Isobaric multiplet mass equation in the $A=31,T=3/2$ quartets

Background: The observed mass excesses of analog nuclear states with the same mass number $A$ and isospin $T$ can be used to test the isobaric multiplet mass equation (IMME), which has, in most cases, been validated to a high degree of precision. A recent measurement [Kankainen et al., Phys. Rev. C 93, 041304(R) (2016)] of the ground-state mass of ${}^{31}\mathrm{Cl}$ led to a substantial breakdown of the IMME for the lowest $A=31,T=3/2$ quartet. The second-lowest $A=31,T=3/2$ quartet is not complete, due to uncertainties associated with the identity of the ${}^{31}\mathrm{S}$ member state.

Purpose: Our goal is to populate the two lowest $T=3/2$ states in ${}^{31}\mathrm{S}$ and use the data to investigate the influence of isospin mixing on tests of the IMME in the two lowest $A=31,T=3/2$ quartets.

Methods: Using a fast ${}^{31}\mathrm{Cl}$ beam implanted into a plastic scintillator and a high-purity Ge $\gamma$-ray detection array, $\gamma$ rays from the ${}^{31}\mathrm{Cl}\left(\beta \gamma \right){}^{31}\mathrm{S}$ sequence were measured. Shell-model calculations using USDB and the recently-developed USDE interactions were performed for comparison.

Results: Isospin mixing between the ${}^{31}\mathrm{S}$ isobaric analog state (IAS) at 6279.0(6) keV and a nearby state at 6390.2(7) keV was observed. The second $T=3/2$ state in ${}^{31}\mathrm{S}$ was observed at $E_x=7050.0\left(8\right)$ keV. Calculations using both USDB and USDE predict a triplet of isospin-mixed states, including the lowest $T=3/2$ state in ${}^{31}\mathrm{P}$, mirroring the observed mixing in ${}^{31}\mathrm{S}$, and two isospin-mixed triplets including the second-lowest $T=3/2$ states in both ${}^{31}\mathrm{S}$ and ${}^{31}\mathrm{P}$.

Conclusions: Isospin mixing in ${}^{31}\mathrm{S}$ does not by itself explain the IMME breakdown in the lowest quartet, but it likely points to similar isospin mixing in the mirror nucleus ${}^{31}\mathrm{P}$, which would result in a perturbation of the ${}^{31}\mathrm{P}$ IAS energy. USDB and USDE calculations both predict candidate ${}^{31}\mathrm{P}$ states responsible for the mixing in the energy region slightly above $E_x=6400$ keV. The second quartet has been completed thanks to the identification of the second ${}^{31}\mathrm{S} T=3/2$ state, and the IMME is validated in this quartet.

Figure 1

Residuals for the quadratic IMME fit of the lowest $A=31,T=3/2$ quartet (Tables 4 and 5) after accounting for the observed isospin mixing in ${}^{31}\mathrm{S}$.

Figure 2

Isospin mixing matrix element, including $1\sigma$ confidence band, of a hypothetical state engaged in isospin mixing with the ${}^{31}\mathrm{P}$ IAS at 6381 keV as a function of the observed excitation energy of the second state. The band is derived under the assumption that the IMME provides a good fit of the data after accounting for isospin mixing. The dotted (left) and dot-dashed (right) lines show the $1\sigma$ bounds obtained using this prediction when the USD mixing matrix element and 6461-keV state energy, respectively, are used as inputs.

Figure 3

High-energy portion of the ${}^{31}\mathrm{Cl}\beta$-coincident $\gamma$ spectrum obtained in Ref. [38]. The transitions from the IAS at 6279 keV, the state at 6390 keV, and the $J^{\pi }=1/2^{+} {}^{31}\mathrm{S}$ state at 7050 keV to the ground state are all labeled with a vertical line. The peak marked with an asterisk at 6539 keV is the first escape peak corresponding to the 7050-keV transition. The peak at 6791 keV is the sum peak between the strong 6280-keV photopeak [38] and the 511 keV annihilation photopeak. The peak at 6255 keV is a photopeak corresponding to a transition from a $T=1/2 {}^{31}\mathrm{S}$ state to the ground state.

Figure 4

Residuals for the quadratic IMME fit of the second-lowest $A=31,T=3/2$ quartet (Tables 7 and 8).