International Journal of High Energy Physics 2018; 5(1): 55-62 http://www.sciencepublishinggroup.com/j/ijhep doi: 10.11648/j.ijhep.20180501.16 ISSN: 2376-7405 (Print); ISSN: 2376-7448 (Online)
The Possibility of Particles Forming from a Bose-Einstein Condensate, in an Intense Magnetic or Gravitational Field
Marius Arghirescu
State Office for Inventions and Trademarks, Bucharest, Romania Email address:
To cite this article: Marius Arghirescu. The Possibility of Particles Forming from a Bose-Einstein Condensate, in an Intense Magnetic or Gravitational Field . International Journal of High Energy Physics . Vol. 5, No. 1, 2018, pp. 55-62. doi: 10.11648/j.ijhep.20180501.16
Received : May 13, 2018; Accepted : May 29, 2018; Published : June 13, 2018
Abstract: In the paper - based on a previous work regarding the cold particles forming process as collapsed cold clusters of gammons- considered as pairs: γ* = (e -e+) of axially coupled electrons with opposed charges, is analyzed the possibility of gammons pre-cluster forming from a Bose-Einstein condensate formed in the magnetic and in the gravitational field of a star. By known relations of a BEC forming, it is argued that- in the magnetic field of a star, the forming of a gammonic BEC with particles density N0 corresponding to those of a pre-cluster of gammons which may generates a particle-like stable cluster, may 3 6 occurs- for a transition temperature TBE ≈ 10 K, in a specific interval of field intensity and of temperature: B = (2.2x10 ÷ 7 -11 -10 8.3x10 ) T and Tp = (4.8x10 ÷ 1.8x10 ) K. The possible mechanism of the formed BEC transforming into pre-clusters of gammons which may become particle-like collapsed BEC, is a pearlitization mechanism, resulted as fragmentation of the formed BEC. It is argued that the particles forming from chiral quantum vacuum fluctuations is possible at T →0K, either by a vortexial, magnetic-like field corresponding to B ≥ 10 4 T or by already formed gammons, in a “step-by-step” process. Keywords: Bose-Einstein Condensate, Bosonic Cluster, Elementary Particles, Magnetic Field Confining, Black Hole, Magnetar
how the specific properties of each resulted particle/ sub- 1. Introduction particle are generated and how is explained the mass spectra It is known that –according to the Superfluid vacuum of the generated particles, (for example, of those called theory (SVT, [1]), sometimes known as the „BEC vacuum "elementary particles", resulted from or by cosmic radiation). theory”, the fundamental physical vacuum is viewed as In a theory developed by author in the book: “The cold superfluid or as a Bose–Einstein condensate (BEC), with Genesis of Matter and Fields” [2, 3] is argued the possibility microscopic structure of fermion and antifermion pairs, of a cold genesis of elementary particles in a very strong describable by a macroscopic wave function, the visible magnetic field, comparable to those of a magnetar or matter appearing as excitations from this superfluid vacuum. gravistar, in accordance with a resulted quasi-crystalline In addition to single-particle excitations, the superfluid model of quark and particle, resulted as Bose-Einstein condensate of N gammons, considered as pairs γ*(e *+ - e*-) of vacuum is capable of having real and virtual bound or * * 2 quasi-electrons with diminished mass me , charge e ≈ ( /3)e quasibound composite excitations which are akin to bosons * and magnetic moment µe , whose etherono-quantonic vortex of integer spin which in particular are quanta of some * of the magnetic moment: Γ µ(r) = ΓA + ΓB, is formed of interactions such as the electromagnetic interactions. -60 sinergonic etherons (m s ≈ 10 kg)- generating the magnetic However, the generation mechanism of real particles with 2 -51 non-null rest mass from virtual states of a quantum vacuum potential A and of quantons (m h = h/c = 7.37x10 kg) - with low density, is not clear, even if the theory of the rest generating vortex-tubes that materializes the B-field lines of magnetic induction. mass generation by the Higgs field gives an answer to this 0 problem. The used electron model is with the charge: e = S /k 1 0 π 2 Also, the SVT not clarify some other problems such as the contained by its surface S = 4 a of radius: a = 1.41fm – nature of force which generates virtual particle-like states, close to the value of the nucleon radius resulted from the 56 Marius Arghirescu: The Possibility of Particles Forming from a Bose-Einstein Condensate, in an Intense Magnetic or Gravitational Field
