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molzeeman.c
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molzeeman.c
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/* ------- file: -------------------------- molzeeman.c -------------
Version: rh2.0
Author: Han Uitenbroek (huitenbroek@nso.edu)
Last modified: Thu Jun 30 15:35:10 2011 --
-------------------------- ----------RH-- */
/* --- Routines to calculate Zeeman splitting patterns and relative
strengths of Zeeman components in molecular transitions.
-- -------------- */
#include <stdlib.h>
#include <math.h>
#include "rh.h"
#include "atom.h"
#include "spectrum.h"
#include "error.h"
/* --- Function prototypes -- -------------- */
double MolZeemanStr(double Ju, double Mu, double Jl, double Ml);
double MolLande_a(double Lambda, double Sigma, double Omega, double J);
double MolLande_b(double Lambda, double S, double N, double J);
/* --- Global variables -- -------------- */
extern char messageStr[];
/* ------- begin -------------------------- MolZeemanStr.c ---------- */
double MolZeemanStr(double Ju, double Mu, double Jl, double Ml)
{
const char routineName[] = "MolZeemanStr";
int q, dJ;
double s;
/* --- Return the strength of Zeeman component (Ju, Mu) -> (Jl, Ml),
where J and M are the total angular momentum and magnetic
quantum numbers of the upper and lower level of a Zeeman split
molecular transition.
See: - G. Herzberg 1950, in "Spectra of Diatomic Molecules", p.301-3
- S.V. Berdyugina and S.K. Solanki 2002, A&A 385, 701-715
- A. Schadee 1978, JQSRT 19, 517-531
Note: Berdyugina & Solanki adhere to the definition that dJ = Jl - Ju
-- -------------- */
q = (int) (Ml - Mu);
dJ = (int) (Jl - Ju);
switch (dJ) {
case 1:
switch (q) {
case 1: s = (Ju + 1.0 + Mu) * (Ju + 2.0 + Mu) /
(2*(Ju + 1.0) * (2*Ju + 1.0) * (2*Ju + 3.0)); break;
case 0: s = (Ju + 1.0 + Mu) * (Ju + 1.0 - Mu) /
((Ju + 1.0) * (2*Ju + 1.0) * (2*Ju + 3.0)); break;
case -1: s = (Ju + 1.0 - Mu) * (Ju + 2.0 - Mu) /
(2*(Ju + 1.0) * (2*Ju + 1.0) * (2*Ju + 3.0)); break;
}
break;
case 0:
switch (q) {
case 1: s = (Ju - Mu) * (Ju + 1.0 + Mu) /
(2*Ju * (Ju + 1.0) * (2*Ju + 1.0)); break;
case 0: s = Mu*Mu /
(Ju * (Ju + 1.0) * (2*Ju + 1.0)); break;
case -1: s = (Ju + Mu) * (Ju + 1.0 - Mu) /
(2*Ju * (Ju + 1.0) * (2*Ju + 1.0)); break;
}
break;
case -1:
switch (q) {
case 1: s = (Ju - Mu) * (Ju - 1.0 - Mu) /
(2*Ju * (2*Ju - 1.0) * (2*Ju + 1.0)); break;
case 0: s = (Ju + Mu) * (Ju - Mu) /
(Ju * (2*Ju - 1.0) * (2*Ju + 1.0)); break;
case -1: s = (Ju + Mu) * (Ju - 1.0 + Mu) /
(2*Ju * (2*Ju - 1.0) * (2*Ju + 1.0)); break;
}
break;
default:
sprintf(messageStr, "Invalid dJ: %d", dJ);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
/* --- The strengths are normalized already. -- -------------- */
return s;
}
/* ------- end ---------------------------- MolZeemanStr_b.c -------- */
/* ------- begin -------------------------- MolLande_a.c ------------ */
