DOI: 10.1063/1.1672572. WKB Solution of Inversion Problems for Potential Scattering

WKB Solution of Inversion Problems for Potential Scattering

10.1063/1.1672572

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The construction of a local, not necessarily monotonic, potential is given in the WKB approximation for the two following sets of “input” information: (1) the phase shift as a function of impact parameter (or orbital angular momentum) at one energy; (2) the phase shift as a function of energy for one value of l, plus the eigenvalues of the potential for this same l. It is also shown that in the high-energy WKB approximation (Eikonal approximation) the energy dependence of the total cross section can be inverted to obtain the potential. Procedures for constructing the classical deflection function (or, equivalently, the phase shift as a function of impact parameter) from the observed differential cross section are also discussed.

Bibliography

Miller, W. H. (1969). WKB Solution of Inversion Problems for Potential Scattering. The Journal of Chemical Physics, 51(9), 3631â3638.

Authors 1

William H. Miller (first)

References 14 Referenced 81

{'key': '2024020905470998500_r1'}
{'key': '2024020905470998500_r2'}
{'key': '2024020905470998500_r2a', 'first-page': '75', 'volume': '10', 'year': '1966', 'journal-title': 'Advan. Chem. Phys.'} / Advan. Chem. Phys. (1966)
{'key': '2024020905470998500_r2b', 'first-page': '389', 'volume': '12', 'year': '1967', 'journal-title': 'Advan. Chem. Phys.'} / Advan. Chem. Phys. (1967)
{'key': '2024020905470998500_r3', 'first-page': '630', 'volume': '99', 'year': '1955', 'journal-title': 'Phys. Rev.'} / Phys. Rev. (1955)
10.1088/0370-1328/89/3/301 / Proc. Phys. Soc. (London) (1966)
10.1063/1.1667946 / J. Chem. Phys. (1968)
10.1103/PhysRev.102.557 / Phys. Rev. (1956)
{'key': '2024020905470998500_r8', 'first-page': '351', 'volume': '12', 'year': '1967', 'journal-title': 'Advan. Chem. Phys.'} / Advan. Chem. Phys. (1967)
10.1063/1.1664543 / J. Math. Phys. (1968)
10.1007/BF02756351 / Nuovo Cimento (1969)
{'key': '2024020905470998500_r12', 'first-page': '2561', 'volume': '39', 'year': '1963', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. (1963)
10.1063/1.1727971 / J. Chem. Phys. (1966)
10.1016/0009-2614(65)80016-1 / Chem. Phys. Letters (1968)

Dates

Type	When
Created	21 years, 6 months ago (Feb. 6, 2004, 2:22 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 1:11 a.m.)
Indexed	3 months, 1 week ago (May 27, 2025, 6:06 a.m.)
Issued	55 years, 10 months ago (Nov. 1, 1969)
Published	55 years, 10 months ago (Nov. 1, 1969)
Published Print	55 years, 10 months ago (Nov. 1, 1969)

Funders 0

None

BibTeX

@article{Miller_1969, title={WKB Solution of Inversion Problems for Potential Scattering}, volume={51}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1672572}, DOI={10.1063/1.1672572}, number={9}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Miller, William H.}, year={1969}, month=nov, pages={3631–3638} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        5,
        27
      ]
    ],
    "date-time": "2025-05-27T10:06:05Z",
    "timestamp": 1748340365655
  },
  "reference-count": 14,
  "publisher": "AIP Publishing",
  "issue": "9",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1969,
        11,
        1
      ]
    ]
  },
  "abstract": "<jats:p>The construction of a local, not necessarily monotonic, potential is given in the WKB approximation for the two following sets of \u201cinput\u201d information: (1) the phase shift as a function of impact parameter (or orbital angular momentum) at one energy; (2) the phase shift as a function of energy for one value of l, plus the eigenvalues of the potential for this same l. It is also shown that in the high-energy WKB approximation (Eikonal approximation) the energy dependence of the total cross section can be inverted to obtain the potential. Procedures for constructing the classical deflection function (or, equivalently, the phase shift as a function of impact parameter) from the observed differential cross section are also discussed.</jats:p>",
  "DOI": "10.1063/1.1672572",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        2,
        6
      ]
    ],
    "date-time": "2004-02-06T19:22:44Z",
    "timestamp": 1076095364000
  },
  "page": "3631-3638",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 81,
  "title": "WKB Solution of Inversion Problems for Potential Scattering",
  "prefix": "10.1063",
  "volume": "51",
  "author": [
    {
      "given": "William H.",
      "family": "Miller",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020905470998500_r1"
    },
    {
      "key": "2024020905470998500_r2"
    },
    {
      "key": "2024020905470998500_r2a",
      "first-page": "75",
      "volume": "10",
      "year": "1966",
      "journal-title": "Advan. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r2b",
      "first-page": "389",
      "volume": "12",
      "year": "1967",
      "journal-title": "Advan. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r3",
      "first-page": "630",
      "volume": "99",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020905470998500_r4",
      "doi-asserted-by": "crossref",
      "first-page": "479",
      "DOI": "10.1088/0370-1328/89/3/301",
      "volume": "89",
      "year": "1966",
      "journal-title": "Proc. Phys. Soc. (London)"
    },
    {
      "key": "2024020905470998500_r5",
      "doi-asserted-by": "crossref",
      "first-page": "464",
      "DOI": "10.1063/1.1667946",
      "volume": "48",
      "year": "1968",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r7",
      "doi-asserted-by": "crossref",
      "first-page": "557",
      "DOI": "10.1103/PhysRev.102.557",
      "volume": "102",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "2024020905470998500_r8",
      "first-page": "351",
      "volume": "12",
      "year": "1967",
      "journal-title": "Advan. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r11",
      "doi-asserted-by": "crossref",
      "first-page": "2050",
      "DOI": "10.1063/1.1664543",
      "volume": "9",
      "year": "1968",
      "journal-title": "J. Math. Phys."
    },
    {
      "key": "2024020905470998500_r11a",
      "doi-asserted-by": "crossref",
      "first-page": "131",
      "DOI": "10.1007/BF02756351",
      "volume": "59",
      "year": "1969",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "2024020905470998500_r12",
      "first-page": "2561",
      "volume": "39",
      "year": "1963",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r12a",
      "doi-asserted-by": "crossref",
      "first-page": "2519",
      "DOI": "10.1063/1.1727971",
      "volume": "45",
      "year": "1966",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020905470998500_r13",
      "doi-asserted-by": "crossref",
      "first-page": "481",
      "DOI": "10.1016/0009-2614(65)80016-1",
      "volume": "2",
      "year": "1968",
      "journal-title": "Chem. Phys. Letters"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/51/9/3631/18865213/3631_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/51/9/3631/18865213/3631_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        9
      ]
    ],
    "date-time": "2024-02-09T06:11:36Z",
    "timestamp": 1707459096000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/51/9/3631/85122/WKB-Solution-of-Inversion-Problems-for-Potential"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1969,
        11,
        1
      ]
    ]
  },
  "references-count": 14,
  "journal-issue": {
    "issue": "9",
    "published-print": {
      "date-parts": [
        [
          1969,
          11,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1672572",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1969,
        11,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1969,
        11,
        1
      ]
    ]
  }
}