The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008
EMPIRIC UNIVERSAL FUNCTION OF a(A) FOR WIGNER MASS
FORMULA
A.M. NURMUKHAMEDOV
Institute o f Applied Physics under the National University o f Uzbekistan,
Aiming on analytical description of empirical universal function of a(A) for Wigner mass formula the analysis of nuclear masses was performed in the framework o f Wigner mass formula:
M (A ,Z ) = a(A) + b(A)C2 + E Cou!(A ,Z ) + Ei (Z ,N ) + E ^ ( Z . t f ) (1)
where a(A) b(A) are Wigner empiric universal functions, C2 is a Casimir operator,
E Coul(A ,Z ) is a Coulomb energy of nuclei, E sl(Z ,N ) is an energy of spin-orbit interaction
and Epcul.(Z ,N ) is a pair energy. To simplify a task there were considered only nuclei with odd mass number ranged in 1 < A < 257 and where E pair (Z, N ) = 0 by definition. As a selection criteria the certain features of a(A) have been used e.g. universality for the given isobar and its smooth dependency from the mass number. Universal functions a(A) have been calculated by the formula:
a(A) = Au + A nucl(A,Tz ) - b (A )C 2 - E Coul(A ,Z), (2)
where A mcl(A,T2)~ is a surplus of nuclear mass recalculated from the surplus of neutral atom [l],Au is a product of the mass number A to the relative isotopic unit of mass. The energy of Coulomb interaction was calculated using formula: E Cmd (A, Z) = 703.2Z 2A~U3 ( 1 - 1 .28A '2 3) keV. The empiric universal Wigner function b(A) for formula (2) obtained from the work [2] and appears as:
b ( A ) = b , e x p (b2A ) + b3 e x p (b4A J 1 - e x p [ - ( 7 ; - 0 .5 ) / 0 .5 ]} . (3) Calculated using expression (2) numeric values of empiric universal function a(A) of the “selected” nuclides [2] which comply with requirement of universality and smoothness of the function a(A) were analyzed using the method of the least squares. Analysis shows that the experimental values of empiric universal function a(A) can be described analytically by the expression:
a(A) = {a, exp(a2A) + a3 exp(a4Â) + a5 exp(a6A) + a7 exp(öaT | 1 - expfHX - 0.5)/0.5]} }A. (4) Constants a, + a 8 for formula (4) have the following numeric values:
a ,= 927368(11) keV/nucleon, a2 =5.11(5) 10'6, a 3 =2147(92) keV/nucleon, a 4 = -0.0214(5), a5 =1995(78) keV/nucleon, a6 = -0.048(1), a 7 =7713(707) keV/nucleon,
Section II. Basic Problems Of Nuclear Physics
The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008
a 8 =-0.22(2). References:
1. G. Audi, A.H. Wapstra and C. Thibault, Nucl Phys. A729, 337 (2003). 2. A.M. Nurmukhamedov, Natural and Technical Sciences magazine, #5, Moscow, “Sputnik”, pp. 116-119, 2007 (in Russian).
Section II. Basic Problems Of Nuclear Physics
