1 of 46. Abbreviated title: [SAP-SVT-Nmsm-g & 137] - Updated on 07 Oct, 09. Shankar V.Narayanan

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1 1 of 46 Subatomic Particls ad thir FOUR Itractios icludig (g &17) (p&) factors with Spac Vortx Thory (A No matrial shll modl) (Part 1 of ) (Th cotts of this txt ar th sam as i ONE EQUATION ad FOUR Subatomic Particls 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 07 Oct, 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 Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

2 of 46 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 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 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 if lctros wr to b poit particls 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 dvlopmt of th subjct. Th xprimts coductd by Sir: J.J.Thomso i attachd at th d of txt alog with th rsults backd by his ow quatio ad that o Kli-Nishia formula substatiats that th lctro radius is its classical radius. Th dtaild low rgy xprimt is rpatabl at ay rasoably quippd laboratory ay tim ay whr. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

3 of 46 Th sam quatios ad photo-lctro scattrig also disprovs Kitic rgy part of currt Spcial Thory of Rlativity. Also kpig i mid studts som aspcts ar strssd with a clos aalogy ad som spcific commts o currt physics ar brought out bcaus it may ot b asily availabl from ducatioal wbsits or from books.. 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] 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 46 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] Fidigs i Modr Sl.N Proprty/ As foud i this proposd physics thory / o Natur thory Exprimt Rfrc 1 Subatomic Particls Poit particl Dyamically stabl Sphrical zo of comprssiv forc & vlopd i a positiv CMP AB-78, AP-JBR-70, 1068 NP-NR-AK 54 NP-IK-64/414 outward lctric fild forc outsid th shll itrfac. Subatomic Poit mass/poit Fiit siz/fiit fild CMP-ABparticl siz charg/ifiit fild itsity. itsity/dyamically stabl. Nuclo Pottial barrir No prcis xprssio hc assumd squar Drivd xprssio with w quatios for spacig, bidig rgy pr uclo. CMP-AB-406 NPNR-AK 94 NP-IK 50 wll. 4 Valu of [Ro] 1. fm Empirical [1.165 fm] at itrfac drivd xprssio NPNR-AK-77 CMP-AB-89 5 Rag of uclar forc Approx [1.7 fm] By Mso thory [1.7 fm] for [0.8 MV to 5 MV] with drivd xprssio. Nutro bcoms gativly chargd i th uclus; hc o mso xchag is dd. 6 Spacig Not prcisly Drivd xprssio CMP-AB-410 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 46 btw kow from thory uclos i a uclus 7. Nuclar Not prcisly Slightly lss tha [0.49fm] 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 [ fm] for uclos kow proto ad (0.484fm) for utro from 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 [but fractioal frmios].th / factor charg frmios] coms aturally 11 Quark (10-15 to )m Ucrtai Ergy Sub- At (1.6 x10-18 )m rgy rag (115 Mv to shlls lvl width (.5 Mv) ad 17,000 Mv) Ergy (-p) distac of (0.49fm) lvl width 1 Wak itractio ad bta dcay attractio, Rag M ma lif 10-5 Scs Rag M s ma lif tim 10-5 Sc. CMP-AB-46,0 497 NP-IK 59 1 Gravitatioal Yt to b likd Du to implosiv cavity POFPGD-PT Nutro Star with othr forcs /ctriptal forc from CMP-AB-, Black hol. isid th cor of th 86.9,499, 504 particl 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 Elctro spi agular momtum dfiitio-g-fi structur costat With Smi Classical Approach Exprimts shows g-factor Nutrios Rquird to xplai bta dcay 15 Tul Rquird to xplai ffct Alpha particl ad dcay ad Casimir attractio btw ffct two plats i mpty spac g-factor (Basd o dcimal placs for physical costats) α 1 ( ).Nw agular momtum ratio dfiitio Nutro Bta dcay- Cosrvatio of rgy violatio-if th lctro siz is lss tha its classical radius. (Smi classical approach) Tul ffct was dd sic uclo siz ad th spacig btw thm is ot v kow. CERN (Appdix (1 of ) Appdix ( of ) Postd as 1) Alpha Particl Dcay- Is it rquird to Tul through th pottial barrir? Not cssary. 16 Elctro Siz Not Cocludd but lss tha (10-18 m) Cocludd ad sam as classical radius of lctro 1.0 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 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 46 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. q m 0C k d q m 0 C k (1.1) d 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 sig hr i quatio (1.1) is ot mat as gativ mass sic this is a o -matrial modl ad by dividig by radius vctor) rprsts iward forc (ctriptal forc) i th cavity of a subatomic particls proposd hr.(that is Implosiv cavity ad a xplosiv lctric fild) Ad this modl is abl to tak us through all four particl itractios ad forms th basis for this proposd o-matrial shll modl. That is rgy rmais i th rgy form ad dos ot tak a matrial or a kot form for th Subatomic Particls ad thir proposd Sub shlls i this modl 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 46 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 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 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 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 Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: kq d [ 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], 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-. 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 19 ] th

