1 of 42. Abbreviated title: [SAP-SVT-Nmsm-g & 137] - Updated on 31 July, 09. Shankar V.Narayanan

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1 1 of 4 ONE EQUATION ad FOUR Subatomic Particls ad thir FOUR Itractios icludig (g &17) factors with Spac Vortx Thory (A No matrial shll modl) (Part 1 of ) (Th cotts of this txt ar th sam as i Subatomic Particls Itractios ad thir FOUR itractios titl oly chagd i ordr to mak it mor xplicit) Abbrviatd titl: [SAP-SVT-Nmsm-g & 17] Corrspodig Author: V Shakar Narayaa - tolratsam@gmail.com Updatd o 1 July, 09 Shakar V.Narayaa Ky Words: 1) Nuclar Particls ) Wak Itractios ) Gravitatio 4) Ds Mattr, 5) Black Hol Physics 6) Elctro lctric dipol momt 7) Smi-classical mthod. 8) Corrctios to a boud lctro ( g factor). 9).Elmtary Particls Abstract This proposd dyamically stabl o- matrial shll modl is a atural outcom from (mass-rgy) to (fild rgy) quivalc for a spiig chargd particl that follows Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

2 of 4 by aalyzig a pair aihilatio procss ad corrlatio with may xprimtal fidigs ad obsrvatios by usig prov laws. I 190, Paul Dirac dvlopd a w vrsio of th Schrödigr Wav Equatio which was rlativistically ivariat, ad prdictd th magtic momt corrctly, ad at th sam tim tratd th lctro as a poit particl. Though Dr: Dirac dalt th lctro as a poit particl oly from a mathmatical tratmt poit of viw, it will b show hr its partial implicatio o uclo forcs ad furthr Ifiit gativ rgy o Gravitatio. Coicidtally th high rgy xprimts idicatig towards a poit particl for lctro is a clar misitrprtatio that is ladig us away from th sidlid classical Physics which may usd to udrstad. Hr agai it will b show why a lctro td to idicat smallr radius at highr ad highr rgis ad what is its tru o rlativistic radius is also show with xprimtal backig. This proposd modl is foud to rplac th prst mpirical formula for uclar siz, itroducs w prcis quatio for uclar pottial barrir, siz ad spacig btw uclos for vry idividual bidig rgy of lmts ad furthr it sms to provid a mor appropriat modl i plac of th prst quarks ad itrrlats all four particl itractios. Howvr may othr xprimtal fidigs hav hlpd i dirctig th dvlopmt of th modl spcially i fixig th uclo siz ad magtic momts- (g ad 17) factors, o utros i utro bta dcay ad hc this modl may b xpctd to prdict particl itractios i a largr prspctiv with a smi classical approach. All this is possibl with Spac Vortx cocpt with a slightly diffrt approach ivolvig simpl mathmatics ad a cospicuous approach ladig to highly accurat rsults although focusd maily o scholarly physicists is also slightly dtaild kpig i mid graduat studts ad itrdiscipliary participatio for furthr all roud for dvlopmt.. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

3 of 4 Classificatio Schm Nos. : PACS Nos (Dr) (1.90+f), (.40-S, Bw) (1.10.g) PACS: 1.0.Jp, 1.0.Js, 1.15xg, 0.0 +p. Itroductio Th ida, that th uivrsality of all mattr could b i [rgy- form] xists right from th first thought giv by th mit scitist Sir:J.J. Thomso ad othr scitists of his tim, ad o th basis of which, thy furthr argud that, thr caot b two kids of masss ad that all mass must b lctrical mass ad such a swpig gralizatio was too prmatur to b accptd at that tim [Though Eisti did ot rfut this thought h had oly isistd that v lctrical rgy mass should td to ifiity as particl vlocity approachs that of light i his Spcial Thory] Rvivig thir thoughts with th hlp of Spac Vortx Thory ad may cotributios mad by mit scitists ad xprimtr s so far, this basic modl procds from strog forc to magtic momts up to gravitatioal attractio ad furthr to rsolv som puzzls i currt physics with a smi classical approach. Summary of th compariso with Currt Physics Rfrcs quotd i th txt for g:-cmp-ab-9 implis [Cocpt of Modr Physics-By Arthur Bisr-Pag-9] Sl.N o Proprty/ Natur Fidigs i Modr physics thory / Exprimt As foud i this proposd thory Rfrc 1 Subatomic Poit particl Dyamically stabl CMP AB-78, Particls Sphrical zo cotaiig AP-JBR-70, 1068 gativ rgy & NP-NR-AK 54 Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

4 4 of 4 vlopd i a positiv NP-IK-64/414 lctric fild rgy shll. Subatomic Poit mass/poit Fiit siz/fiit fild CMP-AB- particl siz charg/ifiit fild itsity/dyamically stabl itsity Nuclar No prcis Drivd xprssio CMP-AB-406 Pottial xprssio NPNR-AK 94 rgy NP-IK 50 4 Valu of 1. fm [1.165 fm] at itrfac NPNR-AK-77 [Ro] Empirical drivd xprssio CMP-AB-89 5 Rag of Approx [1.7 fm] By [1.7 fm] for [0.8 MV to 5 CMP-AB-410 uclar Mso thory MV] with drivd forc xprssio. 6 Spacig Not prcisly Drivd xprssio btw kow from thory uclos i a uclus 7. Nuclar Not prcisly Slightly lss tha [0.7fm] NPNR-AK-96 itractio kow from thory from thory NP-IK-56 chag but Idicativ from AP-JBR-19 from xprimts of attractio about [0.5 fm] to rpulsio. 8. Siz of a Not prcisly About [0.5 fm] from uclos kow thory. 9. Rsoac [549 MV], [78 [549 MV], [78 MV] CMP-AB particls MV] from icludd withi th uclo xprimts for particl structur. msos. 10 Nuclo Agrs with Agrs with xprimts as AP-JBR-1191,18 magtic xprimts Quark Shll substructur modl CMP-AB-91 momt modl [itgral charg Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

5 5 of 4 11 Quark Subshlls Ergy lvl width 1 Wak itractio ad bta dcay attractio, 1 Gravitatioal Nutro Star Black hol. 14 Elctro spi agular momtum dfiitio-g-fi structur costat [but fractioal charg frmios] Rag = M ma lif = 10-5 Scs Yt to b likd with othr forcs With Smi Classical Approach 14 Nutrios Rquird to xplai 15 Tul ffct ad Casimir ffct bta dcay Rquird to xplai Alpha particl dcay ad attractio btw two plats i mpty spac frmios].th / factor coms aturally (10-15 to )m At (1.6 x10-18 )m rgy lvl width (.5 Mv) ad (-p) distac of (0.49fm) Rag = M s ma lif tim =10-5 Sc. Du to gativ rgy /ctriptal forc from isid th cor of th particl g-factor= (Basd o dcimal placs for physical costats) α 1 = ( ) No Nutrios i utro Bta dcay (A Protolctro spi-aomaly) (Smi classical approach) Smi classical approach Ucrtai Ergy rag (115 Mv to 17,000 Mv) CMP-AB-46,0 497 NP-IK 59 POFPGD-PT CMP-AB-, 86.9,499, 504 CERN (Appdix (1 of ) Appdix ( of ) Postd as sparat Appdix Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