double MolLande_a(double Lambda, double Sigma, double Omega, double J)
{
/* --- Lande factor for level in Hund's case a
See: S.V. Berdyugina and S.K. Solanki 2002, A&A 385, 701-715, Eq. 2
-- -------------- */
return (Lambda + 2.0*Sigma) * Omega / (J * (J + 1.0));
}
/* ------- end ---------------------------- MolLande_a.c ------------ */
/* ------- begin -------------------------- MolLande_b.c ------------ */
double MolLande_b(double Lambda, double S, double N, double J)
{
/* --- Lande factor for level in Hund's case b
See: S.V. Berdyugina and S.K. Solanki 2002, A&A 385, 701-715, Eq. 10
-- -------------- */
if (Lambda == 0) {
return 1.0 / (J*(J + 1.0)) *
(J*(J + 1.0) - N*(N + 1.0) + S*(S + 1.0));
} else {
return 1.0 / (J*(J + 1.0)) *
(Lambda*Lambda / (2*N*(N + 1.0)) *
(J*(J + 1.0) + N*(N + 1.0) - S*(S + 1.0)) +
J*(J + 1.0) - N*(N + 1.0) + S*(S + 1.0));
}
}
/* ------- end ---------------------------- MolLande_b.c ------------ */
/* ------- begin -------------------------- MolLande_eff.c ---------- */
double MolLande_eff(MolecularLine *mrt)
{
const char routineName[] = "MolLande_eff";
register double Ml, Mu;
double g_eff, Ju, Jl, norm, Nl, Nu, shift, strength, gLu, gLl;
norm = 0.0;
g_eff = 0.0;
Jl = (mrt->gi - 1.0) / 2.0;
Ju = (mrt->gj - 1.0) / 2.0;
switch (mrt->Hundi) {
case CASE_A:
gLl = MolLande_a(mrt->Lambdai, mrt->Si, mrt->Omegai, Jl);
break;
case CASE_B:
Nl = Jl - mrt->Si + (mrt->subi - 1);
gLl = MolLande_b(mrt->Lambdai, mrt->Si, Nl, Jl);
break;
default:
sprintf(messageStr, "Unsupported Hund's case: %d", mrt->Hundi);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
switch (mrt->Hundj) {
case CASE_A:
gLu = MolLande_a(mrt->Lambdaj, mrt->Sj, mrt->Omegaj, Ju);
break;
case CASE_B:
Nu = Ju - mrt->Sj + (mrt->subj - 1);
gLu = MolLande_b(mrt->Lambdaj, mrt->Sj, Nu, Ju);
break;
default:
sprintf(messageStr, "Unsupported Hund's case: %d", mrt->Hundj);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
for (Ml = -Jl; Ml <= Jl; Ml++) {
for (Mu = -Ju; Mu <= Ju; Mu++) {
if ((Ml - Mu) == 1.0) {
shift = gLl*Ml - gLu*Mu;
strength = MolZeemanStr(Ju, Mu, Jl, Ml);
g_eff += shift * strength;
norm += strength;
}
}
}
return g_eff / norm;
}
/* ------- end ---------------------------- MolLande_eff.c ---------- */
/* ------- begin -------------------------- MolZeeman.c ------------- */
ZeemanMultiplet* MolZeeman(MolecularLine *mrt)
{
const char routineName[] = "MolZeeman";
register int n;
double Jl, Ju, Mu, Ml, norm[3], g_eff, Nl, Nu, gLl, gLu, lambda_air;
ZeemanMultiplet *zm;
/* --- Return a pointer to a ZeemanMultiplet structure with all the
components of a Zeeman split line. The strengths in the line
are normalized to unity for each of the three possible values
of q = [-1, 0, 1].
Convention:
-- q = +1 corresponds to a redshifted \sigma profile
(zm->shift > 0). This redshifted profile has
right-handed circular polarization when the
magnetic field parallel to the line of sight and
points towards the observer.
