The Masses of the $T_z=-3/2$ Nuclei $^{27}$P and $^{29}$S

TL;DR

This study uses isochronous mass spectrometry to precisely measure the masses of $^{27}$P and $^{29}$S nuclei, confirming their consistency with the Isobaric Multiplet Mass Equation and providing insights into isospin symmetry and nuclear forces.

Contribution

First precise mass measurements of $^{27}$P and $^{29}$S using isochronous mass spectrometry, and analysis of isospin multiplet mass relations in light $sd$-shell nuclei.

Findings

New mass excess for $^{29}$S: -3094(13) keV, more precise than previous.

Mass of $^{27}$P remeasured as -685(42) keV.

The ratio of Coulomb radius parameters R ≈ 0.96 is consistent across $T=3/2$ multiplets.

Abstract

Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the $T_z=-3/2$ nuclei $^{27}$P and $^{29}$S. The new mass excess value $ME$($^{29}$S) $=-3094(13)$~keV is 66(52)~keV larger than the result of the previous $^{32}$S($^3$He,$^{6}$He)$^{29}$S reaction measurement in 1973 and a factor of 3.8 more precise. The new result for $^{29}$S, together with those of the $T=3/2$ isobaric analog states (IAS) in $^{29}$P, $^{29}$Si, and $^{29}$Al, fit well into the quadratic form of the Isobaric Multiplet Mass Equation IMME. The mass excess of $^{27}$P has been remeasured to be $ME(^{27}$P$)=-685(42)$ 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 $R\approx0.96$ 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 non-conserving forces in theoretical calculations.