A Strong Force Potential Formula and the Classification of the Strong Interaction

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1 Open Access Libay Jounal 8, Volume 5, e487 ISSN Online: -97 ISSN Pint: -975 A Stong Foce Potential Fomula and the Classification of the Stong Inteaction Zhengdong Huang Hubei Zhouheiya Entepise Development Co., Ltd., Wuhan, China How to cite this pape: Huang, Z.D. (8) A Stong Foce Potential Fomula and the Classification of the Stong Inteaction. Open Access Libay Jounal, 5: e Received: Novembe, 7 Accepted: Januay 6, 8 Published: Januay 9, 8 Copyight 8 by autho and Open Access Libay Inc. This wok is licensed unde the Ceative Commons Attibution Intenational License (CC BY 4.). Open Access Abstact The most difficult poblem in the eseach on stong inteaction is to solve the mechanical expession of stong nuclea foce, thus failing to compehensively descibe the state in and between hadons. In this pape, easonable stong foce potential hypothesis is poposed though analysis, and stong inteaction is classified into 5 types accoding to diffeent stess paticles; then, diffeent intenal symmetical stuctues ae coespondingly obtained, and Diac equation is adopted to descibe the intinsic states of paticles of 5 types; finally, the theoetical value and the expeimental value of the mass atio of the same-chaged paticles and the neutal paticles ae compaed to pove the complete set of eseach method and veify the coectness of the stong foce potential fomula supposed theeby. Subject Aeas Paticle Physics Keywods Stong Inteaction, Stong Nuclea Foce, Stong Foce Potential, Mass Ratio. Intoduction.. Classification of Stong Inteaction... Histoy of Stong Foce Reseach and Solution of Pending Poblem Stong inteaction is an action in o between hadons. Stong foce maintains the stability of intenal stuctue of hadons and the inteaction between hadons, thus contibuting to the enichment of paticles family. Howeve, people have not yet found the suitable beakthough point fo studying the essence of stong inteaction. Many stong inteaction pocessing theoies and methods poposed in the past only have limited achievements, and the mechanical ex- DOI:.46/oalib.487 Jan. 9, 8 Open Access Libay Jounal

2 pession as pefect as that of gavitational foce and electomagnetic foce has not yet been found till now. The autho believes that the key fo solving the stong inteaction poblem is to positively solve stong foce potential, and the suitable mathematical tool- Diac equation can be taken as the diect evidence to pove the mass atio of the same-chaged paticles and neutal paticles ( chaged mentioned in this pape means chage-caying).... Five Types of Stong Inteaction Stong inteaction can be divided into five types accoding to diffeent stess paticles. ) Bayon type stong inteaction in paticles; ) Meson type stong inteaction in paticles; The stess paticles fo the two types of basic stong inteaction in hadons ae quaks, but it does not mean that the stess paticles fo all types of stong inteaction ae quaks, because stong inteaction can be also geneated between hadons. Theefoe, besides the above two types of basic stong inteaction, anothe thee types of stong inteaction ae also included. ) Stong inteaction between bayons is called as inte-bayon type stong inteaction, and the epesentative paticles include deuteon [], titon [] and atomic nucleuses theeof; 4) Stong inteaction between bayon and meson is called as bayon-meson type stong inteaction, and the epesentative paticles include Δ++ () [], Δ+ () [], Δ () [] and Δ () []; 5) Stong inteaction between mesons is called as inte-meson type stong inteaction, and the epesentative paticles include η [] paticle and η [] paticle. Fo the thee types of stong inteaction based on the two types of basic stong inteaction, the action paticles theeof ae hadons (intenal stuctue paticles of hadons ae quaks), so such stong inteaction is also called as combined type stong inteaction.... Intenal Symmetical Stuctue of Hadons Two factos can influence the intenal symmetical stuctues of hadons, namely: paity of quantity of stess paticles and mass diffeence of stess paticles. Hadons have two types of intenal symmetical stuctues. Specifically, one is the plane symmetical stuctue, and such stuctue can be futhe divided into odd symmetical stuctue (as shown in Figue (a) and Figue (e)) and even symmetical stuctue (as shown in Figue (b) and Figue (c)), and it is the most basic, geneal and stable symmetical stuctue in hadons; the othe one is spatial symmetical stuctue (as shown in Figue (d)), and such stuctue is aely seen, and the epesentative paticles include η paticle and η paticle. Bayon type stong inteaction can be futhe divided into bayon type odd DOI:.46/oalib.487 Open Access Libay Jounal