10 10 of 46 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 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 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 46 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 m C r 1 4πε That is ( 1.4) o q r 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 46 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 [rr ] 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 [ECxB] holds good ) Th sphrical shll (rgy-mass) ad its associatd charg at th itrfac is quivalt to a poit mass/ charg at its ctr Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

13 1 of 46 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 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 quivalt poit charg at th ctr of th Sphrical Shll Structur th followig ar th itrprtatio. 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 46 Fig. (GS)- Gaussia Surfac, (S.S.I) Sphrical Shll itrfac of uclos I fig- APpBDr 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] 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). 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 46 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] RE 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 O R 0 [1.165 fm].818fm 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 46 Th valu of is R 0 som what varid, dpdig o th masurmt tchiqu ad th valu ow arrivd at [ R 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

17 17 of 46 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.(not that thr is d to assum roudd corr i currt thoris ad hr w gt this as a atural outcom) [CMP-AB-405/406] 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 bod 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) 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 46 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 BE r D r kq D r...(.6) Whr [r >D>0.7] fm 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. 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 46 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. 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] 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 46 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 (itgral charg) withi, th Nuclos [Quarks- fractioal charg)] 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 fm [4 Mv] ru fm Similarly for th (SS) with [155. MV] Ad for th [SS] with [549 MV] ru fm rd fm Whr ru 1, ad ru ar similar i trmiology as adoptd for up quark which forms th outrmost ad irmost shlls. 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 fm Th radius of [SS] with [669 MV] ru fm ( It may otd that this sub shll would split ito two rgy lvls udr th ifluc of 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 46 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, ad th gyro magtic twic that of orbital which is xprssd as blow [CMP-AB-0] Spi magtic momt of a chargd particl is q ± µ s ± S m 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-0,91] [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. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

22 of 46 I mr Whr m ad r ar th lctric fild rgy-mass ad radius of th shll ad sic its C quatorial vlocity of spi of th shll is C th agular vlocity. r Quatizd Spi agular momtum alog-z-axis [S Z ] mr c r 1 mcr Substitutig for S i th quatio for th spi magtic momt ±µ SZ ± 1 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 fm], [ru fm] ad [rd fm] [Whr, u or d ar up or dow stats i accordac with quark covtio]. 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 1 Momt for a proto alog Z-axis ( µ P ) qc ( r ) Z u1 + ru + rd µ PZ qc( ) fm 14.1x10 J / T By xprimt th valu obtaid for proto magtic momts is qual to.79 x x 10-7 J/T 14.1 x 10-7 J/T [CMP AB-91] Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

23 of 46 Atiproto [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 ] 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 [ 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] 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 46 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. Hc o mso xchag is dd. [CMP- 9, 48] [P-R&H-9] Nutro magtic momt 1 µ Z qc( ru 1 + ( rd 1 + rd ) fm (Not that r d1 ad r d arly cacl out) Nutro Magtic momt alog Z-axis 1 7 qc ( 0.484) fm ( 9.66x10 ) 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] 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 46 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 Btw asct [proto lctro] 9 9x10 x1.60 x x Mv This diffrc i mass rgy btw a utro ad a proto0.78mv 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 ad th proposd structur prmits a cotiuous spctrum. Th spi agular momtum cosrvatio is dtaild i Appdix- ( of ) i ordr to aalyz a d for a atiutrio. It may otd that if lctros ar to b poit particls (<10-18 m) accordig to currt thoris th th stimatd bidig rgy btw th lctro ad th proto will hav to b gratr tha (155Mv) ad bta dcay caot occur. 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 46 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. 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 mtrs 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 46 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] 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 is ot a mr scalar costat but has th dimsios of ivrs of forc-g 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 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] 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 46 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 ad possibly 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 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] Elctro Spi Magtic Momt Aomaly (g, 17) ad a Agular Momtum Dfiitio of Fi Structur Costat, Smi-Classical Approach) Author: V. Shakar Narayaa Shakar V. Narayaa PACS: 1.0.Jp, 1.0.Js, 1.15xg, 0.0 +p. 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 46 ABSTRACT: ABSTRACT: This is a attmpt to rsolv th dcad s log lctro magtic momt aomaly from smi classical approach by aalyzig its ffct at th Bohr radius from first pricipls with classical lctro radius. g- Factor ad α 1 ( ) By xprimt ( ) 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: A lctro is ot a poit particl but has a radius qual to classical radius of lctro 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) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

