{"id":316,"date":"2010-11-01T18:58:28","date_gmt":"2010-11-01T23:58:28","guid":{"rendered":"http:\/\/www.journal-of-nuclear-physics.com\/?p=316"},"modified":"2010-11-01T19:29:26","modified_gmt":"2010-11-02T00:29:26","slug":"agni-avagadros-gravity-for-nuclear-interactions","status":"publish","type":"post","link":"https:\/\/www.journal-of-nuclear-physics.com\/?p=316","title":{"rendered":"AGNI – Avagadro’s Gravity for Nuclear Interactions"},"content":{"rendered":"

By<\/em><\/p>\n

U.V.S. Seshavatharam
\nDIP QA Engineer, Lanco Industries Ltd, Srikalahasti-517641, A.P, India
\nE-mail: seshavatharam.uvs@gmail.com<\/em><\/p>\n

Prof. S. LAKSHMINARAYANA
\nDepartment Of Nuclear Physics, Andhra University, Vizag-530003, AP, India.
\nE-mail: lnsrirama@yahoo.com<\/em><\/p>\n

Direct Download<\/a><\/p>\n

Abstract 1:<\/strong>
\n`N’ being the Avagadro number, it is suggested [2, 3] that strong nuclear gravitational constant (GS<\/em>) is N2 times the classical gravitational constant (GC<\/em>). Elementary charge (e) and the proposed (GS<\/em>) plays a vital role in strong interaction and\u00a0nuclear space-time curvature. Considering the present signi\fcance of Avagadro number\u00a0[4] it is clear that, existence of the classical gravitational constant (GC<\/em>) is a consequence\u00a0of the existence of the strong nuclear gravitational constant (GS<\/em>). It is also suggested\u00a0that there exists 2 kinds of mass units. They can be called as `observed mass units’ and `hidden mass units’.
\nXE<\/em> \u2248\u00a0295.0606339 being the lepton mass generator [1, 2, 3] hidden\u00a0mass unit is XE times smaller than the observed mass unit. This idea can be applied\u00a0to leptons and all the strongly interacting particles. For electron its hidden mass unit\u00a0is 3.087292 x 10^-33 Kg.
\nHidden mass unit of the previously proposed [1, 2, 3] strongly\u00a0interacting fermion (MSf c^<\/em>2 \u2248\u00a0105.3255407 MeV) is \u00a0 MSf c^<\/em>2\/XE \u2248 <\/em>0.35696236 MeV.<\/em>
\nXE<\/em>,\u00a0the strong interaction mass generator = XS <\/em>\u2248\u00a08.803723452\u00a0and 0.35696236 MeV plays a vital role in understanding and coupling the semi empirical mass formula with TOE [2].\u00a0(\u000b\u03b1XE<\/em>) is the ratio of coulomb energy coefficient (Ec) and the proposed (MSf c^2\/XE) .
\nProton and neutron rest masses are co related in a uni\fed approach. GS<\/em>, hidden mass\u00a0units of electron and super symmetric [1] (MSf<\/em> ) play a vital role in the origin of \u045b.
\nElectron`s discrete angular momentum is due the strong nuclear gravity and discrete\u00a0number of super symmetric nucleons or\u00a0(MSf<\/em>).\u00a0All these coincidences clearly suggest that existence of the strong nuclear gravitational constant (GS<\/em>)\u00a0and existence of the strongly interacting fermion (MSf c^2)\u00a0\u2248\u00a0105.3255\u00a0MeV are true and real.<\/p>\n

[1] U. V. S. Seshavatharam and S. Lakshminarayana. Super Symmetry in Strong and Weak interactions. IJMPE, Vol.19, No.2, (2010), p.263-280.<\/p>\n

[2] U. V. S. Seshavatharam and S. Lakshminarayana. Strong nuclear gravitational constant and the origin of nuclear planck scale. Progress in Physics, vol. 3, July, 2010, p. 31-38.<\/p>\n

[3] U. V. S. Seshavatharam and S. Lakshminarayana. Avagadro number and the mystery of TOE and Quantum Theory. Under review of Journal of Nuclear Physics, Italy. (Old version is accepted\u00a0for publication).<\/p>\n

