Strong gravitation is fundamental gravitational interaction at the level of elementary particles, one of the components of the strong interaction in physics according to the gravitational model of strong interaction. It is assumed that strong gravitation and electromagnetic forces are responsible for the formation and integrity of the matter of elementary particles and atomic nuclei, and also participates in the interactions between electrons and nuclei in atoms and molecules. For describing of strong gravitation equations of Lorentz-invariant theory of gravitation are used.
After the discovery of the electron in 1897, of the proton in 1919, and of the neutron in 1932, and of their compositions in the form of atomic nuclei, atoms and molecules, it became necessary to describe the forces acting between the particles and binding their matter. In most cases, the behavior of the electron and proton, placed in the external electromagnetic field, is satisfactorily described by electromagnetic forces. This led to the standard electromagnetic model of the atom. As for the interaction of nucleons in atomic nuclei, the hypothesis of the Japanese physicist H. Yukawa was initially accepted about the binding between the particles by means of mesons, mostly of pions. Then, in the framework of the quark theory all hadrons began to be considered to be composed of quarks.
However the idea, that the fundamental interaction between a set of elementary particles must occur due to the action of another set of elementary particles, belongs to the atomistic theory, but it contradicts the Theory of Infinite Hierarchical Nesting of Matter. Indeed, the reactions between elementary particles follow the laws of conservation of energy, momentum and electric charge; the matter, energy-momentum and the charge of one type of particles transforms into the corresponding quantities of other particles, but this does not mean that the carrier and the cause of the interactions are the elementary particles themselves. The interaction of nucleons with each other by means of pions hardly agrees with quarks and gluons, which are used to describe the integrity of hadrons, due to the problem of non-observability of quarks in the free state and the uncertainty of transformation of the forces between the quarks inside each of the nucleons into the strong interaction between different nucleons in the atomic nucleus. The introduction of virtual particles with their exotic properties (short lifetime, the simultaneous generation of particles and antiparticles, etc.) does not save the situation. Thus, the abstract explanation of the electromagnetic interaction of two charges with the help of virtual photons as the field quanta still remains the statement which is not supported by the concrete model of the interaction process.
Among the attempts to explain the strong interaction in connection with gravitation there is a hypothesis that in the model of hadronic bags the hadrons are de Sitter microuniverses, in which quarks are enclosed. The radius of hadrons corresponding to the radii of these microuniverses, is associated with the strong gravitational constant and the corresponding cosmological constant. To explain the properties of hadrons in the assumption of strong gravitational interaction the analogies between hadrons and Kerr — Newman black holes are described.    
In 1999 Sergey Fedosin, based on the similarity of matter levels, SPФ symmetry and Le Sage's theory of gravitation, according to which black holes are not admitted, postulated the existence of strong gravitation as the fundamental force at the atomic level and found the value of strong gravitational constant m3•s–2•kg–1. 
The equality between the rest energy of the proton and its total energy, which due to the virial theorem is approximately equal to the half of the potential energy of the strong gravitational field, allows us to estimate the radius of the proton :
here is the proton mass, is the speed of light, is the coefficient depending on the distribution of matter, in the case of the uniform matter density of the proton . According to the self-consistent model   for the proton .
The obtained value coincides with the experimentally obtained sizes of the proton and the neutron,  confirming the validity of the idea of strong gravitation. At the same time the given equality implies the explanation of the essence of the rest energy of bodies as the energy associated with the strong gravitation of the nucleons of the bodies’ matter. According to the mass–energy equivalence, the rest energy of the nucleon is proportional to its mass. On the other hand, the total energy of the nucleon includes the energy of the strong gravitational field which is proportional to the squared mass, and the internal energy of the nucleon matter which is proportional to the matter mass in the expression for the kinetic energy. As a result, the total energy is proportional only to the mass just as well as the rest energy.
On the comparison of the maximum angular momentum of the strong gravitational field and the angular momentum of the proton with the uniform matter distribution another estimate of the proton radius is based: 
As the model of emerging of strong gravitation the modernized Le Sage's theory of gravitation is used, which becomes universal taking into account the Theory of Infinite Hierarchical Nesting of Matter.  
At the stellar scale level of matter the analogues of nucleons are neutron stars, the integrity of which is maintained by the ordinary force of gravitation and the pressure force in the matter arising from the repulsion of the nucleons from each other. Similarly, in the matter of nucleons the compensation of the strong gravitation and the internal pressure force takes place (see the substantial neutron model and the substantial proton model). In this picture, for the stability of nucleons and describing their properties quarks are not required, in contrast to the standard quantum chromodynamics. At the same time in the model of quark quasiparticles the quarks are seen not as real particles inside hadrons but as quasiparticles, the constituent elements of the hadrons’ matter which carry the mass, charge and magnetic moment. This ensures the observed symmetry of hadron properties. In turn, the quarks themselves can be reduced to the combinations of two hadronic phases of the matter.  The analysis of the Regge hadron families also shows that they can be explained by taking into account the quantization of the spin and the matter state of the particles, retained by the strong gravitational field.
