Microscopic structure factor of liquid hydrogen by neutron-diffraction measurements

The center-of-mass structure factor of liquid para hydrogen has been measured, using neutron diffraction, in four thermodynamic states close to the triple point. Path integral Monte Carlo simulations have been carried out at the same temperatures and densities. The present experimental data are in reasonable quantitative agreement with the simulations and closer to these results than previous neutron determinations available in the literature. The thermodynamic derivatives of the structure factor, from both experiment and simulation, have been compared to previous measurements obtaining a quantitative consistency.

Figure 1

Diffraction intensity from liquid parahydrogen at $T=17.1\mathrm{K}$ and $p=29.9\text{bar}$. What in the figure appears as a bold line is composed, instead, by the ensemble of the experimental points and their error bars (of the order of 0.1 %). The tiny structure in the region $k\simeq 2{\mathrm{\AA }}^{-1}$ is the signature of the main peak of the intermolecular structure factor $S\left(k\right)$. The dashed line is the calculated self-molecular part, the dash-dotted line represents the Monte Carlo calculation of multiple scattering, and the dotted line is the fitted background. The thin solid line is the sum of the three terms.

Figure 2

Measured intermolecular (center-of-mass) structure factor of liquid parahydrogen at $T=17.1\mathrm{K}$ and $p=29.9\text{bar}$ (open circles with error bars). The value for $S(k=0)$, shown as a black dot, is given in Table .

Figure 3

Comparison between the measured intermolecular (center-of-mass) structure factor of liquid parahydrogen (open circles) and the PIMC simulation results (full lines). The graphs are shown as a function of decreasing density (top to bottom). The black dots at $k=0$ are taken from Table .

Figure 4

PIMC results for center of mass $g\left(r\right)$ of liquid parahydrogen as a function of the Trotter number. The graph shows the superposition of the results with $P=16$ (dots) and $P=32$ (line) for the thermodynamic point 1, using the SG potential. The $P=32$ and $P=64$ results are indistinguishable, even numerically.

Figure 5

Comparison between the present experimental determination for state 1 ($T=17.1\mathrm{K}$ and $n=22.95{\mathrm{nm}}^{-3}$, full squares with error bars) and the data obtained from Ref. 19 ($T=15.2\mathrm{K}$ and $n=22.71{\mathrm{nm}}^{-3}$, open circles). The line represents the present PIMC simulation results. The value at $k=0$ (large black dot) is from Table .

Figure 6

Density derivative, at constant temperature, of the intermolecular structure factor. Comparison between the present experimental determination (open circles, obtained from the data labeled 1 and 2 in Table ) and the results from Ref. 11 (full squares). The line represents the present PIMC simulation results obtained using the SG potential. The value at $k=0$ (full circle) is obtained from the experimental compressibilities.

Figure 7

Temperature derivative, at constant density, of the intermolecular structure factor. Comparison between the present experimental determination (open circles, obtained from the data of states 2 and 4, corrected using the density derivative shown in Fig. 6) and the results from Ref. 11 (full squares). The line represents the present PIMC simulation results, using the SG potential, and obtained using the same procedure as for the experiment data. The value at $k=0$ (full circle) is obtained from the experimental compressibilities.