6 6 of STUCTURE OF SUBATOMIC PARTICLES A Lik btw (mass rgy) ad (fild rgy) A. From th atur of particls ad atiparticls, it is wll stablishd, that a atiparticl has th sam mass, spi ad liftim [If ustabl], but th charg although qual i magitud has th opposit sig. Th aligmt or ati-aligmt btw its spi ad magtic momt ar also opposit to that of a particl. Cosidrig o such pair, th lctro ad a positio for th purpos of aalysis hr, sic thy hav mass togthr with charg, th (fild-rgy) associatd with a particl ca b compard from th kow (mass rgy) xprssio alog with th xprimtally vrifid rst mass-rgy rsult (0.511 MV) for a positro or a lctro. I ordr to valuat th (charg rgy), say for istac, if a positro is ar to a lctro, th two will com togthr udr th ifluc of thir opposit chargs ad i doig so, ad th particls acquir lctric pottial rgy. For th compariso btw th rst mass rgy ad th lctric pottial rgy gai th followig xprssio is cosidrd. m C o 0 m C = = kq d kq d (1.1) Whr 1 K = ad [d] is th distac btw th ctr s of lctro ad positro. 4πε 0 Though th abov quatios ar th sam mathmatically, th physical itrprtatio is as follows Th gativ rgy hr i quatio (1.1) is ot mat as gativ mass sic this is a o -matrial modl ad rprsts a iward forc (ctriptal forc) i th cavity of subatomic particls proposd hr ad this modl is abl to tak us through all four particl itractios ad forms th basis for this proposd o-matrial shll Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

7 7 of 4 modl. That is rgy rmais i th rgy form ad dos ot tak a matrial form for th Subatomic Particls ad thir proposd Sub shlls i this modl. B. Exprimtal obsrvatios ad fidigs Furthr, this procss has b obsrvd to tak plac i amorphous substacs ad it turd out to tak plac maily aftr th positro slows dow i th substac ad dos ot radily aihilat i most of th cass, but forms a boud systm with a xtraous lctro of a ati-paralll spi i th form of a parapositroium for a short tim of about scods ad thy d to com closr so as to mt th cosrvatio of rgy rquirmts (v if thy ar to b poit particls) two particls th thrads ito o aothr ad wh thir combid rgy is qual to (1.0 MV), thy aihilat by simultaously mittig two Gamma ray photos, ach with a rgy of (0.511 MV) ad wr dtctd i xprimts. Th two photos flw strictly i opposit dirctios from th targt irradiatd by positros. Th abov procss is i accordac with cosrvatio of rgy ad th rsultig momtum of th stoppd positro ad lctro is zro, as wll it mts charg cosrvatio [NPNR-AK-55] Thrfor, th (mass-rgy) of aihilatio of th two masss is th sum of thir (mass- rgy) of th pairs ad th (charg rgy) is that cotributd by th chargs o th pairs. From quatio (1.1), th total rgy of masss ad that of chargs ca b writt as blow. Whr, subscripts [p] is for positio ad [] for lctro. Sic th mass ad th charg for th two particls ar th sam umrically, quatio () ca b writt as m C kq = d (1.) Whr, (m o = m p = m = rst mass) ad [d] is th distac btw th particl ctrs This quatio is a rgy trasformatio quatio from pottial rgy to th kitic rgy form of two photos for both positiv lctromagtic rgy ad for th gativ rgy [gravitatioal fild rgy] is put forward i sctio [5.1] aftr gravitatioal attractio Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

8 8 of 4 Pair productio rgy discrpacy: By isrtig th valus for th costats i quatio (1.) ad th kow total mass rgy of (1.0 MV), th distac btw th particl ctrs ds to b qual to (d =.818 x M) i ordr for th particls to gai a total pottial rgy quivalt to th total mass-rgy of (1.0 MV) as show hr Pottial rgy btw th pairs at distac d btw th particls ctrs = = kq d [ = 16.8 x Jouls = 1.04 MV Th abov [ctr to ctr] distac btw th particls is th sam as that of th classical radius of th lctro (Sic w ar dalig with a o matrial modl th classical matrial approach is ot big cosidrd ad th sphrical itrfac at this radius r is th radius at which a stat trasitio from lctromagtic to strog itractio forc is proposd to tak plac for a poit particl approach) ad furthr from Ruthrford s scattrig xprimts with alpha particls o light alumium ucli cofirm th validity of Coulomb s law just about this distac (d)] ad th xprimtal vidc for it is as blow from From xprimts for th cas of a alumium uclus of mass umbr [7], th Coulomb s law was foud to brakdow i xprimts at about [6 to 8] fm, with th valu of ( R 0 = 1,4fm) with alpha particl rgy [NP-IK-64] Now, cosidrig a avrag distac of (7.0fm) from abov, th distac at which th Coulomb s law braks dow is qual to: ( 7 1.4x 7) =. 8 fm Which is i agrmt with th abov said thrshold distac as arrivd at abov. Th valu of R 0 will dpd o bidig rgy as will b dtaild i latr sctio-. 19 ] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

9 9 of 4 Furthr, with th prst matrial cocpt, wh th positro ad th lctro is at a distac of (r ), th total rgy rquird for a pair productio will b qual to ( x rst rgy of lctro + bidig rgy btw th pairs) = ( ) Mv Whras, a pair productio rgy that is foud to b rquird from xprimts is (1.0 Mv) This discrpacy ariss, bcaus th two particls ar big tratd as partly matrial ad partly charg rgy mass. Furthr a photo has all its rgy i lctromagtic form whil i motio ad its rst mass is zro, thrfor it would b appropriat that a liarly movig photo wh mad to slow dow i th strog uclar fild appars to coil up to bcom two chargd /spiig particls formig lctro/positro pairs which also rflct thir rgy i th particl form as lctric ad magtic rgy Thrfor, mass must tirly b fild rgy mass for a spiig chargd particl i ordr to rsolv th abov discrpacy. Th [poit charg] particl cocpt would lad to ifiit lctric fild itsity ad its associatd rgis, whos partial ffcts ar laboratd i sctio [.4] udr th subtitl [A lik btw Coulomb s law ad strog itractio] ad also why possibly th xprimts idicat a smallr d-brogli wav lgths (that is, a poit- lik particl) is also icludd i sctio [.5], [.] Th aforsaid procss of rgy ad agular momtum covrsio with frmios of (+/-half spi) ad photo of (+/- 1 spi) may b rprstd Fig-1 It follows from quatio (1.), that th bidig rgy pr particl at th spcifid distac [r ] would also b qual to th rst rgy Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

