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Penning trap mass measurements to test three-body forces in atomic nuclei Gallant, Aaron T.


Recent theoretical studies have shown that three-nucleon forces are important for understand- ing neutron-rich nuclei, and for the formation of nuclear shell structure. In particular, theory can not reproduce the N = 28 magic number in ⁴⁸Ca using two-body interactions. This magic number is only reproduced with the inclusion of three-nucleon forces. Further along the calcium isotopic chain, the three-nucleon interaction predicts new magic numbers at N = 32 and 34, while calculations with phenomenological interactions predict a magic number at N = 32, but disagree on the magicity of N = 34. An other theoretical tool that has been under significant pressure since the advent of precision mass measurements is the isobaric multiplet mass equation, in which the binding energies of states in an isobaric multiplet should vary quadratically with the z-projection of the isospin. This is a consequence of the isospin dependent component of the nuclear Hamiltonian and Coulomb interactions. We test the predictions of phenomenological and three-nucleon interactions through mass measurements of ²⁰'²¹Mg, ⁵¹'⁵²Ca, and ⁵¹K with the TITAN Penning trap mass spectrometer. The measured mass excesses were ME(²⁰Mg) = 17477.7(18) keV, ME(²¹Mg) = 10903.85(74) keV, ME(⁵¹Ca) = 36339(23) keV, ME(⁵²Ca) = 34245(61) keV, and ME(⁵¹K) = 22516(13) keV. With the calcium and potassium mass measurements, we show that the calculations with three-nucleon forces are able to correctly predict the two-neutron separation energies. In the A = 20 and 21 isobaric multiplets, neither the phenomenological nor the three-nucleon based interactions are able to reproduce the measured behaviour.

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