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Electromagnetic Nature of Nuclear Forces and the Toroid Structure of the Helion and the Alpha Particle

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Electromagnetic Nature of Nuclear Forces and the Toroid Structure of the Helion and the Alpha Particle Vol.4, No.7, 484-491 (2012) Natural Science http://dx.doi.org/10.4236/ns.2012.47065 Electromagnetic nature of nuclear forces and the toroid structure of the helion and the alpha particle Kiril Kolikov Plovdiv University “P. Hilendarski”, Plovdiv, Bulgaria; [email protected] Received 20 May 2012; revised 18 June 2012; accepted 2 July 2012 ABSTRACT in the hydrogen atom, with which he obtained good re- sults for its spectrum within the framework of the old In the present paper, we consider the nucleons quantum mechanics. in the helium-3 and helium-4 nuclei as tori. Additional reasoning to consider the nucleons as spa- These tori rotate with constant angular velocity tially extended objects is the fact that they are located around an axis, which is perpendicular to the close to each other in the atomic nuclei. Thus, we assume rotation plane and passes through the centre of that they are tori and their electric charge can be redis- mass of the nuclei. Based on exact analytical tributed. Essentially, this idea does not contradict to the expressions for the electrostatic interaction be- quark substructure model of nucleons, and it enables us tween two spheres with arbitrary radii and to determine the electrostatic interaction between them. charges derived by us recently, we find that the Based on the exact analytical expressions for the electro- well-known potential binding energy for the static interaction between two charged conducting spheres helion and for the alpha particle is of electro- with arbitrary radii and charges derived for the first time magnetic character. Using the above mentioned in [10], we conclude in [8] that strong interactions are formulae, we find the interaction force in the electromagnetic in nature. nuclei under consideration. Our toroid model In [9], we ascertain that the experimentally determined recovers the basic experimental results not only potential binding energy between nucleons in the deu- for the binding energy, but also for the stability, teron and triton can be obtained taking into account the radii, spins and the magnetic moments of the electrostatic interaction only. To do that, the values of the helion and the alpha particle. experimentally known radii, and masses of the nucleons and the corresponding nuclei have been utilized. In [9], Keywords: Helion; Alpha Particle; Strong the volume and the mass density of nucleons, as well as Interaction; Potential Binding Energy; Electrostatic their interaction force in the deuteron and the triton have Interaction been calculated—important results in nuclear physics pre- sented for the first time. 1. INTRODUCTION Applying the method developed in [8,9], we calculate in the present paper the potential energy and the interac- There are two basic models in the theory of elemen- tion force between the nucleons in the helium-3 and he- tary particles: the standard model [1-3] and the helicon model [4-7]. lium-4 nuclei. Basic experimentally measured character- In [8] and [9] the toroid model of nucleons has been istics such as stability, spin, radius and magnetic moment proposed, which is in certain contradiction with the stan- of the helion and the alpha particle are also explained. According to R. Feynman’s conjecture at distances dard model, however in perfect agreement with the heli- −15 con model. less than 10 m either Coulomb’s law is not valid, or Every nucleon is modelled with an imaginary torus, electrons and protons cannot be considered as point-like which rotates with constant angular velocity around an particles [11]. In accordance with this conjecture, we as- sume that the distance within the corresponding proton- axis z passing through its mass centre (the geometric neutron pairs is less 10−15 m. centre) O and perpendicular to the rotation plane of its central circle. From quantum mechanical point of view, 2. TOROID MODEL OF NUCLEONS the nucleon is not a localized object in configuration space. Therefore, our model is valid in a formal heuristic In [8,9] the nucleons are modeled as tori. Moreover, sense a la Niels Bohr similar to his model for the electron we assume that they rotate with constant angular velocity Copyright © 2012 SciRes. OPEN ACCESS K. Kolikov / Natural Science 4 (2012) 484-491 485 around an axis z passing through their mass (geometric) 2 22 hkk np RR n p . (2) centre O and perpendicular to the rotation plane of their central circle (Figure 1). Obviously, 0 hkpn k . Next, we study the system consisting of a proton and a We assume that the mass and number densities of the neutron and determine the electrostatic interaction be- proton and the neutron are equal, that is p n . If mp tween them. and mn are the masses of Tp and Tn , then The tori corresponding to the proton and the neutron mp mn are denoted by Tp and Tn , while their centres are de- p and n . (3) Vp Vn noted by Op and On , respectively. We assume that the central circles of Tp and Tn lie in parallel or merging According to [12], the volumes of the tori Tp and planes and rotate in the same or opposite direction with T are Vk 2π22R and V 2π22kR, respectively. the same angular velocity ω around the line z, which n p pp nnn Therefore, from p n and from Eq.3 it follows that passes through Op and On being perpendicular to the rotation plane. Then, if OO h, it follows that h 0 mRnp pn kk . (4) (Figure 2). np mRp n Let K p and Kn be the centres of the forming cir- Eqs.3 and 4 contain the proton and the neutron mass cles of the tori Tp and Tn , respectively, and whose values are experimentally known and can be read- ROp pKp, ROnnn K be the radii of the central cir- ily substituted. cles of Tp and Tn . We assume that the distance be- 15 Let q 0 be the radius of the of the empty part of tween Tp and Tn is 0 10 m. According to the available experimental data the pro- the circle with radius equal to that of the proton rp . Then ton radius rp is not greater than the neutron radius rn . That is why we must have RR . p n qr p 2 kp . (5) Let k p and kn be the radii of the forming circles In order to apply the results from [10] derived for the K p and Kn , respectively. It is clear that kRp p and case of spheres, we remodel the tori as in [8,9]. kn Rn. Moreover, Due to the spherical symmetry of the proton charge Rk r and Rk r, (1) p pp nnn [13], we can assume that all its charge p is concen- trated in the geometric centre O of the torus T . where rp and rn are the radii of the proton and the p p neutron in the configuration shown in Figure 2. It is We remodel the proton with a sphere S p having the same centre O lying on the axis z , such that its area worthwhile to note that in some nuclei rp , k p , Rp p is equal to that of the torus T . Moreover, the charge p and rn , kn , Rn may take different values. p of the sphere is spherically symmetric and it can be re- Since OOpn h, simple geometric consideration yields distributed. According to [12] the area Lp of the torus Tp is 2 Lkp 4π ppR. (6) Since the areas of the torus Tp and the sphere S p are equal, from Eq.6 it follows that the radius rP of S p is rkP π ppR. (7) Figure 1. Toroid model of a nucleon. Next, we remodel the neutron Tn whose torus TN has equivalent area and the same centre On . The dis- tance between its surface and that of S p is the same as the distance between Tn and Tp (Figure 3). Let SN be the sphere, whose central circle is forming the torus TN . We denote the centre of SN with KN so that OKnN RN, and let rN be the radius of SN . If OKpN R, then Rr PN r and OOpn h im- plies RR22 h2, that is N Figure 2. Cross section of the system 2 2 containing a proton and a neutron. RrrNPN h. (8) Copyright © 2012 SciRes. OPEN ACCESS 486 K. Kolikov / Natural Science 4 (2012) 484-491 Eq.11 hold because the forming spheres of the torus TN are located symmetrically with respect to the centre of the sphere SP . 3. VOLUME MASS DENSITY OF NUCLEONS Let us consider the proton in a free state as the torus 0 01 5 Tp . According to [14] its radius is rp 0.84184 10 m. Let K 0 is the centre of forming circle of the torus p T 0 and let k 0 is the radius of this circle. Moreover, Figure 3. Cross section of the reduced p p RO00 K. model of the proton-neutron system. p p Utilizing expressions (1) and (5) for different values of Clearly, max Rrr and min Rr . the radius q of the empty part of the circle with radius NpN N N r , we have calculated in [9] the quantities k 0 , R0 The equality of the areas L and L of the tori T p p p N n N 2 0200 and Tn , together with Eq.6 yields and the volume of the proton torus Vkp 2π ppR Rn [12]. The mass of the proton in a free state is rkNn .
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