10 10 of 4 of o particl ad th distac btw th particls [d], i ordr to acquir th total aihilatio rgy is qual to [r ] kq That is m C = (1.) d C. Shll structur ad its dyamic stability: Thus for a pair aihilatio to occur, th distac btw th particls is dd to b qual to th radius of th particls thmslvs (that is [d] = r ) ad hc th sphrical surfacs will hav to ovrlap as show i Fig. 1. I ordr satisfy this rquirmt, a spiig dyamically stabl sphrical Hol lik structur i say Athr (idirct vidc for Athr ar icludd i supplmtary to this papr o Rviw of Spcial Thory of Rlativity ) with a flxibl boudary may b cosidrd, bcaus such a lastic sphrical structur holdig a gativ rgy stat i th cor ad vlopd i a lctric fild rprsts both mass ad th charg o a particl ad at th sam tim its flxibility would prmit th cssary thrshold approach distac btw thir ctrs to abl a pair aihilatio. I additio to this, th vlopig lctric fild itsity aroud such a structur ovrcoms th problm of ifiit lctric fild itsity/rgy ad also abls cotiuity of fild lis. [POFPG-PT-7] 1.4. Dyamic stability of th shll structur: For this shll structur, sic th (mass-rgy) is i fact ow th (charg-rgy) ad ar qual i magitud for a particls as i quatio [1.], th dyamic stability at th particl itrfac ca th b aalyzd as blow By dividig quatio [1.4] by th radius of th particl [r] (say for a lctro) m C r = kq r Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

11 11 of 4 m C r 1 4πε That is = ( 1.4) o q r By dimsioal aalysis, sic 1 ML = ε0 T Q th abov quatio (1.5) turs out as ML T ML T = Thus th trm o th lft sid of th quatio (1.4) is a ctriptal forc dirctd towards th ctr of th shll structur ad that o th right is a outward forc du to th lctric fild itsity. Th ivolvmt of th vlocity factor C shows th dyamic spi stat of th structur. By substitutig umrical valus i quatio (1.4) th followig ar th obsrvatios. a] for r= r, both th iward ad outward forcs ar balacd at th itrfac of th structur which is th stabl stat. b] For [r] > [ r ], m C > r kq r Which rsults is a iward forc ad th structur is rstord to its stabl stat of [r=r ] m C < kq c) For [r] < [r], r r Rsultig i a outward forc that acts to rstor th structur to its stabl stat of [r = r ] d) Th gativ rgy withi th shll is always qual to fild rgy outsid th shll i th form of lctric filds [E] ad magtic filds [B] Furthr sic th spi of a subatomic particl is proposd to b is always at th spd of a lctromagtic wav[c], th classical xprssio [E=CxB] holds good Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

12 1 of 4 ) Th sphrical shll (rgy-mass) ad its associatd charg at th itrfac is quivalt to a poit mass/ charg at its ctr A. Siz of uclos.0 NUCLEON AND NUCLEAR PROPERTIES A Corrlatio btw Rst Ergy with Bidig Ergy pr Nuclo Sic th mass of th protos ad utros ar much havir tha th lctros, thy will b rflctd i thir corrspodig [mass rgis]. Thrfor, th rgy dsity withi a shll structur will rflct as mass-rgy to volum ratio. From th shll structur for a particl as i prvious sctio [1.4], th cor of th particl m C 0 is rprstd by from which it follows that, sic th vlocity C is a costat, r th mass of a particl is ivrsly proportioal to th radius of th structur. With th abov, th rgy dsity xprssio for a uclo ca b corrlatd with that of a lctro whos (mass rgy) togthr with its radius ar kow. Rst rgy of a uclo Rst rgy of a lctro = Volum of a lctro Volum of a uclo r That is RE = RE...(..1) r Th subscripts (- for a lctro), (-for a uclo) ad (RE for th rst rgy of th corrspodig particl) th xprssio (.1), ca b rarragd to obtai a rlatio for th radius of a uclo. RE r = r...(.) RE Whr (r ) - is th radius of a uclo ad (r ) th classical radius of a lctro Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: By drawig quivalc from th pair aihilatio for th itrfac ovrlappig as i Fig (1) ad th ots blow it, ad furthr by xtdig this to (Gaussia surfac) aroud a

13 1 of 4 quivalt poit charg at th ctr of th Sphrical Shll Structur th followig ar th itrprtatio. Fig. (GS)- Gaussia Surfac, (S.S.I) Sphrical Shll itrfac of uclos I fig- AP=p=B=D=r GS Whr (r GS ) Is always lss tha (r ) Th quivalt itrprtatio for uclo at th Gaussia radius from quatios (1.1), (.1), (.) ad figurs [1] ad [] would b Tabl of Equivalc-1 a Th radius of a lctro-positro-[r ] = Th distac btw thir th ctrs [d] b Th rst rgy of lctro-[re] = Bidig rgy pr lctro at [r =d] c Th radius of a GS [r GS ] =Th distac btw th uclo ctrs [D] Equivalc from [a] d Rst rgy withi th GS(REGS) = Equivalc from [b] [BE/] at [D] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

14 14 of 4 Ad thrfor for th itrmdiat bidig rgis pr uclo ad th spacig btw th abov (c) ad (d) ca b xtdd by makig th followig chags to quatio (.1) ad (.) by rplacig (RE ) with (BE ) ad (r ) with (D). I othr words, this is th xtsio of rgy dsity ratio as i sctio [.1], but btw th rgy dsity withi th Gaussia sphr i compariso with lctro rgy dsity Thrfor Bidig rgy/uclo at distac [D] btw ctrs [ / ] = [ r BE D] xre (.) Th distac btw uclo ctrs [D] at th spcifid bidig rgy/uclo RE BE [ D ] = r.....(.4 ) Th quatios (.) ad (.4) ar applicabl oly for valus of [D] = [0.7 to.8] fm byod which th uclar forcs saturat o ithr sid B. Siz of a Nuclus Th siz of a uclus [R] ca b obtaid by multiplyig quatio [.4] by th cub root of th mass umbr of th rlatd uclus. R = r A BE Th siz of th uclus = [ ]......(.5) A workd out xampl for [R 0 ] hr will giv a dirct compariso with th mpirical formula [with typical Bidig rgy of 8 Mv/particl] i cotmporary physics [CMP AB- 88, 97] Th valu for (R O ) so obtaid is approximatly [1. fm] Now from quatio (.4), substitutig for th kow rst rgy of a lctro alog with th avrag bidig rgy/uclo (8 MV/) R RE O =.818fm Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

