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The Correlation between the the Number of Stable Isotopes and Stable Isomers |
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A remarkable fact of nuclear structure is that the numbers for filled shells, the so-called magic numbers, are the same for protons and neutrons. That leads to the conjecture that the numbers of stable isotopes and stable isomers are same or strong correlated for equal numbers of nucleons.
Here is the scatter diagram of the numbers.
As can be seen there is a little but not much correlation of the two quantities.
The actual correlation coefficient is only 0.38. However the regression equation for the data for nucleon numbers 0 to 82 is
The t-ratio for that regression coefficient is 7.05, suggesting that there is definitely a a relationship between the two stability numbers. But that correlation may be nothing more than that both stability numbers rise with the size of the nuclide and hence the magnitude of the nucleon number.
Here is the data for neutrons.
And here for protons.
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