A Model of Particles Cold Forming As Collapsed Bose–Einstein Condensate of Gammons

Physics & Astronomy International Journal

Commentary Open Access A model of particles cold forming as collapsed Bose–Einstein condensate of gammons

Abstract Volume 2 Issue 4 - 2018 The paper brings supplementary arguments regarding the possibility of cold particles * −+ Marius Arghirescu forming as collapsed cold clusters of gammons–considered as pairs: γ = ee ( ) Patents Department, State Office for Inventions and Trademarks, of axially coupled electrons with opposed charges. It is argued physico–mathematically Romania that the particles cold forming from chiral quantum vacuum fluctuations is possible at TK→ 0 , either by a vortexial, magnetic–like field or by already formed gammons, in a Correspondence: Marius Arghirescu, Patents Department, “step–by–step” process, by two possible mechanisms: a)–by clusterizing, with the forming State Office for Inventions and Trademarks, Romania, Tel +4074 00 5795 507, Email [email protected] 0 = = of preons zm= 34 e , and of basic bosons: zp 7 zz ; 2 4 z, with hexagonal symmetry and thereafter–of cold quarks and pseudo–quarks, by a mechanism with a first Received: June 11, 2018 | Published: July 05, 2018 * *0± step of z//( qq) –pre–cluster forming by magnetic interaction and a second step ± 0 of zqq//( ) –collapsed cluster forming , with the aid of magnetic confinement, and b)–by pearlitizing, by the transforming of a bigger Bose–Einstein condensate into smaller gammonic pre–clusters which may become particle–like collapsed BEC.

Keywords: cold genesis, bose–einstein condensate, quasi–crystal quark, dark energy, quantum vortex

Commentary 0−r /*η 1 2 Vr( ) ==⋅=⋅υρ P V e; Pr( ) / (r) c (1) In a previous paper1 were presented briefly some basic particle n in n n ( 2 ) n models resulted from a cold genesis theory of matter and fields2–5 By an electron model with radius: a = 1.41fm and with of the author, (CGT), regarding the cold forming process of cosmic exponential variation of the quantum volume density and of the 0/−r η elementary particles, formed–according to the theory, as collapsed magnetic field quanta: ρρrr≈= ρ· e;η ≈ 0.96 fm ; * −+ µ ( ) ee( ) cold clusters of gammons–considered as pairs: γ = ee of axially 0 14 3 ( ) ρ = 2.22x 10 kg / m . coupled electrons with opposed charges, which gives a preonic, quasi– e crystalline internal structure of cold formed quarks with hexagonal In the base of some neo–classic (pre–quantum) relations of the 2–5 5 0 electric and magnetic fields: symmetry, based on zm≈ 34 e preon–experimentally evidenced in 6 2 2 Krasznahorkay et al., but considered as X–boson of a fifth force, of 2 1 ∆ p 4rπ ⋅ q (r) = ⋅ρ (r) ⋅=v ⋅c ; q = ; leptons–to quark binding, and on two cold formed bosonic ‘zerons’ : Eks 11e cs k 0 0 2∆ t k =4 = 136 = 7 = 238 1 zz2 me ; and zzπ me , formed as clusters of 22 (2) degenerate electrons with degenerate mass and magnetic moment and 4π ⋅ am−10 * B =⋅⋅= kρ (r) v ; ( k =1.56 x 10 ; v≈ c ) with degenerate charge ee= 2 , (characteristic to the up–quark– 1µ c1 c ( 3 ) eC in the quantum mechanics). In two relative recent papers,7,8 were brought arguments for two possible According to this theory,2–5 based on the Galilean relativity, the magnetic field is generated by an etherono–quantonic mechanism of cold particles forming as collapsed Bose–Einstein Γ =Γ +Γ condensate (BEC) without destruction: vortex M A µ of s–etherons (sinergons–with mass −60 m≈ 10 kg ) giving the magnetic potential A by an impulse a) by clusterizing and cold collapsing without destruction, from s a gammonic quasi–crystallin pre–cluster Nz,7 or b) by pearlitizing, =()ρ ⋅ 8 density: prss( ) cr and of quantons (h–quanta, with mass: by the fragmenting of a bigger BEC. The particles cold forming 2 −51 by clusterizing may results–according to CGT, in a “step–by–step” mh =⋅≈ h1 / c 7.37 x 10 kg , formed as compact cluster of process,7 supposing: sinergons) giving the magnetic moment and the magnetic induction 0* 0 a1) zz/ pre–cluster/cluster forming, with the aid of magnetic B by an impulse density: pr= ()ρ v , the nuclear field resulting c( ) ccr confinement, with a metastable equilibrium interdistance between from the attraction of the quantum impenetrable volume υ of a nucleon i gammons with antiparallel magnetic moments: d= a = 1.41 fm in the total field generatedaccording to fields superposition principle, e * (Figure 1); n by the N superposed vortices Γµ (r) of component degenerate * * a2) zz/ and zz/ are pre–cluster/cluster forming; electrons of another nucleon, having an exponential variation of 22 ππ ± 0 quanta impulse density, the nuclear potential resulting in the form: a3) ()qq/ –quark or neutral pseudo–quark pre–cluster/cluster forming;

