Computation of Atomic and Molecular Processes - Introducing the ATOM-M Software Suite PDF
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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 comprehensive manner theory and experiment in the entire field of atoms and moleculesandtheirinteractionwithelectromagneticradiation.Booksintheseries providearichsourceofnewideasandtechniques withwideapplications infields such as chemistry, materials science, astrophysics, surface science, plasma technology, advanced optics, aeronomy, and engineering. Laser physics is a particular connecting theme that has provided much of the continuing impetus for new developments in the field, such as quantum computation and Bose-Einstein condensation. The purpose of the series is to cover the gap between standard 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 Reserved. ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2021 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsofreprinting,reuseofillustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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
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