Computation of Atomic and Molecular Processes - Introducing the ATOM-M Software Suite

464 Pages·2021·7.762 MB·English

by  Miron Y. Amusia, Larissa V. Chernysheva

Springer Series on Atomic, Optical, and Plasma Physics 117
Miron Ya. Amusia
Larissa V. Chernysheva
Computation
of Atomic and
Molecular
Processes
Introducing the ATOM-M Software Suite
Springer Series on Atomic, Optical, and Plasma
Physics
Volume 117
Editor-in-Chief
GordonW.F.Drake,DepartmentofPhysics,UniversityofWindsor,Windsor,ON,
Canada
SeriesEditors
JamesBabb,Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA,USA
AndreD.Bandrauk,FacultédesSciences,UniversitédeSherbrooke,Sherbrooke,
QC,Canada
KlausBartschat,DepartmentofPhysicsandAstronomy,DrakeUniversity,
DesMoines,IA,USA
CharlesJ.Joachain,FacultyofScience,UniversitéLibreBruxelles,Bruxelles,
Belgium
MichaelKeidar,SchoolofEngineeringandAppliedScience,GeorgeWashington
University,Washington,DC,USA
PeterLambropoulos,FORTH,UniversityofCrete,Iraklion,Crete,Greece
GerdLeuchs,InstitutfürTheoretischePhysikI,UniversitätErlangen-Nürnberg,
Erlangen,Germany
AlexanderVelikovich,PlasmaPhysicsDivision,UnitedStatesNavalResearch
Laboratory,Washington,DC,USA
The Springer Series on Atomic, Optical, and Plasma Physics covers in a
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new developments in the field, such as quantum computation and Bose-Einstein
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undergraduate textbooks and the research literature with emphasis on the
fundamentalideas,methods,techniques,andresultsinthefield.
Moreinformationaboutthisseriesathttp://www.springer.com/series/411
·
Miron Ya. Amusia Larissa V. Chernysheva
Computation of Atomic
and Molecular Processes
Introducing the ATOM-M Software Suite
MironYa.Amusia LarissaV.Chernysheva
RacahInstituteofPhysics IoffeInstitute
HebrewUniversity St.Petersburg,Russia
Jerusalem,Israel
ISSN1615-5653 ISSN2197-6791 (electronic)
SpringerSeriesonAtomic,Optical,andPlasmaPhysics
ISBN978-3-030-85142-2 ISBN978-3-030-85143-9 (eBook)
https://doi.org/10.1007/978-3-030-85143-9
Translation from the Russian language edition: ATOM_M, Algoritmy i programmy dl(cid:2)
issledovani(cid:2)atomnyhimolekul(cid:2)rnyhprocessovbyMironYa.Amusia,andLarissaV.Cherny-
sheva,©Sankt-Peterburg«Nauka»2016.PublishedbySankt-Peterburg«Nauka».AllRights
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Preface
Thisbookisdevotedtonumericalmethodsforstudyingthestructureoftheelectron
shellsofatomsanddiatomicmoleculesandtheirinteractionwithvariousparticles—
electrons,positrons,photons,mesons.
Therearetworeasonswhytheproblemsconsideredhereareofsignificantinterest
to scientists and engineers. First, atoms are the main element of various natural
formations,fromhugedistantstarstothesmallestbiologicalandchemicalobjects—
molecules.Thephotonsemittedbyexcitedatomsandmoleculesareasourceofvery
important, if not unique data that carry information about the structure of various
objects, as well as the state and structure of the substance that forms them. The
spectrumofatomicradiationmakesitpossibletodetermine,forexample,whether
a given atom included in the substance under study is neutral or ionized and how
manyelectronsareremovedfromitoraddedtoitduringtheformationofachemical
compound.Thespectraandprobabilitiesofphotoionization(i.e.,theremovalofan
electron from an atom by a photon) are not even a business card, but fingerprints
that allow us to unambiguously identify one or another type of atom or ion in a
polyatomicmoleculeorinamorecomplexobjectunderstudy.
Second,theinteractionoffluxesofdifferentparticlesoflight,i.e.,photonswith
atoms and simplest molecules, is a widespread natural process. Our entire planet,
its atmosphere, is constantly bombarded by streams of cosmic rays, irradiated by
sunlight.And,itisveryimportantfromthepointofviewoflifeitselftoknowhow,
andwithwhatprobability,thisradiationinteractswithatomsandmoleculesofthe
atmosphere, to what extent the radiation passes through almost unchanged, and to
what extent it leads to excitation or ionization of atoms or molecules. Sometimes,
knowingthesefeaturesiscrucial.Forexample,theformationofaheatbalanceonthe
Earth’ssurface,theabilitytoestablishthereasonsforchangesinitstemperature,if
any,isimpossiblewithoutdetailedknowledgeofthecrosssectionsfortheabsorption
ofphotonsbynitrogen,oxygen,andcarbonatomsandmolecules,primarilycarbon
dioxide,ofwhichtheyareconstructed.