30 0 of 46 µ B Bohr Orb Smi. classical ( m VBa0 µ B Bohr Orb Classical (1) 9.74x10 h µ B ( Quatum Orbital) ml ( ) (1A) 9.74x10 m π µ µ S Z S T ( lctro. Spi. Classical Z Axis) ( lctro. Spi. Classical Total) µ By. classical. approach. lt. factor. for µ µ ST Cr ( ) (4) SZ ST h ) π µ SZ ( 1 ( m ( m ) Iω 4 1 ( )( m a V ) x( a J / T ( CMP ) 4 0 J / T ( CMP ) VBa ) Cr 6 ) x mcr () 7.814x10 J / T ) x mcr Cr () 1.54x10 m m 6 J / T 1. so. that. symmtrical. agl. for. Cosθ 45.dg rs. B 0 0 µ V B 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 ) ± π h ) 9.74x10 π Not : That gyromagtic ratio. of. spi. is. twic as. that. of. orbital. quatio(1 A) which.. is. a approximatio that. latr. lad. to. aomaly ( CMP 8,46) h X10 J S π 8 lctro spi Vlocity about. its. ow. axis.( C).998x10 m / s m mass of lctro 9.11x x10 19 ( Coulomb) 1 1 ( kg m 4 J / T (A) ( CMP 0) 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 46 Spi Orbit. Coupld. µ Th. sam. is.xp rssd. as. blow Comparig. Equatios(1) & (4).. µ B BST µ ST ( µ B + ) µ µ ST g. factor g µ BST B ( µ Cr ) 9.841x10 V a J / T Clos. to.xp rimtd. valu. of ( ) Howvr. at. Cosθ 47.7.dg rs. th. rsult. would. b. xactly. as xp rimtd. valu. up. to. all. dcimals. show. abov. I. accordac. with. currt. thory. Cosθ dg rs Cosθ Th. agl. btw. total. agular. momtum. to. its. compot.. o Z axis B + B 0 4 VBa0 Th valu for ( ) Cr turs out to b α 1 ( ) Coclusio for Appdix (1 of ): Th sigificac of th fi structur costat (Plas brows th t for itrstig dtails o this) 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 ordr to apprciat othr fudamtal aspcts plas also fid a figur at th d of this work ad th w fidigs through othr postd works of this author alog with this, with a classical approach. It is also importat to ot hr that v though Quatum thortical calculatios with a arly poit siz lctro approach may agr up to svral dcimal placs with xprimts is otworthy that a classical approach provids clarity ad visibility ad furthr th sam poit particl approach has causd substatial hidracs o othr aspcts too such as itractios lik Nuclar pottial barrir ad its magtic momts, Alpha dcay, utro bta dcay, ad abov all th currt cocpts thmslvs ar dd to challgd. (How a poit lik lctro ca rsult i such accurat agrmt with th xprimt is lft to radrs ow judgmt) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

32 of 46 Th followig has b tak from ducatioal wbsits. It is ot possibl to giv a qualitativ dscriptio of th ffcts which giv ris to th g-factor aomaly of th lctro. Th dtaild thortical calculatio of th quatity is i th domai of quatum lctrodyamics, ad ivolvs th itractio of th zro-poit oscillatio of th lctromagtic fild with th lctro. Compariso of thortical dtrmiatio of a with its xprimtal masurmt costituts th most accurat ad dirct xistig tst of th thory of quatum lctrodyamics. I th sam mar as abov th followig ot shows th cosquc of a poit particl cocpt. Wh th ida of lctro spi was first itroducd i 195, v Wolfgag Pauli had troubl accptig Ralph Kroig's modl. Th problm was ot that a rotatig chargd particl would hav giv ris to a magtic fild, but that th lctro was so small that th quatorial spd of th lctro would hav to b gratr tha th spd of light for th magtic momt to b of th obsrvd strgth. Furthr th postd works of this author o Casimir Effct ad No bta dcay possibl with a poit lctro i fr utro dcay falsifis th cocpt of Zro Poit Oscillatios ad Nutrios. Th aomaly i g-factor of lctro magtic momt as w kow ow was ursolvd bcaus th Plak s agular momtum was hld a costat whil allowig violatio of C is th caus which is far highr i cas of poit particls (a fals otio). This sam aalysis is furthr put forward for utrios i th followig appdix. 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-) Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047