3 Figue. (a) Intenal odd symmetical stuctue diagam of foce-caying paticle (n = ); (b) Intenal even symmetical stuctue diagam of foce-caying paticle (n = ); (c) Intenal Even symmetical stuctue diagam of foce-caying paticle (n = 4); (d) Intenal spatial symmetical stuctue diagam of foce-caying paticle (n = 4); (e) Intenal even symmetical stuctue diagam of foce-caying paticle (n = 4). symmetical stong inteaction (as shown in Figue (a)) and bayon type even symmetical stong inteaction (as shown in Figue (b))..) The epesentative paticle of bayon type odd symmetical stong inteaction is nucleon (including poton and neuton);.) The epesentative paticle of bayon type even symmetical stong inteaction is Σ paticles family [] (including Σ, Σ and Σ ); + Similaly, meson type stong inteaction can be futhe divided into meson type odd symmetical stong inteaction (as shown in Figue (c)) and meson type even symmetical stong inteaction (as shown in Figue (e))..) The epesentative paticle of meson type odd symmetical stong inteaction is neutal K meson [];.) The epesentative paticle of meson type odd symmetical stong inteaction is neutal π meson [] and chaged K meson [];.. Reseach Diection of Stong Inteaction The five types of stong inteaction have coveed all stong inteaction foms known in the wold. This pape aims at compehensively studying the intenal symmetical stuctues of hadons and the foce action fom the aspect of the epesentative paticles of the five types of stong inteaction. The basic eseach thought is as follows: ) Popose elevant hypothesis; ) Infe and demonstate accoding to the hypothesis; ) Compae theoetical value and expeimental value; 4) Obtain the conclusion. The detailed analysis pocess includes nine steps: ) Hypothesis fo basic stong inteaction; DOI:.46/oalib.487 Open Access Libay Jounal

4 ) Analysis of stong inteaction of nucleon (including p and n); ) Analysis of stong inteaction of Σ paticle family; 4) Analysis of stong inteaction of π meson; 5) Analysis of stong inteaction of K meson; 6) Analysis of stong inteaction of atomic nucleus (e.g., deuteon and titon); 7) Analysis of stong inteaction of Δ (); 8) Analysis of stong inteaction of η paticle and η ( 958) paticle; 9) Conclusion.. Hypothesis fo Basic Stong Inteaction.. Intenal Symmetical Stuctues of Hadons ) Chage type quantity of stong foce: quak quantity of neuton o poton is, so the chage type quantity of the coesponding stong foce is ; one neuton and one poton can fom the simplest atomic nuclea stuctue, so the chage type quantity of the coesponding stong foce is. The coesponding chage type of the two types of the most basic stong inteaction is o. n=, ei = i n ei ei = (-) whee e i is chage type; hadons ae usually neutal and can pesent foce action only unde the distance small enough, so the sum of chage types is. It can be poved that the fomula (-) is unsolved in the ange of eal numbe. We must extend the domain fom the eal to complex numbe, and adjust the fomula to have a eal oot. = e i and e ae conjugate complex numbe each othe. i The following fomula is set: ej = aj + bi j ej = aj bi j n=, ( ) ei = (-) i n ei ei (-) a and b ae eal numbes. Fomula (-) ae put into the fomula (-) to obtain: n=, aj + bi j = (-4) i n ( aj + bi j )( aj bi j ) = When n =, a, = ± (-) b = A goup of solutions of chage type of π meson type stong foce DOI:.46/oalib Open Access Libay Jounal

5 e = ± (-) When n =, consideing that neutons and potons can combine to fom stable atomic nuclei, that is to say, thee must be a set of solutions (-), Fomulae (-4), (-) ae combined to solve. a =±, b = a =, b = i a =, b = i A goup of solutions of chage type of nucleon type stong foce, + i i e = e = i, + i e e = = e = e = (-) (-4) when n =, the stong inteaction between thee foced paticles can be decomposed into any two foced paticles. Then we deduce the atio of n = to n = s Stong foce intensity by fomula (-). n= n= n= n= ee j m ej ej ee j j j m j j j = = ee + ( e e ) e e () ) Pesent two types of symmetical stuctues by deuteon as shown in Figue. Figue. Two Types of Intenal Symmetical Stuctues of Hadons... Solution of Stong Foce Potential ) Stong foce potential shall have univesal attibutes as the same as gavitational potential and electostatic potential, namely: V ˆs a (4) ) Special attibutes of stong foce potential: the most significant diffeence DOI:.46/oalib Open Access Libay Jounal

6 between hadons and atoms is that hadons only have gound state, but atoms have multiple states. In ode to ensue the stability of hadons and avoid extenal enegy excitation, a condition fo limiting state tansition shall be added on the basis of Fomula (), namely: a Vˆs F( ϕ ) (5) whee ϕ is the gound state function of hadons, and F ( ϕ ) is the vaiable fo limiting state tansition. ) a value: fo the stong nuclea foce as the most basic foce fo maintaining the intenal stability of hadons, the intensity theeof is appoximate to the poduct of the educed Planck constant and light velocity, and this indicates that stong nuclea foce is cetainly elated to fluctuation. The following hypothesis is made accoding to such elation: a) Stong foce intensity of π meson ħc a= = ħ c (6) b) Stong foce intensity of nucleon ħc a = = ħ c (7) 4) Gound state function of hadons: the state function of hadons is unique and cannot be influenced by stong foce potential, appoximate to o as the same as that of potium atom (Schodinge s equation is adopted to calculate the gound state function of potium atom fo the most accuate compaison). ϕ a, = exp± a (8-) whee and a ae the vaiables elated to distance. The state function is nomalized: ϕ ( a, ) = exp± ( a ) (8-) 5) F ( ϕ ) fomula F ϕ = ϕ = exp± a (9) 6) Solution of stong foce potential: two solutions of stong foce potential can be obtained accoding to Fomulae (4)-(9). a) Stong foce potential fomula of π meson ˆ ħc VS = exp( a) () o ˆ ħc VS = exp+ ( a) () b) Stong foce potential fomula of nucleon ˆ ħc VS = exp+ ( a) () ˆ ħc VS = exp( a) () DOI:.46/oalib Open Access Libay Jounal

