Chaos and Correlation

Transcription

1 Chaos ad Colatio May, Chaos ad Colatio Itatioal Joual, Mayl, Ядерные оболочки и периодический закон Менделеева Nucli shlls ad piodic tds Alxad P. Tuv (Tooto, Caada) Alxad P. Tuv На основе теории ядерных взаимодействий и данных по энергии связи нуклонов для для известных нуклидов установлены параметры, характеризующие периодические закономерности в формировании ядерных оболочек. Ключевые слова: изотопы, изотоны, нейтрон, периодический закон, протон, ядро, ядерная оболочка. Paamts dscibi piodic tds i th fomatio of ucla shlls hav b stablishd basd o th thoy of ucla itactios ad data o th bidi y of uclos fo st of ow uclids. Kywods: Isotops, Isotos, Nuto, Nucli, Nucli Shll, Piodic Tds, Poto. Itoductio Th piodic law discovd by Mdlv i 869, playd a hu ol i th dvlopmt of idas about th stuctu of matt. I o of th fist fomulatios of this law stats that "th poptis of simpl bodis, as wll as th shap ad poptis of th compouds of th lmts, ad thfo th poptis of which thy fom simpl ad complx bodis a i th piodic tabl accodi to thi atomic wiht" []. Usi this law, Mdlv catd th piodic tabl of lmts, but also pdictd w lmts (th mod am of ths lmts - allium, scadium, maium, ad astati), which w lat discovd. Nowadays iitial fomulatio of th piodic law has udo siificat cha, i accodac with a cha i idas about th stuctu of atoms of chmical lmts. I th mod fomulatio poposd by Atoius Va d Bo [] i 9, this law stats that "th poptis of simpl substacs, as wll 5_.pdf

2 Chaos ad Colatio May, as th shap ad poptis of th compouds of th lmts a i piodic dpdc o th chas of th ucli of atoms of lmts." Not that this fomulatio is dictly latd to th modl of th atom, which aos du to th xpimtal discovy of Ruthfod [3] ad his studt Mosly [4]. I this modl, th atom cosists of a ctal, positivly chad uclus ad lcto shlls. Th ul of lcto shlls filld, which is fomulatd by Pauli i 95, bcam th basis fo w itptatios of th piodic law. I th mod piodic tabl of chmical lmts mad t, alo with th atomic wiht ad atomic umb, th cofiuatio of th oud stat ad th ioizatio y - Tabl. Tabl : A famt of th piodic tabl of chmical lmts accodi to [5] Elmt Th cofiuatio of th oud-stat Goud stat Ioizatio y, V 78 Pt [X] 4f 4 5d 9 6s 3 D 3 8, Au [X] 4f 4 8 H [X] 4f 4 5d 6s S / 9,55 5d 6s S, Tl [X] 4f 4 5d 6s 6p P o / 6,8 8 Pb [X] 4 4f 83 Bi [X] 4 4f 84 Po [X] 4 4f 85 At [X] 4 4f 5d 6s 6p 3 P 7,467 5d 6s 6p 3 4 S o 3/ 7,855 5d 6s 6p 4 3 P 8,44 5d 6s 6p 5 P o 3/ 9,5 86 R [X] 4 4f 5d 6s 6p 6 S, F [R] 7s S / 4,77 88 Ra [R] 7s S 5, Ac [R] 6d 7s D 3/ 5,387 9 Th [R] 6d 7s 3 F 6,367 At fist lac, th two fomulatios of th piodic law quivalt, i ay cas, if w assum that th atomic wiht ad cha of th uclus a lid mootoic dpdc. Howv, th psc of isotops claly violats this 5_.pdf

3 Chaos ad Colatio May, quivalc, as th co of isotops of o lmt a difft umbs of utos, with a qual umb of potos, i.. isotops hav difft atomic wiht of a qual cha of th uclus. Cosqutly, th masss of isotops of o lmt diff fom ach oth, that should hav b, bcaus of th piodic law of Mdlv's oiial itptatio, affct thi chmical poptis. But this is i cotadictio with th quatum thoy, i which it is assumd that th stuctu of lcto shlls dpds o th ucla cha oly. Th qustio aiss, what xactly th popty of atomic ucli is maifstd i th piodic law? This qustio ca b fomulatd i vy al tms. Fo this w cosid th atomic uclus, cosisti, accodi to th hypothsis Ivao [6] ad Hisb [7], of N utos ad potos. Th total umb of uclos is dotd A N. This uclus has a lctic cha, ad its mass is xpssd as M A mp mn Eb / c, wh - b E is th bidi y of th uclos i th uclus. Assum that th poptis of matt, o of which is dotd P A, a dfid accodi to th law of Mdlv. I this cas w hav th dpdc P ( ) A PA M A () Not that th dpdc () is mpiical o. It was obtaid by may xpimts i chmisty fo a ctuy. If you us a mod fomulatio of th piodic law, th th popty will also dscib th dpdc of th typ P A PA () () Dpdc () is also mpiical. It is basd o wll-ow law Mosly [4] fo th X-ay spcta of atoms ad umous oth typs of piodic tds dpdi o th ioizatio y of th atomic umb - Fi.. I thoy, ths piodic patts a xplaid, maily, th ul of filli of lcto shlls, which is divd fom Schödi quatum mchaics, ad Pauli picipl. Ivao [8], appatly, was o of th fist who aisd th issu of xpasio of th piodic law to iclud th piodic patts a obsvd i 5_.pdf