[4] Avogadro constant, From Wikipedia, the free encyclopedia.<\/p>\n

\n

<\/p>\n

Abstract 2:<\/strong>
\n`N’ being the Avagadro number, it is suggested that there exists a charged lepton mass unit mL<\/em> = 3.087292 x 10^-33 Kg\u00a0in such way a that its electromagnetic\u00a0and classical gravitational force ratio is N^2. Assuming that N<\/em> neutrons transforms into 1\/2N<\/em> neutrons, 1\/2N<\/em> protons and 1\/2N<\/em> electrons a simple relation is proposed in between\u00a0the lepton mass generator XE<\/em> [1,2] strong gravitational constant GS<\/em> [2],\u00a0classical\u00a0gravitational constant GC<\/em> and the Avagadro number N<\/em>. \u00a0XE<\/em> being the proportionality\u00a0ratio electron rest mass is proportional to its charge e and inversely proportional to\u00a0N<\/em> and \u221aGC.<\/em>
\nM<\/em>uon and tau rest masses are \ftted. With a new (uncertain) quantum\u00a0number at n=3, a new heavy charged lepton at 42260 MeV is predicted.
\nConsidering\u00a0N, 2N, 3N… moles XE<\/em> takes discrete values and it can be shown that \u045b\u00a0is a true uni\fed\u00a0compound physical constant. A simple relation is proposed for estimating [2] the mass\u00a0of strong interaction mass unit MSf c^<\/em>2 \u2248 105.398 MeV.\u00a0From super symmetry [1]\u00a0considering the proposed value of fermion-boson mass ratio = \u03c8 =\u00a02.2623411 values\u00a0of nuclear stability factor Sf<\/em> and strong interaction mass generator XS<\/em> are revised in\u00a0a unifi\fed manner.
\nProton and neutron rest masses are \ftted to 4 decimal places. It\u00a0it is suggested that XE<\/em> sin(\u03b8w<\/em>) \u2248 1\/\u03b1 .\u00a0Finally in sub quark physics [1] the proposed\u00a0strongly interacting fermionic mass unit 11450 MeV is \ftted with ln (N^2).<\/p>\n