7 Five issues shall be explained fo ) and ). ) In actual conditions, π meson only has stong foce potential fomula (); ) The epesentative paticle caying () includes positive and negative K mesons; ) In actual conditions, nucleon only has stong foce potential fomula (); 4) The epesentative paticle caying () includes Σ paticles family; 5) Stong foce potential has fou types, epesented by Fomulae (), (), () and ().. Diac Intinsic Equation of Nucleon.. Desciption fo Intenal Movement of Nucleon Diac equation [4] can be adopted to descibe the intenal movement of hadons iγ mk uk ( x) = ( k= n, pev,, ) x µ (4) µ γ is Diac matix. Diac eigenfunction of nucleon, established on thee-quak model, is combined with positive/negative chage type Diac function of electons unde the action of Coulomb field of potons. Thee-quak model is thee-body symmetical stuctue and positive/negative chage is two-body symmetical stuctue, so a / convesion facto shall be applied between them when the thee-body poblem is conveted into two-body poblem fo elevant eseach. The factos which epesent the attibutes of nucleons, such as mass and caying foce, shall be multiplied with this convesion facto, namely: Hˆ ( ˆ ˆ i = cα p+ mc i β Ve Vs ) (5) whee i= pn, espectively epesent poton and neuton, Ve ( ) and Vs ( ) espectively epesent Coulomb field and stong inteaction in nucleons. In this way, we can establish a Hamilton opeato fo descibing the intenal state of the moving nucleons by simple mass and potential enegy. When H = is tue, namely: nucleon enegy is developed fom nothing, we can obtain the intinsic equation of nucleons... Intenal Symmetical Stuctue of Nucleon Intenal Odd Symmetical Stuctues of Neutons and Potons ae as shown in Figue. Figue. Intenal Odd Symmetical Stuctues of Neutons and Potons. DOI:.46/oalib Open Access Libay Jounal

8 .. Diac Intinsic Equation of Potons Fistly, we analyze potons [5]: potons caying momentum move unde stong foce field and coulomb field in nucleons; then, we solve the common eigenstate function of bound states ( < E< mc p o mc n ) and ( Hˆ, Kˆ, J, J z ). Fistly, Hamilton opeato of poton is as follows: ˆ zzke zzke zzke ħc H= cα p+ mc p β e whee α I p =i ħ, α =, β = α I (7) α and I ae espectively second-ode pauli matix and unit matix, as shown below: α α I α α = = = I ˆ ħk = β Σ l+ ħ = ħ + l whee is the angula momentum opeato of the tack, and ħ is spin angula momentum opeato, namely: I = α (8) I zz zz zz + + is the sum of potential enegy of evey two quaks of the thee quaks, and coefficient is the sum of the obseved values of thee diffeent quaks. Above potential enegy expession includes six physical quantities, namely z, z, z,,,, which cannot be diectly solved though Diac equation. Theefoe, the potential enegy expession must be simplified. Fistly, we shall notice that all chages ae intege multiples of e in coulomb field, but the basic definition is focedly divided into thee pats in quak submodel, namely: ( z, z, z ) =±, ±, ± (9) o Poton chage is e, namely: (6) z, z, z =±, ±, ± () z+ z + z = () The following fomula can be obtained though one goup of values: z =, z =, z = () DOI:.46/oalib Open Access Libay Jounal

9 In poton, thee quaks caying colo chages ae equivalent to positonelecton, and the only diffeence is that two symmetical objects ae changed into thee objects. We can find the cental distance of seveal quaks accoding to the symmety condition in nucleon., and espectively epesent the cental distances of the thee quaks, and is the adius of nucleon, as shown in Figue 4: Figue 4. Symmetical Diagam of Quaks (Coulomb Aveage Potential Enegy = ). = = = () Namely: Ve ( + ) = = Hamilton is changed as follows: ˆ ħc H= cα p+ mc p β e Fomula () is conveted into the following fomula though the algebaic elation of, β, : ˆ ˆ ħc H= cα p + ic ħ Kβ + mc p β e (5) whee p is adial momentum opeato. p = ( p iħ) = iħ + (6) ħ J = l+ (7) ˆ ˆ H, K, J, J can be poven to be mutually commuted, and the eigenvalues z theeof ae as follows: J = j( j+ ) ħ, j =,, J z = mjħ, mj = j, j, ˆ K = K =± j+ =±, ±, As a esult, common eigenfunction of ( Hˆ, Kˆ, J, J z ) can be divided into two types: (4) DOI:.46/oalib Open Access Libay Jounal

