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A program to compute exact hydrogenic radial integrals and Einstein coefficients
An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions F ( a , b ; c ; x ) , which are difficult to calculate directly, when the (negative) integers a, b are large, as in the case of high Rydberg st...
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| Published in: | Computer physics communications 2009-10, Vol.180 (10), p.2020-2020 |
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| container_title | Computer physics communications |
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| creator | Dy, Hoang-Binh |
| description | An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions
F
(
a
,
b
;
c
;
x
)
, which are difficult to calculate directly, when the (negative) integers
a,
b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly
F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.
Program title: ba5.2
Catalogue identifier: ADUU_v2_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 1400
No. of bytes in distributed program, including test data, etc.: 11 737
Distribution format: tar.gz
Programming language: Fortran 77
Computer: PC, iMac
Operating system: Linux/Unix, MacOS 9.0
RAM: Less than 1 MB
Classification: 2, 2.2
Catalogue identifier of previous version: ADUU_v1_0
Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191
Does the new version supersede the previous version?: Yes
Nature of problem: Exact calculation of atomic data.
Solution method: Use of a recurrence relation to compute hypergeometric functions.
Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes.
Summary of revisions: Values of the total Einstein transition probability from an upper level
n to a lower level
n
′
are computed, as well as the radiative lifetime of a level
n.
Running time: About 2 seconds |
| doi_str_mv | 10.1016/j.cpc.2009.06.003 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_03742176v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0010465509001842</els_id><sourcerecordid>34794816</sourcerecordid><originalsourceid>FETCH-LOGICAL-c362t-8c76b2ad30a7f27ece2a71f939ba8af7414f20d467ce8a2161153856b6d4484c3</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKs_wFtOgoddJx9NdvFUil9Q0IOeQ5qdtSnb3Zqkxf57UyoePQ3MPO8L8xByzaBkwNTdqnQbV3KAugRVAogTMmKVrgteS3lKRgAMCqkmk3NyEeMKALSuxYi8TekmDJ_BrmkaqBvWm21Cit_WJbrcN_mEvXc02Mbbjvo-YWa7SG3f0Affx4S-zzFsW-889ilekrM2A3j1O8fk4_HhffZczF-fXmbTeeGE4qmonFYLbhsBVrdco0NuNWtrUS9sZVstmWw5NFJph5XlTDE2EdVELVQjZSWdGJPbY-_SdmYT_NqGvRmsN8_TuTnsQGjJmVY7ltmbI5tf_dpiTGbto8Ousz0O22iE1LWsmMogO4IuDDEGbP-aGZiDZ7My2bM5eDagTPacM_fHDOZvdx6DiQcTDhsf0CXTDP6f9A-OroUX</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>34794816</pqid></control><display><type>article</type><title>A program to compute exact hydrogenic radial integrals and Einstein coefficients</title><source>ScienceDirect Journals</source><creator>Dy, Hoang-Binh</creator><creatorcontrib>Dy, Hoang-Binh</creatorcontrib><description>An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions
F
(
a
,
b
;
c
;
x
)
, which are difficult to calculate directly, when the (negative) integers
a,
b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly
F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.
Program title: ba5.2
Catalogue identifier: ADUU_v2_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 1400
No. of bytes in distributed program, including test data, etc.: 11 737
Distribution format: tar.gz
Programming language: Fortran 77
Computer: PC, iMac
Operating system: Linux/Unix, MacOS 9.0
RAM: Less than 1 MB
Classification: 2, 2.2
Catalogue identifier of previous version: ADUU_v1_0
Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191
Does the new version supersede the previous version?: Yes
Nature of problem: Exact calculation of atomic data.
Solution method: Use of a recurrence relation to compute hypergeometric functions.
Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes.
Summary of revisions: Values of the total Einstein transition probability from an upper level
n to a lower level
n
′
are computed, as well as the radiative lifetime of a level
n.
Running time: About 2 seconds</description><identifier>ISSN: 0010-4655</identifier><identifier>EISSN: 1879-2944</identifier><identifier>DOI: 10.1016/j.cpc.2009.06.003</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Astrophysics ; Einstein coefficients ; Hydrogenic radial integrals ; Lifetimes ; Physics</subject><ispartof>Computer physics communications, 2009-10, Vol.180 (10), p.2020-2020</ispartof><rights>2009 Elsevier B.V.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c362t-8c76b2ad30a7f27ece2a71f939ba8af7414f20d467ce8a2161153856b6d4484c3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03742176$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Dy, Hoang-Binh</creatorcontrib><title>A program to compute exact hydrogenic radial integrals and Einstein coefficients</title><title>Computer physics communications</title><description>An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions
F
(
a
,
b
;
c
;
x
)
, which are difficult to calculate directly, when the (negative) integers
a,
b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly
F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.
