DOI: 10.1103/physreva.33.12. <i>1/R</i>expansion for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal"/></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>: Calculation of exponentially small terms and asymptotics

1/Rexpansion forH2+: Calculation of exponentially small terms and asymptotics

10.1103/physreva.33.12

Crossref journal-article

American Physical Society (APS)

Physical Review A (16)

Bibliography

CÃÅ¾ek, J., Damburg, R. J., Graffi, S., Grecchi, V., Harrell, E. M., Harris, J. G., Nakai, S., Paldus, J., Propin, R. Kh., & Silverstone, H. J. (1986). 1/Rexpansion forH2+: Calculation of exponentially small terms and asymptotics. Physical Review A, 33(1), 12â54.

Authors 10

Jiří Cížek (first)
Robert J. Damburg (additional)
Sandro Graffi (additional)
Vincenzo Grecchi (additional)
Evans M. Harrell (additional)
Johathan G. Harris (additional)
Sachiko Nakai (additional)
Josef Paldus (additional)
Rafail Kh. Propin (additional)
Harris J. Silverstone (additional)

References 25 Referenced 63

{'volume-title': 'Quantum Mechanics', 'year': '1965', 'author': 'L. D. Landau', 'key': 'PhysRevA.33.12Cc1R1'} / Quantum Mechanics by L. D. Landau (1965)
10.1088/0022-3700/1/4/319 / J. Phys. B by R. J. Damburg (1968)
10.1002/qua.560170609 / Int. J. Quantum Chem. by J. D. Morgan (1980)
10.1007/BF01212711 / Commun. Math. Phys. by E. M. Harrell (1980)
10.1103/PhysRevLett.52.1112 / Phys. Rev. Lett. by R. J. Damburg (1984)
10.1103/PhysRevA.32.1341 / Phys. Rev. A by H. J. Silverstone (1985)
10.1016/0550-3213(81)90197-8 / Nucl. Phys. by J. Zinn-Justin (1981)
10.1016/0550-3213(83)90369-3 / Nucl. Phys. by J. Zinn-Justin (1983)
10.1063/1.526205 / J. Math. Phys. by J. Zinn-Justin (1984)
10.1051/jphyslet:019790040019051100 / J. Phys. (Paris) Lett. by E. Brézin (1979)
10.1103/PhysRevA.22.793 / Phys. Rev. A by J. Či$aai žek (1980)
10.1002/qua.560210115 / Int. J. Quantum Chem. by R. Damburg (1981)
10.1002/andp.19263851302 / Ann. Phys. (Leipzig) by E. Schrödinger (1926)
10.1103/PhysRevA.18.1853 / Phys. Rev. A by H. J. Silverstone (1978)
10.1103/PhysRev.51.669 / Phys. Rev. by R. E. Langer (1937)
10.1090/S0002-9947-1950-0034494-3 / Trans. Am. Math. Soc. by T. M. Cherry (1950)
{'volume-title': 'Handbook of Mathematical Functions', 'year': '1964', 'key': 'PhysRevA.33.12Cc19R1'} / Handbook of Mathematical Functions (1964)
10.1007/978-3-642-88396-5 / The Confluent Hypergeometric Function by H. Buchholtz (1969)
{'volume-title': 'Asymptotic Expansions: Their Derivation and Interpretation', 'year': '1973', 'author': 'R. B. Dingle', 'key': 'PhysRevA.33.12Cc21R1'} / Asymptotic Expansions: Their Derivation and Interpretation by R. B. Dingle (1973)
10.1088/0305-4470/16/12/018 / J. Phys. A by W. Byers (1983)
10.1002/qua.560210103 / Int. J. Quantum. Chem. by B. Simon (1982)
10.1103/PhysRevA.32.1965 / Phys. Rev. A by H. J. Silverstone (1985)
10.1103/PhysRevA.32.1338 / Phys. Rev. A by V. Franceschini (1985)
10.1002/qua.560210110 / Int. J. Quantum. Chem. by W. P. Reinhardt (1982)
10.1007/BF02728240 / Nuovo Cimento B by G. Graffi (1971)

Dates

Type	When
Created	23 years ago (July 26, 2002, 7:29 p.m.)
Deposited	8 years, 2 months ago (June 15, 2017, 1:18 a.m.)
Indexed	3 months ago (May 16, 2025, 9:46 a.m.)
Issued	39 years, 7 months ago (Jan. 1, 1986)
Published	39 years, 7 months ago (Jan. 1, 1986)
Published Online	39 years, 7 months ago (Jan. 1, 1986)