Strong gravitation significantly affects the construction of the model of the electron, leading to the substantial model of this particle. In particular, the electron charge is so large, that strong gravitation is not able to keep the electron matter from the Coulomb electric force of repulsion of the charges. Therefore, the stability of the electron in the atom is possible only in the form of a scattered electron cloud (disc) and due to the forces of attraction to the nucleus from strong gravitation and the nuclear charge. Another fact, the quantization of energy levels and of the orbital angular momentum of the electron in the atom, is explained based on the condition that the flux of kinetic energy of the motion of electron matter around the nucleus is equal to the sum of the energy fluxes from the strong gravitation and the electromagnetic field.  This leads to the stationary states of the electron in the atom, in which it does not produce emission. For the hydrogen atom it is also found that the magnetic energy of the nucleus in the magnetic field of the electron equals the energy of the nucleus’ spin in the torsion field of strong gravitation of the electron in case of limiting rotation of the nucleus. 
The interaction of nucleons in the atomic nucleus
The experiments with the scattering of nucleons on each other allow us to estimate the effective potential of strong interaction acting between these particles.  As the distance decreases the interaction force increases rapidly. To describe this force the gravitational model of strong interaction is used, in which the nuclear forces are the sum of the attraction from the strong gravitation, the repulsion of the nucleon spins due to the torsion field of strong gravitation, as well as from the action of electromagnetic forces. At short distances, the repulsive force of the spins dominates, which is inversely proportional to the fourth and then the fifth degree of the distance. At large distances, there is attraction of the nucleons, mainly from the strong gravitation. At distances close to the radius of the nucleon, the neutron and the proton are in the equilibrium state, which gives the deuteron as the simplest atomic nucleus with two nucleons.  Taking into account the strong gravitation allows us to construct the model of simplest nuclei and their geometric configuration, as well as to explain the dependence of the specific binding energy of atomic nuclei on their atomic number due to the saturation effect of the strong gravitational energy and the increase of the electrical repulsive energy of protons.
In quantum chromodynamics, it is assumed that the long lifetime, inherent in some hadrons, is due to the presence of strange quarks in them. However, the models of strange particles can be constructed similarly to the models of atomic nuclei, by connecting nucleons and mesons under the influence of strong gravitation.  The composition of some strange hadrons is described in the model of quark quasiparticles.
The interaction of atoms leads to the formation of molecules, as well as simple and molecular substances. In contrast to the nucleons in atomic nuclei, in the interaction of atoms the strong gravitation acts between the nuclei of all atoms as well as between the electrons, complementing the electromagnetic forces. In this case the electron discs, surrounding the atomic nuclei, due to the rapid rotation in them of the matter, which is charged and oriented by the magnetic field, have the possibility to shield the gravitational forces between the nuclei, reducing them to the level of electrical forces. The equilibrium of atoms in molecules and in substances is achieved in case of the balance of gravitational and electromagnetic forces. With increasing of the distance between the atoms, the so-called Van der Waals force occurs between them in the form of the attraction rapidly decreasing with the distance. The estimate with the help of the Le Sage's theory of gravitation gives the radius of action of strong gravitation in the matter with the density of the order of Earth's density, about 0.7 m. 
1. Salam, A., and Strathdee, J. Confinement Through Tensor Gauge Fields. Physical Review D, 1978, Vol.18, Issue 12, P. 4596-4609.
2. Sivaram, C. and Sinha, K.P. Strong gravity, black holes, and hadrons. Physical Review D, 1977, Vol. 16, Issue 6, P. 1975-1978.
3. Recami, E. and Castorina, P. On Quark Confinement: Hadrons as «Strong Black- Holes». Letters Nuovo Cimento, 1976, Vol. 15, No 10, P. 347-350.
4. Pavsic, M. (1978). Unified Theory Of Strong And Gravitational Interactions. Nuovo Cimento B, Vol. 48, P. 205-253.
5. Oldershaw R. L. Hadrons as Kerr-Newman Black Holes. arXiv:astro-ph/0701006v4, 30 Dec 2006.
6. Fedosin S.G. Fizika i filosofiia podobiia ot preonov do metagalaktik, Perm, pages 544, 1999. ISBN 5-8131-0012-1.
7. Comments to the book: Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages, ISBN 978-5-9901951-1-0. (in Russian).
8. Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, 2012, Vol. 35, No. 4, P. 349 – 363.
9. Hofstadter, Robert, The electron-scattering method and its application to the structure of nuclei and nucleons, Nobel Lecture (December 11, 1961).
10. Fedosin S.G. Sovremennye problemy fiziki: v poiskakh novykh printsipov, Editorial URSS, Moskva (2002).
11. Fedosin S.G. Model of Gravitational Interaction in the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4, No. 1, March 2009, P.1–24.
12. Fedosin S.G. The graviton field as the source of mass and gravitational force in the modernized Le Sage’s model. Physical Science International Journal, ISSN: 2348-0130, Vol. 8, Issue 4, P. 1-18 (2015). http://dx.doi.org/10.9734/PSIJ/2015/22197.
13. Sergey Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9.
14. Ishii N., Aoki S., Hatsuda T. The Nuclear Force from Lattice QCD. – arXiv: nucl-th / 0611096 v1, 28 Nov 2006.
- Infinite Hierarchical Nesting of Matter
- Similarity of matter levels
- SPФ symmetry
- Quantization of parameters of cosmic systems
- Hydrogen system
- Strong gravitational constant
- Strong interaction
- Gravitational torsion field
- Gravitational model of strong interaction
- Model of quark quasiparticles
- Substantial electron model
- Substantial neutron model
- Substantial proton model