Program title: ba5.2
Catalogue identifier: ADUU_v2_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 1400
No. of bytes in distributed program, including test data, etc.: 11 737
Distribution format: tar.gz
Programming language: Fortran 77
Computer: PC, iMac
Operating system: Linux/Unix, MacOS 9.0
RAM: Less than 1 MB
Classification: 2, 2.2
Catalogue identifier of previous version: ADUU_v1_0
Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191
Does the new version supersede the previous version?: Yes
Nature of problem: Exact calculation of atomic data.
Solution method: Use of a recurrence relation to compute hypergeometric functions.
Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes.
Summary of revisions: Values of the total Einstein transition probability from an upper level
n to a lower level
n
′
are computed, as well as the radiative lifetime of a level
n.
Running time: About 2 seconds</description><subject>Astrophysics</subject><subject>Einstein coefficients</subject><subject>Hydrogenic radial integrals</subject><subject>Lifetimes</subject><subject>Physics</subject><issn>0010-4655</issn><issn>1879-2944</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKs_wFtOgoddJx9NdvFUil9Q0IOeQ5qdtSnb3Zqkxf57UyoePQ3MPO8L8xByzaBkwNTdqnQbV3KAugRVAogTMmKVrgteS3lKRgAMCqkmk3NyEeMKALSuxYi8TekmDJ_BrmkaqBvWm21Cit_WJbrcN_mEvXc02Mbbjvo-YWa7SG3f0Affx4S-zzFsW-889ilekrM2A3j1O8fk4_HhffZczF-fXmbTeeGE4qmonFYLbhsBVrdco0NuNWtrUS9sZVstmWw5NFJph5XlTDE2EdVELVQjZSWdGJPbY-_SdmYT_NqGvRmsN8_TuTnsQGjJmVY7ltmbI5tf_dpiTGbto8Ousz0O22iE1LWsmMogO4IuDDEGbP-aGZiDZ7My2bM5eDagTPacM_fHDOZvdx6DiQcTDhsf0CXTDP6f9A-OroUX</recordid><startdate>20091001</startdate><enddate>20091001</enddate><creator>Dy, Hoang-Binh</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope></search><sort><creationdate>20091001</creationdate><title>A program to compute exact hydrogenic radial integrals and Einstein coefficients</title><author>Dy, Hoang-Binh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-8c76b2ad30a7f27ece2a71f939ba8af7414f20d467ce8a2161153856b6d4484c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Astrophysics</topic><topic>Einstein coefficients</topic><topic>Hydrogenic radial integrals</topic><topic>Lifetimes</topic><topic>Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dy, Hoang-Binh</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Computer physics communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dy, Hoang-Binh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A program to compute exact hydrogenic radial integrals and Einstein coefficients</atitle><jtitle>Computer physics communications</jtitle><date>2009-10-01</date><risdate>2009</risdate><volume>180</volume><issue>10</issue><spage>2020</spage><epage>2020</epage><pages>2020-2020</pages><issn>0010-4655</issn><eissn>1879-2944</eissn><abstract>An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions
F
(
a
,
b
;
c
;
x
)
, which are difficult to calculate directly, when the (negative) integers
a,
b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly
F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.
Program title: ba5.2
Catalogue identifier: ADUU_v2_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 1400
No. of bytes in distributed program, including test data, etc.: 11 737
Distribution format: tar.gz
Programming language: Fortran 77
Computer: PC, iMac
Operating system: Linux/Unix, MacOS 9.0
RAM: Less than 1 MB
Classification: 2, 2.2
Catalogue identifier of previous version: ADUU_v1_0
Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191
Does the new version supersede the previous version?: Yes
Nature of problem: Exact calculation of atomic data.
Solution method: Use of a recurrence relation to compute hypergeometric functions.
Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes.
Summary of revisions: Values of the total Einstein transition probability from an upper level
n to a lower level
n
′
are computed, as well as the radiative lifetime of a level
n.
Running time: About 2 seconds</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cpc.2009.06.003</doi><tpages>1</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0010-4655 |
| ispartof | Computer physics communications, 2009-10, Vol.180 (10), p.2020-2020 |
| issn | 0010-4655 1879-2944 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_03742176v1 |
| source | ScienceDirect Journals |
| subjects | Astrophysics Einstein coefficients Hydrogenic radial integrals Lifetimes Physics |
| title | A program to compute exact hydrogenic radial integrals and Einstein coefficients |
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