How to describe a function with an if statement and then integrate it.

Hello,

I am trying to describe a function pretty peculiar and then I need to integrate it. The problem comes in a few ways, and every attend i try result on fail. I allready tried syms variables, anonimous function and "normal fuction" (those defined as-> funtcion [output]=name(input) ..... end).

The context: i am trying to sampling a distribute function, more precisly the diferencial crossection of the rayleight scattering (photons with matter stuff). In some point i have to figure out an angle "theta", or its cosine, its the same.

Inputs: given a Energy ->E , an atomic number ->Z . I suggest to try with E = 1 000 000 (eV), and Z = 11.

Outputs: I need "theta", "E_nueva" should be the same number as E.

My best attempt was:

E = 1e6; Z = 11;
[sigma_rayleigh_valor] = sigma_rayleigh(E,Z)

Conversion to logical from sym is not possible.

Error in solution>sigma_rayleigh (line 33)
if (Z>10) && (f<2) % <-------- Here is where the error happens

function [sigma_rayleigh_valor] = sigma_rayleigh(E,Z)

% Esta funcion devuelve el valor de la seccion eficaz rayleigh para
% una energia dada E y una valor del numero atomico Z.

re = 2.8179e-13; % [cm] Radio del electron clasico. Is a number


% Hay que definir el factor de forma F:
% Definimos la funcion F(x,z):

Tabla1 = readtable("https://de.mathworks.com/matlabcentral/answers/uploaded_files/1214213/Tabla1.xlsx");
a1 = Tabla1{Z,2}; % a number, try for example "8"
a2 = Tabla1{Z,3}; % a number, try for example "7"
a3 = Tabla1{Z,4}; % a number, try for example "6"
a4 = Tabla1{Z,5}; % a number, try for example "5"
a5 = Tabla1{Z,6}; % a number, try for example "4"

syms costheta
x = 20.6074*(E/511000)*(2*(1-costheta))^(1/2); % x=x(E,costheta)


f = Z*(1+a1*x^2+a2*x^(3)+a3*x^4)/((1+a4*x^2+a5*x^4)^2); % f=f(x)=f(Z,E,costheta)

a = (Z-5/16)*(1/137); % a=a(Z)
gamma = sqrt(1-a^2); % gamma=gamma(a)=gamma(Z)
Q = x/(2*a*20.6074); % Q=Q(x,a)=Q(Z,E,costheta)
Fk = sin(2*(gamma)*atan(Q))/((gamma)*(Q)*(1+(Q)^2)^(gamma)); % Fk = Fk(gamma,Q) = ... = Fk(Z,E,costheta)


if (Z>10) && (f<2) % <-------- Here is where the error happens
    
    F = max([f Fk]);
    
else
    
    F = f;
    
end

% El factor de forma F ha quedado descrito.





fun = (1+costheta^2)*(F)^2; % Este es el integrando.

sigma_rayleigh_valor = pi*re^2*int(fun,costheta,-1,1);
sigma_rayleigh_valor = double(sigma_rayleigh_valor); % Con la funcion "double" paso de tener una variable syms a un escalar tipo double.


end

I need to clarify: With Z <= 10 there is no problem at all... the code seems to report a number, not an error ^^". When Z>10 the problem occurs

[Torsten]

We don't have Tabla1, so we cannot test your code.

[Pablo Ortega]

Uploaded, thanks for taking your time.

[Torsten]

f cannot be evaluated to be < 2 or not since it contains an unknown symbolic parameter "costheta".

[Pablo Ortega]

Well, i understand what the problem is. Is there any way to code the function "F" properly?