Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 December 2018 doi:10.20944/preprints201812.0355.v1 Understanding nuclear binding energy with nucleon mass difference via strong coupling constant and strong nuclear gravity U. V. S. Seshavatharam1 & S. Lakshminarayana2 1Honorary Faculty, I-SERVE, Survey no-42, Hitech city, Hyderabad-84, Telangana, India. 2Department of Nuclear Physics, Andhra University, Visakhapatnam-03, AP, India Emails: [email protected] (and) [email protected] Orcid numbers : 0000-0002-1695-6037 (and) 0000-0002-8923-772X Abstract: With reference to electromagnetic interaction and Abdus Salam’s strong (nuclear) gravity, 1) Square root of ‘reciprocal’ of the strong coupling constant can be considered as the strength of nuclear elementary charge. 2) ‘Reciprocal’ of the strong coupling constant can be considered as the maximum strength of nuclear binding energy. 3) In deuteron, strength of nuclear binding energy is around unity and there exists no strong 28 3 -1 -2 interaction in between neutron and proton. Gs 3.32688 10 m kg sec being the nuclear gravitational 2G m Gm2 constant, nuclear charge radius can be shown to be, R s p 1.24 fm. es p e 4.716785 1019 C 0 2 s c c being the nuclear elementary charge, proton magnetic moment can be shown to be, 2 e eGs m p c s 1.48694 1026 J.T -1 . 0.1153795 being the strong coupling constant, p 2m 2 c s Gm2 p s p 1 strong interaction range can be shown to be proportional to exp . Interesting points to be noted are: An 2 s increase in the value of s helps in decreasing the interaction range indicating a more strongly bound nuclear system. A decrease in the value of s helps in increasing the interaction range indicating a more weakly bound nuclear system. From Z 30 onwards, close to stable mass numbers, nuclear binding energy can be addressed 1 2 with, BZ 1 30 31 mmcZn p 19.66 MeV. With further study, magnitude of the As s Newtonian gravitational constant can be estimated with nuclear elementary physical constants. One sample 10 G 1 m G N e F relation is, where GN represents the Newtonian gravitational constant and GF G2 m c mc s p e 10 2 represents the Fermi’s weak coupling constant. Two interesting coincidences are, mpe m exp 1 s and 2Gmc2 G c . se F Keywords: strong (nuclear) gravity, nuclear elementary charge, strong coupling constant, nuclear charge radius, beta stability line, nuclear binding energy, nucleon mass difference, Fermi’s weak coupling constant, Newtonian gravitational constant, deuteron, interaction range, super heavy elements. 1. Introduction the form of ‘residual nuclear force’. At this juncture, one important question to be answered and reviewed Low energy nuclear scientists assume ‘strong at the basic level is: How to understand nuclear interaction’ as a strange nuclear interaction interactions in terms of sub nuclear interactions? associated with binding of protons and neutrons. Unfortunately, the famous nuclear models like, High-energy nuclear scientists consider nucleons as Liquid drop model and Fermi's gas model [2-5] are composite states of quarks and try to understand the lagging in answering this question. To find a way, we nature and strength of strong interaction [1] at sub would like to suggest that, by considering ‘square nuclear level. Very unfortunate thing is that, strong root’ of reciprocal of the strong coupling constant’ interaction is mostly hidden at low energy scales in 1 © 2018 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 December 2018 doi:10.20944/preprints201812.0355.v1 is well established that, strength of strong force s 0.1186 , as an index of strength of nuclear depends on the energy through the interaction or the elementary charge, nuclear binding energy and distance between particles. At lower energies or nuclear stability can be understood. In this direction, longer distances: a) color charge strength increases; we have developed interesting concepts and produced b) strong force becomes ‘stronger’; c) nucleons can many semi empirical relations [6-12]. Even though it be considered as fundamental nuclear particles and is in its budding stage, our model seems to be simple quarks seem to be strongly bound within the nucleons and realistic compared to the new integrated model leading to ‘Quark confinement’. At high energies or proposed by N. Ghahramany et al [13,14]. It needs short distances: a) color charge strength decreases; b) further study at a fundamental level. strong force gets ‘weaker’; 3) colliding protons 2. About Strong (nuclear) gravity