Mirror nuclei

Mirror nuclei are nuclei where the number of protons of element one (Z₁) equals the number of neutrons of element two (N₂), the number of protons of element two (Z₂) equal the number of neutrons in element one (N₁) and the mass number is the same.

In short, Z₁ = N₂ and Z₂ = N₁.

Examples of mirror nuclei:

• ³H and ³He:   J^π = +1/2
• ¹⁴C and ¹⁴O:   J^π = +0
• ¹⁵N and ¹⁵O:   J^π = −1/2
• ²⁴Na and ²⁴Al:   J^π = +4
• ^24mNa and ^24mAl:   J^π = +1

Pairs of mirror nuclei have the same spin and parity. If we constrain to odd number of nucleons(A) then we find mirror nuclei that differ one another by exchanging a proton by a neutron. Interesting to observe is their binding energy which is mainly due to the strong interaction and also due to Coulomb interaction. Since the strong interaction is invariant to protons and neutrons one can expect these mirror nuclei to have very similar binding energies.^[1][2]

References

1. Cottle, P. D. (2002-01-01). "Excitations in the Mirror Nuclei 32Ar and 32Si". Physical Review Letters. 88 (17). doi:10.1103/PhysRevLett.88.172502.
2. Kamat, Sharmila (2002-04-23). "Focus: Gazing into a Nuclear Mirror". Physics. American Physical Society. Retrieved 2016-04-11.