PACS numbers: 12.10-g,21.30.-x.<\/p>\n

Keywords: true grand uni\fcation, classical gravitational constant, strong nuclear\u00a0gravitational constant, lepton mass generator, characteristic lepton mass unit, leptons\u00a0rest mass, new heavy charged lepton, strong interaction mass generator, proton and\u00a0neutron rest masses, strong nuclear fermion, strong nuclear sub quark fermion, fermion-boson mass ratio 2.26.<\/div>\n
.<\/div>\n
\n
1. Introduction<\/strong><\/div>\n
In this paper previuosly [1, 2] de\fned lepton mass generator XE is rede\fned in a uni\fed\u00a0approach and is shown that it is more fundamental than the \fne structure rartio \u000b\u03b1.<\/div>\n
Muon and Tau masses are fi\ftted. With a new (uncertain) quantum number at n=3, a\u00a0new heavy charged lepton is predicted at 42260 MeV. Without considering the classical\u00a0gravitational constant GC<\/em> establishing a relation in between charged particle’s mass and\u00a0charge is impossible. Till now Avagadro number [3] is a mystery. The basic counting\u00a0unit in chemistry, the mole, has a special name Avogadro’s number in honor of the\u00a0Italian scientist Amadeo Avogadro (1776-1856). The commonly accepted de\fnition of\u00a0Avogadro number is the number of atoms in exactly 12 g of the isotope 6C12<\/em> and the<\/div>\n
quantity itself is 6.02214199(47)10^23. Considering N as a fundamental input in grand\u00a0uni\fed scheme authors made an attempt to corelate the electron rest mass and its charge.<\/div>\n
It is also noticed that h is slipping from the net and there lies the the secret of true grand\u00a0uni\ffication.<\/div>\n
\n
As the culmination of his life work, Einstein wished to see a uni\fcation of gravity\u00a0and electromagnetism [4] as aspects of one single force. In modern language he wished\u00a0to unite electric charge with the gravitational charge (mass) into one single entity.<\/div>\n
Further, having shown that mass the gravitational charge was connected with space-time\u00a0curvature, he hoped that the electric charge would likewise be so connected with some\u00a0other geometrical property of space-time structure. For Einstein [5, 6] the existence, the\u00a0mass, the charge of the electron and the proton the only elementary particles recognized<\/div>\n
back in 1920s were arbitrary features. One of the main goals of a uni\fed theory should\u00a0explain the existence and calculate the properties of matter.<\/div>\n
Stephen Hawking – in his famous book- “A brief history of time” [7] says: It would\u00a0be very difficult to construct a complete uni\fed theory of everything in the universe all\u00a0at one go. So instead we have made progress by \fnding partial theories that describe\u00a0a limited range of happenings and by neglecting other e\u000bects or approximating them\u00a0by certain numbers. (Chemistry, for example, allows us to calculate the interactions\u00a0of atoms, without knowing the internal structure of an atoms nucleus.) Ultimately,\u00a0however, one would hope to \fnd a complete, consistent, uni\fed theory that would include\u00a0all these partial theories as approximations, and that did not need to be adjusted to \ffit<\/div>\n
the facts by picking the values of certain arbitrary numbers in the theory. The quest\u00a0for such a theory is known as “the uni\fcation of physics”. Einstein spent most of his\u00a0later years unsuccessfully searching for a uni\fed theory, but the time was not ripe: there\u00a0were partial theories for gravity and the electromagnetic force, but very little was known\u00a0about the nuclear forces. Moreover, Einstein refused to believe in the reality of quantum\u00a0mechanics, despite the important role he had played in its development.<\/div>\n
.<\/div>\n
1.1. Charge-mass uni\fcation<\/em><\/div>\n
\n
The \ffirst step in uni\ffication is to understand the origin of the rest mass of a<\/div>\n
charged elementary particle. Second step is to understand the combined e\u000bffects of its\u00a0electromagnetic (or charged) and gravatational interactions.Third step is to understand\u00a0its behaviour with surroundings when it is created. Fourth step is to understand its\u00a0behaviour with cosmic spce-time or other particles. Right from its birth to death, in all\u00a0these steps the underlying fact is that whether it is a strongly interacting particle or\u00a0weakly interacting particle, it is having some rest mass. To undestand the \ffirst 2 steps\u00a0some how one must implement the gravitational constant in sub atomic physics. Till\u00a0now quantitatively or qualitatively either the large number hypothesis or the string theory\u00a0or the planck scale is not implemented in particle physics.<\/div>\n