4 Chaos ad Colatio May, atomic ucli ad som xotic fomatios, such as xotic atoms. H statd fom th thoy of atomic shlls [7, 9], which at that tim was xpici a piod of daw. Accodi to this thoy, th piodic patts i th ucli a xplaid by aaloy with th lcto shlls, th Pauli picipl, which is applid spaatly fo potos ad utos fill th ucla shlls. It is cla that with this xpasio of th piodic law of its oiial fomulatio () sms mo loical, sic th poptis of th ucli dpds ot oly o th umb of potos but also o th umb of utos. Howv, th xpssio () also has a wll-dfid aa of applicatio i th itptatio of th piodic poptis of chmical lmts. Th mai thi is that th poptis of ucli, ad poptis of atoms of chmical lmts du to th sam typ o th basis of quatum mchaics ad th Pauli picipl [8]. 3 5 Ei, V data [5]. Fi. : Th dpdc of th ioizatio y of th atomic umb of th Th ductio of th Mdlv s piodic law to th Pauli picipl ad quatum mchaics dos ot solv th poblm itslf th psc of piodic patts, but oly ducs it to a hypothtical dsciptio of th poblm of atomic 5_.pdf

5 Chaos ad Colatio May, ad ucla shlls. But ow th poblm of quatum-mchaical dsciptio of atomic shlls of may-lcto atoms is fa fom bi solvd. Fo xampl, th is o quatum-mchaical modl to calculat satisfactoy th ioizatio y of may-lcto atoms, show i Fi.. O th cotay, th thoy of Mills [], basd o classical lctodyamics ad lativistic mchaics, allows us to calculat th bidi y of may-lcto atoms up to lctos with vy hih accuacy - Tabl. Tabl : Th ioizatio y of som 9 ad -lcto atoms calculatd o th modl []. It was show that th Mills thoy [] ca b divd fom Lotz quatum lctodyamics [], obtaid by combii th Lotz classical lctodyamics ad th Kli-Godo quatio. Cosqutly, th Mills thoy dos ot cotadict quatum mchaics, spcially sic it uss th sam Pauli picipl ad hypothsis of th xistc of lctoic shlls, which a assumd to b ifiitly thi i th adial dictio. Th adii of th shlls a calculatd o th basis of th classical quatios of motio of th lcto, tai ito accout th quatum ffcts of spi ad aula momtum (h s a obvious coctio 5_.pdf

6 Chaos ad Colatio May, with Boh's thoy). Thus, th sults obtaid o th basis of th Mills thoy, cofim th hypothsis va d Bo of th dpdc of th poptis of odiay matt o th ucla cha i th fom (). W may otic that th piodic law i th oiial fomulatio of Mdlv is local, as lats poptis of simpl substacs with thi atomic wiht, which at th tim wh th law was fomulatd, was dtmid by wihi i th avitatioal fild of th Eath. Such a colatio poptis of substacs ad thi avitatioal poptis sm asoabl bcaus i macoscopic chmical xpimts, th ucla chas a ot obsvd. I this ss, th colatio poptis of simpl substacs with th cha of thi ucli i th fom () is somwhat abstact, v thouh this hypothsis ad allows you to aa th chmical lmts accodi to th cofiuatio of th atomic shlls - Tabl. But as show abov, th lcto shll of itslf is mo a thotical tha a al phomo, ad v its thotical dsciptio is ot uiqu, as vidcd by Mills thoy []. I additio, th wodi of th piodic law i th fom of () o () ivolvs oly th poptis of th ucli of lmts, but ot th poptis of lctos filli th lctoic shlls. Appatly, w caot au that th poptis of lctos i ay way affct th poptis of simpl substacs; othwis, ths poptis must b flctd i th wodi of th piodic law. I th pst wo is iv xtdd tatmt of th piodic law, combii both his statmts ito o that allows you to oaiz all th chmical lmts ad thi isotops i accodac with a st of quatum umbs chaactizi th ucla shlls. Fo this pupos w dvlopd th modl of ucla itactios [], basd o th fiv-dimsioal uifid thoy of avitatio ad lctomatism [3-4] ad th thoy of fudamtal itactios [5-6]. 5_.pdf