10 ) ) K = j+ K = j+ ϕ A F A φ ϕ jmj φ jmj f B ϕ φ jmj g B G iφ jmj ϕ4 ϕ = = = ϕ B F B φ ϕ jmj φ jmj f A ϕ φ jmj g A G iφ jmj ϕ4 ϕ = = = (8-) (8-) F G and f() =, g = Fo convenient calculation, A B φ jmj and φ g jmj ( ) ae set as two-component θϕ function, ielevant to ). ( J, J z ) eigenfunction (, Fomula (8) is put into intinsic equation of enegy. The following fomula is obtained to establish F, whee α = e Hϕ = Eϕ d F F p = iħ (9) d G simultaneous equations: d mc + E e d ħc mc E d e d ħc F K ( F ) = + G G K ( G ) + = F ħ c is fine stuctue constant. () In following paagaph, F and G actions ae eseached aound singula point =,. When is tue, Fomula () can be appoximately valued as: Theefoe, mc d p + E mc E F dg G, d ħc d ħc p 4 4 mc d p E mc E F 9 dg F, 9 d ħ c d ħ c p Obviously, physically allowable pogessive action of G and F is as follows: F G DOI:.46/oalib.487 Open Access Libay Jounal

11 m pc E c ħ, FG, ~e () When is tue, F and G shall be at the size of the same level accoding to Fomula (). s F C, G~ C () s Above fomula is put into Fomula () to obtain: sk C e C = s+ K C + e C = () C and C cannot be set as at the same time, so the following condition must be met. ( sk) e e ( s+ K) Accodingly, the following solution is obtained: s = ( ) ( e =± K ) When applying the global appoach to find the movement of nucleon in its own field, it is necessay to notice that its static mass is not changed. Namely, when H = o s = is tue, we can obtain a nucleon only influenced by its intenal action, thus avoiding the influence of extenal momentum. ( ) ( e ) K = () In above fomula, the left pat is a continuous value changed along with, and the ight pat is discontinuous value which can be only positive and negative integes. Obviously, the two pats ae unequal to each othe, and the unique feasible method is to set the following equation: ( ) e = constant Namely: = (4) Poton only has one state, namely its gound state. When K = is tue, the following definition is established accoding to the elation between mass and fluctuation: ħ = (5) mc The state equation of poton can be solved as follows: When K = is tue, Above fomula can be met. F p e = G = (6) DOI:.46/oalib.487 Open Access Libay Jounal

12 When K = is tue, F = G = (7) Function convegence equiement cannot be met..4. Diac Intinsic Equation of Neuton Neuton has two states aound decay, namely: neuton state simila to poton state, and poton-electon state afte fission, so thee ae two Hamilton opeatos. z z ke z z ke z z ke ħc ˆ ( ) H = c p+ mc n β e p ˆ e H = c p+ mc e p (8) p and p espectively epesent the pobabilities of the two states, so p+ p = is tue. Similaly to Fomula (4), above fomula can be simplified as follows: e ˆ ˆ ke ħc H c p ic K mc e p ˆ e H = cα p+ mc e p ( / ) = + ħ α β + p β + (9) Thee quaks ae symmetical with each othe and meet the mutual mass cente as shown in Fomula (), the symmetical diagam of quaks as shown in Figue 5. Figue 5. Symmetical Diagam of Quaks. Namely: ( + ) e Ve = e = We find p and p as follows: Fo conveting Fomula (9) into the fine stuctue fom similaly with Fomula (5) fo solution, we fistly need to change s. DOI:.46/oalib.487 Open Access Libay Jounal

13 The following fomula is defined: s = s + s (4) The following fomula can be obtained: s K p 9 s = ( K α ) p ( n ) = α + e Now, we need to find a pobability in decay intemediate pocess to detemine p and p. Thee ae two chages as / u quaks in neuton, and each chage may decay into one negative paticle. Due to the epulsive inteaction between the two paticles, the following two goups of potential enegy can be found. Potential enegy including coulomb field o potential enegy including stong foce field and coulomb field (d Quak Decays into u Quak and Pobably Releases Two Negative Chages Relevant o Ielevant to Each Othe as shown in Figue 6). (4) Figue 6. d Quak Decays into u Quak and Pobably Releases Two Negative Chages Relevant o Ielevant to Each Othe. V V e n ħ = = = α ħc ke ħc( + α ) = + = ke ke ke c Pobability is diectly popotional to the squae of potential enegy, namely: the following fomula can be obtained accoding to above fomula: + α p = + α (4) α p = + α Fomulae (4)-(4) ae combined to obtain: (4) DOI:.46/oalib.487 Open Access Libay Jounal

14 + α α = α + e + ( n ) ( α ) s K K 9 + α + α (44) When H = o s = is tue, we obtain a neuton only influenced by its intenal action, thus avoiding the influence of extenal kinetic enegy. + α α K α ( n ) ( K α ) = + e α + α Similaly with Fomula (5), the following fomula can be defined: ħ = mc Fomula (45) is conveted into: α α ( mp mn) + K = α + e + ( K α ) 9 + α + α At the moment, neuton is unde gound state, namely: K n = K = Accodingly, poton-neuton mass atio is obtained as follows: m m p n 9 = + ln + α ( α ) + α α 4 9 The influence of poton ecoil and weak decay on (45) (46) (47-) (47-) α is not consideed in Fomula (47). Theefoe, we will continuously discuss elevant poblem. ) Influence of poton ecoil on α : Diagam of Recoil Movement between Poton and Electon is as shown in Figue 7. Figue 7. Diagam of Recoil Movement between Poton and Electon. Namely: mpvp= mv e e mpvpe= mv e e e= ħ (48) DOI:.46/oalib Open Access Libay Jounal