12 expression of the nuclear volume: rn ≈1.25 ÷1.5 fm, and with lines of a magnetaric field B→10 T formed around an 0 -r/ η; 0 an exponential variation of its density: ρe = ρe ⋅e with: ρe electronic superdense kernel (centroid). approximated as 3 -18 = 22.24 kg/m and η = 0.965 fm. It is argued that the electron cylindrical, with r0 ≈ 10 m. The electric field intensity E, the * may be formed at cold by an etherono-quantonic Γ µ -vortex electric charge q and the magnetic induction B the results in of magnetic field vortex-tubes which materializes the B-field the form:
π ⋅ 2 2 2 1 ∆ p 4 r 4 π ⋅a− m (r) = ⋅⋅=⋅ρ (r) v2 c ; q = q ; B =⋅⋅== kρ (r) v ; ( k 1.56 x 1010 ; v ≈ c ) (1) Es k1e c k 1 ∆ s 1c1µ c 2 t k 1 e C
The resulted quark/particle model explains the nuclear antineutrino given as pair of electronic centroids (with null force as an attraction of the nucleon’s impenetrable volume υi spin, identical with the electronic neutrino, resulted as p * in the field of N = (2N +1)- superposed vortices Γ µ(r) of Majorana particle), by the loss of the quantum volume of another nucleon, having an exponential variation of quanta quasielectrons, the quasielectron mass resulting of value: me* impulse density: pµ = ρµc, according to equation: = (∆n – 1)/2 ≈ 0.81 me, [2-4, 6].
0 -r/ η* 0 0; 2 0 p - p - 1 - Vn(r) = υiPn =V n ⋅e ; Vn = υiPn Pn(r) = (1/2) ρn(r) ⋅c (2) ne = (N +w ) = (N +e +σ)→ pr + e + νe +∈σ(889keV); (3)
3 with: υi(0.6fm) ≈ 0.9fm - the impenetrable quantum volume The model may explain also the reaction of K-electron 0 p 0 + of the nucleon; ρn ≈ N ⋅ ρe , and with η* = 0.755fm , resulted capture: pr + e → ne + νe, by the conclusion that the * * 2 * by the condition: ρµ(a, e ) ≈ ρe(a, e ) = ( /3)ρe(a, e) ∼ e = electronic neutrino results- in this reaction, by the coupling of 2 ( /3)e, [2-4] . the electron’s superdense centroid with the centroid of the The proton results in CBT by a neutral part with an protonic positron having degenerate magnetic moment, with attached electron (as in the Anderson’s model [5]). the loss of the quantum volume. n 0 The virtual radius: rµ of the proton’s magnetic moment, The theory, which predicted the existence of a preon z ≈ µp, results –in the theory, by a degenerate Compton radius rλ 34 me, experimentally evidenced in 2015 but considered as = λ/2 π = Ћ/mpc of the attached positron, which decreased X- boson of a fifth force, of leptons to quark binding, argues when the protonic positron was included in the Np cluster a preonic model of quarks whose stability was explained by a volume, (N p –the number of quasielectrons of the particle), quasi-crystalline model of z0-preon and of the quark core. e -13 p from the value: rµ = 3.86x10 m, to the value: ri = rµ = By CGT was argued the fact that- in a cold genesis model, 0,59fm , as a consequence of the increasing of the the preon z0 may results as cluster of n = 42 degenerate impenetrable quantum volume mean density in which is electrons with the mass: me* ≈ 0.81 me and with the super- included the protonic positron centrol: m0, from the value: dense kernels (centroids) vortexially confined in a volume of p 0 ρe to the value: ρn ≅ fd⋅N ⋅ρe. radius rz < 0.2 fm, the z cluster being given as a pair of *± This phenomenon may explain the neutron according to a quarcins: c = 21 me*, with hexagonal symmetry ( 7x3 =21 “dynamid” model, with a degenerate electron with quasielectrons). s degenerate magnetic moment: µe = -4.597 µN rotated inside The resulted sub-structure of the fundamental elementary the quantum volume of a proton by the etherono-quantonic particles, considered as formed “at cold”, by quarks with vortex Γ(µp) of its magnetic moment µp, with a speed ve ≈ effective mass (giving the particle’s mass by the sum rule) -2 * 1 1.7x10 c, to an orbital with a radius: re ≈ 1.283 fm [6] under and fractional electric charge q* = (+²/ 3e; - /3e), formed as dynamic equilibrium of forces on tangent and radial preonic clusters, is given by the preon z0 considering also the 0 0 directions. The difference between the neutron’ mass and the existence of the zerons: z1 = 3z = 102 me; z2 = 4z = 136 me; - 0 proton’ mass: ∆n ≈ 2.6 me, is given by a “weson” w zπ = (z 1 + z2) = 7z = 238 me, with the following composed of the attached negatron and a linking gammon: sub-structures [2-4, 6]: σ(e *+ - e*-) which is transformed into an electronic
Table 1. Elementary particles: (theoretic mass) / (experimentally determined mass).