15 15 of 4 R 0 = [1.165 fm] Th valu of is R 0 som what varid, dpdig o th masurmt tchiqu ad th valu ow arrivd at [ R 0 = fm] is wll i accord with xprimts ad furthr idividual bidig rgis ca b substitutd for ach lmt Thus, Equatio (.) ad (.4) is wly itroducd i plac of th prst Squar wll. [CMP-AB-406] Equatio (.4) - Is wly itroducd for spacig btw uclos. Equatio (.5) - Rplacs th prst mpirical formula C. Pottial barrir ad Spacig btw uclos: A pottial barrir ca b costructd from quatio [.5] for a [utro- proto] itractio, similar to th o availabl for a Dutrium for a compariso [CMP -AB- 97/98] Tabl 1 BE/ [R O ] Spacig Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

16 16 of 4 Figur Bidig Ergy/Nuclo Spac ig Bt, Nuc los Not: Th plottig of Figur- is oly idicativ ad is (ot to scal) with rspct to th ratio of (X/Y) axs ad th stpss of fall may v b sharpr i actual scal Nots o th Tabl- 1 a] Th distac btw [-p] ctrs for a dutrium is [.18fm] b] Th spa for th spacig btw [-p] for a bidig rgy rag of (0.511 to 5) MV is ( ) fm= (.1fm) which agrs wll with that calculatd valu basd o a Squar wll from wav mchaics (.1 fm for 5 MV dpth) c] Bcaus of th cotiuity of quatio (.5) with roudd corrs, th spacig ad rag for a strog itractio ca ow b wll dfid to dmarcat from wak itractios [CMP-AB-406] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

17 17 of 4 d) Bidig rgy will howvr dpd o othr factors such as (umbr of uclos to umbr of proto i a uclus), thir pairig ad quadrupol momt. Howvr sic th ma bog rgy is about 8Mv, th kitic rgy of motio of uclos i th ucli is about 5Mv. (NPNR-AK-95,100) (CMP-AB-406,407) f] Coulomb s law would b dirctly applicabl for distac btw uclo ctrs qual to or gratr tha (.8 fm] D. Coulomb s law ad Strog itractio [uclar forc] [Which follows from sctio [.1] that th magitud of th mass rgy closd withi a Gaussia sphr is qual to th charg rgy outsid th Gaussia Sphr] It follows dirctly from th proposd shll structur ad alog with th applicatio of Gaussia surfac aroud th charg ctr of th sphrical shll as show i Fig []; th followig would b applicabl outsid th Gaussia Surfac. a] th lctric fild itsity at th Gaussia surfac will b ivrsly proportioal to its surfac ara ad its pottial ivrsly proportioal to th radius of th surfac. Not: It implis that th [charg] o th shll is a ivariat ad has th magitud of a lctro charg. Equatio [.] is copid hr for asy rfrc Bidig rgy pr uclo BE r = D RE Whr [r >D>0.7] fm BE r = D r kq D r...(.6) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

18 18 of 4 r Hr th first trm D is th cotributio to th bidig rgy du to icras i th lctric fild itsity at D. Th scod trm r D is th cotributio du to th icrasd pottial at D. Kq Th third trm r = Mv is th limit for th Coulomb s law as mtiod i sctio [1] Th abov factors modify Coulomb s law ad it rflcts as strog itractio btw uclos for (r >D>0.7) fm. This is o of th rasos why a poit charg cocpt for th particls was dd to th kpt asid i sctio [1.]. E. Costituts isid uclos [Quarks] Ulik lctros, a proto or a utro has costituts [Substructurs] [SS]. Thrfor, thir ovrall siz will dpd upo th umbr of costituts [Substructurs] ad corrspodigly th rgy cotaid withi ach substructur. Howvr th sum of th idividual rgy cott withi th substructurs isid a uclo must b qual to th rst rgy of th uclo Th charg o vry shll will always b qual to lctro charg ad positiv or gativ will b rflctd i thir dirctio of spi rotatio Th radius of a shll substructur was show to b rlatd to its rst rgy through quatio (.) is copid hr for quick rfrc. RE r = RE r Whr (r, r ) is th radius of a uclo or a lctro ad (RE,) - Rst rgy of uclo or a lctro I ordr to mak a choic o th umbr of substructur [costituts] ad thir rgy cott, th followig factors ar cosidrd. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

19 19 of 4 a) That (o two) costituts (Shlls) hav th sam rgy stat i accordac with xclusio pricipl. b) Sic th radius is ivrsly proportioal to th rgy cott i th substructur, th choic of this rgy has b mad, such that it satisfis th obsrvd xprimtal facts lik rsoac particls tc. c) With th abov cosidratios th sub shll structur cofiguratio for a last rgy stat would b Coctric Substructurs / Sub shll Modl which ar also dyamically stabl from [Sc-1.4] [aalogous to coctric sphrical capacitors] From th abov formula for (r ) th radius of ach sub shll ca b foud by rplacig RE by th proposd rgy cott withi th sub shll. Furthr ths valus hav b chos so that th rsults obtaid from this would b dd to vrify th rsoac particl rgis [ Eta ad ω - msos] also. F. Radius of Sub shlls withi, th Nuclos [Quarks] Proto A proto cosistig of thr coctric sub shlls (SS) of rgy, [4 MV], [155. MV] ad [549 MV] ad ar chos, so that thir sum is qual to th rst rgy of a proto = [98. MV] Th radius of th [SS] cotaiig ru =.818fm [4 Mv] ru 1 = fm Similarly for th (SS) with [155. MV] Ad for th [SS] with [549 MV] ru = fm rd 1 = 0.75 fm Whr ru 1, ad ru ar similar i trmiology as adoptd for up quark which forms th outrmost ad irmost shlls. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

20 0 of 4 rd1 is similarly a dow quark which is th irmost sphrical shll [549 MV]. Th combiatio of [SS] of [549MV] with th [SS] of proto of [4 MV] yilds th valu of [78 MV] th othr rsoac particl [ω mso] Nutro: For a utro, it is proposd with two coctric [SS] of rgy cott [71] MV] ad a [669 MV], th sum of which is qual to th rst rgy of a utro = [940 MV]. Th radius of [SS] with [71 MV] rd 1 = fm Th radius of [SS] with [669 MV] ru 1 = fm ( It may otd that this sub shll would split ito two rgy lvls udr th ifluc of magtic fild of a ighborig proto as will b put forward latr) [CMP AB- 0,9] Th [ctr to ctr] distac btw th proto ad th utro, wh th abov itrfacs ar just i cotact with o aothr, is qual to (0.76 fm). Howvr th closst distac at which a abrupt chag from attractiv uclo forc to rpulsiv should b of ordr of a uclo siz as th particls hav flxibl itrfac ad would dform to som dgr as s i fig-1 ad th xprimtal vrificatio idicats about [0.5 fm]. [AK 96, AP 17] Th split cll will hav radial sparatio of (1.18x10-18 ) ad a rgy lvl width of (.5 Mv) for a (-p) distac of 0.49fm. This radial sparatio abls a virtual rgy of about (17,000 Mv) Th othr fiv radial sparatios btw sub shlls rag from (10-15 to ) m givig ffct to othr valus of Quark itractio forcs ad rgy lvl widths G. Nuclo magtic momt From classical physics a spiig charg givs ris to a magtic momt, which is xprssd as blow [P-R&H-916] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

