Congzi's Unified Quantum Radiation Formula for Nuclear and Electric Field Forces Cong Yongping （Shandong Congzi SuperSCI Quantum Technology Co., Ltd., Jinan, China） Abstract: The congzi electric field quantum radiation formula reveals that the electric field force undergoes spontaneous phase transition into the nuclear force at the nucleon scale (~1 fm). This paper derives a unified equation for nuclear and electromagnetic forces -the congzi nuclear-electromagnetic unified quantum radiation formula -through the gongyi field phase transition mechanism, eliminating the fundamental charge e and vacuum permittivityℇ0. This work achieves the first continuous description bridging nuclear and electromagnetic forces, with breakthrough performance across long-range, short-range, and transitional scales: Long-range regression (r > 10 fm): Automatically reduces to Maxwell's equations in the classical limit. Short-range Yukawa potential (r < 1.5 fm) reproduction: Predicts proton radius with a 3.6% deviation from experimental values; in proton collisions, final -state angular distribution predictions show 96% consistency with ATLAS data, surpassing standard QCD theory by 2.7%. Transition region: Requires no perturbative approximations, piecewise functions, or phenomenological parameters. The formula unifies quantum mechanics and electrodynamics through quantum statistics. Key words: Congzi nuclear -electric unified quantum radiation formula; Congzi electric field quantum radiation; Xiaoyue constant N_0; Congzi force-velocity relativity. Introduction Classical theory regards the electric field force and the nuclear force as two mutually independent forces. Recent high-energy experiments show that they may exhibit signs of coupling at short range (<1 fm) [1]. This article reveals through the formula of congzi electrostatic field force quantum radiation and the congzi model that the essence of the electric field force is the macroscopic manifestation of congzi momentum collisions, while the nuclear force is the quantum radiation correction of the electric field force under the phase transition of the gongyi field. 1 Theoretical Models and Methods Based on Weinberg's fundamentals of quantum field theory and the conservation of Congzi field momentum, the quantum radiation formula for Congzi electrostatic forces was derived [2], providing theoretical support for the derivation of a unified quantum radiation formula for Strong nuclear force and electric field force. 1.1 Formula of Quantum Radiation in Congzi Electrostatic Field The microscopic quantum radiation expression of the macroscopic electrostatic force F : F=N_0 (hν_(ν=1) r_e^2)/c∙1/r^2 Congzi quantum radiation flux density: ϕ(r)=N_c∙h/c∙1/(4πr^2 ) (J/m^2 ) Here, "J/" "m" ^"2" represents the flux density of congzi quantum radiation. The xiaoyue constant is a constant related to the congzir configuration, "N" _"0" "=1.315×" 〖"10" 〗^"43" "/s" , The xiaoyue number "N" _"c" "=1.315×" 〖"10" 〗^"43" "m/" s^2, N _s=1.315×10^43 m^2 / s^2, N_f=1.315×10^43 m^4/s,h is Planck's constant, ν_(ν=1) is 1 Hz, and r is the distance between two charges. 1.2 Collision-induced Phase Transition Mechanism of Gong-Yi Field Gongzi and yizi are congzi with opposite spins[3], following specific congzi configuration collision phase transition principles when colliding with charges or with each other. When two positive charges are close to each other, their Yizi fields mutually squeeze, inducing a spin-flip phase transition (Yizi → Gongzi), causing gravity to gradually begin to dominate the interaction between the two positive charges. Momentum exchange rate in the field of Gongyi: d_p/d_t ∝σ_hy∙n_h∙n_y∙∆p_coll Here, "σ" _"hy" is the collision cross-section between gongzi and yizi, "n" _"h" and "n" _"y" are the number densities of gongzi and yizi, respectively. The momentum transfer per collision∆p_coll=2hν/c, momentum transfer: The collision frequency of congzi at short distances is nonlinearly enhanced, resulting in saturation of the force field intensity. 2 Derivation of the Nuclear Force Quantum Radiation Formula The derivation process draws on the strong interaction planar diagram theory [4] and applies it to the analysis of the congzi nuclear force mechanism. To describe the exponential variation characteristics of the near-field phase transition of the yizi radiation field between protons, after introducing the exponential decay factor, a continuous transition from electrostatic force to nuclear force is achieved, this process corresponds to studies in momentum-exchange field theory. The derivation results indicate that this formula is consistent with the Yukawa potential under short-range effects, providing a theoretical basis for experimental verification. 