There is also great interest in the study of electron interaction processes for
studyingthestructureofatoms(ions),aswellasmoleculesandsolids.Recallthatthe
flowoffastelectronsinteractingwithaspeciallyselectedsolidisthephysicalbasis
v
vi Preface
of an X-ray tube, a kinescope, and a number of other modern electronic devices.
Lasertechnologyalsosignificantlydemandstheknowledgeofthestructureofatoms
and their interaction with electromagnetic radiation. Thoroughly investigating the
electronicstructureofmanyatomsandsimplemoleculesisalsoimpelledbythefact
that often the electron shells are a difficult to remove and by no means always a
usefulfactorthatinterfereswithourstudyoftheatomicverycore—itsnucleus.So,
inthestudyofelectronscattering,wishingtoobtaininformationaboutthenucleus
withahighdegreeofaccuracy,itisimportanttoknowwhatisintroducedbyatomic
electronsandwhatisintroducedbythenucleusitself.
Relatively recently, a new reason has arisen for a detailed study of the atomic
structure.Itturnedoutthattheforcesofinteractionbetweenelectrons,aswellasthe
forcesofinteractionofelectronswiththenucleus,have,alongwithanelectromag-
netic, an additive of different nature. Study of this small parity-violating additive
thatviolatestheequivalencebetween“left”and“right”inourworldrequiresavery
accurateaccountofmuchstrongereffectsofanelectromagneticnature.
Thecomplexityoftheobjectofresearch—theelectronshellofatoms—makesit
necessarytouseintheirstudythecapabilitiesofmoderncomputers,whichnaturally
implies the creation of appropriate numerical models. The simplest molecules are
ofinterest,sincetheirstudy,incomparisonwiththeirconstituentatoms,showsthe
mutual influence of electrons, mainly under the influence of different centers of
attraction.
This book presents numerical methods for solving a wide range of problems
in atomic physics associated with both the structure of the atom and the simplest
molecules,andwiththeirinteractionwiththeelectromagneticfield,electrons,and
otherparticles.TheATOM-Msoftwarepackagediscussedindetailhereisasoftware
systemforautomatingatomicandmolecularcalculationsbasedontheachievements
ofthewell-knownATOMsystemanddevelopingit.TheATOMsystemwasthefirst
to consistently implement numerical methods in the physics of atomic processes
andhasbeenwidelyusedformorethan50yearsfortheoreticalresearchinatomic
physicsandrelatedfieldsofscience.Theprogramsinthesystemwerewritteninthe
ALGOL language, then in FORTRAN, which are widely used in many countries.
Therefore,theprogramsincludedintheATOM-Msystemcanbeeasilytransferred
fromonecomputersystemtoanother.
SincethepublicationofthebookMironYa.AmusiaandLarissaV.Chernysheva,
Computation of atomic processes (IOP Publishing Ltd, Bristol and Philadelphia,
1997),aconsiderabletimehaspassed.Asaresultofthedevelopmentofcomputer
technologyingeneralandthewidespreaduseofpersonalcomputersinparticular,it
becamenecessarytoreviseandradicallymodernizeanumberofexistingprograms
andcreatenewones.Methodsforcalculatingdiatomicmoleculeshavebeendevel-
oped, which required the creation of a number of programs based largely on the
ATOMsystem,andinmanyrespectsbeingitsdevelopment.Allthisledtotheneed
to write this book. Its continuity in relation to its predecessor will be reflected in
referencestoit,as[AC].
As the title of this book suggests, we will focus in it not on obtaining physical
results,butondevelopingalgorithmsandprogramsthatallowustostudyaverywide
Preface vii
range of processes of interaction of atoms and diatomic molecules with photons,
electrons,positrons,andmesons.Therefore,althoughphysicsplaysafundamentally
importantroleinunderstandingthestructureandpropertiesofatomsandmolecules,
inthisbook,itissubordinateandactsasasourceofvariousapproximationsusedand
thecorrespondingequations.Thejustificationfortheseapproximationsisoutsidethe
scopeofthisbook.
Our goal as authors is to teach the reader to calculate what he wants from the
varietyofprocessesthatarediscussedinthebook.Wehopetohelpalsointhecase
whentheprocessisnotdirectlydiscussed,butcanbeconsideredinthesamewayas
wehavedoneinothercases.
