The atomic form factors

Different empirical formulae are used to produce the atomic form factor F(Z,E) data []. For Z = 1-3, 91-99 the empirical expression is: $F\; (\; Z,E\; )\; =\; a$₁E⁷+ b₁E⁶+ c₁E⁵+ d₁E⁴+ e₁E³+ f₁E²+ g₁E + h₁

for Z=100 the formula used is: $F\; (\; Z,E\; )\; =\; a$₂E⁵+ b₂E⁴+ c₂E³+ d₂E²+ e₂E + f₂

for the other elements F is calculated as: $F\; (\; Z,E\; )\; =$

$a$3E3+ b3E2+ c3E + d3	$if\; E\; \le E$c
$a$4E3+ b4E2+ c4E + d4	$if\; E\; >\; E$c

$.$

The value of the energy $E$_c depends on Z and it is set in the array ELIM. The values of the coefficients are stored in the DATA statement in the routine GRAYLI. For each element the fits were performed over 97 tabulated values of the form factors. The accuracy of the fit is estimated to about $\Delta \sigma /\sigma =\; 10$

for $E\; \le 1$ MeV for most of the elements. The integral over the atomic form factors $A\; (\; E$_i) is defined as follows: $A\; (\; E$_i) = 2 ∫₀^E_i| F_T( E ) |²E dE = ∫₀^E_i| F_T( E ) |²dE²

where $F$_T( E ) is the total atomic form factor which is function of the energy E.

PHYS251