21 1 of 4 Spi magtic momt of a chargd particl is = q ± µ s = ± S m Th factor ( ) is proposd to b tak ito radius for uclos whil calculatig thir total agular momtum Whr [±q] rfrs to a positiv or a gativ charg whos magitud is qual to that of th lctro charg, [m] th mass of th particl ad S is th spi agular momtum vctor [CMP AB-9,91] [AP-JBR- 1191] A shll or a [sub- shll] ar frmios of half-spi ad th charg o thm is always qual i magitud to that of a lctro chargs [q = 1.60 x C] ad oly th charg dsity ad pottial that will b diffrt for th idividual shlls dpdig o its radius as show i sctio [.4]. Th momt of Irtia for a sphrical shll, of rgy mass about a axis passig through its ctr is. I = mr Whr m ad r ar th lctric fild rgy-mass ad radius of th shll ad sic its quatorial vlocity of spi of th shll is C th agular vlocity C r Spi agular momtum [S] = mr c = r mcr Substitutig for S i th quatio for th spi magtic momt pr shll ± µ s = ± qcr......(.7) Proto Magtic momt: From prvious sctio a proto was cosidrd to b built up of thr sphrical shll substructurs. Whos workd out radii wr [ru 1 =0.605 fm], [ru = ] ad [rd 1 = fm] [Whr, u or d ar up or dow stats i accordac with quark covtio]. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

22 of 4 By assumig that th irmost [549 Mv] chargd substratum has a opposit spi with rspct to th othr two associatd sub shlls its magtic momt will b [-v], th ffct of which is tak ito cosidratio i its corrspodig radius as rd 1 = [-0.75fm]. Ad th charg [q] is th sam for all th sub shlls, which, for thr [SS] will b [+q]. Thrfor th rsultat magtic Momt for a proto ( µ p) = qc [ ru 1 + ru + rd 1 Substitutig for [µ P ] = 1.60 x x x 10 8 x [ ] fm [µ P ] = 4.49 x 10-7 J/T. Ad masurmt of this alog say a Z-axis will b 14.1 x 10-7 J/T By xprimt th valu obtaid for proto magtic momts is qual to Atiproto.79 x x 10-7 J/T = 14.1 x 10-7 J/T [CMP AB-91] [Th chag of th stats of th abov substructur to th opposit atur [that is by chagig th sig] of a proto lads to a atiproto cofiguratio]. Nutro Magtic Momt Th followig factors obsrvd i th xprimts ar cosidrd i ordr to arriv at th [spi dirctio] of th two costituts i th utro. From th proprtis of a utro, it follows that a] A fr utro is a ustabl particl which has a ma liftim of [889scs] ad dcays by mittig a proto, lctro ad a atiutrio [CMP-AB- 45/47] b] Wh a utro is i a boud stat with a proto [for istac i a dutrium], th ma lif tim of utro is xtdd idfiitly du to xchag of rgy btw thm [CMP-AB-85,410] c] Also from th boud stat of [proto utro] thy hav a strog magtic couplig bcaus of thir clos distacs i a uclus shll modl [CMP ] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: ]

23 of 4 d] Although th ovrall utro charg is zro, th costitut shlls ar quivalt to two oppositly spiig chargd sphr, ad its magtic momt is gativ dpdig o th rsultig gativ charg [CMP-AB-91] [AP-JBR-1191] ) I th absc of a magtic fild, a fr uclo ca hav thir spi i ay arbitrary dirctio but its compots i ay chos rfrc i a uiform magtic fild will b quatizd ad maigful [CMP-AB-09] Thus i ordr to mak a masurmt of th magtic momt of a fr utro a xtral fild would b rquird, whras i a boud stat th utro has a rfrc magtic fild from, that gratd by th ighborig proto. From prvious sctio [.6], th radius for th substructurs was calculatd to b For [71 MV] shll has as radius rd = [-0.48 fm] For [.75 MV] shll has th of radius about rd 1 = [-0.5 fm] Ad for th othr [6.5 Mv ] shll has th radius of about ru 1 = [+4fm] Th [669 Mv] shll of th fr utro splits du to th strog magtic fild from th ighborig proto i th uclos Wh a fr utro is ot udr th ifluc of a magtic fild, th ir shll is assumd to b spiig i th opposit dirctio of th gativ outr shll (-q), so that th rsultat of th two proposd sub shlls, th t charg bcoms zro. Howvr, wh a utro is subjctd to a strog magtic fild du to magtic couplig with a ighborig proto, th ir shll splits ito spi up (+q) ad spi dow (-q) ad its magtic dipol gts aligd with rspct to its ighborig proto, thus givig ffct to a t gativ charg/magtic momt, which is rflctd as a gativ sig o th radius as itrprtd for th proto prviously. [CMP- 9, 48] [P-R&H-9] qc Nutro magtic momt = [ ru 1 + rd 1 + rd ] = x 10 8 x 1.60x10-19 x (0.484) fm Not that ru1 ad rd1 arly cacl out Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

24 4 of 4 = x 10-7 J/T ad th masurmt of this alog say a Z-axis will b 9.66 x 10-7 J/T By xprimtd fidigs= [-1.91 x x 10-7 ] = [-9.66 x 10-7 J/T] Atiutro Th chag of th stats of th substructurs to th opposit atur [that is, by chagig th dirctio of spis of shlls] of a utro lads to a atiutro cofiguratio..0 WEAK INTERACTIONS AND (WIMPS) A. With all th dtails giv for [Nuclar Elctros] i txt book [CMP-AB-88,45,497] Th abov phomo of th [wak itractio], ca ow b aalyzd with th hlp of a [Shll structur] for th particl Rfrrig first ow to th Bta dcay, th avrag kitic rgy of a lctro is about [0. MV] ad sic a lctro i a particl form caot prxist withi a uclus, th Bta dcay rgy of [0. MV] may b vrifid from th outr priphry of th uclus Th abov phomo of th wak itractio ca ow b aalyzd with th shll structur of th particls. Th siz of outr shll of a utro shll ad a proto shll wr calculatd ad foud to b qual to [0.484 fm] ad [ fm] rspctivly, ad that of a lctro is (.818 fm). [Sctio-.6] Th [utro lctro] pottial rgy ca b calculatd from thir ctr-to-ctr distac, wh thir itrfacs ar just i cotact. Thrfor [D] [-] = [ ] fm =.17fm [D] [p ] = [ ] fm =.4 fm. From arlir sctio, th uclo itractio saturats at a distac of [.818 fm] ad hc th Coulombs law is dirctly applicabl for ay distac gratr tha this, thrfor th pottial rgy accordigly will b Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