Weoffertheuserofourprogramsanumberofapproximations,describingqual-
itativelytheirfoundations,advantages,anddifficulties,butweleaveittothereader
to choose what and how to do. In this sense, this book is a user’s guide and not a
detaileddescriptionofvariousproblemsofatomicandmolecularphysics.Itisnot
ourtasktodiscussandshowbywhatandwhyoneapproachisbetterthananother
in describing many processes: the Hartree–Fock method, perturbation theory, the
random phases approximation with exchange, or something else. However, we do
nothideourpreferencesandgivereasonsintheirfavor.
All necessary references for understanding the physical approaches used are
presentedinthebook.However,thisbookisbynomeansatextbookonthephysicsof
atomsandmoleculesandprocesseswiththeirparticipation.Thisbookaimstoshow
howtoapplynumericalmethodsinordertofindwithgoodaccuracymanydifferent
characteristics of atoms, molecules, and processes with their participation. To a
certainextent,webelievethatthereaderhimselfknowswhathereallyneeds:from
textbooks,personalexperience,recommendationsofcolleagues,scientificadvisor,
recommendationfromamanager,etc.
Asinourpreviousbook[AC],thegoalistocreateaunifiedsetofcomputational
programsthatallowtheresearcherhimself,evenonapersonalcomputer,tocalculate
a large number of characteristics of atomic and molecular processes. A distinctive
featureofourapproachisthecreationofasinglecomplexofprogramsthatallowsfor
sequentialexpansionanddevelopmentastasksbecomemorecomplexandcompu-
tationalcapabilitiesincrease.Forexample,itisalreadyeasytoforeseethatnotonly
sphericallysymmetricandaxiallysymmetricatomsandmolecules,butalsoarbitrary
three-dimensionalmoleculeswillsoonbecomeobjectsofstudyusingcomputational
programssimilartothosedescribedinthisbook.
Interestincomputationsisgreat,andcreatingaseparateprogramforonespecific,
evenrelativelysimpletaskisnotjustadifficultandtime-consumingjobforanon-
specialistinprogramming.Sucha"handicraft"program,inevitablyusingtheresults
obtained with the help of programs made by others, can and often lead to a large
computational error due to two or more accounting for the same effects. That is
why it is advisable to use the ATOM-M complex, which contains the entire set of
programsnecessaryuptoacertainlevel.Furthercomplicationandexpansionshould
becarriedoutonthebasisofthiscomplex.
Thereisoftenabeliefamongphysicists,whichweconsideradelusion,thatevery
theoretician can and should create the programs he needs. At the same time, they
viii Preface
proceed from the assumption that the programming technique is simple and quite
accessible to every theoretician. As a result, apart from our book [AC], which is
alreadyoutdated,therearenomorebooksdevotedspecificallytocalculations.And
theneedforthem,asthefateof[AC]hasshown,isgreat.
Letusnoteasignificantdifferenceinthemethodsofcomputationalandtheoretical
physics. The latter are based, as a rule, on the presence of a small parameter that
permitstopresentthecharacteristicsofinterestintheformofaseriesinthepowersof
thisparameter.However,inmostcases,inbothatomicandmolecularphysics,there
isnoclearlyvisibleparameter.Therefore,itisimpossibletojustifytheapplication
of this or that physical approximation a priori. The use of machine computation
onalargescalemakesitpossibletotesttheapplicabilityofthephysicalmethoda
posterioridemonstratinggoodagreement,ifany,betweenthecalculatedresultsand
experimentaldata,andsometimesevenpredictingthem.
Fortheexperimentator,asarule,itisdesirabletohavenottoocrudecalculated
results already before the experiment in order to simplify and refine its planning.
So, the need for the calculation of a given characteristic or process is constantly
increasing, as well as the requirement for the accuracy of such a calculation. As a
rule,thisscientistisinterestedinoneormorespecificprocesses.Thatiswhywetried
tomakethedifferentpartsofthebookasindependentaspossible.Itisunderstood
that the reader of the book will not necessarily study it all, from A to Z, but will
immediatelychoosewhatheneeds.
Webelieve,relying,amongotherthings,onourownvastexperience,thatthere
shouldbeacleardivisionofdutiesbetweenthetheoristandtheprogrammer.Thetask
ofatheoreticalphysicististoselectanobjectofresearch,atheoreticalmodelofits
description,andanassessmentofthelikelihoodofthecalculatedresult.Thetaskof
theprogrammeristofindtheavailableandtodevelopnewalgorithmsandprograms
necessary for solving the problem. Of course, the programmer, who often leads
several theoretical problems at the same time, closely interacts with the physicists
whosettheseproblems.Thisapproachhasmadeitpossibletoconductmanyhundreds
ofstudiesthathaveagoodreputationamongspecialistsallovertheworld.Inthis
book,someoftheresultsobtainedwillbepresentedasanillustrationofthedeveloped
methods.
