Spectroscopic study of ${}^{38}\mathrm{K}$ above the $31.67\mu \mathrm{s}$ isomer

High-spin states of ${}^{38}\mathrm{K}$ above the $31.67\mu \mathrm{s}$ (${\tau }_m$) isomer, populated through the ${}^{12}\mathrm{C}({}^{28}\mathrm{Si},np){}^{38}\mathrm{K}$ reaction with a 110 MeV ${}^{28}\mathrm{Si}$ beam, have been studied by using the Indian National Gamma Array (INGA) facility. Two new levels and four new transitions have been added to the existing level scheme. The spins and parities of most of the levels above the isomer have been assigned, modified, and confirmed from $R_{\mathrm{DCO}}$, $R_{\mathrm{ADO}}$, and linear polarization measurements. The multipole mixing ratios ($\delta$) for a few transitions have been measured. Large-basis shell-model calculations have been performed to understand the microscopic origin of these levels. In our calculations, different particle restrictions in $sd$- and $pf$-shell orbitals were used to reproduce the experimental level energies. Two-nucleon transfer spectroscopic factors have also been calculated for the levels above the isomer to support the new spin and parity assignments. Prediction of collective excitation at high excitation energy in ${}^{38}\mathrm{K}$ is also discussed.

Figure 1

(a) A total projection spectrum of $\gamma$ rays emitted by different nuclei from the present experiment. Background-subtracted coincidence spectra obtained by putting a gate on (b) 328 keV (below the isomer) and (c) 1296 keV (above the isomer) transitions. Transitions marked with $ are from contaminants.

Figure 2

Background-subtracted coincidence spectra obtained by putting a gate on (a) 1796 keV and (b) 2142 keV transitions. Transitions marked with $ are from contaminants.

Figure 3

Partial level scheme of ${}^{38}\mathrm{K}$. Energy levels are given in keV. Newly assigned $\gamma$ transitions and those already observed in light-ion-induced reactions are indicated by $*$ and $\#$, respectively. The spins and parities of the levels below the isomer are taken from Refs. [1, 17]. Since the spin and parity of the 3458 keV level has been established as $7^{+}$ from the results obtained from shell-model calculations, we quote the spin and parity of the levels above the isomer which are confirmed in the present work, without brackets.

Figure 4

Background-subtracted coincidence spectra obtained by putting a gate on (a) 1796 keV (b) 2142 keV, and (c) 1296 keV transitions. The position of the 2286 keV transition in panels (a)–(c) is marked by a dotted line. The background-subtracted coincidence spectrum obtained by putting a gate on the 2286 keV transition is shown in panel (d). These spectra were generated from a ${90}^{\circ }$ vs ${90}^{\circ }$ symmetric matrix.

Figure 5

A schematic representation of (a) DCO and (b) ADO spectra in ${}^{38}\mathrm{K}$. These two spectra (a) and (b) are generated by putting gates on the 1796 keV transition. The ${90}^{\circ }$ spectra have been artificially shifted by 5 keV for a clear view.

Figure 6

Spectra generated from perpendicular and parallel matrices indicating the electric (magnetic) nature of the 2142 keV (1796 keV) transition.

Figure 7

Difference between the experimental $R_{\mathrm{DCO}}$ and theoretical $R_{\mathrm{DCO}}$ values of (a) 972 [ $E2$: $\delta =0$] keV and (b) 1702 [ $E1$: $\delta =-0.002$(1)] keV transitions of ${}^{35}\mathrm{Cl}$ as a function of $\sigma /J$.

Figure 8

Comparison of theoretical (Theo-P1 and Theo-P2) and experimental (Expt.) level energies of positive-parity states in ${}^{38}\mathrm{K}$. All these energies are plotted considering the ground-state energy ($-251.345$ MeV) as zero.

Figure 9

Comparison of theoretical (Theo-N1, Theo-N2, and Theo-N3) and experimental (Expt.) level energies of negative-parity states in ${}^{38}\mathrm{K}$. All these energies are plotted with respect to the ground-state energy ($-251.345$ MeV) as zero.

Figure 10

Calculated spectroscopic factors for (a) $7^{+}$, (b) $8^{+}$, (c) $9^{+}$, and (d) ${10}^{+}$ states in ${}^{38}\mathrm{K}$ to estimate the contribution of the low-lying positive-parity states of the core nucleus, ${}^{36}\mathrm{Ar}$.

Figure 11

Calculated spectroscopic factors for (a) $9^{-}$, (b) ${10}^{-}$, (c) ${11}^{-}$, (d) ${12}^{-}$, and (e) ${13}^{-}$ states in ${}^{38}\mathrm{K}$ to estimate the contribution of the low-lying negative-parity states of the core nucleus, ${}^{36}\mathrm{Ar}$.

Figure 12

Experimental and theoretical $B\left(E3\right)$ values for a few transitions, viz., (a) 4232 keV of ${}^{30}\mathrm{P}$, (b) 4431 keV of ${}^{31}\mathrm{P}$, (c) 5006 keV of ${}^{32}\mathrm{S}$, (d) 4597 keV of ${}^{34}\mathrm{Cl}$, (e) 2418 keV of ${}^{38}\mathrm{Ar}$, and (f) 3597 keV of ${}^{39}\mathrm{K}$, as a function of effective charge.

Figure 13

(a) Calculated excitation energies and (b) $B\left(E2\right)$ values for the positive-parity states generated from 4p-4h excitation in ${}^{38}\mathrm{K}$.