7 Chaos ad Colatio May, Dsciptio of th modl To asw th qustio about th fudamtal causs that lad to a law of piodicity i atu, cosid a al modl of atomic ucli ad atoms of matt []. I this modl, th poptis of matt a dtmid by th paamts of th mtic tso i 5-dimsioal spac, which dpd o a combiatio of cha ad avitatioal poptis of th ctal co i th fom H γ c, Q 3 4 γ M Ac / Q, ε / γ M A / c (3), a th avitatioal costat, th spd of liht ad cha of th uclus, spctivly. About th atu of th cha will b assumd that th souc is a lctic cha, but it ca b scd i vaious atual filds. Th mchaism of sci ad latd filds is discussd blow. I th cas of poto ad lcto paamts of th mtic tso (3) a pstd i Tabl 3. Tabl 3: Paamts of th mtic tso, /m ε max, m mi, m -,7363E-8 4,799488E-43 5,87E7,8799E-5 p,54395e-8,6878e-36 9,48E7,5347E-8 Not that th maximum scal max / i th cas of a lcto xcds th siz of th obsvabl uivs, whil this scal is about liht-yas fo potos. Th miimum is th scal mi ε / / mc cospods to th classical adius of a chad paticl, which i th cas of th poto ad th lcto is compaabl to th scal of wa ad ucla itactios. It is asy to s that th scod paamt of th modl (3) ts dictly ito th fomula of th piodic law i th fom of (). Combii th paamts, w fid th ucla cha Q ε 3/ c / γ. Cosqutly, th piodic law of th fom () ca also b xpssd thouh th paamts of th mtic tso (3). 5_.pdf

8 Chaos ad Colatio May, Th mtic tso ca b xpadd i th viciity of a massiv ct of avity i fiv-dimsioal spac i pows of th distac fom th souc x y z, i th fom paamt G i G i () ~ () ~ G G i i ()... (4) H th dot dots difftiatio with spct to th dimsiolss ~. Cosid th fom of th tso (4) that occus wh holdi th fist th tms i th xpasio of th mtic i th cas of ctal foc fild with th avitatioal pottial i th fom of Nwto. This choic of mtic is ustifid, pimaily bcaus of th spcifid buildi th suppositio picipl holds. Suppos x ct, x x, x 3 y, x 4 z, i this otatio w hav fo th squa of th itval i th 4-dimsioal spac: ds ( ϕ / c ) c dt ( ϕ / c )( dx dy dz ) γ M ϕ Assum that cofficits of th mtic i th fiv-dimsioal spac a chaactizd by a paamt ε G ) G () (this assumptio is quivalt to ( th classical latio btw th mass ad cha of a lcto). Th, assumi (5) that ε / γ M / c, w t th xpssio of th itval dpdi o th paamts of th mtic i th fiv-dimsioal spac: ds ( ε / ) c dt ( ε / )( dx dy dz ) (6) Futh, w ot that i this cas th mtic tso i fou dimsios is diaoal with compots ε / ; ( ε / ) (7) W dfi th vcto pottial of th souc associatd with th ct of avity i th fom u ε /, (8) 5_.pdf

9 Chaos ad Colatio May, H u is a vcto i th dimsioal spacs, which w dfi blow. Hc, w fid th scala ad vcto pottial of lctomatic fild Stti Q Mc ε ϕ, A ϕ u (9) η () ad valuati th mtic tso i 5-dimsioal spac, usi (7) - (8), w fid that i this cas, xpssio (4) cotais i th iht sid, oly th tms of th sis xpasio i pows of G i ~, thus ~ () ~ i i η Gi () G i G i () i () To dscib th motio of matt i th liht of its wav poptis, w assum that th stadad Hamilto-Jacobi quatio i th lativistic mchaics ad Kli-Godo quatio i quatum mchaics ais as a cosquc of th wav quatio i fiv-dimsioal spac [4, 6]. This quatio ca ally b witt as: G x µ GG µ ν x ν Ψ () H Ψ is th wav fuctio dscibi, accodi to (), th scala fild i fiv-dimsioal spac, ad i G is th cotavaiat mtic tso, G i η λ λ λ 3 λ 4 λ 3 4 () λ ( ε λ, / ) ; λ 3 λ, ( ε 3 / ) 4 λ, λ 4 λ λ η. 5 3 λ ( 3 4 ); G η /( ab ); ( ) W futh ot that i th ivstiatd mtics, dpdi oly o th adial coodiat, th followi latio is tu F µ µ ν d µ ν ( GG ) η ( GG ) η µ µ (3) x x d 5_.pdf

