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Theoretical Physics Letters
2024 ° 28(11) ° 11-12
https://www.wikipt.org/tphysicsletters
DOI: 10.1490/77009901.265tpl
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The paper presents a better calculation of the constants and d of the CGT’s unifying bag model, previously published, which explains the strong interaction and the nuclear force without the concept of ‚color charge’ specific to the Standard Model. The recalculation indicates that the pressure of internal ‚naked’ photons on the bag’s surface of radius ai = 0.59, which explains the nucleon's quarks deconfining temperature (~2x1012 K), for a current quark's radius of ordinary nuclear temperature: rq = 0.2 fm, is: Psi0(ai) = 6.688x1033 N/m2, corresponding to a ,bag' constant: Bi l= 41.8 MeV/fm3, value which verify the CGT's model of strong ' interaction between quarks and that between nucleons considered in a vortical model, by a constant of the bag's field variation of value: d = 0.34 fm. The total potential of interaction between two nucleons results in the form of a modified Sombrero-type potential, with an attractive part Va(r) = Va0×e-r/h* and a repulsive part: Vr(r) = Vr0×e-7r/h*, (h* = 0.8 fm). The explanatory model indicates the existence of a bag pressure for each composite particle but also for quarks and the bag’s constant variation with the mass and the intrinsic temperature of the particle’s kernel.
The necessity to explain unitary the strong interaction between quarks and their confining and the nuclear force, that generates the nucleons’ confining in quasi-liquid or solid nuclei, is obvious. In the Standard Model of particles, this aim is fulfilled by the concept of ‘color charge’ of current quarks and by the mechanism of interaction by intermediary ‘gluons’ formed as pairs of virtual current quarks and antiquarks, the nuclear force of interaction between nucleons being explained by an exchange of residual gluons (short lived mesons). But compared to the Electrodynamics- which evidenced a real existence of the electric charge, in the Quantum Chromodynamics the real existence of the considered ‘color charge’ is not proved or strongly argued. In a Cold genesis theory of particles [1], [2] , based on the Galilean relativity, the strong force of quarks confining and the nuclear force were explained by a (multi)vortical model of nucleon, considered as cluster of an even number Np = 1836/0.8095 = 2268 quasielectrons, (integer number of degenerate “gammons”, g*(e*- e*+)), i.e. electrons with degenerate charge (e* = ±(2/3)e), magnetic moment m* and mass: me* = 0.8095 me, resulting by a degeneration of the magnetic moment’s quantum vortex Gm = GA +GB , given by ‘heavy’ etherons of mass ms » 10-60kg and ‘quantons’ of mass mh = h×1/c2 = 7.37x10-51 kg. The considered “gammons” were experimentally observed in the form of quanta of “un-matter” plasma, [3]. The me* -value results in CGT by the conclusion that the difference between the masses of neutron and proton: (mn -mp » 2.62 me) is given by an incorporate electron with degenerate magnetic moment and a linking ‘gammon’ se (g*) = 2me* » 1.62 me , forming a ‘weson’, w- = (se (g*) + e-), which explains the neutron in a dynamide model of Lenard- Radulescu type [1], [2], ( protonic center and a negatron revolving around it by the Gm -vortex with the speed ve* << c, at a distance re* » 1.36 fm [2]- close to the value of the nucleon’s scalar radius: r0 »1.25 fm used by the formula of nuclear radius: Rn » r0×A1/3), at which it has a degenerate meS -magnetic moment and Sen –spin. The used electron model [1] supposes an exponential variation of its density: re(r) =re0e-r/h, (re0 = 22.24x1013 kg/m3) given by photons of inertial mass mf , vortically attracted around a dense kernel m0 and confined in a volume of classic radius a = 1.41 fm, (the e-charge in electron’s surface), the superposition of the (Np+1) quantonic vortices Gm* of the protonic quasielectrons, generating a total dynamic pressure: Pµ(r) = (1/2)rµ(r)×c2 £ (1/2)rn(r)×c2= Pn(r), inside a volume with radius: da = 2.1 fm, (conform to the superposition principle of quantum mechanics) which gives an exponential nuclear potential: Vn(r) = -uiPµ(r) of eulerian form, conform to : Vn(r) = uiPµ(r) = Vn0×e-r/h* ; Vn0 = -uiPµ0 , (1) with: h* = 0.8 fm (equal to the root-mean-square radius of the magnetic moment’s density variation inside a neutron, experimentally determined) and ui(rpi =0.586fm) » 0.843fm3 - the ‘impenetrable’ volume of nuclear interaction [1], [2], the proton resulting as formed by Np » 2268 paired quasi-electrons which give a proton’s apparent density in its center (by the sum rule), of value: rno » fc×Np×reo = 4.54x1017kg/m3, (re0 = 22.24 x1013 kg/m3 ), and an attached positron with degenerate magnetic moment, in the CGT’s model, the density of the Gm -vortex of a free electron having approximately the same density’ variation as the density of photons of its classic volume (of radius a = 1.41 fm), f ≈ 0.9 being a coefficient of mass’ and Gm -vortex’s density reducing