Unifying gravity with the other three interactions would form a theory of everything\u00a0(TOE), rather than a GUT. As of 2009, there is still no hard evidence that nature\u00a0is described by a Grand Uni\fed Theory. Moreover, since the Higgs particle has not\u00a0yet been observed, the smaller electroweak uni\fcation is still pending.The discovery\u00a0of neutrino oscillations indicates that the Standard Model is incomplete. The gauge\u00a0coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a\u00a0common length scale called the GUT scale and approximately equal to 1016 GeV, which<\/div>\n
is slightly suggestive. This interesting numerical observation is called the gauge coupling\u00a0unification, and it works particularly well if one assumes the existence of superpartners\u00a0of the Standard Model particles.<\/div>\n
.<\/div>\n
\n
1.2. Super symmetry<\/em><\/div>\n
In particle physics, a superpartner (also sparticle) is a hypothetical elementary particle.<\/div>\n
Authors proposed and clearly shown that in strong interaction there exists super\u00a0symmetry [1] with a fermion-boson mass ratio,\u00a0\u03c8\u00a0\u2248 2.26\u00a0( but not unity). \u00a0The word superpartner is a portmanteau of the words supersymmetry and partner. Supersymmetry\u00a0is one of the synergistic bleeding-edge theories in current high-energy physics which\u00a0predicts the existence of these “shadow” particles. According to the theory, each fermion<\/div>\n
should have a partner boson, the fermion’s superpartner and each boson should have a\u00a0partner fermion. When the more familiar leptons, photons, and quarks were produced in\u00a0the Big Bang, each one was accompanied by a matching sparticle: sleptons, photinos and\u00a0squarks. This state of a\u000bairs occurred at a time when the universe was undergoing a\u00a0rapid phase change, and theorists believe this state of a\u000bairs lasted only some 10^-35\u00a0seconds before the particles we see now “condensed” out and froze into space-time.<\/div>\n
Sparticles have not existed naturally since that time. In this case also authors shown that\u00a0[1] these sparticles or super symmetric bosons can be seen at any time in the laboratory.<\/div>\n
\n
Boson corresponding to nucleon mass is 415 MeV and considering the basic idea\u00a0of string theory that elementary particle masses are excited states of basic levels, it is\u00a0clearly shown that 493, 547 and 890 MeV etc strange mesons are the excited states of\u00a0415 MeV boson. In the same paper [1] it is suggested that charged W boson is the super\u00a0symmetric boson of Top quark! Finally authors wish to say that there is something\u00a0wrong with the basic concepts of SM. After all from true grand uni\fcation point of view\u00a0there is no independent existence for SM.<\/div>\n
.<\/div>\n
1.3. Planck mass, neutrino mass and Avagadro number<\/em><\/div>\n
\n
It is noticed that ratio of planck mass and electron mass is 2.389 x 10^22 and is 25.2 times\u00a0smaller than the Avagadro number.\u00a0Qualitatively this idea implements gravitational\u00a0constant in particle physics. Note that planck mass is the heaviest mass and neutrino\u00a0mass is the lightest mass in the known elementary particle mass spectrum. As the mass\u00a0of neutrino is smaller than the electron mass, ratio of planck mass and neutrino mass\u00a0will be close to the Avagadro number or crosses the Avagadro number. Since neutrino is<\/div>\n
an electrically neutral particle if one is able to assume a charged particle close to neutrino\u00a0mass it opens a window to understand the combined e\u000bects of electromagnetic (or\u00a0charged) and gravitational interactions in sub atomic physics. Compared to planck scale\u00a0(past cosmic high energy scale), Avagadro number is having some physical significance\u00a0in the (observed or present low energy scale) fundamental physics or chemistry.<\/div>\n<\/div>\n
.<\/div>\n
\n
2. Proposed new ideas in papers [1, 2]<\/strong><\/div>\n
In the previous papers [1, 2] authors collectively proposed the following new ideas.<\/div>\n
1. Strong nuclear gravitational constant can be given as GS<\/em> =\u00a06.94273 x 10^31 \u00a0 \u00a0 m^3\/kg sec^2.<\/div>\n
\n
2. There exists two strongly interacting “confined” fermionic mass units MSf<\/em>c^2 =\u00a0105.38 MeV and MGf<\/em>c^2 = 11450 MeV.<\/div>\n
\n
3. In super symmetry, for strong and weak interactions boson mass is equal to fermion\u00a0mass\/2.26234.<\/div>\n
\n
4. There exists integral charge quark bosons and boso-gluons.<\/div>\n
5. There exists integral charge quark e\u000bective fermions and e\u000bective fermi-gluons.<\/div>\n
6. No two fermions couples together to form a meson. Only bosons couples together\u00a0to form a meson. Light quark bosons couples with e\u000bective quark fermi gluons to form\u00a0doublets and triplets.<\/div>\n
\n
7. Strong interaction mass generator = XS<\/em> = 8.8034856 and it can be considered as the\u00a0inverse of the strong coupling constant.<\/div>\n