15 E 9 mc α 4 = e + Namely, the influence of poton ecoil on 9 4 α me + m p m e m p α is as follows: ) Influence of weak decay on α : z-axis is taken as the obsevation axis; in consideation of the similaity between weak foce and spinning inteaction, the weak foce fomula is set as follows: (49) (5) 8π Vˆ = ee e veσ w e e = S i mc e e e S i = e e mc e + ( α α ) e e x y ( α α ) v v x y (5) The calculation method fo weak potential is as the same as that fo the supefine action between poton and electon unde s state of hydogen atom ( = ). S 4 e Sv e = ħ (5) Finally, the enegy fo weak foce decay is calculated as follows: 4 E = mcα (5) e In consideation of the influence of poton ecoil, the coected enegy is as follows: The influence on E me = α + m p 4 mc e α is as follows: me α + m p The coect poton-neuton mass atio is as follows: m m p n 9 m e = + ln + α ( α ) + α + α α 4 m p 9 The expeimental value of fine stuctue constant is set as α = to obtain the theoetical value of Fomula (5) as The expeimental value of this constant can be checked in NIST mp [] official website as = ( 5). We can find that the mn exp theoetical value has a spectacula accuacy, thus indicating that it is feasible fo (54) (55) (56) DOI:.46/oalib Open Access Libay Jounal

16 us to descibe the intenal movement state of nucleon by Diac equation. Theefoe, this can be taken as the necessay evidence fo us to veify the stong nuclea foce potential fomula. When neuton is unde the gound state s =, the state equation of neuton, solved theeby, can meet Fomula (6)..5. Intenal Stong Inteaction of Σ Bayon.5.. Intenal Symmetical Stuctue of Σ Bayon Σ paticles family includes Σ +, Σ and Σ, espectively coesponding to the quak compositions (uus), (dus) and (dds). s quak is not a stable quak, and ± decays into a stable stuctue accoding to the fom of s K ( K ) + d( u), as shown in Figue 8. Figue 8. Intenal Symmetical Stuctue of Σ bayon..5.. Diac Function of Σ Bayon Hamilton opeato of Σ bayon is as follows: ˆ ˆ ke ħc H c p i c K m c 5 e Σ+ = + ħ α β + Σ+ β + (57) ˆ ˆ ħc H c p i c K m c e Σ = + ħ α β + Σ β (58) ˆ ˆ ke ħc HΣ = c p + i c K + m c 7 + e ħ α β Σ β (59) The pocess fo solving Diac equation of Σ bayon is consistent with the pocess fo solving Diac equation of poton. The state function finally obtained can meet Fomula (6). DOI:.46/oalib Open Access Libay Jounal

17 The mass atio of the thee paticles of Σ paticles family can be obtained as follows: 4 m + : m : m =.5ln α ::.5ln + α Σ Σ Σ 7 7 = ::.8 The expeimental value of mass atio is put to obtain: + Σ exp exp exp (6) m : m : m = ::.4 (6) The expeimental value is basically consistent with the theoetical value..5.. Estimation of Mass of Σ Bayon m = m + m is assumed to estimate the mass of thee Σ bayon paticles, n Σ K and the estimated value is compaed with the expeimental value (as shown in Table ). Table. Thee Σ bayon s mass compaison table. Paticle Name Mass Fomula Theoetical Value A of Mass (Mev) Expeimental Value [] B of Mass (Mev) Eo Rate = (A/B )*% m m.5ln 7 α = + Σ + Σ Σ ±.7.% Σ m Σ ±.4.5% m m 4.5ln 7 α = + Σ + Σ Σ ±..4% Small eo exists between theoetical value and expeimental value. 4. Diac Intinsic Equation of π Meson 4.. Intenal Symmetical Stuctue of π Meson Intenal Even Symmetical Stuctue of π Meson is as shown in Figue 9. Figue 9. Intenal Even Symmetical Stuctue of π Meson. DOI:.46/oalib Open Access Libay Jounal

18 4.. Diac Intinsic Equation of π ± We fistly analyze π ±, and this is simple fo us to undestand, because we have solved Diac intinsic equations of poton and neuton. Hamilton opeato of π ± is as follows: Hˆ c p m c ke = α + ± β + π ħc ( ) e a (6) Figue. (a) Intenal Chage Symmety of Positive-Negative π Meson; (b) Intenal Chage Symmety of Zeo π Meson; (c) Chage Symmety in Zeo π Meson unde Violation of Minimum Chage Value. Notably, two quaks in meson have no electostatic foce action, but unde decay state, electon and anti-electon neutino fom a special electostatic inteaction of the same chage, which seems as an electostatic field between two electons. Anti-electon neutino like a mio pojects an electon with the attibute as the same as that of pimay electon, and then two electons have electomagnetic inteaction (as shown in Figue ). Namely: α I p=iħ, α =, β = α I DOI:.46/oalib Open Access Libay Jounal