10 Chaos ad Colatio May, as Tai ito accout xpssios (), (3), w wit th wav quatio () λ Ψ Ψ i Ψ μ Ψ λ Ψ λ F i μ c t x x (4) 5 4 Not that th last tm i quatio (4) is of th odη < <. Cosqutly, this tm ca b doppd i th poblms, th chaactistic scal which is cosidably lss tha th maximum scal i Tabl. Equatio (4) is maabl i that it dos ot cotai ay paamts that chaactiz th scala fild. Th fild acquis a mass ad cha, ot oly lctic, but also sto i th pocss of itactio with th ctal body, which is du oly to th mtic of 5- dimsioal spac [, 6]. Cosid th poblm of th motio of matt aoud th chad ct of avity, which has a lctical ad sto cha, fo xampl, aoud th poto. I th pocss of solvi this poblm is cssay to dfi th itial mass of matt ad bidi y. Sic quatio (4) is lia ad homoous, this poblm ca b solvd i al. W itoduc a pola coodiat systm (, φ, z) with th z axis is dictd alo th vcto pottial (8), w put i quatio (4) Ψ ψ ( )xp( ilφ i z z iω t i ) (5) Spaati th vaiabls, w fid that th adial distibutio of matt is dscibd by th followi quatio (h w doppd, bcaus of its smallss, th last tm i quatio (4)): λ ω c ψ λ ψ l ψ ψ λ c zψ ψ ω ψ z z ψ (6) Cosid th solutios (6) i th cas wh o ca lct th ifluc of avity, i.. λ λ, but λ ( u ). Ud ths coditios, quatio (6) ducs to ω c ψ ψ l ψ ψ λ c zψ ψ ω ψ z z ψ (7) 5_.pdf

11 Chaos ad Colatio May, I al, th solutio of quatio (7) ca b pstd i th fom of pow sis, as i th aaloous poblm of xcitd stats of th lativistic hydo atom [7-8] a c ~ ~ ~ ) xp( ψ (8) It is idicatd / ~. Substituti (8) i quatio (7), w fid ) ~ ( ~ ~ ~ ) ( ~ ) ( ~ ) ( z u c c a c c K c a c l a κ κ (9) / ) ( u u ε κ, ) / / (, / > c u c K z z ω ε κ ω. Hc, quati cofficits of li pows / ~, w obtai th quatios lati th paamts of th modl i th cas of xcitd stats,, c a l a z u ω κ κ () Th scod quatio () holds oly fo valus of th xpot, fo which th iquality < a is tu. Hc, w fid a quatio fo dtmii th y lvls ) ( 4 c c u a z z z ω ω ε () Equatio () was usd to modl th bidi y of uclos i th uclus fo th ti st of ow uclids []. I th modl [], th uclus cosists of potos, itacti with a scala fild. Pat of th poto is scd by fomi N utos, as a sult th is a atom, cosisti of th lcto shll ad uclus with lctic cha, umb of uclos N A ad th mass 5_.pdf

12 Chaos ad Colatio May, M A A( mp m ) Ebp / c, wh bp E is th y of th uclos i th uclus, which is calculatd o th total umb of uclos, with a total mass of th lcto ad poto. Not that this xpssio of bidi y is ot sstial o, so w ca us stadad xpssio of th mass xcss i atomic uits. Sic i this poblm two typs of chas appa - scala ad vcto, th ffct of sci maifsts itslf ot oly with spct to th scala cha (which lads to th fomatio of utos), but also i tms of th vcto cha, which lads to th fomatio of th uclos. It should b otd that th oiial mtic i th fiv-dimsioal spac dfid by th mtic tso, which dpds oly o th paamts of th ctal body, i of th total cha ad total mass of th uclos. Dpdi o th combiatio of th cha ad mass of th uclus i difft shlls ca b fomd: ) Nuclo shll, i which all chas a scd, thfo - ε / A / Am p c A / m pc ; ) Nuto shll - ε / N / m pc ; 3) Poto shll - ε / / m pc. Usi th lcto mass ad Plac's costat, w dfi th dimsiolss paamts of th modl i th fom α, c S ( ) ( m c), P z, m c E ω m c b X l 4X ( α m / m ) () p ( l ( u ) SX ( α m / ) ) mp H X A, N,, i th cas of th uclo, uto ad poto shlls, spctivly. Solvi quatio () with spct to y, w fid 5_.pdf

13 Chaos ad Colatio May, X X X X Sbl Pu ± i ( Sbl Pu) ( Sbl )( S P Sbl P u ) X E l (3) X ( Sb ) l Not that th paamt i th y quatio (3) ca b both al ad complx valus, which cospod to stats with fiit liftim. Giv that fo most uclids th dcay tim is la ouh quatity, so it ca b assumd that th imaiay pat of th iht-had sid of quatio (3) is a small valu, which cospods to a small valu of th adicad. Hc w fid that fo ths stats th followi latio btw th paamts Substituti (4) i quatio (3), w hav P X S( Sbl ) X (4) Sb ( u ) l E X l 3 / X S bl u X X (5) ( Sb )( Sb ( u )) l l Hc, w fid th dpdc of th bidi y p uclo i th oud stat E X a 3 / S bux / A / A (6) ( Sb X )( Sb X ( u )) It is idicatd b )) (α m / mp ( a. Thus, w hav stablishd a li btw th y of th stat ad paamts of th itactio. Not that th bidi y (5) dpds o th maitud of th vcto cha, which appas i quatios (8) - (9). As show blow, this dmostats th diffc btw th itactio of uclos i ucli, wh th vcto cha paamt u, ad th itactio btw lctos ad atomic ucli, i which u. Nucla shlls ad th bidi y of uclos Fo th bst amt with th data modl [9] i th cas of th uclo shll, put i th quatio (6): X A, S 93; Sb.3; u Equatio (6) ca appoximatly dscib th dpdc of th bidi y of th umb of uclos fo all uclids Fiu. Fo liht ucli, th is a 5_.pdf