\n
8. Lepton mass generator = XE = 294.8183 is a number. It plays a crucial role in\u00a0particle and nuclear physics.<\/div>\n
\n
9. In the semi empirical mass formula ratio of “coulombic energy coefficient” and the\u00a0proposed 105.383 MeV is equal to \u03b1. The coulombic energy constant = EC<\/em> = 0.769 MeV.<\/div>\n
\n
10. The characteristic nucleon’s kinetic energy or sum of potential and kinetic enetrgies\u00a0is close to the rest energy of electron.<\/div>\n
.<\/div>\n
2.1. Nuclear force and charge distribution radii<\/em><\/div>\n
\n
With reference to the assumed strong nuclear gravitational constant GS<\/em>, if it assumedthat charectristic total energy of the nucleon in the nucleus is close to the rest energy of\u00a0electron me<\/em>c^2, the nuclear force is<\/div>\n
\"\"and<\/div>\n<\/div>\n<\/div>\n
\"\"<\/div>\n
\n
Here, MSf<\/em>c^2 is the assumed characteristic strong interaction fermionic mass\u00a0unit=105.383 MeV, RC can be considered as the nuclear characteristic charge\u00a0distribution radius.<\/div>\n
\"\".<\/div>\n
2.2. Nuclear charge radius, Avagadro number and the Bohr radius<\/em><\/div>\n
Quantitatively to a very good accuracy it is noticed that<\/div>\n
\"\"Here, 2GC<\/em>me<\/em>\/c^2 = classical Black hole radius of electron,\u00a0RC<\/em> = Nuclear charge radius \u0018\u2248\u00a01.2157 fermi.\u00a0This equation can be considered as a key observation for the\u00a0implementation of Avgadro number in true uni\fcation. Using this equation value of\u00a0the classical gravitational constant GC<\/em> can be estimated accurately with the microscopic\u00a0physical constants.<\/div>\n
\"\"On simpli\fcation eqation (5) can be written as<\/div>\n
\"\"<\/p>\n
With the proposed lepton mass generator XE and the strong gravitational constant GS <\/em>equation (7) can be simpli\fed as<\/div>\n
\"\"Interestingly,\u00a02GS<\/em>me\/<\/em>c^2 \u0018\u2248\u00a0strong nuclear black hole radius of electron\u00a0\u2248 1:409 fermi\u00a0\u2248 R0, <\/em>can be considered as the nuclear mass distribution radius. RC<\/em> \u2248\u00a01.2157 fermi is\u00a0the nuclear charge distribution radius and geometric mean of RC<\/em> and R0 is \u221a<\/em>R0<\/em>RC <\/em>\u2248 1.309 fermi.\u00a0By considering “1 mole nucleons”, “2 mole nucleons”, “3 mole nucleons”\u00a0etc XE takes “discrete” values like XE,<\/em> 2XE<\/em>, 3XE<\/em>: Using this idea the origin of n\u0016h may\u00a0be understood.\u00a0Considering the nucleus-electron system, interestingly to a very good accuracy it is\u00a0noticed that<\/div>\n
\"\"<\/p>\n
Considering equations (3), (5), (17) and (22) all these observations can be obtained\u00a0in a uni\fed approach. Considering equation (29) the individual roles of MSf<\/em> , GC<\/em> and\u00a0N in the nuclear physics can be understood. Considering equations (7) and (29) it can\u00a0be suggested that, (N=2) represents a measure of uni\fed gauge coupling strength.<\/div>\n
.<\/div>\n
3. Mole neutrons & relation between electron rest mass and its charge<\/strong><\/div>\n
\n
Assuming that N neutrons transforms into 1\/2N neutrons, 1\/2N protons and 1\/2N electrons\u00a0authors tried to establish a relation in between the electron rest mass and its charge.<\/div>\n
This idea may be a hypothesis or might have happened in the history of cosmic evolution.<\/div>\n
For the time being authors request the world science community to consider this idea\u00a0positively.\u00a0Assume that out of N neutrons one neutron transforms into one proton and one\u00a0electron. Focussing our attention to the rest energy of electron it is assumed that<\/div>\n
\"\"On simpli\fcation it can be written as<\/div>\n
\"\"<\/p>\n
Here XE<\/em> is a number and can be called as `lepton mass generator’ and EL<\/em> =<\/div>\n
1.732 x 10^-3\u00a0MeV can be called as the `characteristic lepton potential’.
\nAuthors in the previous papers [1, 2 ] shown many applications of XE<\/em> in particle<\/div>\n
physics and nuclear physics.\u00a0The weak coupling angle can be considered as (\u03b1XE <\/em>)^-1 =\u00a0sin(\u03b8w<\/em>).\u00a0It plays a crucial role in estimating the charged lepton rest masses. Ratio of\u00a0Up and Down quark masses is\u00a0\u03b1XE. <\/em>It plays a very interesting role in \ftting energy\u00a0coefficients of the semi empirical mass formula. It can be used for \ftting the nuclear\u00a0size with “compton wavelength of nucleon”. It is noticed that ratio of “nuclear volume”\u00a0and “A nucleons compton volume” is XE<\/em>. It can be called as the nuclear “volume ratio”\u00a0factor. In this paper in a uni\fed approach XE<\/em> is redi\fned as<\/div>\n
\"\"<\/p>\n
Here, N\/2= half mole neutrons or half mole protons or half mole electrons. GS<\/em> = strong nuclear gravitational constant and GC<\/em> = classical gravitational constant.<\/div>\n
