Calculation of the Atomic Nucleus Mass

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Adriano Antonelli
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1 Calculation of the Atomic Nucleus Mass N. Murata, YojaPanchan Abstract In this paper, the mass derived from the g equation is assumed to be the mass of quark-lepton, and is used to calculate the masses of the atomic nucleus. g equation 1 quark-lepton 1 g equation 1 M = c ϵ 1/ 0 hq π 4πG τ c : velocity of light h : Planck s constant G : gravitation constant q : elementary charge τ : excitation time ϵ : permittivity quark-lepton M (n, ζq ) = 1 c ϵ n hq π 4πG ϵ τ n (ζ 1/ qϵ U n 1 0 ) n ζ q : 1/3, /3, 3/3 n :, 3, 4, τ U = sec quark-lepton mass [kg] n ζ (0/3) : z n ζ (1/3) : d n ζ (/3) : u n ζ (3/3) : g n pending/ rejected, 30 Sep :01:55, www-admin@arxiv.org vixra: Calculation of the Elementary Particle Mass, N.Murata, YojaPanchan,

2 quark-lepton mass [MeV ] n ζ (0/3) : z n ζ (1/3) : d n ζ (/3) : u n ζ (3/3) : g n proton p + neutron n 0 proton p + = (u 5 d 4 ) + u 4 Spin(p + ) = (+1 1 ) + 1 = +1 Charge(p + ) = ( ) + 3 = +1 Mass(p + ) = (u 5 d 4 + u 4 )(1 3b q ) b q = 4π (d 4) + (u 4 ) (u 5 + d 4 + u 4 ) proton p + = (p+ )S = (u 5 d 4 ) S + u S 4 = (u 5 d 4 ) + u S 4 Spin(p + ) = (+1 1 ) 1 = 1 Charge(p + ) = ( ) + 3 = +1 Mass(p + ) = (u 5 d 4 + u 4 )(1 3b q ) b q = 4π (d 4) + (u 4 ) (u 5 + d 4 + u 4 ) Mass(p + ) = Mass(p+ ) = Mass(p+ ) Mass(p + ) = kg = MeV Observation Calculation = MeV = 0.3 KeV neutron n 0 = (u 5 d 4 ) + d A 4 Spin(n 0 ) = (+ 1 1 ) + 1 = +1 Charge(n 0 ) = ( ) 1 3 = 0 Mass(n 0 ) = (u 5 d 4 d 4 )(1 3b q ) b q = 4π (d 4 ) (u 5 + d 4 + d 4 ) neutron n 0 = (n 0 ) S = (u 5 d 4 ) S + d AS 4 = (u 5 d 4 ) d 4 Spin(n 0 ) = (+ 1 1 ) 1 = 1 Charge(n 0 ) = ( ) 1 3 = 0 Mass(n 0 ) = (u 5 d 4 d 4 )(1 3b q ) b q = 4π (d 4 ) (u 5 + d 4 + d 4 ) Mass(n 0 ) = Mass(n 0 ) = Mass(n 0 ) Mass(n 0 ) = kg = MeV Observation Calculation = MeV = 9.44 MeV