Funders 0

None

BibTeX

@article{C_ek_1986, title={1/Rexpansion for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal"/></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>: Calculation of exponentially small terms and asymptotics}, volume={33}, ISSN={0556-2791}, url={http://dx.doi.org/10.1103/physreva.33.12}, DOI={10.1103/physreva.33.12}, number={1}, journal={Physical Review A}, publisher={American Physical Society (APS)}, author={Cížek, Jiří and Damburg, Robert J. and Graffi, Sandro and Grecchi, Vincenzo and Harrell, Evans M. and Harris, Johathan G. and Nakai, Sachiko and Paldus, Josef and Propin, Rafail Kh. and Silverstone, Harris J.}, year={1986}, month=jan, pages={12–54} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        5,
        16
      ]
    ],
    "date-time": "2025-05-16T13:46:57Z",
    "timestamp": 1747403217751,
    "version": "3.40.5"
  },
  "reference-count": 25,
  "publisher": "American Physical Society (APS)",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1986,
            1,
            1
          ]
        ],
        "date-time": "1986-01-01T00:00:00Z",
        "timestamp": 504921600000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "http://link.aps.org/licenses/aps-default-license"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "DOI": "10.1103/physreva.33.12",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T23:29:59Z",
    "timestamp": 1027726199000
  },
  "page": "12-54",
  "source": "Crossref",
  "is-referenced-by-count": 63,
  "title": "<i>1/R</i>expansion for<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\"/></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>: Calculation of exponentially small terms and asymptotics",
  "prefix": "10.1103",
  "volume": "33",
  "author": [
    {
      "given": "Ji\u0159\u00ed",
      "family": "C\u00ed\u017eek",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Robert J.",
      "family": "Damburg",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Sandro",
      "family": "Graffi",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Vincenzo",
      "family": "Grecchi",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Evans M.",
      "family": "Harrell",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Johathan G.",
      "family": "Harris",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Sachiko",
      "family": "Nakai",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Josef",
      "family": "Paldus",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Rafail Kh.",
      "family": "Propin",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Harris J.",
      "family": "Silverstone",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "16",
  "published-online": {
    "date-parts": [
      [
        1986,
        1,
        1
      ]
    ]
  },
  "reference": [
    {
      "volume-title": "Quantum Mechanics",
      "year": "1965",
      "author": "L. D. Landau",
      "key": "PhysRevA.33.12Cc1R1"
    },
    {
      "key": "PhysRevA.33.12Cc2R1",
      "doi-asserted-by": "crossref",
      "first-page": "681",
      "DOI": "10.1088/0022-3700/1/4/319",
      "volume": "1",
      "author": "R. J. Damburg",
      "year": "1968",
      "journal-title": "J. Phys. B"
    },
    {
      "key": "PhysRevA.33.12Cc3R1",
      "doi-asserted-by": "crossref",
      "first-page": "1143",
      "DOI": "10.1002/qua.560170609",
      "volume": "17",
      "author": "J. D. Morgan",
      "year": "1980",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "PhysRevA.33.12Cc4R1",
      "doi-asserted-by": "crossref",
      "first-page": "239",
      "DOI": "10.1007/BF01212711",
      "volume": "75",
      "author": "E. M. Harrell",
      "year": "1980",
      "journal-title": "Commun. Math. Phys."
    },
    {
      "key": "PhysRevA.33.12Cc5R1",
      "doi-asserted-by": "crossref",
      "first-page": "1112",
      "DOI": "10.1103/PhysRevLett.52.1112",
      "volume": "52",
      "author": "R. J. Damburg",
      "year": "1984",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "PhysRevA.33.12Cc7R1",
      "doi-asserted-by": "crossref",
      "first-page": "1341",
      "DOI": "10.1103/PhysRevA.32.1341",
      "volume": "32",
      "author": "H. J. Silverstone",
      "year": "1985",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "PhysRevA.33.12Cc8R1",
      "doi-asserted-by": "crossref",
      "first-page": "125",
      "DOI": "10.1016/0550-3213(81)90197-8",
      "volume": "B192",
      "author": "J. Zinn-Justin",
      "year": "1981",
      "journal-title": "Nucl. Phys."
    },
    {
      "key": "PhysRevA.33.12Cc9R1",
      "doi-asserted-by": "crossref",
      "first-page": "333",
      "DOI": "10.1016/0550-3213(83)90369-3",
      "volume": "B218",
      "author": "J. Zinn-Justin",
      "year": "1983",
      "journal-title": "Nucl. Phys."
    },
    {
      "key": "PhysRevA.33.12Cc10R1",
      "doi-asserted-by": "crossref",
      "first-page": "549",
      "DOI": "10.1063/1.526205",
      "volume": "25",
      "author": "J. Zinn-Justin",