Till now Avagadro number is a mystery. The strange observation is, by considering “1 mole nucleons”, “2 mole nucleons”, “3 mole nucleons” etc XE<\/em> takes “discrete” values like XE<\/em>, 2XE<\/em>, 3XE<\/em>… Using this idea the origin of n\u045b<\/em> may be understood.<\/div>\n
In equation (17) by seeing the strong gravitational constant GS<\/em> every one will be surprised. But it is a fact. In the paper [2] authors proposed many applications of GS<\/em> in nuclear physics. If neutron is a strongly interacting particle and its origin is related to GS<\/em> it is reasonable and a must to implement GS in weak decay of neutron. Considering equation (17) electron rest mass can be given as<\/div>\n
\"\"In this way value of strong nuclear gravitational constant can be estimated from electron rest mass as GS<\/em> \u2248 6.950631729 x 10^31 \u00a0 \u00a0 m^3\/kgsec^2. From equation (15) XE<\/em> can be obtained as<\/div>\n
\"\"If one is able to assume or guess that,<\/div>\n
\"\"From this idea it can be suggested that there exists a charged lepton mass unit
\nmL<\/em> = 3.087292 x 10^-33 Kg in such way a that its electromagnetic and classical gravitational force ratio is N^2. It plays a crucial role in fi\ftting the rest masses of muon and tau.<\/div>\n
.<\/div>\n
4. Fitting of muon and tau rest masses<\/strong><\/div>\n
In the earlier paper [2] authors proposed the following relation for \ftting the muon and tau masses.<\/div>\n
\"\"Here EC<\/em>= coulombic energy coefficient of the semi empirical mass formula =0.769 MeV, EA<\/em>= assymmetry energy coefficient of the semi empirical mass formula=23.86 MeV and XE<\/em> = proposed lepton mass generator = 294.8183 and n = 0, 1, 2. In this paper authors simpli\fed equation (23) as<\/div>\n
\"\"where n=0,1 and 2 and EL<\/em> \u2248 1.732 x 10^-3 MeV.<\/div>\n
Equation (24) is free from all the binding energy coefficients of the semi-empirical mass formula. Authors hope that the \feld experts can easily interpret this expression. See the following Table 1 [8].<\/div>\n
If electron mass is \ftting at n=0, muon mass is \ftting at n=1 and tau mass is
\ntting at n=2 it is quite reasonable and natural to predict a new heavy charged lepton at n=3. Electron was discovered in 1897. Muon was discovered in 1937. Tau was detected in a series of experiments between 1974 and 1977. Positron predicted in 1928 and discovered in 1936. The antiproton and\u00a0 antineutron were only postulated in 1931 and 1935 respectively and\u00a0 discovered in 1956. The charged pion was postulated in 1935 and discovered in 1947 and the neutral pion was postulated in 1938 and discovered in 1950.
\nThe 6 quarks were proposed and understood in between 1964 and 1977. By selecting the proper quantum mechanical rules if one is able to con\frm the existence of the number n=3, existence of the new lepton can be understood.
\nAt the same time one must critically examine the propsed relation for its nice and accurate \ftting of the 3 observed charged leptons. Unfortunately inputs of this expression are new for the standard model. Hence one can not easily incorporate this expression in standard model. Till now in SM there is no formula for \ftting the lepton masses accurately. It seems there is something missing from the SM. Not only that the basic inputs of SM are leptons and quarks. Now in this propsed expression authors tried to \ft and understand the origin of the fundamental building blocks of electromagnetic interaction! Same authors tried to \ft and understand the origin of quarks in the paper [1] with the electron rest mass as a reference mass unit. More interesting thing is that in the paper [1] authors proposed the existence of `integral charge’ qaurk fermions and`integral charge’ quark bosons. Eventhough this idea is against to the SM, observed strong interaction particles charge-mass spectrum can be understood very easily. Super symmetry plays a key role in this.<\/div>\n
\"\"5. Strong interaction mass unit MSf <\/em>c^2<\/strong><\/div>\n
In paper [2] it is proposed that there exists a strongly interacting fermionic mass unit MSf<\/em> c^2 \u2248 105.38 MeV. It is noticed that<\/div>\n
\"\"Accuracy of MSf <\/em>c^2 depends on XE<\/em> and GS<\/em>.<\/div>\n
\"\"6. Proton, neutron rest masses & the nuclear stability factor (Sf <\/em>)<\/strong><\/div>\n
Qualitatively and quantitatively with 99.9 % accuracy it is noticed that<\/div>\n
\"\"where mP<\/em> c^2 = rest energy of proton, mN<\/em>c^2 = rest energy of neutron, me<\/em>c^2 = rest energy of electron and MSf <\/em>= proposed strong interaction fermion mass unit \u2248 105.398 MeV. Interesting thing is that, 2GC<\/em>MSf<\/em>\/c^2 can be considered as the classical black hole radius of MSf<\/em> and \u045b\/MSf <\/em>c is the compton length of MSf <\/em>. This equation clearly suggests the individual roles of MSf <\/em>, GC<\/em> and N in the nuclear physics. On simpli\fcation<\/div>\n
