TLT_IntPiw

 integral in Piwinski Formula for the Lifetime

0001 function I=TLT_IntPiw(u,um,B1,B2) 
0002 % integral in Piwinski Formula for the Lifetime
0003 
0004 
0005 %   in case the Bessel function has too large value (more than 10^251) it
0006 %   is substituted by its exponential approximation:
0007 %   I_0(x)~exp(x)/sqrt(2*pi*x)
0008 
0009 if B2*u<500
0010     I=(...
0011         (...
0012        ((2+1./u).^2).*(((u./um)./(1+u))-1) +...
0013       1 - ...
0014       sqrt((1+u))./sqrt((u./um)) -...
0015       1./(2.*u).*(4+(1./u)).*log((u./um)./(1+u))...
0016       ).*exp(-B1.*u).*besseli(0,B2.*u).*sqrt(u)./sqrt((1+u))...
0017       );
0018 else
0019     I=(...
0020         (...
0021        ((2+1./u).^2).*(((u./um)./(1+u))-1) +...
0022       1 - ...
0023       sqrt((1+u))./sqrt((u./um)) -...
0024       1./(2.*u).*(4+(1./u)).*log((u./um)./(1+u))...
0025       ).*exp(B2.*u-B1.*u)./sqrt(2*pi*B2.*u).*sqrt(u)./sqrt((1+u))...
0026       );
0027 end
0028 
0029 return