Evidence for a breakdown of the isobaric multiplet mass equation: A study of the $A=35,T=3/2$ isospin quartet

Mass measurements on radionuclides along the potassium isotope chain have been performed with the ISOLTRAP Penning trap mass spectrometer. For ${}^{35}\mathrm{K}$ ($T_{1/2}=178$ ms) to ${}^{46}\mathrm{K}$ ($T_{1/2}=105$ s) relative mass uncertainties of $2\times {10}^{-8}$ and better have been achieved. The accurate mass determination of ${}^{35}\mathrm{K}$ ($\delta m=0.54$ keV) has been exploited to test the isobaric multiplet mass equation for the $A=35,T=3/2$ isospin quartet. The experimental results indicate a deviation from the generally adopted quadratic form.

Figure 1

Compilation for the cubic parameter $d$ of the IMME [8, 9, 10, 11]. Top: Values of $d$ as a function of the mass value $A$. Bottom: Relative uncertainty of $d$ where the shaded areas indicate the 1σ, 2σ, and 3σ agreement.

Figure 2

Sketch of the experimental setup of the ISOLTRAP mass spectrometer. Microchannel plate (MCP) detectors are used to monitor the ion-beam transfer (MCP1–2). A newly implemented channeltron detector [22], which can be used in place of MCP3, records the time-of-flight (TOF) resonance curve for the cyclotron frequency determination. The inset shows a resonance curve for ${}^{35}{\mathrm{K}}^{+}$ (with excitation duration of 400 ms) together with the fit of the theoretically expected line shape to the data points [23].

Figure 3

Difference of mass-excess values ($D_{\mathrm{lit}}-D_{\exp }$) of the potassium isotopes taken from this work ($D_{\exp }$; see Table ) and the literature [24, 25]. The experimental value of ${}^{39}\mathrm{K}$ results from a consistency check of the ISOLTRAP data (see text). The shaded area represents the uncertainty of the ISOLTRAP values. The differences of the mass-excess values of ${}^{37-39}\mathrm{K}$ are given as a cross-check. For more details refer to the discussion section.

Figure 4

Partially updated compilation of the coefficient $d$ of the cubic term for multiplets, including this work. The four points shown correspond to the $A=33$ and $A=35$ quartets, and to the $A=32$ and $A=36$ quintets for which at least one member has been measured at ISOLTRAP [8, 10]. The two points on the right-hand side (i.e., the $A=35$ quartet and the $A=36$ quintet) arise from the present work.