in the center of the (quasi)electron at its mass degeneration, its value resulting by the gauge relation of CGT: e = 4pa2/k1 and by the integral of nucleon’s mass –considered as given by confined photons, with a density variation: rn(r) = rn0(0).e-r/h’ with h’ = 0.87 fm, (equal to the proton’s root-mean square charge radius, experimentally determined: 0.84 ¸0.87 fm). The variation of rµ(r) is similar to that of rn(r) because it is given mainly by the vorticity of the photons with mass mf >> mh = h1/c2 which give the main part of the nucleon’s mass, (the mass of the bosonic shell of nucleon’s kerneloid), conform to CGT. The radius rpi of the ‘impenetrable’ quantum volume ui corresponding to the nuclear interaction results in CGT as quasi-equal to the radius of the proton’s magnetic moment: rpi » rmp = 0.586 fm, given by the relation mp = 2.79mN = ½ecrm , (Þrmp/rme = mp/me , with: rme = (h/2pmec) » 386fm; mN- the nuclear magneton) and corresponding in CGT to the maximal speed, c, of the quantons in the Gm -vortex of the magnetic moment mp, without the photonic shell of the nucleon’s kerneloid
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The paper shows that the recalculation of the constants Psi0 and d of the CGT’s bag model, previously published, which for a ‚bag’s radius: ai » 0.59 fm gives: Psi0(ai) = 6.688x1033 N/m2, corresponding to a ‚bag’ constant: Bi » 41.8 MeV/fm3, verify the both CGT’s models: of strong interaction between quarks and the interaction between nucleons, based on the (multi)vortical model of nucleon, by a constant of the bag’s field variation of value: d » 0.34 fm, the explanatory model resulting as unitary, without the need of (semi)formal concepts such as the concept of ‚color charge’ used by the Standard Model of Quantum Mechanics.
The resulting explanatory model of CGT is important because –in a Galilean relativity, the mechanism of paired quarks forming from relativist jets of negatron and positron, experimentally evidenced [21], is explained by the forming of compact clusters of degenerated negatron-positron pairs, (of paired quasi-electrons), corresponding to z0-preons, in CGT [1], and not by the total energy 2me(v)c2 of a single pair of relativist electrons entered in mutual collision, as in the Standard Model, so in this case the forming of the supposed ‘color charges’ of the formed quarks is not explained.
Compared to the value B » 58MeV/fm3 = 9.28x1033 N/m2 obtained by the MIT bag model [6], the lower value Bi » 41.8 MeV/fm3 » 6.69x1033 N/m2 obtained in CGT indicates –by the static equilibrium relation of stellar structures which- in a classic (non-relativist) case, is given by:
dP(r)/dr=-r(r)×g(r); (g(r)=G×m(r)/r2), (28)
and by an equation of state (EoS) of the internal pressure: P(r) = (SPf –B) with Pf -–pressure due to each quark flavor (u; d; s ), that the TOV limit’ (Tolman–Oppenheimer–Volkoff, [22]; [23]) of the neutron stars’ mass is higher than the superior limit of ~3 solar masses [24] obtained by the B-constant of the MIT’ bag model (~58 MeV/fm3 ).
The fact that the shell of the valence (current) quarks is given in CGT by thermalized ‘naked’ photons –instead of gluons as in the S.M., is argued by the possibility to obtain paired quarks from relativist jets of negatrons and positrons (i.e. by the CGT’s model of meson and of baryon) and by the fact that when the internal quark structure of the proton is revealed by deeply virtual Compton scattering [25] (a process in which electrons are scattered off quarks inside the protons), the internal quarks subsequently emit high-energy photons, which are detected in coincidence with the scattered electrons and with the recoil protons.
Even if it was concluded –by the Standard Model of particles, that although the basic bag model does not provide a pion-mediated interaction it describes excellently the nucleon–nucleon forces through the 6 quark bag s-channel mechanism using the P-matrix [26], it results –conform to the observations presented in Chpt. 2, that the value of the current u/d-quark’s radius: rq· = 0.43x10-3 fm –actually considered by the S.M. , is not compatible with the possibility to explain the quarks’ confining without the concept of ‘color charge’ used in Quantum Chromodynamics.
The total potential of interaction between two nucleons results in the form of a modified Sombrero-type potential, with an attractive part and a repulsive part: Vr(r) = Vr0×e-7r/h* -explained in CGT by intrinsic vibrations of the particle’s kernel produced by its current quarks, without the hypothesis of a mediating quantum- considered in the Standard Model as being an isoscalar vector meson omega [31].
The explanatory model indicates the existence of a bag pressure (and a bag constant) for each composite particle but also for quarks and the bag’s constant variation with the intrinsic temperature of the particle’s kernel.
The possible implications in astrophysics are related to the structure and the density of the quark stars and of the cold stars of ‚black hole’ type.
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