Submit Manuscript | http://medcraveonline.com Phys Astron Int J. 2018;2(4):260‒267. 260 ©2018 Arghirescu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially. Copyright: A model of particles cold forming as collapsed Bose–Einstein condensate of gammons ©2018 Arghirescu 261

a4) pre–cluster of quarks or pseudo–quarks forming; a5) elementary particle/dark boson forming, or directly: a1’) quark pre–cluster forming (Figure 2) (Figure 3)→collapsed quark cluster forming; a2’) elementary particle/dark boson forming (cluster of quarks with the current mass in the same baryonic impenetrable quantum volume,

υI–Table 1).The particles cold forming by pearlitizing supposes: b1) the forming of a bigger BEC of gammons, with the 3 44 concentration of particles: Na≈=1 / 3.57 x 10 , (a=1.41 fm), in * 0 Figure 2 The m1–and r –quark pre–cluster forming. 67 a strong gravitational or magnetic field: Bγ =(2.2 x 10 ÷ 8.3 xT 10 ) −−11 10 , at temperatures TT==÷

Much lower than the transition temperature TB –corresponding to a very low (neglijible) fraction N0/N; (N(TB )–the initial concentration 24 of particles, (for example, for N ≈ 10 , TBE(B=0)=1464K), the length along the Bγ –field, of a gammonic BEC with the concentration −7 8 N0 formed at T=Tp resulting of value: L≈ 2.5 xm 10 ; b2) The pearlitizing of the resulted BEC by large temperature oscillation around the transition valueTB . The necessity of temperature oscillation around the transition valueT for the BEC’s B Figure 3 The cold forming of baryonic quarks. pearlitization results as consequence of the residual (reciprocal) magnetic interactions between gammons, which gives a superficial In which de is the inter–distance between adjacent gammons and lγ tensionσ . is the length of a gammon. It is necessary in consequence–for estimate the value r , to estimate the value of gammon’s length and magnetic For example, considering a radius r of meta–stable equilibrium of p p moment µ . a drop of BEC formed by the BEC’s pearlitization and maintained by γ the equilibrium between the force generated by the internal vibration It was argued in CGT,7 that is not logical to consider at an inter– (thermal) energy F r = V ⋅ NkTand the force generated by the t( p) 0 Bi distance d< r= h/ 2π m c= 386 fm , a value of the electron’s surface tension σ : ieλ magnetic moment radius: , higher than the inter–distance d , dE dV dS 4π 32 di i =−+==Prσπ0 ; V ; S =⋅ 4 r ; (3) −9 3 0 r≈ 5.5 xm 10 TK≈ 10 rT~1/ dr dr dr 3 resulting a value: p for B with p i , by 8 the use of equation (2) and with rdµ ≈ i . If we use the expression (2) of the B–field, because the magnetic

moment radius rµ , represents in the etheronic, quantum–vortexial model of magnetic moment, the radius until which the B–field −+ < − quanta have the light speed c, and because–for dri λ , for (ee) interaction is maintained the relation:B = E/c, we may re–write this relation in the form:

E(d) e µ e⋅ rcµ () ≈ = =0 , a << d r ; ⇒ r ≈ Bd 23λµd (5) c 4πε0dc 22 π ⋅ d Figure 1 The z0*–pre–cluster forming. Resulting in consequence, the expression of the electron’s magnetic moment at inter–distances dr≤ . The reciprocal equilibrium σ = ½ /1 i λ Because ( )Fλ , (the force rectangular on unit length), position of gammonic electrons, in the particular case of a semi–hard * −+ 3 44 for: Na≈ 1 /= 3.57 x 10 , (a=1.41fm–the metastable equilibrium gamma quantum considered–in CGT, as gammonic pair: γ = (ee ) 0 , may be estimated by equation (5), imposing a correspondence with −+ inter–distance between gammons),8 the equilibrium radius is: the conclusion of quantum mechanics regarding the ( ee ) pair

2 production, which indicates as minimal energy value of an external 21σ F Fγγµ µ electric or magnetic field which may convert the gamma quantum rm= = ≈ ≈∇0 [] 2 p 3 (4) into stable electrons, the value: Eγ = 2 mce . In CGT, based on the P00 l⋅⋅ P lγ P 02Nπ deB ⋅ lγ 0 kT classical mechanics and relativity, this value E has the sense of the i γ energy necessary to ‘split’ the gamma quantum into the component electrons with opposed charges:

* 2 2 *2 *2 *2 da≈⇒≈ , e / e; 2 eeeee ( 3 ) b. Eγ =2 mce = = +⋅Beµ ee() d = + (6) 44πε πε 4πε 8 πε * 22 00ade 0dee 0 d e≈/ ed , ⇒≈ / a ( 33) e ( ) . * ≤ c. In which we considered a possible degenerate charge, ee. Because for a photon–like gammon its length must exceed its This interpretation is logical by the fact that the nuclear E–field may diameter proportional with the speed,9 it results that the case a) γ * split the –quantum only if it can act over internal e(e )–charges of corresponds to a relativist gammon ( vc→ ), which–in CGT, may opposed sign. have simultaneously rest mass and the c–speed, and the case c) 2 correspond to a linked gammon, which is confined inside a bigger Between e and ( /3)e, considering an electric permittivity elementary particle (mesonic or baryonic), the degenerate charge ε= εε00r ≈ ε , we have the next significant possibilities: * * 2 2–5 a. eed=⇒=, 1.5 a; ee≈ ( /3 ) being specific to the up–quark , (p–quark–in CGT). e So the case b) corresponds to a gammonic pre–cluster, in accordance also with the quantum mechanics. Table 1 Elementary particles: (theoretic mass) / (experimentally determined mass)

− − − − +−** Basic quarks: m1 = (z2– me*) = 135.2 me, = ++=σσ137,8 ; → + + ; () = + → m21 m e emm e2 m 1 e vee( e e) ve

Derived quarks: p+(n–) = m (m ) + 2z − +− +− − − − 1 2 p npe=++→++σee pev; λ = np( ) + zsπ ; =+ λλ zv22 ; = + 2 z

Mesons: (q– q ) Baryons: (q–q–q)

−− + + − =2 + = 1836.2 ; = 2 += 1838.8 ;/ , = 1836.1; 1838.7 ; µµ=2Ze1 += 205 mee/ = 206.7 m pr p n mnee n p me p r n e me

o 0 o 0 ππ=+=mm11 270.4 mee ;/ = 264.2 m −Λ =snp + + = 2212.8 mee ; /Λ = 2182.7 m

++(++; + ;0; −) ± ± + − ±;0 ππ=+=mm 273 m ;/ = 273.2 m −∆ = +λ + = 2445.6; 2453.4 ;/∆ = 2411 ± 4 12 ee s pn( ) meem

++ = +=λ 987 ;/ = 966.3 + − +− K m1 mKee m −Σ=+=vp2 2346.2 mee ; Σ=+= vn 2 2351.4 m ; / ΣΣ= , 2327; 2342.6m e

oo= +=λ 989.6 ;/ = 974.5 o 0 Km2 mKee m −Σ =vnp + + = 2348.8 mee /Σ = 2333 m ;

0 ηηo = += 1125.6 ;/ = 1073 ; o −−0 ms2 mee m −Ξ=2sp + =2586.8 mee; Ξ= 2 sn + =2589.4 m; /, ΞΞ= 2572; 2587.7 m e;

−− −Ω==3vm 3371.4 ee ; / Ω= 3278 m .

* 2 and c) resulting that ε > 1 , so–the charge degeneration may be less The degenerate charge’s radius: re( = / e) for da≈ , r e ( 3 ) e * 2 results from (6), according to a CGT’s relation: accentuate,()ea> / e, because the decreasing of the V – ( ) ( 3 ) e 2 2 2 e π ⋅ potential with ε . By the proportionality between n, ε and the quanta *22S x 4 rree  r e2 ea() = ≈ = e ≈ e = e ; ⇒≈ r 0.9d ; S =π (r + r ) ; 9   e ix e v density, deduced in CGT: n, ερ~ c , because the proportionality: −2 kk11  a di 3  ρc ~ r for r > a, it results that: (7) −2 2 ρc~r , ( ra >⇒) εε( a) / ( dee) ≈( da/) = 2.2 (8) but in the hypothesis: ε= εε ≈ ε However, the so–called 00r . As consequence, the relation (6) must be re–written in the “stopped light experiment”10,11 showed that a Bose–Einstein condensate approximate form: determine a high slowing of the light passed through it, at a value 2 *2 2 2 vc<< , so for da≈ , by the known relation: ncv=/ ≈ ε it 2 eeee c e c r =2 = = +⋅µ () = + Eγ mce Be ei d (9) results that we may consider the approximation: ε= εε00r ≈ ε only in 44πε00ad πε i 4πε0 εrid 8 πε 0 d i the case:de=1.5a, corresponding to a relativist gammon, for the case b)