14 Chaos ad Colatio May, siificat discpacy with xpimt. This is du both to th psc of two oth shlls, ad th fact that th stuctu of liht ucli is laly dpdt o th dtails of th itactio. I paticula, paamts S, b, u a ot costat, as show blow. I this ad, w ot that i thoy [4], th actio i th fiv-dimsioal spac ca b pstd as Σ 5 mcx Σ (x,x,x,x ). Cosqutly, th wav vcto i th fifth dimsio cospods to th mass ad th omalizd vcto - th umb of uit mass. Th calculatd valu S 93 fo th cuv i Fiu, pobably cospods to th lmt with th hihst atomic umb 93 Ei accodi to [9]. 5 Eb/Amc Data [9] Eq. (6) - A Fiu : Th bidi y p uclo as a fuctio of mass umb accodi to [9] ad calculatd accodi to quatio (6). Th ava valu of matic cha u idicats a hih d of colatio of th uclos i th uclus. Th sulti valu of th itactio paamt b -8 ( m / mp ( a)) 3.5 α ivs th ava valu of th aula momt ± l a _.pdf

15 Chaos ad Colatio May, Th oud stat y of th uto shll is dtmid by quatio (5), i which w st X N. Th paamts of th uto shll do ot coicid with th paamts of th uclo shll, but vais fo ach lmt. Usi toth xpssios th bidi y of th uclo ad th uto shll w ca quit accuatly dscib th y of isotops Fiu 3. Th computatioal modl is costuctd as follows. Suppos that, basd o quatio (6) fo th uclo shll faild to accuatly dtmi th bidi y of o isotop of a lmt. Without loss of ality w ca assum that this isotop cotais th miimum umb of utos. Th th bidi y of all oth isotops of a lmt dfid as follows E( N, ) A A N N E a ( N mi, ) Ea ( N, ) Ea ( N mi, ) (7) N N N mi mi Modl (5) - (7) cotais th abitay choic of th itactio paamt, which dos ot dpd o th ucla cha. As a xampl, Tabl 3 shows th modl paamts, calculatd accodi to [9] fo isotops of old. Tabl 3: Paamts q. (5), (7) calculatd fo isotops of old. Sb u S 3/ b u -u Sb (-u ) S /,5,9936 3,6,759 6,38E-5 74,6377,5,9994,49, 6E-5 9,938,56, ,5,6 5,94E-5 67,9489, ,98 5,94E-5 5,94E-5 5,985 5, ,,9E-5 5,94E-5,84, ,4 5,94E-6 5,94E-5 6,45 I cotast, th paamt Sb ( u ) p( ) is almost costat fo a iv lmt, but it dpds o th maitud of th cha. This dpdc is mootoous - th itactio paamt dcass with icasi cha. This sult idicats that th poto ad uto shll ucli itact with ach oth. Th oud stat y of th poto shll is dtmid by quatio (5), i which w st X similaly to (7) with th placmt. Th computatioal modl i this cas is costuctd N. As a sult, w fid: 5_.pdf

16 Chaos ad Colatio May, E( N, ) A A E a ( mi, N) Ea (, N) Ea ( mi, N) (8) N N N mi mi Usi toth quatio (5) ad (8) w ca dtmi th bidi y of uclids with a iv umb of utos - Fiu 4. I this cas also th is abitaiss i th choic of th itactio paamt, which is pactically idpdt of th umb of utos of th uclus. As a xampl, Tabl 4 shows th modl paamts, calculatd accodi to [9] fo N. 7 6,5 6 5,5 Ebp/Am 5 4,5 4 Data [9] Eq. (5), (7) 3,5 3,5 K Ca Sc Ti V C M F Co Co Ni Cu Ga Ga G As As S A Fiu 3: Bidi y p uclo as a fuctio of mass umb calculatd fo a umb of isotops of chmical lmts o th modl (5), (7) ad accodi to [9]. 5_.pdf

