DOI: 10.1063/1.1679070. Integral equation solutions for the classical electron gas

Integral equation solutions for the classical electron gas

10.1063/1.1679070

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The hypernetted chain and Percus-Yevick approximations are used to compute the radial distribution functions and the average potential energy for a classical electron gas. The results are compared with Monte Carlo calculations. The Percus-Yevick equation gives poor results above Γ = 1.0; Γ = e2/kTa, where a is the ion-sphere radius. The hypernetted chain equation was solved for 0.05 ≤ Γ ≤ 50. The results agree qualitatively with the Monte Carlo calculations everywhere except at very small Γ, where they agree with the Debye-Hückel approximation. Definite short-range order is predicted for Γ&gt;3.0, but the size of the peak in the radial distribution function is underestimated. The error in the peak size is about 9% at Γ = 50. The average potential energy is in error by less than 2% for 1 ≤ Γ ≤ 50.

Bibliography

Springer, J. F., Pokrant, M. A., & Stevens, F. A. (1973). Integral equation solutions for the classical electron gas. The Journal of Chemical Physics, 58(11), 4863â4867.

Authors 3

J. F. Springer (first)
M. A. Pokrant (additional)
F. A. Stevens (additional)

References 22 Referenced 171

10.1063/1.1727895 / J. Chem. Phys. (1966)
10.1103/PhysRev.131.1406 / Phys. Rev. (1963)
10.1063/1.1696505 / J. Chem. Phys. (1965)
10.1063/1.1762149 / Phys. Fluids (1967)
10.1103/PhysRevA.7.1 / Phys. Rev. A (1973)
10.1016/0031-8914(59)90004-7 / Physica (Utr.) (1959)
10.1063/1.1703652 / J. Math. Phys. (1960)
10.1143/PTP.24.588 / Prog. Theor. Phys. (1960)
{'key': '2024020910255138300_r6c', 'first-page': '920', 'volume': '20', 'year': '1959', 'journal-title': 'Prog. Theor. Phys.'} / Prog. Theor. Phys. (1959)
10.1143/PTP.21.361 / Prog. Theor. Phys. (1959)
10.1143/PTP.23.175 / Prog. Theor. Phys. (1960)
10.1143/PTP.23.829 / Prog. Theor. Phys. (1960)
10.1143/PTP.23.1003 / Prog. Theor. Phys. (1960)
{'key': '2024020910255138300_r6h'}
10.1007/BF02726040 / Nuovo Cimento (1960)
10.1016/0031-8914(60)90020-3 / Physica (The Hague) (1960)
{'key': '2024020910255138300_r7'}
{'key': '2024020910255138300_r8', 'first-page': '185', 'volume': '24', 'year': '1923', 'journal-title': 'Z. Phys.'} / Z. Phys. (1923)
10.1103/PhysRev.110.1 / Phys. Rev. (1958)
10.1103/PhysRevLett.8.462 / Phys. Rev. Lett. (1962)
{'key': '2024020910255138300_r10'}
10.1063/1.1731166 / J. Chem. Phys. (1960)

Dates

Type	When
Created	21 years, 6 months ago (Feb. 4, 2004, 5:30 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 6:24 a.m.)
Indexed	1 year, 1 month ago (Aug. 1, 2024, 9:15 a.m.)
Issued	52 years, 3 months ago (June 1, 1973)
Published	52 years, 3 months ago (June 1, 1973)
Published Print	52 years, 3 months ago (June 1, 1973)