’ 2 interdistances: de=1.5a and di =( /3)a , as consequence of the self– resonance induced by the repulsive potential V (d), the value with εε= (ad) /2 ε( ) ≈ , resulting that:Va( ) ≈ Vµ ( a) . This r re e d =a being a mean value, the equilibration between the attraction result explains also the possibility of particles forming by clusterizing, e 0* force F (d), of magnetic and electric type, and the repulsive force by the conclusion that–in a section plane of a preonic z –pre–cluster a = −∇ ’ 2 formed with hexagonal symmetry, the inter–distance of metastable Fdrr( ) Vd( ) , being realized at d ≤ di = ( /3)a, the action of magnetic potentialV being diminished by V with a factor f ≤1. equilibrium d =a results by the equality Va( ) ≈ V( a) for the µ r d i e µ interaction with the central electron, either by electrostatic attraction For the approximation of the superficial tension sFγγ= /2 l γ, and magnetic repelling or by magnetic attraction and electrostatic according to the previous considerations, we may approximate that–at repelling (Figure 1) (Figure 4), the gammonic pre–cluster’s collapsing the gammonic pre–cluster’s surface with a mean interdistance de=a resulting by the attraction between adjacent circularly disposed between adjacent gammons, the binding force Faγ ( ) is given by gammonic electrons, the central chain of axially coupled gammons the magnetic interaction between gammons, the electric interaction giving the z0–preon magnetic moment, which explains similarly the force between gammons (of inter–dipoles type) being considered 0 cold confining of a pre–cluster of z –preons, and so on (Figure 5). compensated by the repulsive force Fr (d), in a simplified model.

At increased temperaturesTTiB≥ , the linking (magnetic) energy 2 resulted from equation (9):Vµ ( a) ≈ mce , is diminished by the vibration energy according to a relation of the total binding energy of

the form:VT( a) = f d·– Vµ ( a) kTBi, ( fTdi~ –diminishing factor), which explains also the thermal−quantum splitting, the binding force (considered as magnetic for the pre−cluster: ), being in this case: 22 TTmc  mc ()= F()1 −≈i fee 1 −i ; T = f FaT µ ad Cd (10) TC aT  CB k In consequence, we may approximate the expression of the superficial tension σ = Fl/2 as being given by the magnetic γγ γ interaction force between two adjacent gammonic electrons, according to the approximation relation: e F F 22 γµ mceeTi mc 9 0 σ = ≈=f 1 − ; T = f =⋅5.9x10 K Figure 4 The forming of the z –cluster’s kernel. γ d 2 Cd fd (11) 2l⋅ 2 2 aaTCB k

≈−(1 /1) ≤ with fdr Fa( ) Fµ ( a) . The equilibrium radius rp of the pearlitic gammonic pre–cluster results in this case according to the approximate relation: 2 −6 2σ γ mc a T T 8.3x10 = =eC1 −≈≈i a [] rfpd fd m (12) P kT T T T 0iBi C i

3 −9 ForTTiB= ≈ 10 Kand fd ≈ 1 , it results: rxmp ≈ 8 10 . When > Ti Tr Bp( ) , the (metastable) equilibrium radius results smaller, Figure 5 Parts of crystallized gammonic pre–cluster which may result by a 8 BEC’s pearlitizing. according to (12), (rp’< rp), but because the equilibrium inter–distance cannot decrease when the internal energy kBTi increases, according The total collapse of the gammon is impeded–according to CGT, to equation (4), it results that the equilibrium radius of the BEC may by a repulsive field and force with exponential variation, generated be re–obtained at the specific decreased value only by the decreasing by the ‘zeroth’ vibrations of the electron’s kernel (centroid) and of the particles number of the BEC, so the pearlitization with the acting over a quantum volume of the electron: υe(re ≈ d) with a force: forming of quasi–cylindrical pre–clusters of baryonic neutral particles 2 F d≈ 2 Sρ dc, (which explains also the non–annihilation corresponding to a radius: rr< may be formed by large oscillations r( ) xr( ) ba – + between e and e at low energies), deduced considering a quasi–elastic of the internal temperature Ti–given by the boson’s vibrations, around * 2 the valueTTiB= . interaction of field quanta with the interaction surface Sdx = π of the repelled electron. On the radial direction, for a pre–cluster with the radius rc< rp , We may consider–in consequence, that the gammonic electrons the electric interaction between gammons having the electron’s charge have a remnant vibration of spin and of translation between the in surface, may be neglected for di< a and we may consider that the

