First Penning trap mass measurement of ${}^{36}\mathrm{Ca}$

Background: Isobaric quintets provide the best test of the isobaric multiplet mass equation (IMME) and can uniquely identify higher order corrections suggestive of isospin symmetry breaking effects in the nuclear Hamiltonian. The generalized IMME (GIMME) is a novel microscopic interaction theory that predicts an extension to the quadratic form of the IMME. Only the $A=20,32$ $T=2$ quintets have the exotic $T_z=-2$ member ground state mass determined to high precision by Penning trap mass spectrometry.

Purpose: We aim to establish $A=36$ as the third $T=2$ isobaric quintet with the $T_z=-2$ member ground state mass measured by Penning trap mass spectrometry and provide the first test of the predictive power of the GIMME.

Method: A radioactive beam of neutron-deficient ${}^{36}\mathrm{Ca}$ was produced by projectile fragmentation at the National Superconducting Cyclotron Laboratory. The beam was thermalized and the masses of ${}^{36}\mathrm{Ca}^{+}$ and ${}^{36}\mathrm{Ca}^{2+}$ were measured by the time-of-flight ion cyclotron resonance method in the LEBIT 9.4 T Penning trap.

Results: We measure the mass excess of ${}^{36}\mathrm{Ca}$ to be $\mathrm{ME}=-6483.6\left(56\right)$ keV, an improvement in precision by a factor of 6 over the literature value. The new datum is considered together with evaluated nuclear data on the $A=36$, $T=2$ quintet. We find agreement with the quadratic form of the IMME given by isospin symmetry, but only coarse qualitative agreement with predictions of the GIMME.

Conclusion: A total of three isobaric quintets have their most exotic members measured by Penning trap mass spectrometry. The GIMME predictions in the $T=2$ quintet appear to break down for $A=32$ and greater.

Figure 1

Schematic of the NSCL gas cell and LEBIT facility. For further discussion, see Ref. [22].

Figure 2

Time-of-flight resonance of ${}^{36}\mathrm{Ca}^{2+}$ with 50 ms excitation time. The smooth curve shows the fit of the theoretical curve used to extract ${\nu }_c$ [30].

Figure 3

Mass excess of ${}^{36}\mathrm{Ca}$ determined by measurements of ${}^{36}\mathrm{Ca}^{+}$ and ${}^{36}\mathrm{Ca}^{2+}$ and their $1\sigma$ error bars. The horizontal lines show the $1\sigma$ error band from the AME2016 (dot-dashed red) [11, 15] and this work (solid blue). Note the near overlap of lower-bound lines near ME $\approx -6490$ keV.

Figure 4

$d$ and $e$ coefficients of the $T=2$ quartic IMME. The star points come from GIMME theory [9]. The circular points are from the experimental literature [10, 12] and the square point is the update to the $A=36$ quintet from this work. Those quintets with experimental error bars larger than the figure are omitted. Update to Fig. 3 from Ref. [9].