25 5 of 4 Btw asct [proto lctro] = 9 9x10 x1.60 x x10 19 = 0.445Mv This diffrc i mass rgy btw a utro ad a proto=0.78mv of which th bidig rgy ad magtic couplig btw th proto ad th lctro ar to b ovrcom ad th rst is carrid of as kitic rgy of lctro. Th spi agular momtum cosrvatio is dtaild i Appdix- ( of ) ad o utrio is cratd i th abov procss. Th diffrc btw ay two substructurs withi th uclos ad that btw th outrmost structur of th utro ad th proto ar mostly i th rag of [10-17 to ] mtrs, i accordac with th charactristic rag of th Wak Itractio" i th figur blow. Th ir sub shll of (669 Mv) of utro with two shlls would split i th clos proximity of Proto B. Wak itractig massiv particls [Wimps] Th charactristics of th itrmdiat vctor bosos hav a Rag = M Ad rgy >80 tims th proto rst rgy for [Wimp s] [CMP-497] This ca b dirctly applid to th Shll structur from quatio [.] for th radius of a uclo. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

26 6 of 4 r RE =.818fm For a W [+/-], 0 Z - th rgy is 80 tims th proto rst rgy or gratr. Thrfor RE = [80 x 98 MV] = 75,040 M V Substitutig, i th abov quatio for r 17 r w = Th phomo is basd o th ivrs proportioality btw th rgy ad th volum as drivd i sctio [] Such a phomo is xpctd for all th othr virtual stats ad thy should also shrik i siz, which is why, wh particl siz dducd from high rgy [lctrolctro] scattrig xprimts quit possibly idicat as if thy ar poit charg Howvr, ths stats big o th dcay mod, th particl siz will bouc back to its stabl siz as i sctio [1.4] mtrs 4.0 UNIVERSAL LAW OF GRAVITATION A.Th forc of attractio btw two masss i accordac with Nwto s Law is, F = Gm1m D F = G C m C D m C D 1 4 (4.1) Th itrprtatio of this is as blow, Th first costat trm has th dimsios of ivrs of forc Th scod ad th third trms ar th ctriptal forc from th cor of th gativ rgy stat isid th corrspodig subatomic particls. Thrfor th ractio forc Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

27 7 of 4 btw particls is idpdt of spi dirctio of th cor of th particls ad will always b attractiv, ad furthr this xplais th ivrs squar law of forcs. It may b rcalld that th Spac Tim Curvatur was a suitabl optio as bcaus Sir: Isaac Nwto s law of gravitatio had o immdiat xplaatio for Actio at a distac. [P-R&H-Vol-1-88] [POFPG-PT] Sic th lctric ad magtic ffcts ar ullifid at th atomic lvl itslf i most of th objcts, th oly domiat forc that prvails is that of gravitatio. W kow th complxity for this applicatio to mor tha two objcts; though th itractio of th rst of th Uivrs will b rflctd i th local ffcts of th Earth s gravitatio B. Nutro Star, Black Hols: Fig [4] I th cas of a utro star whos atoms hav b so comprssd that, most of thir protos ad lctros hav fusd ito utro, for which this shll modl appars to b mor appropriat. Th W[±] ad Z virtual particls ivolvd i th wak itractio, shows o sig of saturatio of th lctric fild aroud th shll structur, bcaus th particl boucs back to its origial stabl siz,du to th dyamic stability of th shll structur as s Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

28 8 of 4 i sctio. Howvr, at a much dpr lvl th lctric fild may radiat away [Hawkig Radiatio] ad a imbalac may st i with th rsult that a iward pull will th domiat accordig th proposd shll structur. [CMP-4, 86,1,9,496,504] (Appdix- 1 of 1) Elctro Spi Magtic Momt Aomaly (g, 17) ad a Agular Momtum Dfiitio of Fi Structur Costat, Smi-Classical Approach) PACS: 1.0.Jp, 1.0.Js, 1.15xg, 0.0 +p. ABSTRACT: This is a attmpt to rsolv th dcad s log lctro magtic momt aomaly by aalyzig its ffct at th Bohr radius from first pricipls at radius qual to th classical lctro radius. g- Factor = ad α 1 = ( ) I coclusio it r-mphasizs that lctros ar ot poit particls. Cocpts of Modr Physics-Fifth Editio-Arthur Bisr-Mc-Graw-Hill,Ic (CMP-) rfrs to pag umbr () of th Book. Ky Words: 1) Elctro lctric dipol momt ) Smi-classical mthod. ) Corrctios to a boud lctro ( g factor). 4). Elmtary Particls INTRODUCTION: Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

29 9 of 4 A lctro is ot a poit particl but has a radius qual to classical radius of lctro drawig a clar idicatio from uclo itractio ad magtic momt agrmt s so far. Th total orbital magtic momt coupld with th spi magtic momt at th Bohr orbit ca b xprssd i trms of charg, vlocitis, radii ad th multiplyig factors for thir rspctiv momt of irtia as proposd blow. (CMP-10,,8,9,0) µ µ Bohr S. Classical = ( B B µ ( Quatum Orbital) = m µ B SZ. ST m VBa µ Bohr S. Classical = ( m h ) = π ( Spi. S. Classical. Z Axis) = ( m µ ( Spi. S. Classical. Total) = V B l 0 (1) = 9.74x10 ) h ( m (1A) = 9.74x10 m Cr Cr = () = 7.814x10 Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: b x ) x 1 ( m ) Iω = 1 ( m 4 Cr mcr ) = )( m a V ) x( a VBa ) = J / T ( CMP ) 4 0 J / T ( CMP ) (1B ) = x10 6 ( Orbital. Vlocity. at. Bohr. radius) =.188x10 m / s ( CMP 15) 11 a 0( Bohr. radius) = 5.9x10 m ( CMP 11) Spi ( Quatum Spi) = m spi ( m ) h = 9.74x10. a approximatio that. latr. lad. to. aomaly ( CMP 8,46) bar = ± 1 ( m B J / T J / T J / T J / T (A) ( CMP 0) Not : That gyromagtic ratio. of. spi. is. twic as. that. of. orbital. quatio(1 A) which.. is µ ST Total.( orbital + Spi). Magtic. Momt. at' a0 '( µ BST ) = ( µ B + ) = 9.80x10 µ B h 4 = X10 J S π 8 lctro spi Vlocity ( C) =.998x10 m / s m = mass of lctro = 9.11x10 = 1.60x10 19 ( Coulomb) 1 kg ) h bar 4 4