Theinterestinthealgorithmsandprogramsdiscussedinthisbookisdetermined
bythefactthattheconsideredcharacteristicsofatomicandmolecularprocessescan
inmanycasesbecalculatedwithveryhighaccuracyandreliability.Atthesametime,
thisbookisnotatextbookeitheronthephysicsoftheprocessesunderconsideration
orontheprogrammingofmathematicalformulasforcalculatingthecharacteristics
oftheseprocesses.Therefore,thetheoreticaldescriptionofeachprocessconsidered
inthebookisbriefandincludesonlytheformulationofthemainideasunderlying
the methods used, as well as key formulas, which then become the object for the
developmentofcomputationalprograms.Asfortheprograms,onlythemainideas
of their creation and the formation of the input database are given. The Appendix
tothisbookcontainsproperreferencetoSpringerdatabasethatdirectthereaderto
working versions of all programs and test cases, as well as gives explanations for
enteringtheinitialdataforthecalculation.
Preface ix
We assume that this book will be useful to very many people, from qualified
specialiststostudents,theorists,andexperimentators,toallthosewhoareinterested
inatomicandmolecularcalculations,aswellasinotherareas,forexamplenuclear
physics,wherethemethodsdevelopedinthisbookcanbeapplied.
Entirely,wewillpresentinthisbookalotofcomputationalprogramsforvarious
physicalprocesses,almostallassociatedwiththeinteractionofatomsandionswith
photons, electrons, and positrons and also consider the probabilities of decay of
atomicvacancies.Formostoftheseprocesses,wepresentthenecessarycomputa-
tional programs that make it possible to carry out calculations in the one-electron
Hartree–Fock (HF) approximation and taking into account many-electron correla-
tionsintheframeworkoftherandom-phaseapproximationwithexchange(RPAE)
ormany-bodyperturbationtheory(MBPT).
As reference books on quantum mechanics and electrodynamics in describing
the structure of atoms and processes with their participation, we will use the
followingtwofundamentalagelessguides—books:L.D.LandauandE.M.Lifshits,
Quantum Mechanics. Nonrelativistic Theory (Pergamon Press, Oxford, 1977) and
V. B. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Quantum Electrodynamics
(Butterworth-Heinemann,Oxford,1982).Asareferencebookoncomputing,wewill
useS.BerezinandN.P.Zhidkov,ComputingMethods.VolumeIand II.(Pergamon
Press,Oxford—London—Edinburgh—NewYork—Paris—Frankfurt,1965).
Whencalculatingatomiccharacteristicsandscatteringcrosssections,theradial,
angular,andspinvariablesareusuallyseparatedandtheintegrationovertheangular
variables and the summation over the spin projections are performed analytically.
As a guide for these actions, one can even now use the ageless book by I. I.
Sobel’man,Introductiontothetheoryofatomicspectra(PergamonPress,Oxford,
1972).Furtherreferencestoallthesesourceswillbegivenas[LL],[BLP],[BZ],and
[IS],respectively.
Thereissignificantoverlap,especiallyinnotations,diagramsthatrepresentphys-
ical processes, and in the presentation of the mathematical formulas used in this
book,withpreviouspublications:M.Ya.Amusia,AtomicPhotoeffect(PlenumPress,
NewYorkandLondon,1990),M.Ya.AmusiaandL.V.Chernysheva,Computation
of atomic processes (IOP Publishing Ltd., Bristol and Philadelphia, 1997), and
M. Ya. Amusia, L. V. Chernysheva, and V. G. Yarzhemsky, Handbook of theoret-
icalAtomicPhysics,Dataforphotonabsorption,electronscattering,andvacancies
decay (Springer, Berlin, 2012). References to these books willbe given as [AM],
[AC],and[ACY].Amuchshorterinitialversionof[ACY]waspublishedinRussian
as M. Ya. Amusia, L. V. Chernysheva, and V. G. Yarzhemsky, Photon absorption,
electronscattering,vacanciesdecay(Nauka,Saint-Petersburgbranch,St.Petersburg,
2010)[ACYr].
Throughout the book, we use the so-called atomic system of units, assuming
Planck’sconstantè,electronchargee,anditsmassmtobeequalto1,sinceotherwise
formulas,calculations,andexpressionswillbeoverloadedwithdifferentpowersof
è, m, i e. When passing to the SI system of units, the following numerical values
of the charge and mass of the electron are used: e = 1.6·10−19C, m = 9108·10−31
kg, as well as the relationship of the basic SI units with atomic units: length a =
0