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5
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84926868348
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At the beginning of each of Secs. III–VI we list the main characteristics of the best available EOS data for systems of hard D-spheres with D = 2 – 5, respectively.
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-
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8
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84926868347
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For the hard-disk system the best available estimates for the higher-order virial coefficients have been derived in the following articles for B5, B6, and B7, respectively;
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-
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12
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84926853318
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The corresponding estimates for hard spheres are also due to Kratky [, ]. All of these estimates are listed in Table I.
-
(1977)
Physica
, vol.87 A
, pp. 584
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13
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84926803767
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Two exceptional cases are the hard D-sphere systems for D = 0,1. For the first of these systems [, ] XI (x) = -1 - ln (1 - x)/x, so that Bnstar= 1/n. For the second system , 2, 38, K. F. Herzfeld, M. Goeppert-Mayer, J. Chem. Phys.
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(1934)
J. Phys. A
, vol.19
, pp. L585
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Luban, M.1
Baram, A.2
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15
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84926802899
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The analyticity of ζ (x) in a region which includes the origin of the x plane follows directly from the assumption that the virial expansion (1) possesses a nonzero radius of convergence.
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17
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84926824555
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We have chosen to give equal weights to the data for zeta given that there are two different sources for this data. In fact, it is quite difficult to provide a reasonable estimate of the uncertainties for the data that are derived from the Levin T approximant.
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-
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20
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0039055130
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The results for XI given in Ref. 13 for hard 4-spheres were obtained using the estimate B4/(B2)3apeq 0.1513(2), calculated over two decades ago by Monte Carlo integration methods [, ]. We find that upon incorporating the exact value of B4 (Table I, present work) within an approximant of the form proposed by Baus and Colot yields estimates (Table IV, column 4 of the present work) which are substantially closer to the results of the present method than are those reported in Ref. 13 (see their Table VI).
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(1964)
J. Chem. Phys.
, vol.40
, pp. 2048
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Ree, F.H.1
Hoover, W.G.2
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22
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0000093401
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Baus and Colot (see Ref. 13) have adopted the values B4/(B2)3= 0.0746 and B5/(B2)4= 0.0148 for hard 5-spheres. These values were obtained by B. C. Freasier and D. J. Isbister [, ] using Monte Carlo integration methods. In fact, the latter give their results as 0.0746(7) and 0.0148(8), respectively, where their errors are described as constituting two standard deviations from the mean. By contrast, Ree and Hoover (see Ref. 14), also using Monte Carlo methods, obtained B4/(B2)3= 0.0761(1), which is in excellent agreement with the exact analytical result listed in Table I. The data we list in the fourth column of Table V are obtained using an approximant of the form Z3 proposed by Baus and Colot, which utilizes values of B2, B3, and B4, but we have substituted the exact values of B2, B3, and B4.
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(1981)
Mol. Phys.
, vol.42
, pp. 927
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