19 When H = is tue, namely: when we obtain a static π ±, a goup of necessay conditions can be obtained as follows: K = ħ (6) a = m c π ± When K = is tue, F G e π = = ± can meet the equiement. When K = is tue, F G e π = = ± cannot meet function convegence equiement. 4.. Diac Intinsic Equation of π Hamilton opeato of π is as follows: H c p m c ke ħc ˆ ( a) = α + π β 4 + e ± Namely: α I p =iħ, α =, β = α I When H = is tue, namely: when we obtain a static π ±, a goup of necessay conditions can be obtained as follows: K = ħ (65) a = m c π ± At the moment, m ln ( 8α ) π± = (66) m π ln ( + α ) When K = is tue, F G e π = = ± can meet the equiement. When K = is tue, F G e π = = ± cannot meet function convegence equiement. The condition shown in Figue (c) is not consideed in above fomula, and the specific value of such condition and common symmety condition is exactly the specific value of stong foce and electostatic foce, namely::8α, so the above fomula is coected as follows: m ln ( 8α 8α 9) π± = =.487 (67) m π ln ( + α ) The expeimental value of the mass atio of chaged π meson and neutal π meson cannot be found in efeences, so the expeimental value of the mass atio of the two K mesons is obtained though the mass [] division: mπ exp ±.5 ± = =.4 ± (68) m ±.6 π exp (64) DOI:.46/oalib Open Access Libay Jounal

20 Fomula (59) is divided by Fomula (6) to obtain:.487 % = = (69) Eo ate is.5, thus indicating the theoetical value is consistent with the expeimental value. 5. Diac Intinsic Equation of K Meson 5.. Intenal Symmetical Stuctue of K Meson [6] Figue. Intenal Even Symmetical Stuctue of K Meson. Figue. Intenal Chage Symmety of K Meson. 5.. Diac Intinsic Equation of K Meson The pocess fo solving Diac equation of K meson is simila with the pocess fo solving the same of π meson. But such pocess is independently descibed in following paagaph fo thee puposes: ) wide applicable scope of the pape: except K meson which also includes s quak, othe paticles in this pape ae composed of two quaks-u and d quaks, so the intoduction to such pocess can futhe widen the applicable scope of stong inteaction veified in this pape; ) the intenal symmetical type of chaged K meson is odd symmety, and such stuctue aely exists among mesons; ) the stong foce potential of chaged K meson is as shown in Fomula (), thus poving the existence of such stong foce potential (as shown in Figue, Figue ). Finally, the fomula fo the mass atio of chaged K meson and neutal K meson is as follows: DOI:.46/oalib.487 Open Access Libay Jounal

21 m m K± K ( α ) +.5ln 4 =.5ln + = ( α ) Z. D. Huang The expeimental value of the mass atio of chaged K meson and neutal K meson cannot be found in efeences, so the expeimental value of the mass atio of the two K mesons is obtained though the mass [] division: mk exp ±.6 ± = =.99 ± (7) m ±.4 K exp Fomula (7) is divided by Fomula (7) to obtain: %.4 4 = = (7).99 Eo ate is.4, thus indicating the theoetical value is consistent with the expeimental value. 6. Stong Inteaction of Atomic Nucleus Intenal stong foce action of atomic nucleus is souced fom π meson exchange between poton and neuton. The eaction fomula is expessed as follows: n p+ π ± (7) The intenal stong inteaction of deuteon is geneated by π meson exchange between single poton and single neuton though eplacement eaction as shown in Fomula (7). Notably, π meson exchange also exists between two neutons, but the eplacement between two neutons cannot be distinguished, so thee is no foce effect o foce action (as shown in Figue ). The intenal stong inteaction of deuteon is the most basic intenal stong inteaction of atomic nucleus. The fou most epesentative and simplest paticlesdeuteon, titon, He- and He-4 will be eseached in following paagaph to explain the foce action in atomic nucleus (as shown in Figue ). (7) Figue. (a) π Meson Loop-exchange State in Deuteon; (b) π Meson Loop-exchange State in Titon; (c) π Meson Loop-exchange State in He-; (d) π Meson Loop-exchange State in He-4. DOI:.46/oalib.487 Open Access Libay Jounal

22 6.. Stong Inteaction of Deuteon Classical theoy is adopted to solve the combined potential of deuteon. Deuteon is an atomic nucleus fomed by the combination of one poton and one neuton unde stong action, and the intenal stuctue of deuteon can meet angula momentum consevation and stess balance (as shown in Figue (a) and Figue 4). Figue 4. π meson elease and absoption states always exist in deuteon. In consideation of continuous movement of π meson between poton and neuton, the balance state in deuteon is namely the elease state theeof. Unde such state, two potons make cicula movement aound nucleus, and π meson locates at the cente of the cental cicle. The mechanical fomula fo such state can be established as follows: m p v = ħ (74) mv p The following fomula is set: k = a b = ( a) ( α ) ħc = e + 4 m π ± m p (.5ln ( + α )) (75) (76) DOI:.46/oalib.487 Open Access Libay Jounal