17 Chaos ad Colatio May, Ebp/Am 5, 5 4,8 4,6 4,4 4, 4 3,8 N N N N N N N N N N N N N N N Data [9] Eq. (5), (8) Fiu 4: Bidi y p uclo as a fuctio of mass umb calculatd fo N,, o th modl (5), (7) ad accodi to [9]. Tabl 4: Paamts q. (5), (8) calculatd fo N. Sb u S 3/ b u -u Sb (-u ) S /,,984 9,385,335,34 944,5,997 45,5454,579,9 93,5,, ,395,898,9 64,5, ,567,58,9 7,, ,377,88,88 96,4, ,6,44,88 38,59 3, ,567 9,6E-5,88 3,9 6, ,385 4,8E-5,88 79,89, ,693,9E-5,9 6,7 Th qustio aiss, what mod of itactio is alizd i atomic ucli - with a la o small valu of th paamt of itactio Sb? To asw this 5_.pdf

18 Chaos ad Colatio May, qustio, w calculat th chaactistic scal appai i th quatios (). Solvi th thid quatio () with spct to siz, w fid fom (4) - (5) that m c P S E Sb m ce X l m cp u u z (9) I Fi. 5 shows th stadad ucli siz ad modl scal fo th isotops of old. Ths data imply that th modl scal fo old will b cosistt with th al siz of ucli at Sb. Th stadad siz of th ucli dpds o th umb of uclos [8, ]: /3 5 ( A) A, (..4) m. A A Cosqutly, th poto shll is implmtd with th valu of th itactio paamt Sb. It was foud that th obital aula momtum has a valu clos to ½ fo Sb - Tabl 5. Thus, th iitial scala fild acquis th cha ad mass, ad spi, li fmios, which claifis th atu of th lcto spi. Tabl 5: Paamts of quatio (6), calculatd fo som isotos. N Sb u S / f(n) a L,8 5,36,499583, ,95 67,44375,499734, ,964 55,9,774,499778, ,979 5,8,4559,499798,499798,994 69,4,566,49974,49974,998 84,9,3796,499663, , ,598,49964, ,99937,6,499559, , ,5,9,49958, , ,5,688,49955, ,9997 3,56,499479, , ,48,499388, ,9998 4,4,49944,49944, ,3,49935,499354, ,54,49934, , ,46,49965, , ,88,4995, _.pdf

19 Chaos ad Colatio May,,5E-4 (A), m E-4,5E-4 E-4 5E-5 (A) (A) Sb5 Sb Sb.56 Sb A Fiu 5: Gold ucli isotop adius ad th chaactistic scal of th modl as fuctio of mass umb.,,,, y,698x 59,483 R, N y,4438x -,56 R,9937 f(n) S^/ Линейны й (S^/) Степенн ой (f(n)) Fiu 6: Itactio paamt f ( N) Sb ( u ) ad paamt S / / m c chaactizi th motio of matt i th fifth dimsio as a fuctio of umb of utos at Sb. 5_.pdf

20 Chaos ad Colatio May, Not that i th cas of Sb a paamt chaactizi th itactio of th matic typ, Sb ( u ) f ( ) dcass mootoically with icasi N umbs of utos by a pow law, ad a paamt S / / m c chaactizi th motio of matt i th fifth dimsio, almost lialy dpdt o th umb of utos - Fi. 6. W hav show that th ucla shlls, cosisti of uclos, utos ad potos, spctivly, allow modlli th bidi y as a fuctio of uto, poto ad mass umb. Data show i Fiu 6, ad Tabl 5, idicat that th poto shll itacts with th uto shll. Th qustio aiss which of th ucla shll mo siificat ffcts o th poptis of atomic ucli ad chmical lmts? Th uto ad poto shll ca qually b usd to modl th bidi y, ad it is cosistt with th picipl of isotopic symmty of ucla focs. Howv, th lcto shlls dpd o th umb of poto ucli, which implis that th poto shll has a at ifluc o th atomic scal, ath tha a uto shll. This sult is compatibl with mod fomulatio of th piodic law i th fom (). Elcto shll W cosid th al xpssio of y (3) i th cas of th poto shll, ad subct to full sci of matic cha, i.. put i th iht-had sid of (3) X, u. Th sult is ± ( Sbl )( P S) E l, ( Sb ) l b l 4 ( α m / m ) (3) p ( l S ( α m / ) ) mp O th oth had, i th cas of hydo atom th is th Sommfld- Diac fomula fo th y of a lativistic lcto [7-8, ] 5_.pdf

21 Chaos ad Colatio May, ) ( m c E α α φ (3) Compai (3) ad (3), w fid that fo amt of ths fomulas should b put l m m S S P E p l > φ, ) / (, ) / (,, (3) Not that a diffc i a si of th adical l α aiss du to th choic of th si of th paamt i th xpssio of th wav fuctio (8), wh i al cas, w should put u l a κ ±. I th ucli stuctu poblm w hav chos a positiv si, whas fo atomic shlls ta ativ si. I th latt cas w fid fom (3) that th fist quatio (3) coicids with th Sommfld-Diac quatio (3): ) ( m c E E l α α φ (33) Thus, w hav show that th xpssio (3) is uivsal o. I th io u this xpssio dscibs th y of th uclos i th ucli, whil at th coditio u it dscibs th y of lativistic lctos i atomic shlls. Th is a spcial cas of stats of th hydo atom - hydio [, 7-8], which is also dscibd by (3). Th fist tms i th xpasio of (33) i pows of small paamt ) ( < < α dscibi th y lvls of hydo atoms, icludi hydo, i this cas w hav [] ( ) ( ) l m c E E φ φ φ φ α α 4 3 ) (... (34) Equatio (34) dscibs th X-tms, th quadatic dpdc o th ucla cha has b dtmid xpimtally by Mosly [4], which svd 5_.pdf

