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A dynamical description of spectral shifts and widths of positron planar-channeled radiation is presented. The presence of we11-defined valence electron collective oscillations or plasmons as documented in electron-loss spectroscopy is proposed as one mechanism for experimentally observed negative shifts. Qualitative comparison with the experimental data at 55 MeV for diamond, silicon, and LiF is indicated. Relativistic planar-channeled positrons in crystals may occupy bound energy eigenstates in the transverse direction. Spontaneous transitions between these discrete states yield intense, narrow-width, strongly forward-peaked xray radiation. ' Channeling radiation from positrons of approximately 55 MeV has been observed in silicon, diamond, germanium, and LiF. According to the harmonic potential model of Pantell and Alguard, a single spectral envelope should be observed. This composite structure results from a set of closely spaced spectral lines arising from weak anharmonicity and the associated natural line-broadening mechanisms. In most experiments to date on positron channeling, such a structure has indeed been observed but with a perceptible negative shift. This paper examines these negative shifts, as well as the accompanying spectral widths, from a dynamical approach by using a density-matrix treatment. We have recently shown that in the case of high-energy electron planar channeling, the presence of nondegenerate transition frequencies can yield negatively shifted spectral lines. Specifically, each bound eigenstate effectively repels the adjacent level through intermediate or virtual transitions by an amount significantly depending on the bound electron energy level. In the case of positron channeling, however, the transition frequencies are nearly degenerate, and the effects of intermediate bound-bound (b-b) transitions on spectral shifts nearly cancel. This motivates our investigation here of the influence of intermediate bound-free (b-f) transitions on spectral line shifts. In previous studies of electron planar channeling, the electric field fluctuations associated with the thermal motion of the ions, i.e., phonons, were emphasized because the channeled electrons are localized near the ionic planes. ' For positron channeling, however, the relevant electric field fluctuations are principally associated with the valence electrons since the positrons are confined near the ionic midplanes. ' Electron-loss spectroscopic (ELS) studies have documented that the valence electrons collectively behave in the form of relatively long-lived plasmon excitations for the crystalline samples we shall consider. These experimental results are of essential importance in our identification of the electric field fluctuations with coherent plasmon phenomena. Because the samples are ordinarily around room temperature ( ~ eV) or less and the valence plasmon energies are typically greater than 15 eV, the valence electrons have only zeropoint collective motions with plasmon occupation number zero. As the channeling positron traverses the crystal, virtual processes result where plasmons are created and subsequently annihilated. The effect of these virtual transitions on the spectral characteristics of the channeling radiation is to yield dynamical line shifts and widths. These are understood most conveniently through a densitymatrix formulation which we employ here. " For the three low-Z samples to which we apply this simple formalism, qualitative agreement with the experimentally observed negative shifts and widths is found. In the case of higher-Z elements such as germanium or tungsten (W) (Ref. 12), the presence of more complicated band structures prevents us from reliably applying the theory as presented here. The paper is organized as follows. In Sec. II a densitymatrix equation of motion is obtained for the channeling positrons interacting with the valence electrons of the crystal. In Sec. III the line shifts and widths of the channeling radiation are obtained from the ensemble-averaged density-matrix equation of motion. Section IV uses a simplified density fluctuation model for comparing our results with the experimental data at 55 MeV for diamond, silicon, and LiF.

Valence-band plasmon effects on line shifts and widths in positron planar-channeling radiation