Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the $T_z=-3/2$ nuclei ${}^{27}\mathrm{P}$ and ${}^{29}\mathrm{S}$. The new mass excess value $\text{ME}\left({}^{29}\mathrm{S}\right)=-3094\left(13\right)\mathrm{keV}$ is 66(52) keV larger than the result of the previous ${}^{32}\mathrm{S}({}^3\mathrm{He},{}^6\mathrm{He}){}^{29}\mathrm{S}$ reaction measurement in 1973 and a factor of 3.8 more precise. The new result for ${}^{29}\mathrm{S}$ together with those of the $T=3/2$ isobaric analog states in ${}^{29}\mathrm{P}, {}^{29}\mathrm{Si}$, and ${}^{29}\mathrm{Al}$ fit well into the quadratic form of the isobaric multiplet mass equation (IMME). The mass excess of ${}^{27}\mathrm{P}$ has been remeasured to be $\text{ME}\left({}^{27}\mathrm{P}\right)=-685\left(42\right)\mathrm{keV}$. By analyzing the linear and quadratic coefficients of the IMME in the $T_z=-3/2 sd$-shell nuclei, it was found that the ratio of the Coulomb radius parameters is $R\approx 0.96$ and is nearly the same for all $T=3/2$ isospin multiplets. Such a nearly constant $R$ value, apparently valid for the entire light mass region with $A>9$, can be used to set stringent constraints on the isovector and isotensor components of the isospin nonconserving forces in theoretical calculations.

• Received 26 September 2017
• Revised 7 May 2018

DOI:https://doi.org/10.1103/PhysRevC.98.014315