- - - - +* -* Basic quarks: m 1 = (z 2- me*) = 135. 2 m e, m2 = m 1+e +σe = 137,8 m e; m 2 → m1 + e +νe; (σe = (e +e )→νe) + - - + - + - - - - Derived quarks: p (n ) = m 1 (m 2) + 2z π n = p +e + σe → p +e +νe; λ = n (p) + z π;; s = λ + z 2; v = λ + 2z 2 Mesons: (q- q) Baryons: (q-q-q) - - + + µ = 2Z 1+e = 205 m e/ µ = 206.7 m e -pr = 2p + n = 1836.2m e; n e = 2n + p =1838.8m e; / p r , ne=1836.1; 1838.7m e; o 0 o 0 π = m 1 +m1 = 270.4m e;/ π = 264.2 m e -Λ = s + n + p = 2212.8 m e; / Λ = 2182.7 m e + + (++;+;0;-) ± ± + - ±;0 π = m 1 +m2 = 273 m e;/ π = 273.2 m e -∆ = s + λ + p (n ) = 2445.6; 2453.4 m e; /∆ = 2411 ±4 m e + + + - + - K = m 1 +λ = 987 m e;/ K = 966.3 m e -Σ = v+2p = 2346.2me; Σ = v+2n =2351.4me;/Σ , Σ =2327; 2342.6 me o o o 0 K = m 2 +λ = 989.6 m e;/ K = 974.5 m e -Σ = v + n +p = 2348.8 m e / Σ = 2333 m e; o 0 o - 0 - η = m 2 +s = 1125.6 m e;/ η = 1073 m e; -Ξ = 2s+p = 2586.8 m e; Ξ = 2s+n = 2589.4 m e; /Ξ , Ξ =2572; 2587.7 m e; - - -Ω = 3v = 3371.4 m e; / Ω = 3278 m e.
The classical, pre-quantum mechanism of the preonic cold explained in a relative recent paper of the author [7] by the quarks forming and of dark matter bosons forming was cold genesis of two preonic bosons with hexagonal International Journal of High Energy Physics 2018; 5(1): 55-62 57
0 0 symmetry: zπ = 7z ; z2 = 4z , by the magnetic interaction as Bose-Einstein condensate produced in the magnetic and between constituents, as a mechanism with the next steps: the gravitational field of a star which ensures at its surface 0*/ 0 a)z z -pre-cluster/cluster forming, with the aid of the condition: T < TBE . * * magnetic confinement; b) z2 / z2- and zπ /zπ- pre- cluster/cluster forming; c) (q ±/q0)- quark or pseudo-quark pre- cluster/cluster forming; d) pre-cluster of quarks or pseudo- 2. The Bose-Einstein Condensate of quarks forming; e) elementary particle/dark boson forming. Gammons in a Magnetic Field The total collapsing is impeded- according to the model, by a repulsive force of a scalar field generated by remanent According to a pre-quantum analyze of the forming thermal vibrations of the electronic centroids (kernels) which process of a collapsed cluster of gammons considered as γ* - + determines a local increasing of the quantum static pressure. gammonic pairs: = (e e ) of axially coupled electrons with The formed structures corresponds- according to the opposed charges [7], it resulted that –under a specific Bose- model, to an organized (quasi-crystallin) collapsed Bose- Einstein condensate forming temperature, TBE , the magnetic Einstein condensate [7], with quasi-crystallin kernel given by interaction between the gammons is enough for the gammons an arrangement with hexagonal symmetry of the electronic pre-cluster forming and self-confining, with the forming of a centroids, having- in the model, a barel-like form, with a stable particle-like cluster, if the external magnetic field B diameter of 10 -18 m [2-4]. not exceed a critical value Bc given by the condition that the γ* γ* γ* The possibility of Bose-Einstein condensate forming in a VB (B- ) potential to be lower than the Vγ( - ) potential: µ ≤ µ µ 2 π 3 magnetic field and in a gravitational field was studied in VB = e·B Vγ(r) = 0 e /2 r . some reference papers [8, 9]. The gammonic pairs may results –in the magnetic field of γ The collapsing of a BEC, corresponding to a sharply a neutronic star, from nuclear -emissions resulted + → γ density increasing of the formed condensate, was obtained particularly by K-electron capture: pr + e ne + and by experimentally with ∼15000 atoms of 85 Rb cooled in a combinations between electrons resulted from attracted β+ magnetic trap at ∼3nK with B ≈ 162Gs [10], being observed atoms and positrons resulted as -radiation emitted by → + ν a remnant condensate as fraction of the initial condensate and protons