Inconsistancy between xray_edge() and f2_chantler()

[luriol]

I'm not sure if I'm misunderstanding the database, or if this is really an issue. I would expect that the value of the "jump ratio" given by the xray_edge() function, should give the same jump ratio as when it is calculated directly from the ratio of the cross sections given by the f2_chanler() function. However these values differ by more than would be expected. See the code snippet below and the associated output. Does this indicate an inconsistency in the database?

import numpy as np import xraydb as xdb (energy, yfield, jump_ratio) = xdb.xray_edge('W','L1') Jump = xdb.f2_chantler('W',energy+50)/xdb.f2_chantler('W',energy-50) print('jump_ratio = {0:7.3f} jump calculated from f2 = {1:7.3f}'.format( jump_ratio,Jump))

jump_ratio = 1.155 jump calculated from f2 = 1.137

[newville]

@luriol Hi, I think that a few things are going on.

First, the "jump ratio" in XrayDB is from the Elam et al tables, and I believe that is from extrapolating the XCOM data (ie, the values from mu_elam()), while f2_chantler is from the FFAST/Chantler databases. So, the tabulations are just from different databases. I am inclined to believe that FFAST/Chantler is generally more accurate in the 1 to 100 keV range, but they should be close.

Second, f2 should be proportional to mu*E, so maybe the comparison in jumps should be with mu_chantler or f2_chantler/E - that should be a very small effect.

I think the biggest effect here is that the Chantler data is broadened (with a core-level width Gamma of around 5.6 eV, I believe), which might be a noticeable effect when using +/-50 eV.

If I do this:

import numpy as np
import xraydb as xdb
import matplotlib.pyplot as plt

(e_l3, yfield, jump_l3) = xdb.xray_edge('W','L3')
(e_l2, yfield, jump_l2) = xdb.xray_edge('W','L2')
(e_l1, yfield, jump_l1) = xdb.xray_edge('W','L1')

print(f"W L3, L2, L1: E= {e_l3}, {e_l2}, {e_l1}, Jump = {jump_l3}, {jump_l2}, {jump_l1}")

(energy, yfield, jump_ratio) = xdb.xray_edge('W','L1')


print(f'jump_ratio reported for W L1 = {jump_ratio:7.3f}')

jump_mue = xdb.mu_elam('W',energy+1)/xdb.mu_elam('W',energy-1)
print(f'jump_ratio from mu_elam edge+/-1 eV = {jump_mue:7.3f}')

jump_mue = xdb.mu_elam('W',energy+50)/xdb.mu_elam('W',energy-50)
print(f'jump_ratio from mu_elam edge+/-50 eV = {jump_mue:7.3f}')

jump_muc = xdb.mu_chantler('W',energy+50)/xdb.mu_chantler('W',energy-50)
print(f'jump_ratio from mu_chantler edge+/-50 eV = {jump_muc:7.3f}')

jump_muf2 = xdb.f2_chantler('W',energy+50)/xdb.f2_chantler('W',energy-50)
print(f'jump_ratio from f2_chantler edge+/-50 eV = {jump_muf2:7.3f}')


e = np.linspace(-200, 200, 201) + energy

mu_e = xdb.mu_elam('W', e)
mu_c = xdb.mu_chantler('W', e)
f2_c = xdb.f2_chantler('W', e)
f2_ce = f2_c/e

plt.plot(e, mu_e/mu_e.min(), label='mu_elam')
plt.plot(e, f2_c/f2_c.min(), label='f2_chantler')
plt.plot(e, f2_ce/f2_ce.min(), label='f2_chantler/energy')
plt.plot(e, mu_c/mu_c.min(), label='mu_chantler')

plt.ylabel('f2/f2.min(),  mu / mu.min()')
plt.xlabel('Energy (eV)')
plt.title('f2, mu for W L1')
plt.axvline(energy-50)
plt.axvline(energy+50)
plt.legend()
plt.show()

I get this output

W L3, L2, L1: E= 10207.0, 11544.0, 12100.0, Jump = 2.613, 1.4, 1.15478
jump_ratio reported for W L1 =   1.155
jump_ratio from mu_elam edge+/-1 eV =   1.153
jump_ratio from mu_elam edge+/-50 eV =   1.130
jump_ratio from mu_chantler edge+/-50 eV =   1.125
jump_ratio from f2_chantler edge+/-50 eV =   1.137

and this plot

So, the reported edge jump is pretty consistent with mu_elam() which is not broadened, and when extrapolating right at the edge energy. I think the slight differences in slopes between FFAST/Chantler and XCOM/Elam are probably just from differences in those calculations.

But, I think that also really means that those values for "jump ratio" will tend to be high-ish estimates, especially for L edges as they ignore broadening.

[luriol]

Thanks, that makes sense.