generate ‘scattered free quarks leading to ‘Quark Asymptotic freedom’. Based on these points, low Microscopic physics point of view, one very energy nuclear scientists assume ‘strong interaction’ interesting concept is that- elementary particles can as a strange nuclear interaction associated with be considered as ‘micro black holes’. ‘Strong binding of nucleons. High-energy nuclear scientists (nuclear) gravity’ concept proposed by Abdus Salam, consider nucleons as composite states of quarks and C. Sivaram, K.P. Sinha, K. Tennakone, Roberto try to understand the nature and strength of strong Onofrio, O. F. Akinto and Farida Tahir [15-20], interaction at sub nuclear level. seems to be very attractive. The main object of unification is to understand the origin of elementary With reference to the picture of ‘Strong (nuclear) 38 particles mass, (Dirac) magnetic moments and their gravity’[15-20], if Gf 10 G N , forces. Right now and till today ‘string theory’ with 10 dimensions is not in a position to explain the 1) Schwarzschild radius of nucleon mass can be unification of gravitational and non-gravitational 2Gf m p forces. More clearly speaking it is not in a position to addressed with, R0 1.2 fm . c2 bring down the Planck scale to the nuclear size. The 2) Strong coupling constant can be expressed with most desirable cases of any unified description are: 2 c 0.115 a) To implement gravity in microscopic physics and s 2 to estimate the magnitude of the Newtonian Gf m p gravitational constant GN . 3) Characteristic temperature associated with b) To develop a model of microscopic quantum nucleon can be expressed with, gravity. 3 c 12 c) To simplify the complicated issues of known Tproton 10 K physics. 8kGmB f p d) To predict new effects, arising from a combination of the fields inherent in the unified Note: Considering the relativistic mass of proton, it is description. 4 2 1 v possible to show that, 1 where v s 3. About quantum chromo dynamics (QCD) mp c can be considered as the speed of proton. The modern theory of strong interaction is quantum Qualitatively, at higher energies, strength of strong chromo dynamics (QCD) [21]. It explores baryons interaction seems to decrease with speed of proton. and mesons in broad view with 6 quarks and 8 gluons. According to QCD, the four important 4. About the semi empirical mass formula properties of strong interaction are: 1) color charge; Let A be the total number of nucleons, Z the 2) confinement; 3) asymptotic freedom [22]; 4) short- -15 number of protons and N the number of neutrons. range nature (<10 m). Color charge is assumed to According to the semi-empirical mass formula be responsible for the strong force to act on quarks [2,3,4], nuclear binding energy: via the force carrying agent, gluon. Experimentally it 2 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 December 2018 doi:10.20944/preprints201812.0355.v1 2 2/3 ZZ( 1) ( AZ 2 ) ap 2Gs m p B av A a s A a c a a 1 R 1.24 fm (3) A1/3 A 0 2 A c Based on this relation, Here av = volume energy coefficient, as is the surface energy coefficient, a is the coulomb energy R c2 c G 0 3.32688 1028 m 3 kg -1 sec -2 (4) s 2m coefficient, aa is the asymmetry energy coefficient p and a is the pairing energy coefficient. If we 2 p c consider the sum of the volume energy, surface s 0.1153795 (5) G m2 energy, coulomb energy, asymmetry energy and s p 2 pairing energy, then the picture of a nucleus as a drop e G m es p e 4.716785 1019 C (6) of incompressible liquid roughly accounts for the s s c observed variation of binding energy of the nucleus. By maximizing B AZ, with respect to Z , one can 7. New concepts and semi empirical relations find the number of protons Z of the stable nucleus of atomic weight A as, We would like to suggest that, A0.4 A2 Z2/3 and AZ 2 2 1) Fine structure ratio can be addressed with, 2 ac 2 aA a A 200 e2 c s 7.297348 103 2 2 4 Gm Gm By substituting the above value of Z back into B 0 s p s p one obtains the binding energy as a function of the 2) Proton magnetic moment can be addressed with e eG m atomic weight, B A. Maximizing BA / A with s s p 1.48694 1026 J.T -1 p 2m 2 c respect to A gives the nucleus which is most strongly p bound or most stable. 3) Neutron magnetic moment can be addressed with e e s 9.805 1027 J.T -1 . 5. Three simple assumptions n 2m n With reference to our recent paper publications and 4) Nuclear unit radius can be expressed as, conference proceedings [6-12], [23-33], we propose 2Gm e s p s R 0 2 the following three assumptions.