transformed into neutrons: pr ne + e + , which a missing atoms part. are trapped in the star’s magnetic field, in which has the The stability of the remnant condensate that was observed Hamiltonian: during the collapse of attractive BECs was explained by the (p - e⋅ A ) 2 e ⋅ ℏ p2 existence of an absolute stable minimum that appears only if H= −σ ⋅= B λ −⋅ µ B (4) 2m 2 m 2 m the energy is nonlocal, as consequence of the condensate’s transition which occurs when the scattering length ‘a’ from with A, B, pλ -the magnetic potential, the magnetic induction the Gross-Pitaevskii equation is tuned from zero scattering and respective-the canonic impulse. length to a negative scattering length, determined by the Is of particular interest to know which category of stars magnetic field, as a linear function of 1/(B - B0), where B0 is may offer conditions for particles cold genesis. the Feshback resonance position [11]. It is known that the quantum nature of a cold gas is evident It was shown also that the transition temperature of a BEC when the distance between particles is smaller than the formed in a magnetic field, decreases with the strength of the thermal wavelength, i.e: l = N-1/3 ≤ λ = h/p , (p =√(2mE ) ). 2 i t k k k B-field, according to the relation: (B̅ ) = 0[1− ( /5)· (B̅ )], In a magnetic B-field, the energy of a charged particle, m, is: with (B̅ ) ∼ 1 + (B̅ ) 2. 2 EB = p /2m + µe·B; (µe = eħ/2m·c). It was considered theoretically also the possibility to Because that in CGT the gammons have a magnetic describe the dark matter as a non-relativistic, Newtonian moment µγ given by the axially coupling of negatron and Bose-Einstein gravitational condensate, [12] but at the atomic positron, according to the similitude principle, we may use level and the possibility to consider a black hole as a Bose- for the proposed study a relation of the TBE as those deduced Einstein condensate of gravitons [13]. by Rojas and Villegas for the non-relativistic case (E k = In the present paper we analyze the possibility of πkBT) of charged particles [8], of the form: gammons pre-clusters forming, specific to cold formed quarks or pseudo-quarks (corresponding to neutral bosons),
L4π23ℏ c 2 π 24 ℏ ≅υ ⋅ N; ⇒ T = N = N ; µ = µ ⋅ BkT >> (5) λ B ⋅ µ 2 1 e B teBm k B L 1m kB L
N λπ λλπh⋅ c ℏ2 h 0 =t ; N = ; υ ==t t ; λ = ; (6) ⋅ µυµ⋅ µ t π ⋅ N L 1 1 e B1 m 2 mk B T in which: TB - the temperature necessary for having a system parallel to the external magnetic B- field; N; N0 - the macroscopic fraction of the total density of charged particles density of m- particles outside and in the B-E condensate; λt - in the ground state; L - the dimension of the ground state the thermal wavelength; υ = λthc/eB- the elementary cell and 58 Marius Arghirescu: The Possibility of Particles Forming from a Bose-Einstein Condensate, in an Intense Magnetic or Gravitational Field
eBħ/2m·c = µ1 - the effective chemical potential, interaction between ‘residual’ magnetic moments of the corresponding to a magnetic potential: µ1 = µe·B. gammonic bosons [7]. For T< 2 2 4 3 L µ µ mγ k T L µ2πℏ µ π ⋅ℏ N 2 π N=1 N = 1 B B ; ⇒ λ µ = h 1 = N ; 1 = 0 (9) λ0π2 4 t1 π ⋅ 2 0 3 t 2 ℏ 2mkTγ B pmkTγ B B T p T B mk B 3 -11 5 With TB ≈ 10 , it results that: λt√µ1 = 1.9x10 and surface of a massive “black hole” of mass M ≥ 10 solar √(T p/µ1) = 2.7xT B, with Tp - the temperature to which the pre- masses may radiate (may emits Hawking’s radiation). c cluster P of gammonic particles density N0 is formed. We may conclude also that the dynamic pressure of the Choosing some values for TB and B, will results the quantonic vortex-tubes which materializes the magnetic corresponding values for µ1 = µγ·B and for Tp. For example, induction field lines – according to CGT, may decrease the 3 6 -11 for TB = 10 K and B = 10 T, it results that Tp ≈ 2.2x10 