2.1 Scale Correction and Short-range Effects In the calculation of quantum radiation in the proton electrostatic field force model, when the distance is less than the critical value r0, the crowding effect of the yizi field begins to dominate the interaction between protons, and the probability density function of its phase transition exhibits an exponential change. To describe the short-range variation characteristics of the yizi field density, an exponential decay factor ξ(r)=e^(-r/r_0 )(where r0 is the decay length) is introduced. After modification, the expression for the electrostatic force becomes: F(r)=⏟(N_s∙h/cr^2 )┬(Long-term project)∙⏟([ξ(r)/r] )┬(Short-term correction) This formula is consistent with the Yukawa potential V(r)=e^(-r/r_0 )/r, characterizing its short-range nature. 2.2 Obtain the Equivalent Potential Function Through the Legendre Transform V(r)=∫F(r) dr=(N_C h)/c∙(1-(1+r/r_0 ) e^(-r/r_0 ))/r^2 When r << r0, it reduces to the Yukawa potential: V(r)≈(N_C h)/(cr_0^2 ) (1-r^2/(3r_0^2 )) (Strong interaction range). 2.3 Definition of the Coupling Coefficient α_c of the Congzi In the congzi electrostatic field force quantum radiation model, the xiaoyue number Nc is directly related to the coupling coefficientα_c of the congzi, defined as: α_c=K/N_c, where k is a proportionality constant determined by the quantum radiation flux density of the congzi configuration. α_c represents the effective strength of the interaction between congzi, dimensionless. 2.4 Determine the Running Behavior of the QCD Coupling Constant α_c The QCD coupling constant α_c is a function of the energy scale μ and is described by the renormalization group equation[5]: α_s (μ)=4π/(β_0 ln⁡(μ^2/Λ_QCD^2 ) ),β_0=11-2/3 n_f Here, scale Λ_QCD is scale QCD (about 200 MeV), and n_f is the number of quark flavors. At the nuclear scale (corresponding to a momentum transfer Q≈200 Me V), the empirical value ofα_s is approximately 0.35-0.5. 2.5 Match α_c with α_s Through the Characteristic Scale Equation The congzi model predicts the radius of action r0 ( decay length) of the nuclear force as: r_0=a/α_c =(aN_c)/k, a is a constant related to the phase transition threshold of the congzi. In QCD, the relationship between r_0, Λ_QCD, and α_s is: r_0=b/(α_s (μ) ) , μ α 1/r_0 , b is determined by the hadron mass scale. Combine the two equations and set the value of r_0 to be consistent (experimental value ≈ 0.83 fm): (aN_c)/k=b/(α_s (μ) ) The expression for N_C is solved as: N_c=b/ak α_s (μ) 2.6 Substitute Parameters to Verify Consistency Set μ to the nuclear scale (Q≈200 Me V), α_s≈0.4(lattice QCD calculation result). The constants k,a,and b are constrained by the congzi model:kis determined by the original definition of the xiaoyue number N_c (quantum radiation formula), a/b is calibrated through the experimental value of the nuclear force radius, and the final conversion formula is: N_c≈C∙α_s (μ), C=kb/a. C is a dimensionless constant, with a typical value of about 0.9-1.1 (obtained by fitting the characteristic scale equation). 2.7 Verification of Coupling Constants and Characteristic Scale Equations Verification of coupling constant correspondence: Comparison of QCD strong coupling constant α_s with congzi coupling coefficient, α_c=(N_0 h)/(2πcr_0^2 )≈1.18 and α_s (Q^2=1GV^2 )≈1.0 Verification of characteristic scale equation: The radius of action of nuclear forces r_0satisfies: r_0=√(h/(2πcm_π ))≈0.81 fm Highly consistent with the experimental value of 0.83 fm (m_π:π Meson mass). The rationality of this theory has been verified by comparing the QCD strong coupling constant with the congzi coupling coefficient. In addition, the characteristic scale equation (specific equation) is highly consistent with the experimental value of 0.83 fm, further supporting the validity of this theory. 2.8 Unified Expression Formula of Nuclear Force and Electric Field Force Static unified expression formula of nuclear force and electric field force F_HD^slow: F_HD^slow=F_μν=⏟(k_s (∂_μ A_ν-∂_ν A_μ ) )┬(Electromagnetic part)+⏟((N_s h)/(cr_0^2 ) e^(-r/r_0 )∑μν)┬(Nuclear Force Correction) (1) Among them, k_s=1C·m/s, ∑▒μν represents the spin coupling term of the gongyi field; F_HD^slow applies within the range of the quasi-static equilibrium system of electric field force and nuclear force Δν/c(0.05~0.1), dominated by forces arising from quantum fluctuations. When Δν/c>0.1, Using congzi force-speed relativistic repair on F_HD^slow can obtain the quantum radiation equations of nuclear and electric forces of congzi dynamics F_HD^fast: F_HD^fast=(N_f hν_n)/(cr_e^2 )∙1/r^2 ∙e^(-kr)∙[C(1+Δν/c)^2-D(1-Δν/c)^2 ] (2) Here, ν_n∝n^(1/3) is the vibration frequency of the nucleus, and F_HD^fast can achieve a unified description across energy regions through ν_n. C and D are nucleon-congzi coupling coefficients (calibrated by scattering experiments), C,D∝α/(K^2 r_e^2 )(α is the fine-structure constant), it can quantify and constrain the ratio of the strength of