Experiments were carried out at the NSCL in 2014 to measure the mass of ⁴⁸Ar and ⁴⁹Ar via the time-of-flight technique. [1] We can use this new data together with the mass data on the more stable argon isotopes (AME 2012) to make a plot of the odd-even staggering in the masses in terms of the D_n(N) = (-1)^N+1[S_n(N+1)-S_n(N)] where S_n are one neutron separation energies and N are the number of neutrons. The physical interpretation of D_n is relatively simple. [2] The peak at N=28 indicates that there is a shell gap at this neutron number with a value of 4.5 MeV. Away from the shell gap the average value of D_n is proportional to the effective number of m states that can be connected with the nuclear pairing Hamiltonian. The average value below N=28 where the structure is dominated by the f_7/2 orbital with m=8 is about twice the average value above N=28 where the structure is dominated by the p_3/2 orbitals with m=4 . The experimental results are in good agreement with theoretical predictions based on the SDPF-U [3] and SDPF-MU [4] Hamiltonians.

The puzzle lies in the 0⁺ to 2⁺ B(E2) value for ⁴⁶Ar. Usually when then is a shell gap the B(E2) value is reduced relative to the neighboring nuclei. This expectation is in agreement with three consistent and independent Coulomb excitation measurements. [1] However, as shown in Fig. 3 of [5] the theoretical B(E2) with the SDPF-U and SDPF-MU Hamiltonians do not decrease and are almost two times larger than obtained in the Coulomb excitation experiments. (There is a low-statistics lifetime measurement shown in Fig. 3 of [5] that is in agreement with theory.) The deviation between theory and the Coulomb excitation results indicate that the proton-neutron interaction strengths of these shell-model Hamiltonians are too strong. This would have important consequences for the shell-model preditions of properties of the lighter isotones with N=28.

References

[1] Mass Measurements Demonstrate a Strong N=28 Shell Gap in Argon, Z. Meisel et al., Phys. Rev. Lett. 114, 022501 (2015). link to paper

[2] Nuclear Pairing Gap, How Low Can it Go? B. A. Brown, Phys. Rev. Lett. 111, 162502 (2013). link to paper

[3] F. Nowacki and A. Poves, Phys. Rev. C 79, 014310 (2009). link to journal

[4] Shape Transitions in Exotic Si and S Isotopes and Tensor-Force-Driven Jahn-Teller Effect, Y. Utsuno, T. Otsuka, B. A. Brown, M. Honma, T. Mizusaki and N. Shimizu, Phys. Rev. C 86, 051301 (2012). link to paper

[5] Quadrupole Collectivity Beyond N=28: Intermediate-Energy Coulomb Excitation of ^47,48Ar, R. Winkler et al., Phys. Rev. Lett. 108, 182501 (2012). link to paper