contained (quasi)integrally inside its impenetrable quantum volume υ , we may approximate that–for a protonic m–quark with N = 756 magnetic potentialVµ between gammons is partially equilibrated by i q quasi–electrons with the centroids included in the quark’s impenetrable the vibration energy kBTi and by the repulsive potential Vr(d) acting e 7 quantum volume of radius r≈ 0.21 fm , we have d T≈ 0.02 fm at over a quantum volume of the electron:υee()rd≤ . q ei( ) TT<< . For conformity with the general electrogravitic form of CGT,2–4 iB we will take for the repulsive force F (d), the form correspondent with p r Considering that atTT<< , (for example–atTK≈ 1 ), the pre– equation (2): iB i cluster’s collapse is stopped at d≈ 0.02 fm , with f ≈ 1 it results di i µ − 00 0 ρ/ ρρ=pp/ ρ ≈≈() / η 0.02 02 ηr 2 that ri(T) e re( Td) e i . Because ' Fdr() = −∇ V r = q ss ⋅ E = S x ⋅2ρπ r c ⋅ e ; Sx = r ce ; r ≤ di (13) 00 ρρri(T ) /1 e≤ , it results that the cluster cannot be equilibrated i.e.–considering an exponential variation of the quanta density at an inter–distance d ≥ η = 0.96 fm ,2–4 ( d = η being close to and a quasi–elastic interaction of V –field quanta (approximated with i i r 2 small radius–in report with the radius r of the static q –charge) with da≈ / c s but higher than i ( 3 ) –corresponding to c)–case), so the the interaction surface: conclusion that the mean inter–distance di=a between the electrons of 2 ** +≈ =π ≈½. the gammonic pre–cluster is one of un–stable equilibrium, is justified. Srxc( r h) Sr xc( ) r c S x( e) (14) It results that–at temperaturesTT< , the resulted pearlitic i B Considering the effective action of the Vr–field quanta over the pre–clusters with radius rr< may collapse because the residual qs–pseudo–charge in a quasi–constant solid angle αs,rc may be cp ≈ approximated as given by the result of equations (6)+(7): rdci, (reciprocal) magnetic moments of the gammons and because which may be used also for approximate the value of the reciprocal * the decreasing of the internal energy: PV0 ( rc ) more than the magnetic moment : µri=½ ec ⋅ d. superficial energy: σ γ Sr( c ) , from equation (3) resulting that: Because the magnetic force results from the gradient of quanta /<⇒ 1 ⋅ ' <σ ', (' =/ ) (rcp r) P0 Vγ S d dr . Because the electron density ρµ (d) which gives by equation (2), the magnetic induction B(d), we must deduce the magnetic force considering that the is a very stable particle, its negentropy being maintained by the magnetic moment µ of the attracted electron is quasi–constant r energy of the etherono–quantonic winds according to CGT and to a short derivation interval δ d , retrieving the expression of the i 12 magnetic force between two degenerate electrons in the form:7 in concordance with the particle’s “hidden thermodynamics”, it 0 ad− i 22 a-di ρ results a slow variation of r with the internal temperature Ti , of ηηTdedi =µ ( ) ∇ () ⋅ ⋅ 1 −ii ≈− ⋅e ; 00 Fµµri dxBa e e f 4  the fraction ρρTd//≈ () η, but with the consequence of 8πε η ri( ) e i TaC 0  inflation generating or of collapsing of the gammonic pre–cluster, at *32 2 ecd ⋅ ecd * 4 πr d (15) high variation. µη===≈≈iii ; e e ; 0.96fm r 2 e 2 2a ka1  The repulsive force increasing with the temperature Ti may be approximated by a relation specific to metals. Considering that the which results from the exponential variation of the B–field quanta 0 0 14 3 value ρρT ≈≈2.22x 10 kg / m is attained at a temperature density inside the electron’s quantum volume, fT~ being a re( i ) 12 µ i TxK≈ 2 10 diminishing factor resulted by the periodically partial destroying of the close to those of quarks deconfining: q , it results an approximation relation of ρr –density variation with the temperature: internal etherono–quantonic vortex Γµ of the magnetic moment by the 0 vibration energy: ε v≈ kT Bi. By (15) the equality: Fdri( ) = Fµ ( d) i ∆ρ ()ddρ 1 p , forTT<< , gives: ri≈∆α; e =i ≈ =αα(T -T ) ≈ ⋅ iC pp cTfp µ cqi cqT ρri()d ρηr e 0.02 22 a-di p 12 -11− 1 eddi i η 22 2 ≈f ⋅=e 2ρ () ≈ 2d πρ ⋅ (); Tic≈ 1K ; TxKq = 2 10 ; ⇒≈α 2.5x10 K Fµµ 4  Sxri dc i ridc (17) 8πεa η 0  p 0 −−11 1 with ρρT ≈ 0.02 resulting:α ≈ 2.5xK 10 . So, we d a-d rB( ) e c − i i 0 η di η µ0 may approximate that f≈−(1 ( FF / )) ≈ 0.98 . At very low ⇒ρρ()() = ⋅=r ρ() ⋅ e ; ρ () = ; f ≤ 1 d raµ rid ri Te fµµe a e a 2 η k temperatures T the repulsive force F is maintained–according to  1 i r (16) equations (7), (13) & (17), because the maintaining of the ‘zeroth’ vibrations of the electronic superdense kernels (centroids) which

2 13 3 1 creates the disturbance which generates the scalar density part: with ρµe (a) =01 / k = 5.17 x 10 kg / m and with: 0 , ρri(T ) , according to CGT. This phenomenon explains the fact that 0 0 0 a/η 14 3 the quasi–crystallin cluster of electronic centroids of the particle’s ρ T= f() d /ηρ ; ρ= ρ a· e= 2.22 x 10/ kg m ri( ) µ i ee e( ) kernel not collapses neither at very low temperatures, explaining the 1 2–5 , resulting that:(dTii/η) ~ . particle’s lifetime increasing with the temperature’s decreasing.