K, temperature Th of the quantum vacuum. -2 31 λt = 1.12x10 m and N = 1.38x10 . Also, if we choose a lower transition temperature TB, for 2 6 The previous conclusion of the gammon’s magnetic example: TB = 10 K, by eqn. (8) and with B = Bl = 2.2x10 T 3 moment value is based on the CGT’s conclusion that the (or with TB = 10 K but with a lower B-field), will results a c -13 etherono-quantonic vortex Γµ = 2πrλc induced by the temperature of the P –pre-cluster forming: Tp = 4.8x10 K- chirality of the electron’s superdense kernel (centroid) is the lower than the considered limit Th. 3 cause of the electron’s charge forming and not inverse. So, maintaining the test temperature TB = 10 K, it results Linde [14] suggested that very high values of the magnetic that we have an interval: B = (2.2x10 6 ÷ 8.3x10 7) T in which 11 ± field, exceeding 10 T, may generate the condensation of W is fulfilled the condition: Tp ≥ Th and which corresponds by -11 -10 bosons resulted from the electro-weak interaction theory. eqn. (8) to: Tp = (4.8x10 ÷ 1.8x10 ) K. 11 In our case, a magnetic field B ≈ 10 T gives- with TB = The gammonic particles concentration N corresponding to 3 -6 3 6 7 10 K, a value Tp ≈ 2.2x10 K. But- according to CGT, for the the values: TB =10 K; B = (2.2x10 ÷ 8.3x10 )T, results- from c P -pre-cluster collapsing the potential µ1 must be lower than eqn. (8), of value: 31 33 24 the potential of magnetic interaction between gammons at a N = N0 L⋅µ1/λt√µ1 = (3.1x10 ÷ 1.17x10 ) > 10 - much rougly approximate distance dλ = λ/2 π with λ = h/m γc = higher than the limit imposed by the eqn. (7) of TBE (B =0). -13 2 2 -16 1.93x10 m: Vµ = µ0/2 π(µγ /d λ ) = 2.5x10 J, resulting that- Because that- according to the last astrophysical data, the for the pre-cluster’s forming, it is necessary a B –field lower determined values of the “black hole” magnetic field are 7 than a critical value: Bc = 8.3x10 T or a supplementary force much lower than those predicted by the theoretical models that may compensate the repulsion between the gammonic [15], it results that the previous deduced conditions for B and magnetic moments oriented parallel with the field B > Bc. Tp may exists only in the outer space at enough far distance The inferior limit of the B-field is given by the conclusion of a magnetaric star. that the quantum vacuum temperature is given by quantons, For example, if we have- according also to eqn. (1), a -51 2 (m h = 7.37x10 kg) according to the relation: kBTh ≈ mhc magnetaric field: -11 resulting that Th ≈ 4.8x10 K, which corresponds by eqn. (8) 3 6 R2 R R 3 and by T = 10 K, to B = 2.2x10 T and which is =ρ = ρ 0 0 = 0 (10) B l B(R) k1cc10 v k c B 0 comparable with the Hawking’s temperature at which the R R R International Journal of High Energy Physics 2018; 5(1): 55-62 59 11 with B0 ≈ 10 T at the magnetar’s surface, S0(R 0), it results fulfilled. that the values: B= (2.2x10 6 ÷ 8.3x10 7) T are attained in the Also, we may hypothesize that such specific conditions for interval: ∆RT = (35 ÷10,6)R 0. B-field and Tp may be generated also by a rotational black Taking into account also the cooling effect of the magnetic hole with electrically charged surface, (model permitted by field, resulted according to CGT and by the effect of the µ1 the general relativity). potential, it results that in the outer space of a magnetar, in In a Gross-Pitaevskii equation, of the BEC’s wave the distance interval ∆RT, the specific condition: Tp = function: (4.8x10 -11 ÷ 1.8x10 -10 ) K, of Pc -pre-clusters forming, may be ℏ2∂ 2 4π ⋅ℏ2a -++VrVar ( ) ( ) ψµψ ( ) =⋅ ( r ) ; Va ( ) = s ψ2 ; N = ∫ ψ 2 dr3 (11) 2 is is p 2m ∂ r m specific to temperatures much smaller than TBE , in which: m potential VMG decreases the value of the B-field at which a is the boson’s mass, as is the scattering length, µ is the BEC with gammons may be