\"\"Here, 2GS<\/em>MSf\/<\/em>c^2 can be considered as the strong nuclear black hole radius of MSf <\/em>. Considering the average mass of nucleon<\/div>\n
\"\"From equation (18)<\/div>\n
\"\"<\/div>\n
Hence, in the above equation (31) denominator 2 can be eleminated as<\/div>\n
\"\"Here, e^2\/4\u03c0\u03b5\u03b8me<\/em>c is the classical radius of electron. On simpli\fcation<\/div>\n
\"\"All these equations suggests that the proposed strong nuclear gravitational constant GS<\/em> and the strong interaction mass unit MSf<\/em> plays a key role in understanding the origin of rest mass of nucleon.<\/div>\n
.<\/div>\n
6.1. Fitting of nucleon rest masses upto 4 decimal places<\/em><\/div>\n
In paper [2] authors prosed a new number called as nuclear stability number Sf<\/em> = 2XS<\/em>^2 \u2248 155.0 and XS<\/em> = Strong interaction mass generator \u2248 \u221a(GS<\/em>M^2Sf<\/em>\/\u045bc). It is noticed that proportionality constant being \u221a(1\/Sf<\/em>) ratio of rest energy of proton and charged lepton potential can be given as<\/div>\n
\"\"where mP<\/em> c^2 = Rest energy of proton, EL<\/em> = characteristic charged lepton potential \u2248 1.732 x 10^-3 MeV.<\/div>\n
\"\"Considering proton-electron mass ratio<\/div>\n
\"\"If Sf is fundamental compared to XS<\/div>\n
\"\"\"\"This equation can be written as<\/div>\n
\"\"If it is assumed that (mP<\/em> c^2 + mN<\/em>c^2) is more appropriate than 2mP <\/em>c^2,<\/div>\n
\"\"Neutron-proton mass di\u000berence can be given as<\/div>\n
\"\"See the reference [1]. In super symmetry in strong and weak interactions for every fermion there exists a corresponding boson of mass = (fermion mass\/\u03a8). Authors clearly shown this in paper [1]. The most interesting idea is that fermion makes 13 jumps in one revolution and comes to the initial position and boson makes 13 revolutions with 6 jumps in each incomplete revolution. Here angle of jump for fermion can be assumed as sin^-1(1\/\u03b1XE<\/em>)\u224827.67394^0 and angle of jump for boson is 55.34788^0. Boson in one cycle makes 78 jumps and this is very close to XS<\/em>^2\u224877.6.<\/div>\n
Considering \f decay it is known that neutron transforms into stable proton, stable electron and stable neutrino. Authors proposed that neutron is a combination of proton and Up quark boson [1]. The Up boson transforms into an electron. The important observation is that \u03c8<\/strong> plays a crucial role in neutron and proton mass generation. Its square root value is just crossing 1.5. This number 1.5 can also be attributed to the energy ratio of proposed [2] nuclear coulombic energy constant 0.769 MeV and the electron rest mass 0.511 MeV. But it is also not giving the correct values of mP and mN<\/em>. Values of
\nmP<\/em> and mN<\/em> depends on Sf,<\/em> XE<\/em> and me<\/em>. To a very good accuracy it is noticed that<\/div>\n
\"\"where \u03c8<\/strong> = proposed strong interaction fermion – boson mass ratio – 2.2623412 \u2248 ln(6+\u221a13) and \u221a\u03c8 = <\/strong>1.504108104. <\/strong><\/div>\n
\"\"<\/strong>This value of XS<\/em> is very close to the original de\fnition of XS<\/em> = \u221a(GS<\/em>MSf^<\/em>2\/\u045bc) = 8.809788028.<\/div>\n
The obtained values are mP<\/em> = 1.672641849 x 10^-27 Kg and mN<\/em> = 1.67493932 x 10^-27 Kg. The co-data recommended [9] values are mP<\/em> = 1.672621637 x 10^-27 Kg and mN<\/em> = 1.674927211 x 10^-27.<\/div>\n
.<\/div>\n
6.2. Nucleon-proton stability<\/em><\/div>\n
Stable isotope AS of any Z or proton-nucleon stability relation can be given as<\/div>\n
\"\"This can be compared with the existing nucleon- proton stability relations [10]<\/div>\n
\"\"\"\"Here NS=Stable neutron number, ZS<\/em>=Stable proton number corresponding to mass number A. By considering A as the fundamental input its corresponding stable Z can be obtained as<\/div>\n
\"\"AS <\/em>can be called as the stable mass number of Z. After rounding o\u000b for even (Z)
\nvalues, if obtained AS<\/em> is odd consider AS<\/em> – 1, for odd (Z) values if obtained AS<\/em> is even, consider AS<\/em> – 1. For very light odd elements this seems to be not \ffitting. Hence for Z\u22649 this correction idea is not applied. At Z = 47 obtained AS <\/em>= 108.24. Its round o\u000b value is 108 which is even. Its nearest odd number is 108-1=107. At Z = 92 obtained AS<\/em> = 238.56. Its round o\u000b value is 239 which is odd. Its nearest even number is 239-1=238. At Z = 29 obtained AS<\/em> = 63.42. Its round o\u000b value is 63 which is odd. Correction is not required. At Z = 68 obtained AS = 165.81. Its round o\u000b value is 166 which is even. Correction is not required.<\/div>\n
.<\/div>\n