23 The expeimental values of poton, π meson and fine stuctue constant can be put into the fomula to find constant b. b = (77) Fomulae (7), (74) and (75) ae combined and simplified as follows: 4 ( k ) e + α = k 4b The potential enegy fomula of deuteon is as follows: Kinetic enegy of each nucleon is as follows: V ( e a α ) ħc = + (78) (79) Fomulae (76) and (77) ae put into the following fomula to obtain: E = V E = 5.5 MeV (8) Deuteon has a pobability of / espectively fo two states absoption state and elease state. Unde absoption state, the sum of the chages caied by potons and neutons theein is zeo, so thee is no any inteaction; potons and neutons ae espectively unde fee state, and the binding enegy is also zeo, and the binding enegy of deuteon shall be the mean value unde the two states. E = E.576 MeV + = (8) But the influence of the mass of π meson located at the cente is not consideed in above fomula. Notably, the mass of this π meson is not a constant. The influence of two factos may be consideed fo the estimation theeof. e ) π ± e + υ is tue, so the mass of π meson will not be lowe than that of electon. Theein, the pobability of π meson unde elease state in deuteon is / (intenal quak composition of poton is (uud), π meson can be only absobed by u quaks to geneate d quak; the pobabilities fo π meson unde absoption state and unde elease state ae espectively / * / = / and / = /). E > E =.47 MeV (8) π ± e ) Influence of intenal stess action inside deuteon on π meson E = En Ep E =.9.88 =.5 MeV (8) π ± Fomulae (8) and (8) ae compehensively consideed to obtain the estimated mass of π meson: E = E + E =.457 MeV (84) ± π e ± π Finally, the binding enegy of deuteon is obtained as follows: EDthe = E+ m π ± =. MeV (85) The expeimental value is put into the fomula: DOI:.46/oalib.487 Open Access Libay Jounal

24 EDexp = EDexp Enexp Epexp =.5 MeV (86) Eo is as follows: = E exp E the =+.5 MeV (87) D D Eo ate is as follows:. = % = % =.% E Dexp.5 ED the η (88) The theoetical value is basically consistent with the expeimental value. 6.. Estimation of Binding Enegy of Thee Atomic Nucleuses Titon, He- and He-4 have complex intenal spatial stuctue, so the binding enegy can be only estimated. He- has two potons and a neuton, when the neuton elease a pion, the stong nuclea foce will spead between thee potons, Stong inteaction of He- is equivalent to the stong inteaction of thee pais of deuteon (as shown in Figue (c)), and the binding enegy theeof is thee times of that of deuteon. Consideing the influence of the electostatic potential diffeence, the binding enegy of he- can be obtained. ( + ) α EHe-the = ED the + E m ±.5ln + π 4k = ( ( α )) = 7.55 MeV Stong inteaction of titon is simila with that of He- (as shown in Figue (b)), but it is necessay to conside the epulsive inteaction between two potons in He-, and its binding enegy is slightly lowe than that of He-. ( + ) α EHe-the = EDthe + E m ±.5ln + π k = ( ( α )) = 8.4 MeV The intenal spatial stuctue of He-4 is a nomal tiangula pyamid (as shown in Figue (d)), and each face of the nomal tiangula pyamid is equivalent to the intenal symmetical stuctue of a He-, so its binding enegy is fou times of that of He-. Additionally, two faces ae lack of π mesons, so the influence of two pais of poton-poton foce must be consideed. Specifically, the binding enegy is measued and calculated as follows: E = 4 E + E E T He-4the He-4the He-4the the = = 8.48 MeV The compaison between the theoetical value and thee expeimental value of the binding enegy of thee atomic nucleuses is shown in the following Table. (89) (9) (9) DOI:.46/oalib Open Access Libay Jounal

25 Table. Binding enegy Compaison Table fo Thee Atomic Nucleuses. Paticle Name Theoetical Value A of binding enegy (MeV) Expeimental Value B of binding enegy (MeV) Eo = A B Eo Rate = (A/B )*% He % Titon % He-4 [7] % Remaks: ) The expeimental value of He- binding enegy cannot be found, so it is obtained though deducting the mass [] of two neutons and one poton fom the mass [] of He-. ) The expeimental value of titon cannot be found, so it is obtained though deducting the mass [] of two neutons and one poton fom the mass [] of titon. Accoding to the compaison between the theoetical value and the expeimental value of the binding enegy of thee atomic nucleuses, we find significant eo and high eo ate, but we cannot deny that such thought can be used fo analyzing the intenal nucleus action of atomic nucleuses, thus pesenting impotant efeence value. 7. Δ() Stong Inteaction 7.. Δ() Intenal Symmetical Stuctue Δ () paticles family includes fou types of paticles, espectively Δ++ (), Δ+ (), Δ () and Δ (). Δ () paticles family plays a special ole, and foms the complete bayon family of u and d quak stuctue togethe with potons and neutons. Accoding to the mass infomation analysis, Δ () paticles family, diffeent fom poton and neuton which ae usually diectly composed of quaks, is composed of poton o neuton and two π mesons. In othe wods, the stong inteaction theeof belongs to bayon-meson stong inteaction. Δ () paticles family has intenal odd symmetical stuctue, as the same as the intenal symmetical stuctue of poton and neuton (as shown in Figue 5). 7.. Δ () Mass Ratio and Mass Estimation Δ () intenal symmetical stuctue can be also descibed by Diac equation, but the specific pocess is simila with the pocess fo the mentioned paticles, so it will not be epeatedly explained in this chapte. Theoetical values of the masses of the fou types of paticles ae as follows: m ++ : m + : m : m = +.5ln α : +.5ln α : +.5ln α : +.5ln α =.66 ::: (9) DOI:.46/oalib Open Access Libay Jounal