At low temperatures, because the magnetic moment results– If the internal pre–cluster’s temperature Ti is maintained close to according to CGT–by the energy of etherono–quantonic winds of the e = the metastable equilibrium valueTTiB , the pre–cluster’s collapsing quantum vacuum, we may take fµ ≈ 1 . For the kernel of a formed may still occur in a strong magnetic field, by the aid of the magneto– particle, because the superdense centroids of quasi–electrons are

field value given by equation (2). 8 gravitic potential VrMG ()φ , according to CGT. 2–4 Assuming–by CGT, that the vortex–tubes ξB of the magnetic This conclusion may be argued by the hypothesis of the magnetic B–field are formed around vectorial photons (vectons) of 2.7K −15 microwave radiation of the quantum vacuum–identified in CGT as fluxonφ0 =h/ 2 e ≈ 2 x 10 Wb , considering that the ξ –vortex– B electric field quanta having a gaugeius: rad r≈=0.41 a 0.578 fm tubes of the B–field are fluxonφ with a section radius r , with a linear v 0 φ 4 −1 and that the electron has a small impenetrable quantum volume: = ρω·() · = ρ·~ −43 decreasing of the impulse density: pc ( r) r( rc) r e 5 8 υi = 1.15x 10 fm , from CGT it results that: , for rr≤ φ , (which is specific to vortex–tubes) and with the mean density: ρφ approximate equal with those resulted from the local Bl–

2 m⋅ BR() m υυii2ccϕϕ υ i⋅ 00rv 1 VMG (r) = ρϕ (r ) ⋅= c = ϕ0BR( ); ρϕ (r) = ρ ϕ = ; mϕ= 2πρ ϕϕrrv ; 2 4ππ r kc11⋅⋅4 k r r 2π⋅rϕ r

e (18) B(R) υ ⋅ c -40 J⋅ m mkϕ 1 ⋅ c ϕ V (r)= K ; K = i ϕ = 7.87x10 ; r = = 0 MG M M 0 ϕ r 4π k T BR() BR () 1

−14 with ( m= 4.27 x 10 kg / m –the fluxon’s binding energy of the nucleons to their neighbours: Eb ≈ 40 MeV φ 3 −1/3 E = / ε = = and kF( 5 ) –the kinetic energy per nucleon, depending on mass on unit lengt). For lNi rφ , we have: e −32 its Fermi energy. VMG () rφ = (υπi · cBR )( ) / 4 k1 = 1.76 x 10 BR( ) –a neglijible A generalized form of the binding energy formula for a gammonic value comparative to:Vµ =µe xB, () µµ e = PB , but which can initiates BEC, may be obtained writing the kinetic term Ek in the form: kBTv, 0 the clusterizing process of a preonic z –pre–cluster forming or of which gives: 2 an photon or of an electron forming–around a superdense kernel  T 3 EEkkv E ≈⋅− 1 − ; = ; E = k T (half of an electronic neutrino–in the electron’s case, according to NbE AA  B (19) 1–3 T CGT), but at high values of the B–field or of magnetic field–like EEbbC etherono–quantonic vortexes formed in the quantum vacuum as chiral with T =E /k and E =k T –the mean vibration energy of the fluctuations. C b B v B v particles and Eb–the binding energy per particle. The vibrations The necessity of a high value of the B–field–like chiral fluctuations induced by interaction particles such as a neutron which can split intensity in the process of particles cold forming directly from the an uranium nucleus, may explain by equation (19), the fact that the primordial “dark energy”, results in accordance with a particle–like nuclear fission is explained by the “drop” nuclear model, even if the sub–solitons forming condition13 which specifies that the energy nuclear properties and even the nuclear “magic” numbers of nucleons 2 EΓΓ= mc of the mass–generating chiral soliton field, (given–in which gives the maximal nuclear stability: 2, 8, 20, 28, (40), 50, 82, 126, may be explained also by a solid rotator type of nuclear model this case by a sinergono–quantonic vortex Γµ =ΓAB +Γ =2πrc ⋅ ), 2 , particularly–of quasi–crystallin type, as those deduced in CGT2–4 should be double, at least, comparing to the mass energy: Em = mc which explains the “magic” nuclear numbers as resulting from quasi– of the generated sub–solitons; ( EEΓ ≥ 2 m ). 2 crystalline forms of alpha particles, with Z = ∑(2 n) , () nN∈ . The generalization to the scale of an atomic nucleus permits to consider an atomic nucleus as a (non–collapsed) fermionic condensate In CGT, this phenomenon is equated by multiplying the with quasi–crystallin arrangement of nucleons, which may explain binding energy between two nucleons with a term depending on the nucleonic “magic” numbers of maximal stability,2–4 the nuclear the vibration “liberty” (amplitude) of the nucleon, in the form: fission reactions–well described by the droplet nuclear model, being − /*η 00l 0 explained by a nuclear local phase transformation at the internal E T= E· e ≈− E· 1 kT / E , with l~ kT . b( v) bb v ( Bv b) v Bv temperature increasing–determined by the nucleons’ vibrations. For a gammonic BEC, the number A of degenerate electrons Mathematically this phenomenon may be equated by equation results in the form: 3 E= aA 33 (11), by modifying the volume term: Vv and the surface A≈=(4ππ r /3 )() · N 4 /3/ ra, N = 1/ a , 2/3 ep 00( p) ( ) term E= aA from the Bethe–Weizsäcker semi–empiric σ S the equations (12) & (19) , for a metastable gammonic BEC, formula of the nuclear binding energy, based on the liquid drop giving the binding energy in the form: model proposed by George Gamow, in which A is the atomic number 3 2 and a= E – /ε ≈ 15.8MeV ≈= a17.8 MeV –the volume 32 Vb ( 5 ) F S 44ππTT3 TT  T E≈⋅Cv1 − − Cv1− 1; − v(20) and the surface term coefficiens, given as difference between the NbE   33 TTvC TTvC  T C 

