Electron scattering from the ground state of mercury

We give a short review of e-Hg scattering and present some results of our recent closecoupling calculations. We look at the challenges facing theorists in the calculation of elastic scattering and excitation of the 6s6p P1 levels. INTRODUCTION In the field of electron-atom scattering the e-Hg collision systems is one of more interesting and important cases. Mercury is an important constituent of various industrial plasmas where electron collisions play crucial role in many technologically important processes, as, for example, in fluorescent and high intensity discharge lamps [1, 2]. Additionally, as a heavy atom, mercury is a useful target in studies of relativistic effects in electron-atom scattering (see Andersen et al. [3] for a recent review). In this report we would like to give a short review of the present status of e-Hg scattering and present some of our recent results for this scattering system concentrating on elastic scattering and excitation of the 6s6p P1 levels. THEORETICAL METHODS Electron scattering form mercury presents a serious challenge to theorists. Comparing to light atoms, where good agreement between theory and experiment was established, there are a number of processes which make the theoretical modelling substantially more difficult. These difficulties originate from the fact that mercury is a heavy atom of nuclear charge Z = 80. For such an atomic system it is important to to take into account relativistic effects, as well as to model electron-electron correlations between two active outer electrons and the rest of the electrons. Relativistic effects There are two different aspects to relativistic effects, the description of the target states and the scattered electron. While both are important and observed in experiments, an adDownloaded 08 Mar 2010 to 134.115.152.130. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp equate description of the mercury wave functions seems to be the most important. The two most prominent relativistic effects relevant to the accurate description of elastic scattering and excitation of the 6s6p P1 levels of mercury are the relativistic contraction of the orbitals which leads to an increase in the ionization energy (experimental value is 10.43 eV) by about 1.5 eV, and the singlet-triplet mixing between the nonrelativistic 6s6p P1 and 6s6p P1 configurations (the mixing coefficient is 0.171). The most consistent way to account for the relativistic nature of mercury is to use methods based on the Dirac equation. This approach was employed for the study of elastic scattering by Walker [4], Sin Fai Lam [5], Haberland and Fritsche [6], McEachran and Stauffer [7], Sienkiewicz [8], Sienkiewicz [9], and McEachran and Elford [10]. Excitation of the 6s6p levels has been studied by Srivastava et al. [11] using distorted wave approximation. Wijesundera et al. [12] have applied a five-state fully relativistic Dirac R-matrix method to study low energy e-Hg scattering and have provided elastic and excitation (6s6p P0,1,2) cross sections. Breit-Pauli approximation has been used extensively in e-Hg scattering calculations. Bartschat and Madison [13] have studied excitations of the 6s6p P1 levels using a distorted-wave Born approximation (DWA) and Scott et al. [14], Bartschat et al. [15] have used five-state R-matrix method (RM(5)) to calculate elastic scattering and excitation. In all these calculations only a one-body spin-orbit term was used to model relativistic effects. The present calculations use the CCC method [16] to study e-Hg scattering. The relativistic contraction of the Hg orbitals has been modelled by means of a short-ranged potential. Singlet-triplet mixing in the 6s6p P1 manifold has been accounted for in the semi-relativistic approximation by combining nonrelativistic amplitudes for the 6s6p P1 and 6s6p P1 states with appropriate mixing coefficients [17]. Electron correlations In most of the calculations the mercury atom is modelled as two active electrons above a frozen inert Hg++ core of [Xe]4 f 145d10. Within this approximation it is important to include configurations with the “inner” electron being described by a combination of the 6s, 6p and 6d orbitals. The “outer” electron is expanded using sufficiently many Laguerre based orbitals. Such an approach leads to a good ground state and excited levels based on the [Xe]4 f 145d10 core. However, the mercury discrete spectrum contains a number of states corresponding to the excitation out of 5d10 shell. The importance of such core excitations can be appreciated by noting that about one-third of the mercury ground state static dipole polarizability (αd = 34.4 a.u. [18]) comes from the 5d 96s2nl manifold. Opening of the 5d10 shell also leads to a reduction of the optical oscillator strength f for the 6s6p P1 level by nearly a factor of two [12]. An error in the value of α d or f can substantially affect scattering calculations, as will be discussed later. Only the Dirac R-matrix method of Wijesundera et al. [12] attempted to take into account valence-core correlations directly by allowing excitation out of the 5d10 shell. Most of the theoretical methods applied to e-Hg scattering take no account of core excitations. Our calculations use twoand one-electron polarisation potentials to model Downloaded 08 Mar 2010 to 134.115.152.130. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp valence-core correlations, which leads to a good agreement for the 6s6p P1 level optical oscillator strength, but the error in the value of α d remains. Channel coupling There are very few calculations of e-Hg scattering which take into account channelcoupling. These are the Dirac R-matrix method of Wijesundera et al. [12] and the BreitPauli R-matrix method of Scott et al. [14], Bartschat et al. [15]. Both calculations have included only five low lying states of Hg. Such calculations are expected to be accurate only at low energies where states not included in the calculations are closed. The present CCC calculations include 54 states (nine 1S, eight 3S, 1,3De, 1,3Po, two 3Pe and one 1Pe, 1,3Do) comprising both the discrete spectrum states and the positive-energy states modelling the target continuum. RDD Kaussen et al. S scattering angle θ (deg) 150 120 90 60 30 0 1