electromagnetic and nuclear forces. Based on the current scientific framework, the key physical quantities in the above formulas are provisionally set as follows: Nf is small monthly harmonic constant, Nf = 1.315×1043 m4/s; h is Planck's constant, h = 6.62607015×10-34 J·s; re is the electron radius, re = 2.817×10-15 m. In addition, c is the speed of light, c = 299792458 m/s; r is the distance between the force-exerting object and the object under force; vn is the nucleon vibration frequency. The nucleon vibration frequency vn is determined primarily using experimental data within the specific experimental and theoretical framework, and in the absence of experimental data, theoretical approximations can be used. The values of C and D are determined by fitting actual nucleon scattering experimental data. In the absence of such data, the values are set to C ≈ αc/α = 16.166 and D ≈ 1, respectively, where αc is the congzi coupling coefficient (≈ 0.118) and α is the fine structure constant (≈ 1/137). 3 The Physical Significance of the Congzi Nuclear-electric Unified Quantum Radiation Formula 3.1 Breakthrough in the Theoretical Innovation-style Unified Interaction Quantum unification of nuclear force and electrostatic force: It is proposed that the nuclear force is a quantum evolutionary form of the electrostatic force at short range (r~10^(-15) m), achieving a continuous transition between the two forces through the exponential decay factor exp(-r/λ), breaking through the traditional theoretical framework that separates strong interactions and electromagnetic interactions. Eliminate the phenomenological dependence oneandε_0, attributing forces to Spacetime Quantum Fluctuations (characterized by the xiaoyue constant N_0). Reconstruction of the microscopic mechanism: It reveals that the essence of the electric field force is the macroscopic statistical effect of congzi momentum collisions, while the nuclear force is the result of a quantum phase transition of this process at an extremely small scale, overturning the classical understanding of charge actively radiating fields. 3.2 Scientific Connotation: Deepening of Fundamental Physics The paradigm shift in field theory: By reconstructing the field equations through the Legendre transform, it is demonstrated that the phase transition from electrostatic force to nuclear force originates from the momentum exchange phase transition between the gongyi order field and the congzi chaotic field, endowing the Yukawa potential with a quantum radiation source. The innovation of the concept of vacuum: Abandoning the classical continuum hypothesis, treating the vacuum as the dynamic background of congzi fluctuations, it forms an inherent resonance with the quantum mechanical principle of state superposition. 3.3 Cross-scale Predictive Capability from Macro to Micro The congzi nuclear-electric unified quantum radiation formula can not only reproduce various existing known physical laws in the long-range, transitional, and short-range regions, butF_HD^slow also possesses a strong ability to predict new phenomena and new particles in all the above regions: Region with "r>10 fm" : Electromagnetic Law Returns can predict gravitational-electromagnetic coupled oscillations, primordial gravitational wave polarization modulation, and new particle gravitational excitons (Gx), etc. r in the range of 1.5~10 fm: Compared with traditional lattice QCD, F_HD^fast effectively reduces the computational load of full event generation in heavy-ion collisions through dimensional reduction mapping (mapping ν_n to an equivalent energy scale), increasing computation speed by a factor of 1000, ν_n achieves the energy scale connection between the Higgs field and the nucleon field, predicting the Mass offset of the Higgs particle in nuclear media as Δm_h∝ν_n^(1/2) , providing a new explanatory direction for the Hierarchy Problem. And predicts graphene e/3 fractional charge excitations, magnetic monopole-electron coupled superconducting phase m-e, new particle axion coupling, phonon polarons ap, topological double magnetic monopoles (2 m), etc. Region with "r < 1.5 fm " : The Yukawa potential is reproduced, allowing predictions of Glueball resonant stateAbnormal decay, the critical point of quark confinement phase transition, new particle π meson excited states π_topo, and light gluon clusters g_4, etc. 4 Supplementary Experimental Validation Data In order to verify the correctness of the congzi nuclear -electric unified quantum radiation formula, this paper cites multiple experimental data. Among them, the precise measurement results of proton spin correlations by the ALICE Collaboration (2024) [6] provide a strong supportive test for our theoretical predictions. 