is, however, also rather complicated [150]. A simpler system with similar characteristics is a doubly excited state in few-body systems, as helium. Here, it is possible [151-153] to simulate the whole sequence of events that take place when the interaction with a short light pulse first creates a wave packet in the continuum, including doubly excited states, and the metastable components subsequently decay on a timescale that is comparable to the characteristic time evolution of the electronic wave packet itself. On the experimental side, techniques for such studies are emerging. Mauritsson et al. [154] studied recently the time evolution of a bound wave packet in He, created by an ultra-short (350 as) pulse and monitored by an IR probe pulse, and Gilbertson et al. [155] demonstrated that they could monitor and control helium autoionization. Below, we describe how a simulation of a possible pump-probe experiment, targeting resonance states in helium, can be made. 

The panels in the first and last columns in Figure 5.11 correspond to two selected consecutive times at which a wave front originates close to the nucleus, 14.51 and 15.63 fs, while the central column corresponds to a time halfway between these two. In the upper row of Figure 5.11, we show the electron density within 15 Bohr radii from the nucleus its breathing motion is evident At f = 14.51 fs (a) the central part of the wave packet is at the peak of its contraction. At f = 15.09 fs (b) it reaches its maximal expansion. Finally, at f = 15.63 fs (c), it is contracted again. Thus, the relation between the breathing of the electron density at small radii and the ejection of isolated electron density bursts is more subtle than the obvious correspondence between their periodicities. Indeed, the instants at which the wave fronts are born in the vicinity of the nucleus correspond closely to the stages of maximum contraction of the localized part of the metastable wave packet. This evidence supports the idea that the collisional description of the autoionization dynamics of the doubly excited state of helium holds down to the least excited ones. 

Figure 5.14 The helium ionization yield for the ion being left in the He+(2s) and He+(2p) excited states as a function of the time delay between the initial XUV pump pulse and the IR probe pulse. The oscillations are due to breathing between different doubly excited states (resonances).

E. Lindroth, Calculation of doubly excited states of helium with a finite discrete spectrum, Phys. Rev. A 49 (1994) 4473. 

D.R. DeWitt, E. lindroth, R. Schuch, H. Gao, T. Quinteros, W. Zong, Spectroscopy of highly doubly excited states of helium through dielectronic recombination, J. Phys. B 28... 

N. Elander, E. Yarevsky, Exterior complex scaling method applied to doubly excited states of helium, Phys. Rev. A. 57 (1998) 3119. 

The most recent advance in the theory of the helium atom was the discovery of its classically chaotic nature. In connection with modern semiclassical techniques, such as Gutzwiller s periodic orbit theory and cycle expansion techniques, it was possible to obtain substantial new insight into the structure of doubly excited states of two-electron atoms and ions. This new direction in the application of chaos in atomic physics was initiated by Ezra et al. (1991), Kim and Ezra (1991), Richter (1991), and Bliimel and Reinhardt (1992). The discussion of the manifestations of chaos in the helium atom is the focus of this chapter. 

The doubly excited states of helium are amenable to theoretical studies, and some of those states can be studied spectroscopically. Nevertheless, by any reasonable criterion, these transient states are rather exotic. They illustrate a phenomenon of atomic structure that was not heretofore expected, and, in so doing, open our minds to thinking of atomic structure in more general terms. They force us to ask whether other atoms, expecially atoms with two valence... 

The development of a full angular momentum, three dimensional, smooth exterior complex dilated, finite element method for computing bound and resonant states in a wide class of quantum systems is described. Applications to the antiprotonic helium system, doubly excited states in the helium atom and to a model of a molecular van der Waals complex are discussed. 2001 by Academic Press. 

Fragmenting levels for a known three-body problem - doubly excited states in the normal helium atom. 

The role of electron-electron interaction is one of the main topics of atomic, molecular physics and quantum chemistry. The normal helium atom is then naturally one of the most fundamental systems. Doubly excited states are as almost bound states of special interest since the role of the electron-electron interaction is important in describing energies and also autoionization rates. Dielectronic recombination processes where one of the two excited electrons falls down to a lower level while the other is ejected appears to be a fundamental process where electron-electron interaction plays a dominant role[6]. The recently built electron-cooler storage rings [7] have made it possible to study dielectronic recombination and thereby doubly excited states with high experimental accuracy. 

Having tested our formalism and code on the two coulomb interacting systems antiprotonic helium and doubly excited states in normal helium we were ready to attack a model of predissociating triatomic molecule. We choose the NelCl van der Waals complex as our triatomic test molecule since a number of more and more accurate studies had been performed on zero-angular momentum levels of this system[38, 39, 40, 41, 42]. 

The doubly-excited state of helium is some 160 000 cm above the ground state (78). Apply the spreadsheet approach to obtain a best estimate of this energy difference. 

Other helium-like systems also were investigated. Ho (99) considered doubly excited states of C between the N = 2 and N = 3 C thresholds. He computed both resonance positions and total widths for odd parity states of total angular momentum L — 0,. .,5 and for even parity states of L = 1,. .,4. Ho also computed the doubly excited autoionizing states of S XV ion converging on the N = 2 to IV = 4 thresholds of S XVI ion (100). He gave positions and widths of 77 resonances of i = 0,. .,6. 

V. Mujica, O.Goscinski and E. Sangfelt Election Correlation in Doubly Excited States of Helium and Extensions to Beryllium and Magnesium. Chem. Phys. 87, 473 (1984). 

Doubly excited discrete states that are stable to autoionization are known in helium and these probably have radiative lifetimes characteristic of optically allowed transitions/If such states also exist in argon, these lifetimes would be such that a small contribution to HeAr would be observed at the pressures used by Munson et Experiments utilizing separated excitation and reaction regions indicate that no contribution to HeAr arises from excited argon. Not unexpectedly, therefore, one concludes that the doubly excited states in argon proposed by Munson et have lifetimes less than 10 sec. 

In their measurements of electrons emitted after double excitation of the (2p ) D and (2s2p) P states of helium by 1.84 MeV/amu electron and proton impact, Pedersen and Hvelplund [6.23] observed that the yield of autoionized electrons was considerably smaller in the forward direction for electron impact than for proton impact. The authors do not believe that this can be due to a postcollision effect like that seen by Skogvall and Schiwietz [6.29] since the projectile electron velocity in their case is much larger. They suggest that the reason is instead a difference in the excitation of the doubly excited states, combined with the effect of interference between the amplitudes for ionization after double excitation and direct ionization. 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

Figure 5.13 Helium photoelectron angular distribution in the He+(2p) channel (logarithmic scale). x-Axis cosine of the electron ejection angle relative the laser polarization, y-axis total energy (1 a.u. 27 eV). (a) After the XUV-pulse after the IR-pulse for three different time delays, separated from each other by half the IR-pulse period, 15.53 fs (b), 16.87 fs(c), and 18.21 (d). The fringes in (b)-(d) arise due to the interference between the (XUV-pulse) direct ionization from the ground state and the (IR-pulse) ionization from the doubly excited populated by the XUV-pulse.

A. Burgers, D. Wintgen, J.-M. Rost, Highly doubly excited S states of the helium atom, J. Phys. B 28 (1995) 3163. 

---