      "year": "1984",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "PhysRevA.33.12Cc12R1",
      "doi-asserted-by": "crossref",
      "first-page": "L",
      "DOI": "10.1051/jphyslet:019790040019051100",
      "volume": "40",
      "author": "E. Br\u00e9zin",
      "year": "1979",
      "journal-title": "J. Phys. (Paris) Lett."
    },
    {
      "key": "PhysRevA.33.12Cc13R1",
      "doi-asserted-by": "crossref",
      "first-page": "793",
      "DOI": "10.1103/PhysRevA.22.793",
      "volume": "22",
      "author": "J. \u010ci$aai \u017eek",
      "year": "1980",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "PhysRevA.33.12Cc14R1",
      "doi-asserted-by": "crossref",
      "first-page": "191",
      "DOI": "10.1002/qua.560210115",
      "volume": "21",
      "author": "R. Damburg",
      "year": "1981",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "PhysRevA.33.12Cc15R1",
      "doi-asserted-by": "crossref",
      "first-page": "437",
      "DOI": "10.1002/andp.19263851302",
      "volume": "80",
      "author": "E. Schr\u00f6dinger",
      "year": "1926",
      "journal-title": "Ann. Phys. (Leipzig)"
    },
    {
      "key": "PhysRevA.33.12Cc16R1",
      "doi-asserted-by": "crossref",
      "first-page": "1853",
      "DOI": "10.1103/PhysRevA.18.1853",
      "volume": "18",
      "author": "H. J. Silverstone",
      "year": "1978",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "PhysRevA.33.12Cc17R1",
      "doi-asserted-by": "crossref",
      "first-page": "669",
      "DOI": "10.1103/PhysRev.51.669",
      "volume": "51",
      "author": "R. E. Langer",
      "year": "1937",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "PhysRevA.33.12Cc18R1",
      "doi-asserted-by": "crossref",
      "first-page": "224",
      "DOI": "10.1090/S0002-9947-1950-0034494-3",
      "volume": "68",
      "author": "T. M. Cherry",
      "year": "1950",
      "journal-title": "Trans. Am. Math. Soc."
    },
    {
      "volume-title": "Handbook of Mathematical Functions",
      "year": "1964",
      "key": "PhysRevA.33.12Cc19R1"
    },
    {
      "key": "PhysRevA.33.12Cc20R1",
      "doi-asserted-by": "crossref",
      "DOI": "10.1007/978-3-642-88396-5",
      "volume-title": "The Confluent Hypergeometric Function",
      "author": "H. Buchholtz",
      "year": "1969"
    },
    {
      "volume-title": "Asymptotic Expansions: Their Derivation and Interpretation",
      "year": "1973",
      "author": "R. B. Dingle",
      "key": "PhysRevA.33.12Cc21R1"
    },
    {
      "key": "PhysRevA.33.12Cc22R1",
      "doi-asserted-by": "crossref",
      "first-page": "2709",
      "DOI": "10.1088/0305-4470/16/12/018",
      "volume": "16",
      "author": "W. Byers",
      "year": "1983",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "PhysRevA.33.12Cc23R1",
      "doi-asserted-by": "crossref",
      "first-page": "3",
      "DOI": "10.1002/qua.560210103",
      "volume": "21",
      "author": "B. Simon",
      "year": "1982",
      "journal-title": "Int. J. Quantum. Chem."
    },
    {
      "key": "PhysRevA.33.12Cc24R1",
      "doi-asserted-by": "crossref",
      "first-page": "1965",
      "DOI": "10.1103/PhysRevA.32.1965",
      "volume": "32",
      "author": "H. J. Silverstone",
      "year": "1985",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "PhysRevA.33.12Cc26R1",
      "doi-asserted-by": "crossref",
      "first-page": "1338",
      "DOI": "10.1103/PhysRevA.32.1338",
      "volume": "32",
      "author": "V. Franceschini",
      "year": "1985",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "PhysRevA.33.12Cc27R1",
      "doi-asserted-by": "crossref",
      "first-page": "133",
      "DOI": "10.1002/qua.560210110",
      "volume": "21",
      "author": "W. P. Reinhardt",
      "year": "1982",
      "journal-title": "Int. J. Quantum. Chem."
    },
    {
      "key": "PhysRevA.33.12Cc28R1",
      "doi-asserted-by": "crossref",
      "first-page": "313",
      "DOI": "10.1007/BF02728240",
      "volume": "4",
      "author": "G. Graffi",
      "year": "1971",
      "journal-title": "Nuovo Cimento B"
    }
  ],
  "container-title": "Physical Review A",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.aps.org/article/10.1103/PhysRevA.33.12",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevA.33.12/fulltext",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2017,
        6,
        15
      ]
    ],
    "date-time": "2017-06-15T05:18:00Z",
    "timestamp": 1497503880000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://link.aps.org/doi/10.1103/PhysRevA.33.12"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1986,
        1,
        1
      ]
    ]
  },
  "references-count": 25,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          1986,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1103/PhysRevA.33.12",
  "relation": {},
  "ISSN": [
    "0556-2791"
  ],
  "subject": [],
  "container-title-short": "Phys. Rev. A",
  "published": {
    "date-parts": [
      [
        1986,
        1,
        1
      ]
    ]
  }
}