Funders 0

None

BibTeX

@article{Springer_1973, title={Integral equation solutions for the classical electron gas}, volume={58}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1679070}, DOI={10.1063/1.1679070}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Springer, J. F. and Pokrant, M. A. and Stevens, F. A.}, year={1973}, month=jun, pages={4863–4867} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        8,
        1
      ]
    ],
    "date-time": "2024-08-01T13:15:08Z",
    "timestamp": 1722518108441
  },
  "reference-count": 22,
  "publisher": "AIP Publishing",
  "issue": "11",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1973,
        6,
        1
      ]
    ]
  },
  "abstract": "<jats:p>The hypernetted chain and Percus-Yevick approximations are used to compute the radial distribution functions and the average potential energy for a classical electron gas. The results are compared with Monte Carlo calculations. The Percus-Yevick equation gives poor results above \u0393 = 1.0;\u2009\u0393 = e2/kTa, where a is the ion-sphere radius. The hypernetted chain equation was solved for 0.05 \u2264 \u0393 \u2264 50. The results agree qualitatively with the Monte Carlo calculations everywhere except at very small \u0393, where they agree with the Debye-H\u00fcckel approximation. Definite short-range order is predicted for \u0393&amp;gt;3.0, but the size of the peak in the radial distribution function is underestimated. The error in the peak size is about 9% at \u0393 = 50. The average potential energy is in error by less than 2% for 1 \u2264 \u0393 \u2264 50.</jats:p>",
  "DOI": "10.1063/1.1679070",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        2,
        4
      ]
    ],
    "date-time": "2004-02-04T22:30:48Z",
    "timestamp": 1075933848000
  },
  "page": "4863-4867",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 171,
  "title": "Integral equation solutions for the classical electron gas",
  "prefix": "10.1063",
  "volume": "58",
  "author": [
    {
      "given": "J. F.",
      "family": "Springer",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Physics and Astronomy, University of Florida, Gainesville, Florida 32601"
        }
      ]
    },
    {
      "given": "M. A.",
      "family": "Pokrant",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Physics and Astronomy, University of Florida, Gainesville, Florida 32601"
        }
      ]
    },
    {
      "suffix": "Jr.",
      "given": "F. A.",
      "family": "Stevens",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Physics and Astronomy, University of Florida, Gainesville, Florida 32601"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020910255138300_r1",
      "doi-asserted-by": "crossref",
      "first-page": "2102",
      "DOI": "10.1063/1.1727895",
      "volume": "45",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020910255138300_r2",
      "doi-asserted-by": "crossref",
      "first-page": "1406",
      "DOI": "10.1103/PhysRev.131.1406",
      "volume": "131",
      "year": "1963",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020910255138300_r3",
      "doi-asserted-by": "crossref",
      "first-page": "3489",
      "DOI": "10.1063/1.1696505",
      "volume": "43",
      "year": "1965",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020910255138300_r4",
      "doi-asserted-by": "crossref",
      "first-page": "565",
      "DOI": "10.1063/1.1762149",
      "volume": "10",
      "year": "1967",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024020910255138300_r5",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1103/PhysRevA.7.1",
      "volume": "7",
      "year": "1973",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020910255138300_r6",
      "doi-asserted-by": "crossref",
      "first-page": "792",
      "DOI": "10.1016/0031-8914(59)90004-7",
      "volume": "25",
      "year": "1959",
      "journal-title": "Physica (Utr.)"
    },
    {
      "key": "2024020910255138300_r6a",
      "doi-asserted-by": "crossref",
      "first-page": "192",
      "DOI": "10.1063/1.1703652",
      "volume": "1",
      "year": "1960",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "2024020910255138300_r6b",
      "doi-asserted-by": "crossref",
      "first-page": "588",
      "DOI": "10.1143/PTP.24.588",
      "volume": "24",
      "year": "1960",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6c",
      "first-page": "920",
      "volume": "20",
      "year": "1959",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6d",
      "doi-asserted-by": "crossref",
      "first-page": "361",
      "DOI": "10.1143/PTP.21.361",
      "volume": "21",
      "year": "1959",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6e",
      "doi-asserted-by": "crossref",
      "first-page": "175",
      "DOI": "10.1143/PTP.23.175",
      "volume": "23",
      "year": "1960",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6f",
      "doi-asserted-by": "crossref",
      "first-page": "829",
      "DOI": "10.1143/PTP.23.829",
      "volume": "23",
      "year": "1960",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6g",
      "doi-asserted-by": "crossref",
      "first-page": "1003",
      "DOI": "10.1143/PTP.23.1003",
      "volume": "23",
      "year": "1960",
      "journal-title": "Prog. Theor. Phys."
    },
    {
      "key": "2024020910255138300_r6h"
    },
    {
      "key": "2024020910255138300_r6i",
      "doi-asserted-by": "crossref",
      "first-page": "77",
      "DOI": "10.1007/BF02726040",
      "volume": "18",
      "year": "1960",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "2024020910255138300_r6j",
      "doi-asserted-by": "crossref",
      "first-page": "259",
      "DOI": "10.1016/0031-8914(60)90020-3",
      "volume": "26",
      "year": "1960",
      "journal-title": "Physica (The Hague)"
    },
    {
      "key": "2024020910255138300_r7"
    },
    {
      "key": "2024020910255138300_r8",
      "first-page": "185",
      "volume": "24",
      "year": "1923",
      "journal-title": "Z. Phys."
    },
    {
      "key": "2024020910255138300_r9",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1103/PhysRev.110.1",
      "volume": "110",
      "year": "1958",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020910255138300_r9a",
      "doi-asserted-by": "crossref",
      "first-page": "462",
      "DOI": "10.1103/PhysRevLett.8.462",
      "volume": "8",
      "year": "1962",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024020910255138300_r10"
    },
    {
      "key": "2024020910255138300_r11",
      "doi-asserted-by": "crossref",
      "first-page": "456",
      "DOI": "10.1063/1.1731166",
      "volume": "33",
      "year": "1960",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/58/11/4863/18885080/4863_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/58/11/4863/18885080/4863_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T11:24:44Z",
    "timestamp": 1707477884000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/58/11/4863/87448/Integral-equation-solutions-for-the-classical"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1973,
        6,
        1
      ]
    ]
  },
  "references-count": 22,
  "journal-issue": {
    "issue": "11",
    "published-print": {
      "date-parts": [
        [
          1973,
          6,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1679070",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1973,
        6,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1973,
        6,
        1
      ]
    ]
  }
}