3 Mass(p + ) Mass(n 0 ) = MeV, Mass(p + ) > Mass(n 0 ) 3 Z p + N n0 B (N, Z) Z 1, N 0 B (N, Z) = B M B S B C B G B M : p + n0 B S : p + n0 Spin B C : d S 4 + u 4 Coulomb B G : B M p + n0 p+ n0 B M N = Z = 1 N = 0 B M = 0 α B α B = 0 (N=0), 1 (N>0) N Z : B M = α B ( Z (Mass(p + ) Mass(n0 )) (Mass(p + ) Mass(n0 )) ) = α B (Z 1)(Mass(p + ) Mass(n0 )) N < Z : B M = α B ( N (Mass(p + ) Mass(n0 )) (Mass(p + ) Mass(n0 )) ) = α B (N 1)(Mass(p + ) Mass(n0 )) B M B S Spin Spin N Z : n 0 = n 0 + (d 4 + d A 4 ) = n0 + γ (d4 d A 4 ) γ (d4 d A 4 ) Mass(d 4 + d 4 ) B S = N Z Mass(d 4 + d 4 ) N < Z : p + = p+ + (u 4 + u A 4 ) = p+ + γ (u 4 u A 4 ) γ (u4 u A 4 ) Mass(u 4 + u 4 ) B S = Z N Mass(u 4 + u 4 ) q Coulomb B C q d S 4 + u 4 l 1/c Z = 1 B C = 0 p + = n0 + ( d A 4 + u 4) = n 0 + (d S 4 + u 4) l = h c Mass(d S 4 + u 4) B C = 3 5 (Z 1) q 4πϵ 0 (l/ + l/) 1 c = 3 5 α fs (Z 1) Mass(d S 4 + u 4) α fs = q 4πϵ 0 hc 3

4 B G N = Z N = 0 B G = 0 B G = α B ( Z Mass(p+ ) + N Mass(n0 ) Z + N = α B Z N (Z + N) (Mass(p+ ) Mass(n0 )) Mass(p+ ) + Mass(n0 ) ) B (N, Z) B (N, Z : N Z) = + α B (Z 1 Z N (Z + N) ) (Mass(p+ ) Mass(n0 )) N Z Mass(d 4 + d 4 ) 3 5 α fs (Z 1) Mass(d S 4 + u 4) B (N, Z : N<Z) = + α B (N 1 Z N (Z + N) ) (Mass(p+ ) Mass(n0 )) Z N Mass(u 4 + u 4 ) 3 5 α fs (Z 1) Mass(d S 4 + u 4) atom (N, Z) Mass(atom (N, Z : N Z) ) = Z Mass(p + ) + N Mass(n 0 ) B (N, Z : N Z) Mass(atom (N, Z : N<Z) ) = Z Mass(p + ) + N Mass(n 0 ) B (N, Z : N<Z) 4 quark-lepton MKSC unit system kg MeV C 1 N = 0, Z = 1 N = 104, Z = MeV +50 MeV A = N + Z d S 4 + u 4 ha c Mass(atom (N, Z) ) m h c Mass(d S 4 + u 4) = m 3 ATOMIC MASS DATA CENTER The 01 Atomic Mass Evaluation 4

