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Coulomb crystals in the harmonic lattice approximation
Plasma Physics · Submitted 23 Dec 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The HL method can serve as a useful tool complementary to MC and other numerical methods.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.81 | 0.95 | 0.27 | asserted 1.00 |
| s1 | 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. | contribution 0.59 | 0.94 | 0.08 | asserted 1.00 |
| s2 | 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. | result 0.94 | 0.80 | 0.12 | asserted 0.99 |
| s3 | The HL Coulomb energy is calculated for classical and quantum bcc and face-centered cubic crystals, and anharmonic corrections are discussed. | contribution 0.65 | 0.95 | 0.09 | asserted 0.99 |
| s4 | 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. | result 1.00 | 0.93 | 0.13 | asserted 1.00 |
| s5 | The type of the singularities is different in classical and quantum cases. | result 0.98 | 0.85 | 0.07 | asserted 1.00 |
| s6 | The HL method can serve as a useful tool complementary to MC and other numerical methods. | interpretation 0.90 | 0.33 | 0.42 | hedged possibility 0.83 |
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Original 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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