22 Chaos ad Colatio May, as th basis fo th catio of quatum mchaics ad mod fom of th piodic law. Not that th al xpssio (3) cotais f paamts, which i mod quatum thoy ta th paticula valus of (3). Giv ths valus, w fid that th xpssio (33) dscibs ot oly th y of th boud stats of a lcto i a hydo atom (34), but th y of a f lcto du to its st mass. Equatio () dscibs th motio of a scala fild, which dos ot possss, o cha o mass o spi. Cosqutly, w hav show that th lcto st mass, its cha ad spi motio du to a scala masslss fild i th fivdimsioal spac with a spcial mtic (), dpdi o th cha ad mass of th ctal co. Nucla shll ad piodic tds Cutly, th a at last 473 vsios of th piodic tabl []. A mod id of piodic tabl with uclids i th pla (N, ) icludd basic poptis of ucli [6]: ) Spi ad paity J π ; ) Mass xcss M A A calculatd with spct to isotop C; 3) Half-lif, o width, ad abudac of a lmt i atu (%); 4) Dcay mod. Not, th piodic tabl ca b lid to ifomatio thoy [3-4] basd o a ida of chaos ad od, topy ad ifomatio coctd with complxity of th obct, which is dfid as th miimum lth of aloithmic poams dd to t som Y of X [5]. I this ad, w ot that i this thoy, a aloithm fo obtaii th atomic y lvls is o difft fom th aloithm of obtaii th y lvls of th uclus. Cosqutly, it is assumd that a atom is aad ot mo complicatd tha uclus ad a uclus is o mo complx tha a atom. 5_.pdf

23 Chaos ad Colatio May, Usi th thoy dvlopd abov, w ca dtmi th od of lmts ad isotops, all of thm, cosidi both th pocss of filli of poto ad lcto shlls. Th icas i ucla cha by o poto lads to a cha i ucla mass ad bidi y of uclos ad lctos, which i tu lads to a cha i th chmical ad physical poptis of chmical lmts. As show i fiu 6 paamts of poto shll dpd o th umb of utos. Usi th quatio of th td fo th data i Fi. 6, w ca dtmi how to cha th paamts f ( N), S( N) with spct to th td li s Fius 7-8: Vf ( N) VS S /.56 f ( N)* N /.4438 ( N) /(.698N ) (38),5,5 VS Vf(N) Maic Numbs, N Fiu 7: Fluctuatios i th modl paamts (8) ov td lis:.56 Vf ( N) f ( N ) * N /.4438; VS S / /(.698 N ) Ths chas hav a cla piodic compot that allows to slct i th tabl of uclids thi ow piods. Ths piods ca b associatd with uto shll, which, accodi to th ucla shll modl [9], filld i th sam way as th filld lcto shlls. I such a cas should b allocatd th maic umbs, 8, 5_.pdf

24 Chaos ad Colatio May,, 8, 5, 8, 6, 84. Idd, accodi to Fi. 7, w ca idtify piods associatd with th filli of shlls with uto umb btw ad 8, 5 ad 8, 8 ad 6, 6 ad 7, which cospods to th d, 6 th, 7 th ad ihth shll. Maic umbs ca b compad with th sam poits i th cuvs i Fiu 7. Th lvat data a collctd i Tabl 7. Ths umbs do ot match xactly th maic umbs, althouh thy a clos to thm. Tabl 7: Numb of utos cospodi to maximal ad miimal valus of paamts (38) ad maic umbs. VSmax VSmi Vfmax, Vfmi Maic umbs, 8, 8, ,5,5 VS Vf(N) Maic Numbs, N Fiu 8: Fluctuatios i th modl paamts (8) ov td lis i th cas of liht ucli. 5_.pdf

