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Description
The yrast negative-parity states of the T$=1/2$ mirror pairs $^{35}$Cl–$^{35}$Ar and $^{39}$K–$^{39}$Ca display Mirror Energy Differences (MEDs) exceeding 200 keV at high spin ($J$ ≥ 11/2⁻) [1,2]. This is in contrast to the <100 keV deviations characteristic of positive-parity states in this mass region. Existing shell-model decompositions attribute the high-$J$ enhancement to the electromagnetic spin–orbit (EMSO) term, which is single-particle in origin and maximized for the cross-shell $0d_{3/2}\to 0f_{7/2}$ excitation [1,3]. Direct experimental constraints on the single-particle content of the relevant intruder states have remained limited.
Three single-neutron transfer measurements addressing this question will be discussed and reported. Simultaneous $^{34g}$Cl($d$,$p$) and $^{34m}$Cl($d$,$p$) reactions were performed with the HELIOS spectrometer and two different ground-state to isomeric-state beams produced by the ATLAS in-flight facility [4]. The $^{38}$K($d$,$p$)$^{39}$K reaction was also measured with the ISOLDE Solenoid Spectrometer (ISS) located at the HIE-ISOLDE facility at CERN. In both cases, angular distributions were extracted from the proton spectra and analyzed within a DWBA framework, confirming $\ell=3$, $0f_{7/2}$ neutron transfer to the yrast 11/2⁻ and 13/2⁻ states in $^{35}$Cl and $^{39}$K. The aligned 13/2⁻ configuration carries the dominant single-neutron strength in both mirrors. Setting C$^2$S(13/2⁻) = 1, the values for the lower-$J$ negative-parity states ($J$ = 7/2⁻ – 11/2⁻) were found to have C$^2$S $\lesssim 0.2$. Therefore, the extracted spectroscopic factors have a direct correlation with the magnitudes of the experimental MEDs, consistent with the aligned ($0d_{3/2}$)$^2$($0f_{7/2}$)$^1$ neutron configuration and the EMSO term as the structural origin of the large high-$J$ MEDs in the $A=35$ and $A=39$ $T=1/2$ systems.
[1] F. Della Vedova et al., Phys. Rev. C 75, 034317 (2007).
[2] J. Ekman et al., Phys. Rev. Lett. 92, 132502 (2004).
[3] M. A. Bentley et al., Phys. Rev. C 92, 024310 (2015).
[4] C. R. Hoffman et al., Nucl. Instrum. Meth. A 1023, 166612 (2022).