30 0 of 4 µ BST µ ST = ( µ B + µ Th. sam. ca. b. rframd. as. blow Comparig. Equtios(1) & ().. µ µ g. factor = g = µ B ) = ( ) x10 BST B = J / T Cr V a Clos. to.xp rimtd. valu. of ( ) BST = ( µ + B B = 9.80x ) = 9.80x10 J / T 4 J / T VBa0 Th valu for ( ) Cr turs out to b α 1 = ( ) Coclusio: Th sigificac of th fi structur costat is wll kow to may disciplis of scic ad hr w gt a clar w dfiitio with th abov total magtic momt ratio, i othr words, wh rprstd i trms of total agular momtum by rplacig with m. This i additio mphasizs that lctros ar ot poit particls ad idd hav classical radius of lctro. I th abov aalysis ivolvig both classical ad quatum physics, it is limitd to thr dcimal placs hr for physical costats i ordr to vrify th Fi Structur Costat. Th magtic momt for a half itgral lctro spi valu turs out to b as i quatio (1A). Som high rgy xprimts it sms appar to idicat that thr is possibly a chag to th Fi Structur Costat du to th chag of lctro charg could v b du to chag i mass ad cosqutly o charg mass ratio. Howvr v so, part ( of ) postd o this sam wbsit dscribs th atur of charg ad ca accommodat such a chag to lctro charg. (It may b otd that thr is o clar itrisic dfiitio for a charg so far ad its possibl atur is icludd with Athr proprtis i Spcial thory of Rlativity as (part-) (a figur showig th furthr sigificac of 17 factor ivolvmt ca b foud at th d). Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

31 1 of 4 Appdix ( of ) No Nutrios i utro Bta dcay (A Proto-lctro spi-aomaly) (Smi classical approach) Abstract: This scop of this cocis work is a attmpt to show that cratio of a half spi utrio durig a bta dcay procss would compltly distort th cosrvatio of spi agular momtum durig bta dcay of a utro wh spi vlocity is maitaid a costat at C. PACS Numbr: g, St, 14.0Dh,.40Bw Ky Words:1) Elmtary particls ) Wak Itractios ad lptos ) Nutrios 4) Bta Dcay Aalysis: Is basd o 1) Violatio of C is ot accptd as it will challg mass rgy quivalc as wll as ucrtaity pricipl. Th followig work shows th xtt to which C is violatd by maitaiig (h/pi) a costat ad th dgr of dpartur for magtic momts from a Classical approach. ) This is basd o a o matrial shll modl for subatomic particls whos spi momt of irtia is (/)mr ad that th orbital vlocity of lctros ad uclos ar far lss tha C ad thrfor rlativistic ffcts for mass icras ar isigificat. Dfiitio of Plack s agular momtum (h/pi) = mvr Whr (m- is th mass of a subatomic particl), (V B - Orbital vlocity of th particl ad Vs- quatorial vlocity of spi of a particl a costat) ( C =.998x10^8m/s), (radius of th particl udr cosidratio markd with subscript -for lctro,-p-for proto..) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

32 of 4 Th umrical valu of h =1.0546x10-4 J-S π 1) At Bohr radius Quatum ad Classical agular momtum ar th sam. By rplacig charg with lctro mass w gt th ratio agular momtum. Sic, th magtic momts ar xprimtally vrifid ad furthr thm big dirctly proportioal to agular momtum th aalysis is proposd to bgi by Comparig magtic momts. VBa0 4 µ B Bohr Classical = (1) = 9.74x10 J / T ( CMP ) h 4 µ B ( Quatum Orbital) = ml ( ) (1A) = 9.74x10 J / T ( CMP ) m π V B 6 ( Orbital. Vlocity. at. Bohr. radius) =.188x10 m / s ( CMP 15) 11 a 0( Bohr. radius) = 5.9x10 m ( CMP 11) h 1 1 VB mvba = Iω = ( m a0 ) x( ) = 4π a 0 0 µ SZ. ( Spi. Classical. Z Axis) = ( m At classical radius of lctro (r ) Cr x mcr ) = (1B ) = 4.51x10 6 J / T By rplacig charg with mass of lctro i quatios (1) ad (1B) abov hbar mvba0 Th valu for = ( ) h m Cr spi turs out to b α 1 = ( ) Thus it r-mphasizs th sigificac of lctro classical radius. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

33 of 4 ) Elctro (g-factor aomaly) th first idicator of dviatio of Quatum with Classical agular momtum for boud lctros i a atom. From its rlatio for lctro spi h = Iω = ( mr π V ) x( r spi mv ) = spi V Thrfor quatorial spi vlocity = C r () spi h = 4π. m r C = 05.5 () Thus by maitaiig (h/pi) a costat th xtt of violatio of C is carrid ovr to th magtic momts as blow µ B By comparig quatios (1A) with (1B) = ( ) = 05.5 (4) µ sz If th lctro wr to b a poit particl th violatio of C far xcds byod ay justificatio. ) For uclos Quatum ad Classical agular momtum. Th costacy of spi vlocity C is violatd v for hadros which hav a structur of radius (0.5 fm) as show blow for Baryos, of siz approximatly (1 fm across) (V/C) =0.6 (CMP-AB-481) May virtual particls hav diffrt masss ad sizs which agai will hav to rflct o th spi vlocity. Now by maitaiig th costacy of th spi vlocity of light C th variatio of agular momtum is as follows for lctro ad uclos. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

34 4 of 4 h ( Spi Classical agular momtum lctro) = ( m Cr ) = 7.696x10 h ( Spi Classical agular momrtum Pr oto) = ( m h ( Spi Classical agular momtum utro) = ( m r p ( r =.818 fm ( lctro classical radius) p = 0.51fm),( r Cr ) =.548x10 Cr ) = 1.749x10 J S (5) J S (7) = 0.48 fm) ar clos to 0.5 fm xp rimts ( CMP 481) p p J S (6) µ. µ pz z = = m m p x m x m p Cr Cr = 14.1x10 = 9.66x10 Th rsults of (8 & 9) cofirms th validity of quatios (6 & 7) Half Plack Spi is about = 0.5x10 p 7 7 J / T (8) sam as J / T (9) sam as foud i xp rmt 4 J S foud i xp rimt Th radius for thr sub shlls for uclos i plac of Quarks is dtaild i th omatrial subatomic particl modl (Part-1 Sap-Nmsm by this author i this wbsit.). By comparig from abov valus for uclos agular momtum with that of lctro is lss by a factor of (8) folds for proto, (7) for utro ad (17/) folds with rspct to half Plack s spi ad thus its ffct durig bta dcay is ot flt ad thrfor th agular momtum cosrvatio is arly mt btw utro ad th proto itslf ad if ay half spi particl such as utrio wr to b prst th rsult would b compltly distortd as (h bar/) is tak uiformly for all particls i currt thoris But th qustio is what th valu is for half spi agular momtum? Th discrpacis for lctro magtic momt ad hr for utrio as w kow is bcaus Plak s agular momtum is hld a costat ad allowig violatio of C which is far highr i cas of poit particls. Ad is xplaid i Quatum Thory i trms of zro Poit oscillatios that dos ot giv ay clu of a particl bhavior. This aspct is somwhat aalogous with lctro (g-factor Bohr magto) aomaly but hr btw th uclos ad th lctro (g N.-Nuclo magto). A positiv sig is tak for lctro, bcaus i this procss th lctro is movig away from th proto ad as th fr utro is charg lss its magtic momt is zro for quatio (10) blow. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