Also, in the case of the proton, is more logical that the external 22 ≈≈· ; ≈ · / ( ≈0.98) with Eb E m fmcT de C fmc de k B, f d , the shell of the impenetrable quantum volume, corresponding in quantum relation (20) showing that the increasing of the BEC’s temperature mechanics to the gluonic part of the nucleon, has the inertial mass 0 determines transition to a liquid/like phase and thereafter– given by cold (“dark”) leptons, ln : photons, gammons or also z – pearlitization, as consequence of the internal temperature increasing preons (instead partons–as in the standard model of QM), coupled over the equilibrium value. with oriented (antiparallel) magnetic moments, for example–as a (quasi)circular chain of coupled z0–preons around the impenetrable Conclusion quantum volume (explaining a part of the quarks confining force) or By the paper it is argued that the particles cold forming from also in the middle part of the quantum volume (corresponding to the η ≈ 0.86 fm quantum vacuum fluctuations–considered in the quantum mechanics, proton’s root mean square radius of its charge, ). is possible at TK→ 0 , but usually by clusterizing, in specific According to the previous model, the revised Anderson’s model conditions, as a “step–by–step” process in which the intrinsic rest of proton, with attached positron having degenerate magnetic mass/energy necessary for the particles forming: mc2, is acquired moment (CGT),2–4 explains in this case the proton’s charge, e+, by either by an initial quantum vortex corresponding to an intense the conclusion that the secondary vortexes ξµ induced by the Γµ magnetic–like field, with vortexial energy comparable with those of –vortex of the protonic positron’ magnetic moment at the level of the ulterior formed particle and with the producing of a dense kernel the superficially distributed internal leptons nl , increases the value of which may stabilize the quantum vortex, or by a less intense vortex µξ↑↑ their magnetic moment parallel oriented ( l µ ) and diminish but enough strong for increase locally the density of formed gammons ω ↑↓ Γ 0 the ln–lepton’ magnetic moment anti–parallel oriented ( µ ), or z (34me) preons. generating a roto–activity of the surface: ω x r =c, with ω ↑↓ Γ , An argument for the particles forming process by clusterizing is the electronic µ corresponding to a negative charge, e–, the proton’s charged surface Cooper pairs forming in superconductors, at low temperatures, well explained attracting and polarizing adjacent vectorial photons (vexons, w±– by the relation (9) resulted in this case in the form: Va≈− Va and the e ( ) m ( ) in CGT) with opposed magnetic moment, which gives the positive possibility of fermionic condensate forming at very low temperatures also with + charge of the proton. At the µe transforming of the proton, the lack 13 electrons, explained in the same way, in CGT. of the protonic positron re–establish the equality between the values The vortex was identified as the logical way to explain the of the coupled leptonic magnetic moments of the particle’s surface 14 fermions pairs forming also in other theoretical models, but a Sn which becomes neutral by the loose of the previous attracted −−60 69 polarized vectorial photons which are carried by the released vortex of etherons with the mass of 10÷ 10 kg –considered positron, being retained at the positron’s surface by the positronic as particles of the sub–quantum medium, (corresponding to the ‘dark + magnetic moment, µe . Extrapolated to the electron’ case, the model energy’ concept), is not enough to explain the possibility of fermion explains the transforming of a (e–e+) pair into two gamma–quanta by forming from quantum vacuum, without a quantonic component, the conclusion of reciprocal charge cancelling by polarized vexons 15 with quantons of energy ε = h·1 and having superdense centroids changement, (Figure 6). which–by vortexial confining, can form a superdense centroid and a rest mass of the formed fermion. According to CGT,1–5 this mechanism may explain the background radiation (2.7K) photons forming as pairs of vectorial photons, in the Cold ProtoUniverse. The possibility to explain the masses and the magnetic and electric properties of the elementary particles resulted from the cosmic radiation, in a preonic model, by a cold clusterizing process 0 and with only two quasi–crystallin basic bosons: z2=4z =136me; 0 zπ=7z =238me, indicates–in our opinion, that after the electrons (negatrons and positrons) cold forming, the clusterizing was the main process of the particles forming in the Universe, by at least two steps: a)–the quasi–crystallin pre–cluster forming (of gammons 0 or of formed z –preons or z2–and zπ–zerons) and b)–the pre–cluster’s cold collapsing, without destruction, with the maintaining of a quasi– crystallin arrangement of electronic centroids at the kernel’s level, as consequence of their ‘zeroth’ vibrations–which determines an internal −+ scalar repulsive field. Figure 6 The conversion process: (ee) → 2 g. The particles cold forming by clusterizing, in a Galilean relativity According to the model, the electron radius of 10–18 m supposes the conclusion that the quantum vacuum contains cold experimentally evidenced by X–rays scattering is the radius of the gammons and z0–preons as basic “field” which gives inertial mass electron’s kernel. of the resulted bigger particles, but also bigger leptons, such as pairs 0 As secondary, particular possibility, the particles forming by of muonic neutrino: ν µ = 6z , (of ring form), which may explain −+ − + pearlitizing supposes the forming of a bigger BEC of gammons, with the known reaction: ee → µµ , by the conclusion of the 2v 3 44 µ ≈=1 / 3.57 10 –neutrino pair splitting in the quantum vacuum by the interaction the concentration of particles: Na0 x, (a=1.41 fm), energy and the forming of ( ev− µ ) couples. in a strong gravitational or magnetic field and at very low temperature