-- q = 0 corresponds to an unpolarized \pi profile
-- -------------- */
zm = (ZeemanMultiplet *) malloc(sizeof(ZeemanMultiplet));
if (mrt->g_Lande_eff != 0.0) {
/* --- In case an effective Landee factor has been specified, or
the the inputs.use_effective_Lande parameter has been set
in the input -- -------------- */
zm->Ncomponent = 3;
zm->q = (int *) malloc(3 * sizeof(int));
zm->strength = (double *) malloc(3 * sizeof(double));
zm->shift = (double *) malloc(3 * sizeof(double));
/* --- Normal Zeeman triplet -- -------------- */
for (n = 0; n < 3; n++) {
zm->q[n] = -1 + n;
zm->strength[n] = 1.0;
zm->shift[n] = zm->q[n] * mrt->g_Lande_eff;
}
} else {
/* --- Anomalous Zeeman splitting. First, count the number of
components -- -------------- */
Jl = (mrt->gi - 1.0) / 2.0;
Ju = (mrt->gj - 1.0) / 2.0;
switch (mrt->Hundi) {
case CASE_A:
gLl = MolLande_a(mrt->Lambdai, mrt->Si, mrt->Omegai, Jl);
break;
case CASE_B:
Nl = Jl - mrt->Si + (mrt->subi - 1);
gLl = MolLande_b(mrt->Lambdai, mrt->Si, Nl, Jl);
break;
default:
sprintf(messageStr, "Unsupported Hund's case: %d", mrt->Hundi);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
switch (mrt->Hundj) {
case CASE_A:
gLu = MolLande_a(mrt->Lambdaj, mrt->Sj, mrt->Omegaj, Ju);
break;
case CASE_B:
Nu = Ju - mrt->Sj + (mrt->subj - 1);
gLu = MolLande_b(mrt->Lambdaj, mrt->Sj, Nu, Ju);
break;
default:
sprintf(messageStr, "Unsupported Hund's case: %d", mrt->Hundj);
Error(ERROR_LEVEL_2, routineName, messageStr);
}
/* --- Determine the number of components -- -------------- */
zm->Ncomponent = 0;
for (Ml = -Jl; Ml <= Jl; Ml++) {
for (Mu = -Ju; Mu <= Ju; Mu++)
if (fabs(Mu - Ml) <= 1.0) zm->Ncomponent++;
}
zm->q = (int *) malloc(zm->Ncomponent * sizeof(int));
zm->strength = (double *) malloc(zm->Ncomponent * sizeof(double));
zm->shift = (double *) malloc(zm->Ncomponent * sizeof(double));
/* --- Fill the structure and normalize the strengths -- -------- */
for (n = 0; n < 3; n++) norm[n] = 0.0;
n = 0;
g_eff = 0.0;
for (Ml = -Jl; Ml <= Jl; Ml++) {
for (Mu = -Ju; Mu <= Ju; Mu++) {
if (fabs(Ml - Mu) <= 1.0) {
zm->q[n] = (int) (Ml - Mu);
zm->shift[n] = gLl*Ml - gLu*Mu;
zm->strength[n] = MolZeemanStr(Ju, Mu, Jl, Ml);
if ((Ml - Mu) == 1)
g_eff += zm->strength[n] * zm->shift[n];
norm[zm->q[n]+1] += zm->strength[n];
n++;
}
}
}
for (n = 0; n < zm->Ncomponent; n++)
zm->strength[n] /= norm[zm->q[n]+1];
mrt->g_Lande_eff = g_eff / norm[2];
}
vacuum_to_air(1, &(mrt->lambda0), &lambda_air);
sprintf(messageStr, " -- %2s line at %9.4f nm has %3d "
"Zeeman components, gL_eff = %7.4f\n", mrt->molecule->ID,
lambda_air, zm->Ncomponent, mrt->g_Lande_eff);
Error(MESSAGE, routineName, messageStr);
return zm;
}
/* ------- end ---------------------------- Zeeman.c ---------------- */