26 Figue 5. (a) Δ++ () Intenal odd symmetical stuctue; (b) Δ+ () Intenal odd symmetical stuctue; (c) Δ () Intenal odd symmetical stuctue; (d) Δ () Intenal odd symmetical stuctue. Table. Δ () s mass compaison table. Paticle Name ++ Mass Fomula ( ) m = m +.5ln α m = m +.5ln α Theoetical Value A of Mass (MeV) Expeimental Value [] B of Mass (MeV) Eo Rate = (A/B )*% ±.89% ±.97% m = m +.5ln α ±.97% m = m +.5ln α ±.97% The expeimental values of fou types of Δ () paticles ae all ± MeV, and the specific value theeof is basically as the same as Fomula (9). m = mp + m π ± is assumed to estimate the masses of the fou types of Δ () paticles, and the estimated value is compaed with the expeimental value (as shown in Table ). The theoetical value is basically consistent with the expeimental value. DOI:.46/oalib Open Access Libay Jounal

27 8. Stong Inteaction of η Paticle and η (958) Paticle Intenal tiangula-pyamid symmetical stuctue of η paticle is as shown in Figue 6(a); intenal dual tiangula-pyamid symmetical stuctue of η ( 958) paticle is as shown in Figue 6(b). η paticle has intenal tiangula-pyamid symmetical stuctue and is composed of fou π mesons which geneate inte-meson type stong inteaction. η paticle has dual tiangula-pyamid symmetical stuctue combined by two η paticles, and is composed of seven π mesons which geneate inte-meson type stong inteaction. Without consideing electostatic foce, the mass of the two types of paticles is namely the sum of the mass of π mesons included theein. Figue 6. (a) Intenal tiangula-pyamid symmetical stuctue of η paticle; (b) Intenal dual tiangula-pyamid symmetical stuctue of η (958) paticle. Table 4. Δ () s mass compaison table. Paticle Name Mass Fomula Theoetical Value A Expeimental Value B of Mass (MeV) of Mass (MeV) Eo Rate = (A/B )*% η m ( m m η π± π ) ( 958) m m 4m ± = ±..4% η = ±.4.7% η π π DOI:.46/oalib Open Access Libay Jounal

28 The theoetical value is basically consistent with the expeimental value in Table Summay As implied by the title of the pape Reseach on Stong Inteaction, the pape aims at solving stong foce potential fomula. Fistly, the stong inteaction is globally divided into five diffeent types accoding to diffeent stess paticles, and types of diffeent epesentative paticles ae selected fo diffeent types of stong inteactions, thus pesenting the compehensiveness of the eseach objects. The fist pat of the main text is the hypothesis fo stong foce potential. Chage type of stong foce, elation between stong foce intensity and fluctuation, hadon state and its limitation cause ae eseached to popose easonable stong foce potential fomula, but the applicability of stong foce potential fomula shall be veified unde specific paticle state. Two tools ae needed fo solving paticle state, namely: intenal symmetical stuctue diagam of eseach object, which is used fo peliminaily integating stong foce potential and electostatic potential opeatos; Diac equation which is undoubtedly successful fo solving high-enegy state of paticles. Stong foce potential and electostatic potential opeatos peliminaily integated ae put into Diac equation to impove solution efficiency. The second pat of the main text is the veification of the applicability of stong foce potential fomula. The gound state function fo the chaged paticle can be obtained though Diac equation desciption, but the most effective evidence fo this pat is the theoetical value of the mass atio of chaged paticle and neutal paticle, and it is geatly accuate to compae the theoetical value of the mass atio with the coesponding expeimental value to judge a seies of mentioned pocesses and hypotheses. Eo o eo ate between the theoetical values of the mass atios of paticles and the coesponding expeimental values is vey small (the eo ate between the theoetical values of η paticle and η ( 958) paticle and the coesponding expeimental values is vey small). In othe wods, the theoetical value is consistent with the expeimental value, thus poving the validity of stong foce potential fomula. Hadon state o the state fo foming stable stuctue between hadons is descibed by state function which can meet Fomula (6). By obseving the stong inteaction law of the above hadons, we found that all the stong inteactions have the paticipation of meson (pion o kaon), which is the medium of stong nuclea foce. It is speading the ole of powe between quaks, Mesons, bayons, Meson and bayon, so the meson is not only the stess paticles, but also the media. Refeences [] CODATA Intenationally Recommended 4 Value of the Fundamental Physical DOI:.46/oalib Open Access Libay Jounal

29 Constants. [] Amsle, C., et al., Paticle Data Goup. (7) The Review of Paticle Physics. Chinese Physics C, 4,. [] Eidelman, S., et al., Paticle Data Goup. (4) Physics Lettes B, 59,. [4] Diac, P.A.M. (98) The Quantum Theoy of the Electon. Poceedings of the Royal Society of London. Seies A, Containing Papes of a Mathematical and Physical Chaacte, 7, [5] Diac, P.A.M. (9) A Theoy of Electons and Potons. Poceedings of the Royal Society A: Mathematical, Physical and Engineeing Sciences, 6, 6. [6] Huang, Z.D. (7) The Reseach on Relationship between Neueinos and Weak Foce. Moden Physics, 7, [7] Nogga, A., Bogne, S.K. and Schwenk, A. (4) Physical Review C, 7, Aticle ID: 6. DOI:.46/oalib Open Access Libay Jounal