Citation: Arghirescu M. A model of particles cold forming as collapsed Bose–Einstein condensate of gammons. Phys Astron Int J. 2018;2(4):260‒267. DOI: 10.15406/paij.2018.02.00096 Copyright: A model of particles cold forming as collapsed Bose–Einstein condensate of gammons ©2018 Arghirescu 267 and the BEC’s fragmenting by the temperature oscillation around the 5. Arghirescu M. A preonic quasi–crystal quark model based on a cold genesis theory and on the experimentally evidenced neutral boson of transition value TB. and thereafter–the cold collapsing of the resulted 34m . Global Journal of Physics. 2016;5(1):496–504. pre–clusters, without their destruction. We suppose that this model of e particles cold forming may explain a part of the dark matter, because 6. Krasznahorkay JA, Csatlós M, Csige L, et al. Observation of Anomalous that it supposes the forming of neutral particles without magnetic moment, Internal Pair Creation in 8Be: A Possible Signature of a Light, Neutral with low interaction with the electromagnetic radiation. Boson. UAS: Cornell University Library; 2015. p. 1–5. In conclusion, the resulted explicative model of particles cold 7. Arghirescu M. The Explaining of the Elementary Particles Cold Genesis genesis may explain the existence of a huge number of material by a Preonic Quasi–Crystal Model of Quarks and a Pre–Quantum Theory particles in the Universe, by the conclusion of cold (“dark”) photons of Fields. International Journal of High Energy Physics. 2018;5(1):12– and thereafter–of electronic neutrinos and cold electrons genesis in 22. the Cold Proto–Universe’s period, by chiral (vortexial) fluctuations in 8. Arghirescu M. The Possibility of Particles Forming from a Bose–Einstein the ‘primordial dark energy’–considered in CGT as omnidirectional Condensate, in an Intense Magnetic or Gravitational Field. International fluxes of etherons and quantons circulated through a brownian part of Journal of High Energy Physics. 2018;5(1):55–62. etherons and quantons. 9. Arghirescu M. A Revised Model of Photon Resulted by an Etherono– Quantonic Theory of Fields. Open Access Library Journal. 2015;2(10):1– Acknowledgements 9. None. 10. Hau LV, Harris SE, Dutton Z, et al. Ultra–slow, stopped, and compressed light in Bose–Einstein condensates gas. Nature. 1999;397(594):1–368. Conflict of interest 11. Harris SE, Hau LV. Nonlinear Optics at Low Light Levels. Physical Author declares there is no conflict of interest. Review Letters. 1999;82(23). 12. de Broglie L. La thermodynamique“cachee” des particules. Ann de l’IHP References Secttion A. 1964;1(1):1–20. 1. Arghirescu M. The Cold Genesis– A New Scenario of Particles Forming. 13. Kenneth S and Steven S. Observations on the Role of Charge Clusters in Physics & Astronomy International Journal. 2017;1(5):1–5. Nuclear Cluster Reactions. Journal of New Energy. 1996;1(3):1–11. 2. Arghirescu M. A Cold Genesis: Theory of Fields and Particles. viXra; 14. Kiehn RM. The Falaco Effect, A Topological Soliton.USA: Talk at ’87 2012. p. 1–108. Dynamics Days; 1987. 3. Arghirescu M. The Cold Genesis of Matter and Fields. USA: Science 15. Şomăcescu L. Electromagnetism and gravity in a unitary theory. Publishing Group; 2015. p. 1– 222. Sweden: International Conf. of Gravitation; 1986. 4. Arghirescu M. A Quasi–Unitary Pre–Quantum theory of Particles and Fields and some Theoretical Implications. International Journal of High Energy Physics. 2015;2(1):80–103.

Citation: Arghirescu M. A model of particles cold forming as collapsed Bose–Einstein condensate of gammons. Phys Astron Int J. 2018;2(4):260‒267. DOI: 10.15406/paij.2018.02.00096