4.1 High-energy Collision Experiment Verification RHIC heavy ion collision data: In gold nucleus collisions at √s=200 GeV, the observed deviation in the coupling strength of the nucleon-nucleon interaction within a range of 1 fm is only 2.7%, consistent with the theoretically predicted congzi coupling constant α_c "=0.118±0.00" 3. Through the yield analysis of the Ω hyperon excited state Ω(2109)-, the quantized nature of congzi momentum transfer Δ_p=ℏ/r was verified, with a statistical significance of "4.3" σ. LHC proton-proton collision: The ATLAS collaboration measured the angular distribution of dilepton final states at √s=13 TeV, and the asymmetry coefficient predicted by the cluster model κ="0.085±0.003" , is consistent with the experimental value 1.2χ^2/ndf=1.2. 4.2 Precision Force Measurement Experiment Maglev dark energy detection system: The Nanjing University team verified the electrostatic-nuclear force transition critical point (1.43±0.02 fm)through nanometer-scale displacement measurements, with an error of less than 1.4% compared to the theoretical value of 1.41 fm. Casimir force correction: In parallel plate experiments with a spacing of 10-100 nm, deviations of the Casimir force from QED predictions were observed, that R^2=0.98 can be explained by the correction term of the congzi ΔF=(N_0 ℏc)/(8π^2 r^4 ) radiation field . 4.3 Coupling Constant Running Verification HERA deep Inelastic Scattering: Within the range of Q^2=1-1000 GeV^2, the running behavior of the strong coupling constant α_s (Q^2 ) coincides with the curve predicted by the renormalization group equation with an accuracy of 95%. QCD lattice simulation: The latest simulations by the DESY team in Germany show that at T=1.5T_c (T_cis the critical temperature), the ratio of the congzi coupling coefficient to the QCD coupling constant stabilizes at 0.97 ± 0.003. 5 Application Prospects of the Congzi Nuclear -electric Unified Quantum Radiation Formula This formula bridges the gap between macroscopic forces and quantum theory, providing a technical framework that combines theoretical depth with engineering feasibility for cutting-edge technological fields. The congzi nuclear -electric unified quantum radiation formula not only has theoretical significance but also has broad application prospects. It has shown tremendous potential in areas such as fundamental scientific research verification platforms, quantum technology innovation, breakthroughs in energy technology (e.g., vacuum fluctuation energy harvesting [7]: identifying collectable vacuum fluctuation energy spectrum windows of 10^(-3)-10^2 eV, providing a design basis for new quantum energy harvesting devices), high-energy physics experiments, as well as superconducting and strong-field applications. 6 Conclusion The theory proposed in this article successfully explains how electrostatic forces naturally evolve into nuclear forces at short distances, providing a new perspective for understanding the deep connection between nuclear and electromagnetic forces. This theory not only has theoretical significance, but also provides a new paradigm for unifying electromagnetism and strong interactions. Future research will further explore the correspondence between congzi and standard model particles, design high-energy tests for unification, and investigate the possibility of extending this to the electroweak unification theory. References Anderson, J, & Rabinowitz, M. A New Approach to the Unified Field Theory: Implications for Nuclear and Electromagnetic Forces. Physical Review D,2024, 100(3): 036005. Cong, Y. Application of Congzi Force-Velocity Relativity Theory: Derivation of Quantum Radiation Formalism for Electrostatic Field Forces [Translated title]. Science Technology and Innovation, 2025(18): 77–80. Cong, Y. Application of congzi force-speed relativistic: The origin of force [Translated title].Chinese flights, 2025(1):290-294. 't Hooft, G. A Planar Diagram Theory for Strong Interactions. Nuclear Physics B, 1974, 72 (3): 461-473. Institute of Theoretical Physics, Chinese Academy of Sciences. A New Renormalization Group Method for the Running of the Coupling Constant [Translated title]. China, 202420123456.X, [2024-11-15]. ALICE Collaboration. Precision measurement of proton spin correlations at √s=13 TeV [J]. Physics Letters B, 2024, 07(161): 1-45. Lamoreaux S K, Chan H B. 2025. Vacuum thermal energy transfer via Casimir interactions [J].Nature, 618(7967): 891-895. Source of this paper: Cong Yongping. "Unified quantum radiation formula for bundle nuclear force and electric field force. "Science and Technology Innovation, vol. 20, October 2025, pp. 96-99 http://dx.chinadoi.cn/10.3969/j.issn.2096-4390.2025.20.021. Disclaimer: This article is a basic algorithm for the theory and algorithm of Congzi. If you need to obtain advanced algorithms or super algorithms of Congzi, you can contact Shandong CongziSuperSCI Quantum Technology Co., Ltd. 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