def test_Er_LaF3():
"""
Tests that we give the same results as Carnall 1989 for Pr:LaF3
"""
#energy levels from Carnall's paper
carnall_levels = [-22, 27, 92, 176, 193, 289, 375, 420,
6612, 6637, 6686, 6699, 6732, 6771, 6830,
10300, 10314, 10336, 10351, 10365, 10405]
carnall_levels = np.array(carnall_levels)
carnall_levels = carnall_levels -np.min(carnall_levels)
nf = 11 # 11 f-electrons means we're dealing with Er
Er = dieke.RareEarthIon(nf)
cfparams = dieke.readLaF3params(nf)
# Number of levels and states
numLSJ = Er.numlevels()
numLSJmJ = Er.numstates()
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in cfparams.keys():
if k in Er.FreeIonMatrix:
H0 = H0+cfparams[k]*Er.FreeIonMatrix[k]
# Add in the crystal field terms
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Er.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq) # B_{k,-q}
Ckq = Er.Cmatrix(k, q)
Ckmq = Er.Cmatrix(k, -q)
# See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
# Diagonalise the result
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
calc_nrg_levels = calc_nrg_levels[::2]
print(' Jevon Carnall Difference')
for k in range(len(carnall_levels)):
print("%9.1f %9.1f %6.1f"%(np.real(calc_nrg_levels[k]),carnall_levels[k],np.real(calc_nrg_levels[k]) - carnall_levels[k]))
# Assert that they all agree within 1.1 wave number
assert(np.max(np.abs(
calc_nrg_levels[0:len(carnall_levels)]-carnall_levels))
< 1.1 )
def test_Pr_LaF3():
"""
Tests that we give the same results as Carnall 1989 for Pr:LaF3
"""
#energy levels from Carnall's paper
carnall_levels = [0.2, 71, 95, 138, 183, 221, 333, 444, 463,
2126, 2158, 2191, 2284, 2290, 2295, 2318,
2399, 2412,2438, 2540, 4179,4200, 4283,
4321, 4384, 4467, 4478, 4496]
carnall_levels = np.array(carnall_levels)
nf = 2 # 2 f-electrons means we're dealing with Pr
Pr = dieke.RareEarthIon(nf)
cfparams = dieke.readLaF3params(nf)
# Number of levels and states
numLSJ = Pr.numlevels()
numLSJmJ = Pr.numstates()
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in cfparams.keys():
if k in Pr.FreeIonMatrix:
H0 = H0+cfparams[k]*Pr.FreeIonMatrix[k]
# Add in the crystal field terms
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Pr.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq) # B_{k,-q}
Ckq = Pr.Cmatrix(k, q)
Ckmq = Pr.Cmatrix(k, -q)
# See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
# Diagonalise the result
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
# Assert that they all agree within one wave number
assert(np.max(np.abs(
calc_nrg_levels[0:len(carnall_levels)]-carnall_levels))
< 1.0 )
# Testing Hermitian stuff
ckeys = [
'C20', 'C21', 'C22', 'C40', 'C41', 'C42', 'C43', 'C44', 'C60', 'C61',
'C62', 'C63', 'C64', 'C65', 'C66'
]
for ckey in ckeys:
mike_test = np.matrix(mikemats[ckey])
if np.linalg.norm(herm_test - herm_test.H) < EPS:
print("Mikes %s is Hermitian" % ckey)
else:
print("Mikes %s is not Hermitian" % ckey)
# Read in a a set of crystal field parameters from Er:LaF3
# dieke reads these from (incomplete) carnall89params.xls
cfparams = dieke.readLaF3params(nf)
#change most of the parameters to those in eryso_cf paper
#leave some from carnall89
cfparams['E0'] = 35503.5 #this is ignored
cfparams['ZETA'] = 2362.9
cfparams['F2'] = 96029.6
cfparams['F4'] = 67670.6
cfparams['F6'] = 53167.1
cfparams['B20'] = -149.8
cfparams['B21'] = 420.6 + 396.0j
cfparams['B22'] = -228.5 + 27.6j
cfparams['B40'] = 1131.2
cfparams['B41'] = 985.7 + 34.2j
def test_ErYSO():
"""
Tests that we give the same as Sebastians calcs for ErYSO
(arXiv:1809.01058)
"""
#energy levels from Paper
seb_levels = [15, 47, 75, 130, 199, 388, 462, 508,
6522, 6560, 6583, 6640, 6777, 6833, 6867,
10206, 10236, 10267, 10339, 10381, 10398]
seb_levels = np.array(seb_levels)
nf = 11 # 11 f-electrons means we're dealing with Er
Er = dieke.RareEarthIon(nf)
# Number of levels and states
numLSJ = Er.numlevels()
numLSJmJ = Er.numstates()
cfparams = dieke.readLaF3params(nf)
cfparams['E0'] = 35503.5 #this is ignored
cfparams['ZETA'] = 2362.9
cfparams['F2'] = 96029.6
cfparams['F4'] = 67670.6
cfparams['F6'] = 53167.1
cfparams['B20'] = -149.8
cfparams['B21'] = 420.6+396.0j
cfparams['B22'] = -228.5+27.6j
cfparams['B40'] = 1131.2
cfparams['B41'] = 985.7+34.2j
cfparams['B42'] = 296.8+145.0j
cfparams['B43'] = -402.3-381.7j
cfparams['B44'] = -282.3+1114.3j
cfparams['B60'] = -263.2
cfparams['B61'] = 111.9+222.9j
cfparams['B62'] = 124.7+195.9j
cfparams['B63'] = -97.9+139.7j
cfparams['B64'] = -93.7-145.0j
cfparams['B65'] = 13.9+109.5j
cfparams['B66'] = 3.0-108.6j
cfparams['A'] = 0.005466 #this is ignored
cfparams['Q'] = 0.0716 #this is ignored
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in sorted(cfparams.keys()):
if k in Er.FreeIonMatrix:
print("Adding free ion parameter \'%s\' = %g" % (k, cfparams[k]))
H0 = H0+cfparams[k]*Er.FreeIonMatrix[k]
# Add in the crystal field terms and diagonalise the result
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Er.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq)
Ckq = Er.Cmatrix(k, q)
Ckmq = Er.Cmatrix(k, -q)
#See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
calc_nrg_levels = calc_nrg_levels[::2] # ignore every second element
E0seb = np.min(seb_levels)
seb_levels = seb_levels-E0seb
print(' Jevon Sebastian Difference')
for k in range(len(seb_levels)):
print("%9.1f %9.1f %6.1f"%(np.real(calc_nrg_levels[k]),seb_levels[k],np.real(calc_nrg_levels[k]) - seb_levels[k]))
# This isn't much of a test at the moment because there seems to be
# an issue with the free ion parameters
assert(np.max(np.abs(
calc_nrg_levels[0:len(seb_levels)]-seb_levels))
< 26.0 )
# This is more of a test because it it only looks at the ground multiplet
assert(np.max(np.abs(
calc_nrg_levels[0:8]-seb_levels[0:8]))
< 0.6 )