35 5 of 4 µ N h = m bar p = 5.05x10 7 J / T (10)( CMP AB 91) µ sz µ p = ( µ N + ( ) = (5.05 ( ) x10 J / T = 14.0x10 J / T µ 5.05 N For vrifyig th rgy cosrvatio durig a bta dcay a simpl cas of fr utro is cosidrd. Hr agai a corrctio to (h/pi) is dd by about 0.95 tims to corrlat with xprimts. Rst Ergy (utro) - (proto + lctro) =0.78Mv with which th asct lctro ds to ovrcom th lctric bidig rgy of th asct proto of about a distac of ( )fm with Coulombs law ad has also to ovrcom th magtic couplig btw thm put togthr is about (0.6)Mv) ad th rst is carrid off as lctro kitic rgy. Coclusio: With abov aalysis it sms icorrct to hold a spcific umrical valu for (h/pi) ad th rsults so obtaid may bcom qustioabl. I this cotxt th followig quatio (.) copid hr from (part-1 of Sap-Nmsm)) prmits to valuat th siz of a particl ad its substructurs (Quarks) by substitutig th mass rgy of a chos particl ca b dtrmid ad thrfor th agular momtum accuratly i plac of (h/pi) ad furthr it dos ot violat C or charg q. Th corrlatio Plack s costat (h) for bosos with (h/pi) is ot i th scop of this work. Hc a smi classical approach ca oly b satisfactory ad prcis. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

36 6 of 4 r RE = RE...(..1) r RE r = r...(.) RE From Cor Ctr 1) First itrfac of Cor of Proto (0.75fm) It appars as though a positro is shildd by a atiproto is a utro of (0.484fm) ) Scod Itrfac of Proto (0.605fm) ) Outrmost Itrfac of Proto (0.4194fm) 4) Elctro Itrfac (.818fm) 5) Plack s (h/pi) -d- Brogli-Compto wavlgth (.86x10-1 m) (h/pixm C) 6) Eisti- Radius (5.9x10-1 m) (Commt-4 - blow) 7) Plack s-bohr Orbit (5.9x10-11 m) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

37 7 of 4 Agular momtum/radius ad (17 factors) 1) Th ratio of agular momtum btw (7) ad (4) =17 ) Th ratio radius btw (7) ad (4) =17 ) Plack s d Brogli- Compto wavlgth Ratio at (h/pi) = 17 4) Eisti- radius at which spis vlocity is C ad at which agular momtum will b 05.5 (=1.5x17) tims lss tha half spi. 5) Itrstigly v th ratio btw th agular momtum of utro to proto quatios (7)/ (6) o pag () = (1.7/) 6) This factor is also ivolvd i Thomso lctro cross sctio 7) Coditio for stabl atomic orbits = ( ) (clos to dcimal placs) π. x10 x17 Som of abov may alrady xist ad a thig to otic with this umbr is its coicidc with svral stabl stats that may ivolv a rsoac phomo. Coclusio: Sic this papr is dalig oly with th fudamtal cocpts, th coclusios ar limitd to th followig Th lctro radius is o doubt its classical radius which has b alrady xprimtally vrifid with low rgy lctromagtic radiatio at o rlativistic vlocitis as prdictd by Thomso Drivatio as wll as Th Kli-Nishia formula is xpctd to b clos to th tru valu ad ot with aothr chargd particls or high rgy photos. Th spi of th particl is du to mobility of Athr ad is always at C maifstig its itimat coctio with th rst of th uivrs. This spi has its ow xplaatio i Quatum Thory Th proposd structur for a subatomic particl is applicabl both for xplicitly chargd particls or a combiatio of positiv ad gativ costitut chargd particls as i Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

38 8 of 4 utral os ad th photo itractios with particls such as momtum ar of lctromagtic i atur. A photo itslf may b viwd as som sort of a rvrs ffct of ormal Crkov divrgig co radiatio that may abl a sphrical wav frot to covrg to tak th form of a photo that is mittd upo a atomic xitd stat ad lctromagtic radiatio this is obsrvd whil chargd particls ar acclratd i particl acclrators a prdictio of classical thory is a visibl proof of Athr. Furthr assumig a xitd lctro xpads its rgy lvl aroud th uclus (aalogous to a largd balloo agaist Athr) could th rstor th lctro alog with its rgy lvl to its iitial stat. Durig a pair productio it appars as though th liar photo taks a coild form that projcts as a sub atomic particls ad durig a pair aihilatio th mittd photos ar xpctd to hav th sam cofiguratio (Cosrvatio of rgy) of a combiatio of positiv lctromagtic rgy ad a gativ gravitatioal rgy cor as has b s for lctro though sprad out i spac. Th [Shll structur] o acquirig ithr sustaid rgy or impuls rgy (rcallig ucrtai rgy/positio) would Shrik i siz, which implis mass icras i a trasitio mod such as Muo,Tau,Pio,--- fially dcay ito stabl particl form. Thrfor high rgy particls will td to idicat as (poit- lik) particl. [CMP-AB-48] Th cor of subatomic particls is similar to a pottial wll ad o th ir surfac of th itrfac has comprssiv prssur ad outsid of th itrfac a outward prssur. Furthr for valus lss tha th classical radius of lctro [.8fm] it is also turs out to b th startig of th Gravitatioal pottial wll at th particl lvl apart from big a uclar pottial wll Itrstigly (by tratig µ 0 a spac proprty ad C ) a costat, th lctro charg has co-rlatio with Plak s lgth [h pl], by th rlatio [Q is proportioal h pl C/µ 0 ] i th radial dirctio at th itrfac du to two opposig forcs which could crat a strai o Athr as xprssd by Michlso i o of his lcturs i th yar 1899.Th umrical valu so valuatd with (h pl 1.616x10-5 m]) for th charg is about 4 tims (I a way comparabl with Hook s Costat) lss tha lctro charg. Th valu with Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047