7. Estimation and signi\fcance of sin (\u03b8w<\/em>)<\/strong><\/div>\n
\"\"Empirically it is noticed that<\/div>\n
\"\"Its more appropriate form seems to be<\/div>\n
\"\"8. Estimation of the strongly interacting subquark fermion MGf<\/em> c^2 and the strongly interacting subquark boson MGb<\/em>c^2<\/strong><\/div>\n
In the paper [1] it is proposed that there exists a strongly interacting fermionic mass unit MGf <\/em>c^<\/strong>2 \u2248 11450 MeV in subquark physics by using which quark gluon masses can be estimated. It is noticed that<\/div>\n
\"\"It’s corresponding strongly interacting boson mass MGb<\/em>c^<\/strong>2 can be given as<\/div>\n
\"\"where\u00a0\u03c8<\/strong> =proposed strong interaction fermion-boson mass ratio=2.2623412.<\/div>\n
\"\"Authors shown the applications of these two mass units in particle physics paper [1]. MGf <\/em>c^2 plays a crucial role in estimating the strongly interacting fermi-gluonic masses of e\u000bective quark fermions as<\/div>\n
\"\"where QGfe<\/em>=e\u000bffective quark fermi-gluon mass and Qfe=eff\u000bective quark fermion mass. MGb<\/em>c^2 plays a crucial role in estimating the strongly interacting boso-gluonic masses of quark bosons as<\/div>\n
\"\"where QGb<\/em>=quark boso-gluon mass and Qb<\/em>=quark boson mass.<\/div>\n
.<\/div>\n
Conclusions<\/strong><\/div>\n
If one is able to develop a relation between electron rest mass and charge certainly it can lead to the true grand uni\fcation. To understand the mystery of true grand uni\fcation Avagadro number can be given a chance. The characteristic nucleon’s kinetic energy or sum of potential and kinetic enetrgies is close to the rest energy of electron. Authors request the world science community to kindly look into these new ideas for further analysis.<\/div>\n
.<\/div>\n
Acknowledgements<\/strong><\/div>\n
Authors are very much grateful to the editors and referees of paper [1] and paper [2] for publication. First author is very much thankful to Prof. S. Lakshminarayana, Department of Nuclear Physics, Andhra University, Visakhapatnam, India, for his kind encouragement and guidance at all times. Finally \frst author is very much thankful to his loving brother B. Vamsi Krishna (Software professional) for encouraging, providing technical and \fnancial support. Authors are very much thankful to the Wikipedia for the nice presenting of the `grand uni\fcation’ information.<\/div>\n
References<\/strong>
\n[1] U. V. S. Seshavatharam and S. Lakshminarayana. Super Symmetry in Strong and Weak interactions. IJMPE, Vol.19, No.2, (2010), p.263-280.
\n[2] U. V. S. Seshavatharam and S. Lakshminarayana. Strong nuclear gravitational constant and the origin of nuclear planck scale. Progress in Physics, vol. 3, July, 2010, p. 31-38.
\n[3] Avogadro constant, From Wikipedia, the free encyclopedia. http:\/\/en.wikipedia.org\/wiki\/Avogadro constant.
\n[4] Einsteins Last Dream: The Space -Time Uni\fcation of Fundamental Forces, Physics News, Vol.12, No.2 (June 1981), p.36. (Address by Professor Abdus Salam at the UNESCO Celebration of the Centenary of Einstein’s birth, 7 May 1979, Paris.)
\n[5] Tilman Sauer. Einsteins Uni\fed Field Theory Program. The Cambridge Companion to Einstein, M. Janssen, C. Lehner (eds), Cambridge University Press.
\n[6] David Gross. Einstein and the search for Uni\fcation. http:worldscibooks.com\/etextbook\/6259.
\n[7] Hawking S.W. A Brief History of Time. Book. Bantam Dell Publishing Group. 1988.
\n[8] Particle Data Group (W.-M. Yao et al.), J. Phys. G 33 (2006) 1, http:\/\/pdg.bbb.gov.
\n[9] P.J. Mohr and B.N. Taylor. CODATA Recommended Values of the Fundamental Physical
\nConstants.2007. http:\/\/physics.nist.gov\/constants.
\n[10] P. Roy Chowdhury et al. Modi\fed Bethe-Weizsacker mass formula with isotonic shift and new driplines. (http:\/\/arxiv.org\/abs\/nucl-th\/0405080v4)<\/div>\n
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By<\/p>\n

U.V.S. Seshavatharam DIP QA Engineer, Lanco Industries Ltd, Srikalahasti-517641, A.P, India E-mail: seshavatharam.uvs@gmail.com<\/p>\n

Prof. S. LAKSHMINARAYANA Department Of Nuclear Physics, Andhra University, Vizag-530003, AP, India. E-mail: lnsrirama@yahoo.com<\/p>\n

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Abstract 1: `N’ being the Avagadro number, it is suggested [2, 3] that strong nuclear […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/posts\/316"}],"collection":[{"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=316"}],"version-history":[{"count":14,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/posts\/316\/revisions"}],"predecessor-version":[{"id":327,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=\/wp\/v2\/posts\/316\/revisions\/327"}],"wp:attachment":[{"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.journal-of-nuclear-physics.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}