obtained, resulted from the -11 3 chemical potential and N is the number of bosons, the obtained equation: λt√µ1 = 1.9x10 , with: TB = 10 K and Tp -11 possibility of bosons confining in an etherono-quantonic ≈ Th =4.8x10 K. For equate this effect, we may use the -15 vortex-tube ξB which materializes the magnetic field lines, hypothesis of the magnetic fluxon φ0 = h/2e ≈ 2x10 Wb, can be equated by considering a negative value of the considering that the ξB -vortex-tubes of the B-field are fluxon coherent scattering lengt (a) –corresponding to an attractive φ0 and that they have a linear decreasing of the impulse interaction, the external potential V (r) being- in this case, a density: pc = ρ(r)·( ω·r) = ρ(r)·c for r ≤ rφ (specific to the magneto-gravitic potential VMG given by the local gradient ∇r vortex-tubes) and a mean density: ρφ approximate equal with (ρΓc) of the etherono-quantonic vortex-tubes ξξξB that those resulted from the local Bl –field value resulted from 0 3 materializes the field lines of magnetic induction B, [2-4]. eqn. (1): Bl = k1ρBc, ρB (R) = ρB (R 0/R) . 2 For a surface S = 1m , the fluxons number nφ rectangular 3. The Gravito-Magnetic Potential of the on S are given according to the equation: φ φ ⇒ φ Magnetic Field Lines = B·S =B·1 = nφ 0; nφ = B·1/ 0; (12) Considering an unit length of the fluxons: lφ = 1m, the When the total attractive potential: Va = -(VMG + Vi) is fluxon’s mass on unit length mφ is given according to the much higher than kBT, we have: µ ≈ µ1 = Va, which is –in this case, the effective chemical potential. relations: If Vi = µγ·B, it results that the considered magneto-gravitic 2 r BRBR() ()1 ϕ h− − m m = ∫ 2πρrdrr00 =⋅⋅=⋅ π 2 ρπ r 2 = ===0 4.27 xkgm 1014 / ; k = 1.56 x 10 10 (13) ϕ ϕ ϕϕϕ ⋅ ⋅ ⋅ 1 r kckcnkcekc11ϕ 12 1 C It results also that: rφ = √(m φk1c/B (R)). For example, for B around vectorial photons (vectons) of 2.7K microwave 6 -11 ≈ 10 T it results: rφ = 4.47x10 m –corresponding- by the radiation of the quantum vacuum, identified in CGT as 30 11 equality: li = 2r φ, to N = 1.4x10 and for B = 10 T it results: electric field quanta having a gauge radius: rv ≈ 0.41a = -13 rφ = 1.41x10 m –corresponding -by the equality: li = 2r φ, to 0.578fm [4] and that the electron has a small impenetrable 37 44 e -4 3 N = 4.45x10 , (compared with N0 = 3.57x10 ). Assuming- quantum volume: υi = 1.15x10 fm [6], from eqn. (12) it according to CGT [2-4], that the vortex-tubes ξξξB are formed results by the eqns. (2) and (12) that: 2 υ υcmBRϕ ⋅ ( ) υ ⋅ c r m ϕ 1 V (r) =⋅= i ρ (r ) c2 i = i ϕ B ( R ) ; ρ (r) == ρ0v ; m = 2 πρ 0 r r ; (14) MG ϕ π⋅ π ⋅0 ϕϕ π ⋅ ϕϕϕv 2 4 rkck1 4 1 r r2r r ϕ with: e B(R) υ ⋅ c J⋅ m mϕ k⋅ c µ =⋅+ µ B(R) K ; K ==i ϕ 7.87x10 -40 ; r = 1 (15) 1γ M M0π ϕ r 4 k1 T B( R ) -1/3 -31 -34 For li = N = rφ, we have: magnetic moment, of the order of 10 ÷10 J/T, as those of e -32 -10 VMG (r φ) = (υi ·c) B(R)/4 πk1 = 1.76x10 B(R)- the neutrino: µν ≈ 10 µB or those of photons and may i.e- a neglijible value comparative to: explain- in the last case, the electron’s forming as collapsed -24 VB = µe·B ≈ 3x10 B(R). Bose-Einstein condensate of photons with super-dense kernel But the magneto-gravitic potential VMG (r) may be in a magnetaric-like field [2-4]. important for the confining of bosons with small or null Also, we may conclude that in the case of neutral mesons 60 Marius Arghirescu: The Possibility of Particles Forming from a Bose-Einstein Condensate, in an Intense Magnetic or Gravitational Field and baryons having small or null magnetic moment but an If the internal pre-cluster’s temperature T i is maintained -2 3 impenetrable quantum volume of the size order: (1 ÷10 )fm , close to the metastable equilibrium value T B, the pre-cluster’s the potential VMG may generates dark matter bosons in a collapsing may still occur in a strong magnetic field, by the magnetaric-like field, by mesons cold confining. aid of the magneto-gravitic potential V MG (r φ), according to π For example, for the confining of π-mesons with υi ≈ the model. 