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Has the latest update to IsotopeData caused a loss of precision?

Posted 1 month ago

In version 14.2, the outputs of IsotopeData that produce fractional answers (e.g., isotope abundances, decay branching ratios), have suffered a change in format (compared to version 13.2). The new format not only is less convenient, but also appears to cause a loss in precision.

For example, in version 13.2, the isotope abundances of lithium-6 and lithium-7 print as 0.0759 and 0.9241, respectively. The abundances of all other lithium isotopes output 0. (with a decimal point). These values agree with other databases.

In version 14.2, the isotope abundances of lithium-6 and lithium-7 print as 0. % (with a red square outline) and 1. x 10^2 %. The abundances of the other lithium isotopes are printed as 0%, without the decimal point or a red outline.

This suggests there has been some rounding that caused some values to lose all precision. It is also worth noting that the version 13.2 outputs, with the simple fractions, were more convenient for calculations.

There is a way to recover something similar to the outputs of version 13.2 in version 14.2, and that is to add 0.0 to the result.

With this trick, in version 14.2, the isotope abundances of lithium-6 and lithium-7 print as 0.0485 and 0.9515, respectively (no more percentages). While these values add to 1, as they should, they are different from the values obtained in version 13.2.

It is possible that these differences are the result of an update of our knowledge of the abundances of the lithium isotopes, but, to my knowledge, other databases have not changed their values. It seems to me that this is the result of an unsuccessful attempt to standardize the reported precision of these data.

There are many similar fractional outputs in this database that are close to zero (many isotopes are extremely rare, so that their abundances will be close to zero, and many others have decay modes that occur extremely seldom, causing very small branching ratios). The concern is that all these outputs will lose accuracy and be reported as zero, and a simple attempt to recover these values seems to lead to incorrect outputs.

Does anybody have an explanation for this? Is this just a bug? Is there a way to control this behavior with some precision or formatting option?

Thanks in advance for your time, Otto Linsuaín

P.S. The outputs mentioned above can be obtained with commands like: IsotopeData["Lithium6","IsotopeAbundance"]

For the branching ratios one should use an unstable isotope, for example: IsotopeData["Neptunium239","BranchingRatios"]

POSTED BY: Otto Linsuain
2 Replies
Posted 1 month ago

Thanks a lot for your reply. This helps a lot. It seems to me that they have tried to incorporate the uncertainty range, which is a good thing, but one can have a poor implementation of a good idea, and it seems that is what has happened here.

The factor of 1.73 may be related to making the assumption of a uniform distribution, as explained here: https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc541.htm

There are serious shortcomings in the implementation:

  1. The default output one gets does not reflect the mean or the range or the scatter of the distribution. One gets 0 and 1, which are very poor approximations.

  2. If one tries to get the best estimate value using, for example, the N function in your reply, one gets the mean of the minimum and the maximum (0.0485 for lithium-6). Normally, the value used for the best estimate for the abundance of lithium-6 is about 0.0759 (the value printed in previous versions), which probably means that the underlying distribution is not symmetric, but this seems to be ignored in the new implementation.

Anyway, thanks a lot again for your input. In a sense, you have put my suspicions on a firmer basis. I really feel I cannot use the new database for any serious calculations.

Best,

Otto LinsuaĆ­n

POSTED BY: Otto Linsuain
Posted 1 month ago

I don't understand how isotopes abundances are determined or how the uncertainties in the measures are modeled probabilistically, But the following comes very close to reproducing the intervals for the isotopes found at https://www.ciaaw.org/lithium.htm:

IsotopeData["Lithium6", "IsotopeAbundance"]/100 // QuantityMagnitude // 
 N@# + 10^-Accuracy[#] 1.73 {-1, 1} &
(*  {0.018917, 0.078083}  -- cf. [0.019, 0.078] (CIAAW) *)

IsotopeData["Lithium7", "IsotopeAbundance"]/100 // QuantityMagnitude // 
 N@# + 10^-Accuracy[#] 1.73 {-1, 1} &
(*  {0.921917, 0.981083}  -- cf. [0.922, 0.981] (CIAAW) *)

I cannot explain the 1.73 scaling factor. It is close, but not very close, to the $z$-score of 1.645, used in say, constructing a 95%-confidence interval. It's closer to $\sqrt{3}$, which means nothing to me.

My understanding extends no farther than the intervals are rather close to the CIAAW intervals, and that the precision in the arbitrary-precision quantities most likely encodes the uncertainty of the value in some form.

POSTED BY: Updating Name
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