TLT_IntPiw_k

 integral in Piwinski Formula for the Lifetime with u=tan^2(k)

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