33 of 46 (A figur showig th furthr w fidigs o 17 factor ca b foud at th d). 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) Agular momtum/radius ad (17 factors) 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 46 1) Th ratio of agular momtum (w) btw (7) ad (4) 17 ) Th ratio radius btw (7) ad (4) 17 ) Plack s d Brogli- Compto wavlgth rlatio (5) x17 (7) 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 (6)/(7) o pag () (1.7/) xm 6) Coditio for stabl atomic orbits (xh/pi) (1.058x 10-4 ) ( ) π. x10x17 7) Multiplyig (6) by (pi) as w kow is Plack s costat h 6.649x10-4 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. Rfrcs: 1) Cocpts of Modr Physics-Fifth Editio-Arthur Bisr-Mc-Graw-Hill,Ic ) Msur d précisio du magétism d l'élctro URL: 000: Th Amrica Physical Socity No Nutro Bta dcay (If lctros ar lss tha its classical radius) (Smi classical approach) Corrspodig Author: V. Shakar Narayaa Abstract: 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 46 This scop of this cocis work is a attmpt to show that bta dcay of a utro is ot possibl if lctros ar to b lss tha its classical radius ad furthr to show that by holdig Plack s spi agular momtum a costat as i currt thoris lads to mor discrpacis o magtic momts of subatomic particls. 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. 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 ( whr m is lctromagtic rgy mass)ad that th orbital vlocity of lctros ad uclos ar far lss tha C ad thrfor rlativistic ffcts for mass icras ar isigificat. Furthr this particl modl also provs that durig high-rgy scattrig xprimts th sub atomic particls would momtarily shrik posig as though thy ar poit particls (particularly lctro). Aalysis: 1) If lctros ar to b tratd as poit particls i accordac with currt thoris,, th bta dcay is impossibl? O cosrvatio of rgy frot, sic lctros ar clos to poit particls (<10^ -18m) accordig to currt thoris th bidig rgy btw a asct proto ad a lctro durig a fr utro dcay th distac btw thm ar about (0.51) fm ad at this distac th bidig rgy btw thm should b gratr tha (9 Mv). Hc how a fr utro ca dcay at all if lctros wr to b poit lik particls? Howvr at th proposd classical radius for lctros th followig ar th outcom. Rst Ergy (utro) - (proto + lctro) 0.78Mv with which th asct lctro ds to ovrcom th lctric bidig rgy of th 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 46 asct proto of about a distac with classical radius for lctro is ( ) fm with Coulombs law is about (0.445 Mv) ad th rst is carrid off as lctro kitic rgy which is i agrmt with xprimts. ) Aalysis o Agular momtum of utrio: Dfiitio of Plack s agular momtum (h/pi) mvr Whr (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..) Th umrical valu of h x10-4 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. V B 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 6 ( Orbital. Vlocity. at. Bohr. radius).188x10 m / s ( CMP 15) a ( Bohr. radius) 5.9x10 m ( CMP ) h 1 1 VB mvba Iω ( m a0 ) x( ) 4π a At classical radius of lctro (r ) 0 0 µ Sz ( Spi. Classical. Total) ( m ) x mcr Cr (1B ) 7.814x10 6 J / T 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 46 ( Agular Momtum). h π Iω m r C x( ) r 1 mcr 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. ) 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 π Iω ( mr V ) x( r spi mv ) V Thrfor quatorial spi vlocity C spi spi r () h 4π. m r C () µ B By comparig quatios (1A) with (1B) ( ) (4) µ Thus by maitaiig (h/pi) a costat th xtt of violatio of C is carrid ovr to th magtic momts which xplais th aomalous-g-factor- Zma ffct. 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) 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 46 (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. Plack' s. agular. momtum." h" Th. rsultig. agular. momtum. of.(5,6 & 7) x10 r ( r h ( Spi Classical agular momtum lctro) h ( Spi Classical agular momrtum Pr oto) h ( Spi Classical agular momtum utro).818 fm ( lctro classical radius) p p 0.51fm),( r mcr 1 ( mcr ) 4.44x10 1 ( m 1 ( m J S which.. is. lss. tha. half. spi 0.48 fm) ar clos to 0.5 fm xprimts ( CMP 481) 4 p 7 Cr ) x10 p 4 Cr ) x10 J S (5) J S (6) 4 J S (7) µ. µ pz z m m p x m x m p Cr Cr 14.1x x10 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 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 (119) folds with rspct to half Plack s spi ad thus its ffct durig bta dcay is ot flt ad thrfor th cosrvatio of agular momtum (h bar/) that is big tratd a costat uiformly for all particls i currt thoris bcoms qustioabl. But th qustio is what th valu is for half spi (spior) is? Ad furthr this mchaical uit is ot a masurabl quatity. Subatomic Particls ad Four Itractios (A omatrial shll modl (Part -1 of STR-GTR-Athr-(Part of ) ad) CopyrightDposit.com,umbr: 00047