Proton-hole states in the $N=30$ neutron-rich isotope ${}^{49}\mathrm{K}$

Excited states in the $N=30$ neutron-rich isotope ${}^{49}\mathrm{K}$ have been studied using multinucleon transfer reactions with thin targets and the PRISMA-CLARA spectrometer combined with thick-target $\gamma$-coincidence data from Gammasphere. The $d_{3/2}$ proton-hole state is located 92 keV above the $s_{1/2}$ ground state, and the proton-particle $f_{7/2}$ state is suggested at 2104 keV. Three other levels are established as involving the coupling to $2^{+}$ of two neutrons above the $N=28$ shell. The measured or estimated lifetimes served to reinforce the interpretation of the observed level structure, which is found to be in satisfactory agreement with shell-model calculations.

Figure 1

$\gamma$ spectra measured in coincidence with the PRISMA-CLARA spectrometer. Inserts show selection of the mass window from the distribution of potassium isotopes. (a) Low-energy part of the $\gamma$-ray spectrum obtained for ${}^{47}\mathrm{K}$. Indicated lines were known from thick-target experiments [12]. Note the absence of an intense 1660 keV transition due to the 7 ns half-life of the corresponding state. (b) $\gamma$-ray spectrum associated with ${}^{49}\mathrm{K}$. All indicated lines are observed for the first time.

Figure 2

Selected parts of coincidence spectra obtained from triple-$\gamma$ coincidence data in thick-target experiment ${}^{238}\mathrm{U}+$ 330 MeV ${}^{48}\mathrm{Ca}$. Double-gate energies are indicated.

Figure 3

${}^{49}\mathrm{K}$ level scheme established in the present study. For the 1011 keV transition, the alternative placement as feeding the ground state is possible. Indicated as tentative, the spin-parity assignments are strongly supported by several experimental facts as discussed in the text. The theoretically calculated level energies using the large space shell-model approach (see text) are shown to the right.

Figure 4

$\gamma$-ray spectrum of ${}^{49}\mathrm{K}$ obtained in plunger experiment devoted to measure lifetimes in the ps range. The spectrum was obtained by summing all runs performed with various target-degrader distances. The observed clear enhancement of the 92 keV line intensity compared to that in Fig. 1b indicates a state lifetime in the ns range. Broad lines at 575 and 771 keV have two components arising from decays before and after plunger degrader.

Figure 5

Doppler-corrected $\gamma$-ray spectra showing the 575 and 771 keV lines at various target-degrader distances as indicated in (a)–(c). Separation of components arising from $\gamma$ emission before (shifted to low energy) and after (properly corrected) the degrader foil served to form ratios $R=I_{\mathrm{after}}/(I_{\mathrm{before}}+I_{\mathrm{after}})$ used to determine lifetimes (see inserts).

Figure 6

Systematics of the lowest $1/2^{+}$, $3/2^{+}$, and $7/2^{-}$ states in a series of potassium isotopes including the presently obtained ${}^{49}\mathrm{K}$ results.