Method

For a compound ( NLMAT < 0), the molecular weight and charge are:

$A$_mol= ∑_in_iA_i&sp;Z_mol= ∑_in_iZ_i

where $n$_i = WMAT(I) is the number of atoms of the $ith$

component of the molecule. In this case the proportion by weight is:

$p$_i= {n_iA_iA_mol}

where $p$_i = WMAT(I) in output. From the relative weights, GSMIXT works out the effective atomic weight and atomic number according to the following formulas:

$A$_eff= ∑_ip_iA_i&sp;Z_eff= ∑_ip_iZ_i

which are stored in the JMATE data structure [CONS199] together with the radiation length.

The radiation length is computed according to the EGS manual [], formula 268 (37), for an element:

₀}=4 αr₀²N_Av{1A}Z(Z+ ξ(Z)) [ ln{183Z^1/3}-F_c(Z) ]

where

$X$₀

radiation length (in cm);

$\rho$

density (in g $cm-3$ );

$\alpha$

fine structure constant;

r

classical electron radius (in cm);

$N$_Av

Avogadro's number;

A

atomic weight;

Z

atomic number;

$F$_c(Z)

Coulomb correction function.

$F$_c(Z) = (αZ)²[ {1 1+( αZ)²}+0.20206-0.0369( αZ)²+0.0083(αZ)⁴-0.0020(αZ)⁶]

$\xi (Z)\; =\; \{ln\{1440Z2/3\}ln\{183Z1/3\}-\; F$_c(Z)}

for a compound or mixture:

$\{1\rho X$₀}=∑_i{p_iρ_iX_0i}

where $p$_i is the proportion by weight of the $ith$ element. For more information on the organisation of the data in memory see [CONS199].

The effective absorption length $\lambda$ is defined as the interaction length of a 5GeV pion in the material:

Once this value has been determined, an effective hadronic atomic weight ($A$_h-eff ) is calculated by the routine GHMIX [] and stored in the data structure.

R.Brun, M.Maire CONS199