Isospin purity of $T=1$ states in the $A=38$ nuclei studied via lifetime measurements in ${}^{38}\mathrm{K}$

The Doppler Shift Attenuation Method was used to measure lifetimes for levels in ${}^{38}\mathrm{K}$ at excitation energies of 1698, 2404, 2830, 2996, and 3671 keV, populated using the ${}^{40}\mathrm{Ca}$(d, α)${}^{38}\mathrm{K}$ reaction at a beam energy of 4.5 MeV. Values of 109(29), 95(22), 457(63), 130(40), and 160(50) fs, respectively, were measured and are compared with previous values obtained using different stopping powers. The matrix element for the transition between the $J^{\pi }=2_{T=1}^{+}$ and $0_{T=1}^{+}$ states in this $T_z=0$ nucleus is compared with the analogous transition in the other nuclei in the $T=1$ triplet, ${}^{38}\mathrm{Ca}$ ($T_z=-1$) and ${}^{38}\mathrm{Ar}$ ($T_z=+1$), and with the results of shell-model calculations.

Figure 1

The first excited 2${}_{T=1}^{+}$ states for nuclei in the $A=38$ isobaric triplet.

Figure 2

Matrix elements for the $2_{T=1}^{+}\to 0_{T=1}^{+}$ transition in $T=1$ triplets from $A=22$ to $A=42$. The straight lines correspond to the best fits calculated using the least-squares method. Data are taken from Refs. [1, 2, 3, 4, 5, 6]. For some nuclei ($T_z=1$ and ${}^{30}\mathrm{P}$ ) the error bar is smaller than the data point.

Figure 3

Partial level scheme for ${}^{38}\mathrm{K}$ showing the excited states and transitions observed in this work.

Figure 4

Particle spectra obtained by gating on (a) the 2700 keV, (b) the 1568 keV, and (c) the 329 keV transitions depopulating the 2830, 1698, and 459 keV levels, respectively.

Figure 5

The measured energy of the 1944 keV transition from the 2404 keV state as a function of cos θ. The straight line corresponds to the best fit.

Figure 6

Positive-parity levels below 2.5 MeV in ${}^{38}\mathrm{K}$ compared with the results of shell-model calculations (see text for details).

Figure 7

Comparison between the empirical matrix elements for the $2_{T=1}^{+}\to 0_{T=1}^{+}$ transition for the $A=38$ isobaric triplet and the results of shell-model calculations using (left) the USD interaction and (right) the IOKIN.SDPF.SI35 interaction and allowing two particles across the $A=40$ shell gap. The error bar for the $T_z=1$ data point (${}^{38}\mathrm{Ar}$) is smaller than the symbol.