A318999 - OEIS

A318999

Number of stable nuclides with neutron excess n, i.e., (neutron number) - (proton number) = n.

0, 0, 0, 0, 0, 0, 0, 2, 13, 16, 12, 5, 9, 7, 9, 4, 9, 5, 10, 9, 10, 6, 8, 4, 8, 3, 6, 3, 7, 4, 6, 6, 10, 5, 9, 2, 7, 3, 7, 5, 7, 3, 8, 5, 6, 3, 4, 4, 4, 2, 3, 3, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0

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OFFSET

-8,8

COMMENTS

Radioactive nuclides with a half-life of 700 million years or greater (i.e., half-life longer than or equal to that of uranium-235) are included.

n = -8 represents the most proton-rich nuclide known (nickel-48), n = 61 represents the most neutron-rich nuclides known, although there are many unconfirmed nuclides with neutron excess 62 or 64.

Sum_{n=-8..61} a(n) = 286, which is the number of known stable nuclides.

Note that if a nuclide has Z protons and N neutrons then its mass number is A = Z + N while its neutron excess is D = N - Z, so A == D (mod 2). This means that the total number of stable nuclides with an even neutron excess is 176 (the same as that of stable nuclides with an even mass number), while for odd mass number it's 110.

The only odd k such that a(k) > 5 are a(13) = a(23) = 6, a(5) = 7, a(11) = 9 and a(1) = 16, while there are only 6 even numbers such that a(k) <= 5.

LINKS

Table of n, a(n) for n=-8..61.

Wikipedia, Table of nuclides.

Wikipedia, Isodiapher.

EXAMPLE

Stable nuclides with neutron excess n:

n = -1: hydrogen-1, helium-3;

n = 3: chlorine-37, potassium-41, calcium-43, scandium-45, titanium-47;

n = 17: cadmium-113, indium-115, tin-117.

CROSSREFS

Cf. A179301 (proton number), A318997 (mass number), A318998 (neutron number).