5 MKSC unit system : Masses [kg] gcc -o Atom. exe Atom.c -lm include <stdio.h> include stdlib.h> # include < string.h> # include <math.h> # define pi ( e +00) /* \ pai */ # define pc ( e +08) /* velocity of light */ # define ph ( e -34) /* Planck s constant bar */ # define pq ( e -19) /* elementary charge */ # define pe ( e -1) /* permittivity */ # define pg ( e -11) /* gravitation constant */ # define ut ( e +17) /* age of the Universe : electron (4, 3/3) */ # define fs (( pq * pq) / (4.0 * pi * pe * ph * pc )) /* fine - structure */ # define MeV (+1.0 / e -30) /* MeV */ # define nnmax ( 6 + ) # define iimax ( 4 + ) # define aamax (104 + ) double mql [ nnmax ][ iimax ]; /* quark - lepton Mass */ double tql [ nnmax ][ iimax ]; double lql [ nnmax ][ iimax ]; double mat [ aamax ][ aamax ]; /* Atom Mass */ double bat [ aamax ][ aamax ]; /* Atom Binding Energy */ double Mp; /* proton Mass */ double Mn; /* neutron Mass */ void xzero ( void ); void xmassql ( void ); double xsurface ( double, double ); void xmasspn ( void ); void xmassatom ( void ); void xprintql ( void ); void xnndc ( void ); void main () { xzero (); xmassql (); xmasspn (); xprintql (); xmassatom (); xnndc (); void xzero ( void ) { int nn, ii; for ( nn = 0 ; nnmax > nn ; nn ++){ for (ii = 0 ; iimax > ii ; ii ++){ mql [nn ][ ii] = tql [nn ][ ii] = lql [nn ][ ii] = 0.0; for ( nn = 0 ; aamax > nn ; nn ++){ for (ii = 0 ; aamax > ii ; ii ++){ mat [nn ][ ii] = bat [nn ][ ii] = 0.0; void xmassql ( void ) { double aa, bb, mm; int nn, ii; aa = sqrt ((( pq * ph) / sqrt (4.0 * pi * pg )) * (.0 * pi / ut )) / (.0 * pc ); for ( nn = ; nnmax > nn ; nn ++){ mm = 0.0; for (ii = 1 ; 3 >= ii ; ii ++){ bb = sqrt (pow ((( double )ii / 3.0) * sqrt (pe), (double )nn) / (double )(nn - 1)); mql [nn ][ ii] = aa / bb; lql [nn ][ ii] = (ph / pc) / mql [nn ][ ii ]; mm -= mql [nn ][ ii ]; mql [nn ][0] = mm; lql [nn ][0] = (ph / pc) / mm; double xsurface ( double sr, double sr) { return ( 4.0 * pi * pow (sr / sr,.0) ); void xmasspn ( void ) { double mm, ww, rr, bb; mm = + mql [5][] + mql [4][] - mql [4][1]; rr = + mql [5][] + mql [4][] + mql [4][1]; bb = xsurface (1.0 * mql [4][], rr) + xsurface (1.0 * mql [4][1], rr ); Mp = mm * ( * bb ); mm = + mql [5][] - mql [4][1] - mql [4][1]; rr = + mql [5][] + mql [4][1] + mql [4][1]; bb = xsurface (.0 * mql [4][1], rr ); Mn = mm * ( * bb ); void xmassatom ( void ) { double qq, ss, mm; double cq, cs, cm, cg; int nn, zz; mm = (Mp - Mn ); qq = ( mql [4][1] + mql [4][]) * fs; for ( nn = 0 ; aamax > nn ; nn ++){ for (zz = 1 ; aamax > zz ; zz ++){ cs = (double )(int )(( double )abs (nn - zz) /.0); cq = (3.0 / 5.0) * ( double )( zz - 1) * ( double )( zz - 1); cg = ( double )( zz - nn) / (.0 * ( double )( nn + zz )); if( nn >= zz ){ ss = ( mql [4][1] + mql [4][1]); cm = ( double )( zz - 1) - cg; if( nn < zz ){ ss = ( mql [4][] + mql [4][]); cm = ( double )( nn - 1) - cg; if( 0 == nn ){ cm = 0.0; bat [nn ][ zz] = + cm * mm - (cq * qq + cs * ss ); mat [nn ][ zz] = + (( double )zz * Mp + ( double )nn * Mn) - bat [nn ][ zz ]; 5