25 Chaos ad Colatio May, Thfo w ca sust that piodic poptis of chmical lmts dpd o th umb of potos (cha), ad o th umb of utos (mass) as wll i accodi with oiial Mdlv's piodic law. Fially ot, that stadad thoy of ucla shll [9] i which th actual motio of th uclos i th uclus calculatd o th modl of a quatum hamoic oscillato, is cosistt with this thoy, i which th motio of uclos is calculatd o q. (). Howv, fo liht ucli, th is a discpacy that ca b s fom th data show i Fi. 8. W ca assum that i th cas of thid, fouth, ad fifth shll piodic law is mo complicatd tha that pdictd by th stadad thoy of ucla shlls. Autho xpsss his atitud to Pofsso V.D. Dzhuushaliv ad Pofsso E.V. Lutso fo usful discussios. Rfcs. Менделеев Д. И., Периодический закон. Основные статьи. М.: Изд-во АН СССР, 958, с... Va d Bo. Th Numb of Possibl Elmts ad Mdléff's Cubic Piodic Systm// Natu 87 (77), E. Ruthfod. Th Scatti of α ad β Paticls by Matt ad th Stuctu of th Atom// Philosophical Maazi. Sis 6, vol.. May H. G. J. Mosly, M. A. THE HIGH FREQUENCY SPECTRA OF THE ELEMENTS// Phil. Ma., p. 4, W.C. Mati, A. Musov, S. Kotochiova, ad J.E. Sasotti (), Goud Lvls ad Ioizatio Eis fo th Nutal Atoms (vsio.3). [Oli] Availabl: [Wdsday, 8-Ma- 9:33:3 EDT]. Natioal Istitut of Stadads ad Tcholoy, Gaithsbu, MD. 6. Iwao, D.D. Th uto hypothsis// Natu, 9, 93, Гейзенберг В. Замечания к теории атомного ядра// УФН (), Иваненко Д.Д., Периодическая система химических элементов и атомное ядро // Д.И.Менделеев. Жизнь и труды, АН СССР, М., 957, с Maia Goppt-May. O Closd Shlls i Nucli/ DOE Tchical Rpot, Phys. Rv. Vol. 74; 948. II DOE Tchical Rpot, Phys. Rv. Vol. 75; 949. Mills, Radll L. (Ju 8). Th Gad Uifid Thoy of Classical Physics. Blacliht Pow. Alxad P. Tuv. Lotz quatum lctodyamics// Научный журнал КубГАУ [Электронный ресурс]. Краснодар: КубГАУ,. (75). С Режим доступа: P. Tuv. Th stuctu of atomic ucli i Kaluza-Kli thoy // Политематический сетевой электронный научный журнал Кубанского государственного аграрного университета (Научный журнал КубГАУ) [Электронный ресурс]. Краснодар: 5_.pdf

26 Chaos ad Colatio May, КубГАУ,. (76). С Режим доступа: 3. Kaluza, Thodo. um Uitätspoblm i d Physi. Sitzusb. Puss. Aad. Wiss. Bli. (Math. Phys.) 9: Ю. Б. Румер. Исследования по 5-оптике. М., Гостехиздат, с. 5. V. Dzhuushaliv (6 Dcmb 996). Multidimsioal Gomtical Modl of th Elctical ad SU() Colou Cha with Splitti off th Supplmtay Coodiats// 6. Трунев А.П. Фундаментальные взаимодействия в теории Калуцы-Клейна// Научный журнал КубГАУ. Краснодар: КубГАУ,. 7(7). С Режим доступа: 7. Naudts, Ja (5 Auust 5). O th hydio stat of th lativistic hydo atom. axiv:physics/ Domby, Noma (8 Auust 6). Th hydio ad oth ulily stats. Physics Ltts A 36: 6. axiv:physics/ Natioal Nucla Data Ct Wb Sit, Maslo Aloso, Edwad J. Fi. Fudamtal Uivsity Physics. III Quatum ad Statistical Physics. Addiso-Wsly Publishi Compay, Ландау Л.Д., Лифшиц Е.М. Теоретическая физика: Учебное пособие. В т. Т. IV/В.Б. Берестецкий, Е.М. Лифшиц, Л.П. Питаевский. Квантовая электродинамика. 3-е изд., испр. М.: Наука, Гл. Ред. Физ.-мат. Лит., 989, - 78 с.. Th INTERNET Databas of Piodic Tabls, 3. Луценко Е.В. Универсальный информационный вариационный принцип развития систем / Е.В. Луценко // Политематический сетевой электронный научный журнал Кубанского государственного аграрного университета (Научный журнал КубГАУ) [Электронный ресурс]. Краснодар: КубГАУ, 8. 7(4). С Шифр Информрегистра: 48\9. Режим доступа: 4,8 у.п.л. 4. Вяткин В.Б. Информационно-синергетический анализ электронных систем атомов химических элементов.часть. Структурная организация электронных систем в плоскости подоболочек / В.Б. Вяткин // Политематический сетевой электронный научный журнал Кубанского государственного аграрного университета (Научный журнал КубГАУ) [Электронный ресурс]. Краснодар: КубГАУ, 9. 4(48). С Шифр Информрегистра: 49\36. Режим доступа: у.п.л. 5. А.Н. Колмогоров. Алгоритм, информация, сложность. Москва, «Знание», JAGDISH K. TULI. NUCLEAR WALLET CARDS (Svth ditio). Apil 5, NATIONAL NUCLEAR DATA CENTER, 5_.pdf