dorsal/arxiv
View SchemaCoulomb crystals in the harmonic lattice approximation
| Authors | D. A. Baiko, D. G. Yakovlev, H. E. De Witt, W. L. Slattery |
|---|---|
| Categories | |
| ArXiv ID | physics/9912048 |
| URL | https://arxiv.org/abs/physics/9912048 |
| DOI | 10.1103/PhysRevE.61.1912 |
Abstract
The dynamic structure factor ${\tilde S}({\bf k},\omega)$ and the two-particle distribution function $g({\bf r},t)$ of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multi-phonon excitation and absorption. The static radial two-particle distribution function $g(r)$ is calculated for classical ($T \gtrsim \hbar \omega_p$, where $\omega_p$ is the ion plasma frequency) and quantum ($T \ll \hbar \omega_p$) body-centered cubic (bcc) crystals. The results for the classical crystal are in a very good agreement with extensive Monte Carlo (MC) calculations at $1.5 \lesssim r/a \lesssim 7$, where $a$ is the ion-sphere radius. The HL Coulomb energy is calculated for classical and quantum bcc and face-centered cubic crystals, and anharmonic corrections are discussed. The inelastic part of the HL static structure factor $S''(k)$, averaged over orientations of wave-vector {\bf k}, is shown to contain pronounced singularities at Bragg diffraction positions. The type of the singularities is different in classical and quantum cases. The HL method can serve as a useful tool complementary to MC and other numerical methods.
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"abstract": "The dynamic structure factor ${\\tilde S}({\\bf k},\\omega)$ and the\ntwo-particle distribution function $g({\\bf r},t)$ of ions in a Coulomb crystal\nare obtained in a closed analytic form using the harmonic lattice (HL)\napproximation which takes into account all processes of multi-phonon excitation\nand absorption. The static radial two-particle distribution function $g(r)$ is\ncalculated for classical ($T \\gtrsim \\hbar \\omega_p$, where $\\omega_p$ is the\nion plasma frequency) and quantum ($T \\ll \\hbar \\omega_p$) body-centered cubic\n(bcc) crystals. The results for the classical crystal are in a very good\nagreement with extensive Monte Carlo (MC) calculations at $1.5 \\lesssim r/a\n\\lesssim 7$, where $a$ is the ion-sphere radius. The HL Coulomb energy is\ncalculated for classical and quantum bcc and face-centered cubic crystals, and\nanharmonic corrections are discussed. The inelastic part of the HL static\nstructure factor $S\u0027\u0027(k)$, averaged over orientations of wave-vector {\\bf k},\nis shown to contain pronounced singularities at Bragg diffraction positions.\nThe type of the singularities is different in classical and quantum cases. The\nHL method can serve as a useful tool complementary to MC and other numerical\nmethods.",
"arxiv_id": "physics/9912048",
"authors": [
"D. A. Baiko",
"D. G. Yakovlev",
"H. E. De Witt",
"W. L. Slattery"
],
"categories": [
"physics.plasm-ph",
"astro-ph"
],
"doi": "10.1103/PhysRevE.61.1912",
"title": "Coulomb crystals in the harmonic lattice approximation",
"url": "https://arxiv.org/abs/physics/9912048"
},
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