2.5x10 -2fm 3 [5] by a magnetaric field: B ≈ 10 11 T, it results So, it is argued the conclusion that also a static but strong -13 -19 from eqn (13), that: rφ = 1.4x10 m and VMG (r φ) ≈ 3.8x10 J magnetic field may create conditions for BEC forming and- ≈ 2.4 eV, corresponding to a confining force: FMG (r φ) = particularly, for particle-like collapsed BEC forming, by -6 2.7x10 N. bosons capturing with the ξB-vortex-tubes which materializes In the same-time, it results that-by the VMG potential, the the B-field lines. ξB-vortex-tubes helps the pearlitization of a formed BEC into pre-clusters with N0- density of particles and relative small number of bosons and the gammonic pre-clusters’ collapsing and their transforming into particles. For example, considering a radius r p of meta-stable equilibrium of a drop of BEC formed by the BEC’s pearlitization and maintained by the equilibrium between the force generated by the internal thermal energy F (r ) = t p V⋅N0kBTi and the force generated by the surface tension, σ: Figure 1. Part of a crystallized gammonic pre-cluster which may result by a dE dV dS 4π BEC’s pearlitizing, (CGT). =−P +=σ0 ; V = r 3 ; S =⋅ 4 π r 2 ; (16) dr0 dr dr 3 It results-in consequence, two plausible scenario of because that σ = (½)F γ/l, (the force rectangular on unit particles cold genesis-according to CGT: a) by clusterization, 3 44 0* length), for: N0 ≈ 1/a = 3.57x10 , (a = 1.41 fm- the from z - preonic pre-clusters, in a step-by step scenario, by * 0* metastable equilibrium inter-distance between gammons [7]), steps of z -/q - pre-clusters cold collapsing, or: b) by the and because the antiparallel magnetic moments of two pearlitization of a bigger BEC, by the temperature oscillation adjacent gammons of a precluster have a residual (reciprocal) around the value T B, with the cold collapsing of the resulted 2 * e * e * value given by: E γ =2m ec ≈ Ve(a,e ) +V µ(a,e ) ≈ 3V µ(a,e ) BEC pre-cluster but without destruction. * 2 and: B(d) ≈ E(d)/c, [7], giving: e ≈ √( /3)⋅e, it results that: Relative to the particles genesis from quantum vacuum fluctuations, considered in SVT but also in CGT- as chiral m e*c⋅ d 2 d ℏ 4πππ (0.9d) 2 2 µ(a) =e =⋅ µ ; r == ; e* = e ; d = a (17) (vortexial) fluctuations, contrary to the scenario of r BP ⋅ λλλ mγ232m rck λ e 1 3 spontaneous particles-antiparticles pairs forming from virtual particle-like pairs, supposed by the Heisemberg’s and–by CGT, because m c2 = e 2/8 πε a, it results that: e 0 nedetermination relation of quantum mechanics, it results – *2 2F Fe µµµ µµµ 2 2 from the previous analyze, that the fermions and bosons e e2 eγ µµγµ 0 2 BP e (18) Vµµµ ( a ) =− =− ; ⇒ ≈ = = πε πε π 2 3πεπεπε 3 forming process is possible only by enough strong vortexial 80a 38 0 a l a 23 rλλλ a12 0 a fluctuations in the etherono-quantonic quantum vacuum- and because the electric force between gammons may be which determine also the speed of the process and the mass neglected, the meta-stable equilibrium radius has the form: of the formed particles, resulting as more plausible a “step- by-step” scenario of particles forming by chiral fluctuations, 2 2− 6 2σFγγγ µ µ 1 µ µ 1 10 r ==≈0BP = 0 BP ≈ 5.5x [ m ] (19) beginning with the vectorial photons forming- process p ⋅ π2 3 π 2 PlP0 03rλ a NkT 0 Bi 3 r λ kT BB T B possible also at lower density of the quantum vacuum, ρ ≈ 3 -9 comparable with those of a lower magnetic field: B(B) For T B ≈ 10 K it results: r p≈5x10 m, so the pearlitization ρ(m p). with the forming of quasi-cylindrical pre-clusters of baryonic For example, for the cold genesis of a quantum of 2.7K neutral particles corresponding to a radius: r b < r a may be radiation, if it is formed from two vectorial photons named formed by large oscillations of the internal temperature T i - -40 “vectons” in CGT, with mass: mv = 2.3x10 kg and given by the zeroth vibrations, around the value T = T B. considered with an inertial mass of gauge radius: r = 0.41a = If we consider a BEC of z 0-preons- formed by clusterizing v 0.6fm- in the free state, it results that: ρB(B) ≈ ρ(m v) = and collapsing process as neutral couple of two quarcins (m q 2.5x10 5 kg/m 3, resulting that a vortexial magnetic-like field ≈ * 17m e) with degenerate charge e , axially coupled, with the ρ ≈ 4 ’ corresponding to Bv = k1 Bc 10 T may generates vectons same value N 0 and with T B ≈86K –given by (8), it results ’ -11 from the primordial dark energy- composed of etherons and from eqns. (17)-(19), that: µz ≈ µγ/17 and: rp ≈ 4x10 m. 2 quantons (m hc = h·1), according to CGT, the cold genesis of Under this value r p of metastable equilibrium, because the electrons being possible at higher values of magnetic-like decreasing of the internal energy, the residual (reciprocal) energy density, in a magnetaric-like field, [9, 10]. magnetic moments of the gammons generates the pre- It results- according to CGT, that the forming of virtual cluster’s collapsing, without destruction- conform to CGT. particles from the energy of quantum vacuum by chiral International Journal of High Energy Physics 2018; 5(1): 55-62 61 fluctuation and their transforming into real particles involve with antiparallel chiralities axially coupled, it results in either a magnetic-like (vortexial) field of values higher than a consequence –according to the cold genesis quasi-crystallin 4 critical value: Bv ≈ 10 T, or already formed gammonic pairs quark model of CGT, the possibility of particles forming γ*(e -e+) and a low temperature: T<< 10 3K, and because that starting with the forming of a Bose-Einstein condensate of the relative stability of its specific structure is ensured only electronic centroids with antiparallel chiralities axially and by the existence of superdense kernels (centroids), resulted parallely coupled (on axial, respective-on radial direction), from confined quantons- in CGT, which stabilizes the formed which- after the pearlitization of the BEC, may forms vortex(es) and its vortexial structure. mesonic or baryonic quasi-crystallin kernels which initiates The explaining of the strong interaction with mass excess, the forming of etherono-quantonic vortexes around their in which the total mass of resulted particles exceed the total center, by the action of quantum and sub-quantum winds, mass of particles entered in reaction, results as in the case of corresponding to magnetic moments which attracts- by the 2 reaction: resulted self-potential V = V0|ψ| , some photons of the - + - o o π (m1+m2) + pr(2p + n ) + Q → Λ (s+n+p) + K (m 2 +λ), quantum vacuum, (previously formed), which- in this way, by the participation of real bosons of quantum vacuum, generates the quantum volume of the resulted composite particularly-dark matter bosons, formed by quark-antiquark particle, according to CGT. 2 pairs, with the intrinsic energy mbc lower than the The previous conclusions argues the possibility of dark interaction energy, Qi, [3,4,7]. matter bosons genesis in the field of a black hole or of a For a Bose-Einstein condensate in a gravitational potential magnetar-type star- at an enough long distance from its Vg = m·g·y, because that the transition temperature is surface. increased by the presence of the gravitational field [9], for the forming of a gammonic pre-cluster with a density of 3 44 4. Conclusions gammons: N0 ≈ 1/a = 3.57x10 we may conclude that in the gravitational field of a black hole with a surface temperature In the present paper, based on a previous work [7] regarding γ Tt