6 void xprintql ( void ) { int nn; printf ("\ n\n "); printf ("*= - YojaPanchan -=*\n"); printf (" quark - lepton [ MeV ]\n"); printf (" n : z : d : u : g :\n"); for (nn = ; 6 >= nn ; nn ++){ printf ("% d : %+9.6 e : %+9.6 e : %+9.6 e : %+9.6 e :\n", nn, mql [nn ][0] * MeV, mql [nn ][1] * MeV, mql [nn ][] * MeV, mql [nn ][3] * MeV ); printf (" quark - lepton [kg ]\n"); printf (" n : z : d : u : g :\n"); for (nn = ; 6 >= nn ; nn ++){ printf ("% d : %+9.6 e : %+9.6 e : %+9.6 e : %+9.6 e :\n", nn, mql [nn ][0], mql [nn ][1], mql [nn ][], mql [nn ][3]); printf (" quark - lepton [m]\n"); printf (" n : z : d : u : g :\n"); for (nn = ; 6 >= nn ; nn ++){ printf ("% d : %+9.6 e : %+9.6 e : %+9.6 e : %+9.6 e :\n", nn, lql [nn ][0], lql [nn ][1], lql [nn ][], lql [nn ][3]); void xnndc ( void ) { # define Op ( e -7) /* e +0 */ # define On ( e -7) /* e +0 */ # define AMU ( e -7) printf ("\ n\n "); printf (" Proton \n "); printf (" observ - calcu = %+9.8 e - %+9.8 e = %+9.8 e [kg ] :\n", Op, Mp, fabs (Op) - fabs (Mp )); printf (" observ - calcu = %+9.8 e - %+9.8 e = %+9.8 e [ MeV ] :\n", Op * MeV, Mp * MeV, fabs (Op * MeV ) - fabs (Mp * MeV )); printf (" Neutron \n "); printf (" observ - calcu = %+9.8 e - %+9.8 e = %+9.8 e [kg ] :\n", On, Mn, fabs (On) - fabs (Mn )); printf (" observ - calcu = %+9.8 e - %+9.8 e = %+9.8 e [ MeV ] :\n", On * MeV, Mn * MeV, fabs (On * MeV ) - fabs (Mn * MeV )); printf ("\ n\n "); # define rfile " mass. mas1 " /* In File */ # define wfile " Atom. dat " /* OutFile */ FILE FILE *fr; *fw; char bf [56 + ]; char bs [56 + ]; char el[ 4 + ]; char fo[ 4 + ]; double mo bo; double mc bc lc; aa; int int zz nn, ii, jj; if( NULL!= (fr = fopen ( rfile, "r ")) ){ if( NULL!= (fw = fopen ( wfile, "w ")) ){ for (ii = 0 ; 40 > ii ; ii ++){ fgets (bf, 56, fr ); Head while ( NULL!= fgets (bf, 56, fr) ){ strcpy (fo, " "); sprintf (bs, "%c%c%c%c%c", bf[ 4], bf[ 5], bf[ 6], bf[ 7], bf[ 8]); nn = atoi (bs ); sprintf (bs, "%c%c%c%c%c", bf[ 9], bf [10], bf [11], bf [1], bf [13]); zz = atoi (bs ); sprintf (bs, "%c%c%c%c%c", bf [14], bf [15], bf [16], bf [17], bf [18]); aa = atoi (bs ); sprintf (el, "%c%c%c", bf [0], bf [1], bf []); for (ii = 0 ; 56 > ii ; ii ++){ bs[ii] = 0 x00 ; for (ii = 0, jj = 0 ; 14 > ii ; ii ++){ if( # == bf [51 + ii] ){ strcpy (fo, "#"); break ; else { bs[jj] = bf [51 + ii ]; jj ++; bo = atof (bs) * 1e -3; [ MeV ] for (ii = 0 ; 56 > ii ; ii ++){ bs[ii] = 0 x00 ; for (ii = 0, jj = 0 ; 14 > ii ; ii ++){ if( # == bf [96 + ii] ){ strcpy (fo, "#"); break ; else { if(!= bf [96 + ii] ){ bs[jj] = bf [96 + ii ]; jj ++; mo = atof (bs) * 1e -6 * AMU * MeV ; [ MeV ] bc = (( double )zz * Op + ( double )nn * On - mat [nn ][ zz ]) * MeV / ( double )aa; Definition lc = (( double )aa * ph) / (pc * mat [nn ][ zz ]); fprintf (fw, "%s %3d %3d %3d %9.8 e %+9.8 e %+9.8 e\n", el, aa, nn, zz, mat [nn ][ zz] * MeV, bc, bat [nn ][ zz] * MeV ); fclose (fw ); fclose (fr ); - N.Murata, YojaPanchan - 6

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