Cloudy & Associates

Commit 699245c8 authored by Marios Chatzikos's avatar Marios Chatzikos
Browse files

Add comment to explain treatment of Lebedev eqn

The implementation omits the exponential term that appears in Eq. (8.30)
of Lebedev & Beigman, as it is folded in its conversion to a collision
strength.  Comment clarifies this point.
parent 66d1ae06
......@@ -469,28 +469,34 @@ double hydro_Lebedev_deexcit(long ipISO, long nelem, long nHi, long nLo, double
double npn = (double)nHi + (double)nLo;
double npn2 = npn*npn;
double xn = IP_Ryd_Lo*TE1RYD/phycon.te;
double e1expxn = 0.;
double e1expxn = expe1(xn);
e1expxn = expe1(xn);
double theta = phycon.te / TE1RYD/pow2(Z);
//
// these are the two terms in the curly brackets in Eq. (8.30)
//
double phi = 2.*pow2(nHi*nLo/npn2)/deltan*(4*deltan - 1.)*e1expxn/deltan;
phi += pow3(2.*nLo/npn)*npn*(deltan - 0.6)*(1.33+pow2(nLo)*deltan)*(1.-xn*e1expxn)/deltan/pow2(nLo)/pow2(nHi);
double theta = phycon.te / TE1RYD/pow2(Z);
double ftheta = log(1.+nLo*theta/(Z*deltan*sqrt(theta)+2.5));
ftheta /= log(1.+nLo*sqrt(theta)/Z/deltan);
double rate = 2.*BOHR_RADIUS_CM*BOHR_RADIUS_CM*FINE_STRUCTURE*SPEEDLIGHT*SQRTPI;
rate *= double(nLo)*pow3((double)nHi/deltan/Z)/sqrt(theta)*phi*ftheta;
//
// NB NB
//
// Eq. (8.30) gives the excitation rate coefficient, and involves the
// term exp(-DE/kT). Omit that term here to obtain its product with the
// excitation rate coeff, q(exc)*exp(+DE/KT), stored in rate_x_exp.
//
// Omission gives the impression we compute the CS incorrectly.
// Tripped over this twice already. Added comment for clarity.
//
double rate_x_exp = 2.* pow2(BOHR_RADIUS_CM) * FINE_STRUCTURE * SPEEDLIGHT * SQRTPI;
rate_x_exp *= double(nLo)*pow3((double)nHi/(deltan*Z))/sqrt(theta)*phi*ftheta;
double gLo = get_iso_statw( ipISO, nLo );
double col_str = rate/COLL_CONST*phycon.sqrte*gLo;
double col_str = rate_x_exp / COLL_CONST * phycon.sqrte * gLo;
ASSERT (col_str >= 0);
......
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