Helium, autoionizing states

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. 

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. 

Manning and Sanders (33) used the Z-dependent perturbation theory combined with the complex rotation method to calculate the resonance position and width for the 2s2p autoionizing states of all members of the helium isoelectronic sequence. 

The double excitation (DE) process for a helium target has recently been investigated by Pedersen and Hvelplund [6.23] and by Giese et al. [6.24]. These two groups recorded the spectrum of electrons emitted from several autoionizing states of He following bombardment of e , p", at 1.84 MeV/... 

If this argument holds true, already the frozen planet configurations of planar helium should exhibit enhanced autoionization rates as compared to the ID case. In figure 2 (right) we therefore compare the decay rates of our 2D frozen planet states with the earlier ID and 3D results. Clearly, the 2D rates are of the same order of magnitude as the 3D rates,... 

Figure 3. Contour piot of the eiectronic density of a (tripiet) eigenstate strongly scarred by the antisymmetric stretch orbit (left), in 2D configuration space (spanned by the electrons distances ri and r-2 from the nucleus, in the collinear configurations considered here). This eigenstate belong to the N = 9 series. The solid lines depict the associated classical periodic orbit. Autoionization rates of antisymmetric stretch singlet states (right) of the Nth autoionizing series of the helium spectrum, in ID (squares), 2D (circles), and 3D (diamonds) configuration space.

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. 

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)...

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. 

L. Argenti, Rydberg and autoionizing triplet states in Helium up to the N = 5 threshold, At. Data Nucl. Data Tables 94 (2008) 903. 

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. 

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. 

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