Interplay between single-particle and collective excitations in argon isotopes populated by transfer reactions

New $\gamma$ transitions have been identified in argon isotopes in ${}^{40}$Ar + ${}^{208}$Pb multiple transfer reactions by exploiting, in a fragment-$\gamma$ measurement, the new generation of magnetic spectrometers based on trajectory reconstruction coupled to large $\gamma$ arrays. The coupling of single-particle degrees of freedom to nuclear vibration quanta was discussed. The interpretation of the newly observed states within a particle-phonon coupling picture was used to consistently follow, via their excitation energies, the evolution of collectivity in odd Ar isotopes. The proposed level schemes are supported by the results of $sd$-$pf$ shell-model calculations, which have been also employed to evaluate the strength functions of the populated states.

Figure 1

Mass distribution of argon isotopes populated in ${}^{40}$Ar $+{}^{208}$Pb at $E_{\mathit{lab}}=$ 255 MeV and at ${\theta }_{\mathit{lab}}=$ 54${}^{\circ }$ in coincidence with $\gamma$ rays. A mass resolution of $\Delta A/A\sim$ 1/160 was obtained. The insert displays the same mass distribution in logarithmic scale.

Figure 2

Doppler corrected $\gamma$-ray spectra for ${}^{40,41,42,43}$Ar populated in ${}^{40}$Ar $+{}^{208}$Pb by detecting the $0n$, $+1n$, $+2n$, and $+3n$ channels in Prisma and the coincident $\gamma$ rays in Clara. The strongest transitions are marked in the figure, with the spin and parity as listed in Ref.[19]. New transitions that have been identified in this work, $(9/2^{-}\to 7/2^{-})$, $(11/2^{-}\to 7/2^{-})$ in ${}^{41}$Ar and ${}^{43}$Ar, and $(6^{+}\to 4^{+})$ in ${}^{42}$Ar, are listed in more details in Table , together with the here preferentially assigned spin $4^{+}$ for the 2413-keV state in ${}^{42}$Ar [$(3^{-},4^{+})$ in Ref.[19]]. The label “Pb” refers to the wrongly Doppler corrected $\gamma$ rays of the heavy partners.

Figure 3

$\gamma$-ray spectra in coincidence with ${}^{42}$Ar zoomed in the range of interest (top panel), and with additional gates (particle-$\gamma$-$\gamma$ coincidences) on 1205–1208-keV (middle panel) or 1150-keV (bottom panel) transitions. The 1208(1)- and 1205(1)-keV lines are in coincidence with each other, and at least one of them, probably both, are in coincidence with the 1150.4(3)-keV line.

Figure 4

The experimental (left) and SM calculated (right) level scheme of ${}^{42}$Ar, populated via $+2n$ channel. Relative $\gamma$-ray intensities (left) are indicated by the width of the arrows. Only $\gamma$ transitions observed in our measurement are plotted. The energy, spin, and parity of levels, their branching ratios, and energy of transitions, where known, are as in Ref.[19]. We propose $\left(6^{+}\right)$ for the new state at 3563 keV, and the spin $\left(4^{+}\right)$ for the 2413-keV state [$(3^{-},4^{+})$ in Ref.[19]]. SM calculations for all positive parity states with the energy up to 3323 keV are plotted (right).

Figure 5

The experimental and SM calculated level scheme of ${}^{41}$Ar populated via the $+1n$ channel for positive parity states (left), negative parity states (middle), and calculated (right) are plotted. Relative $\gamma$-ray intensities (left and middle) are indicated by the width of the arrows. Only $\gamma$ transitions observed in our measurement are plotted. The energy, spin, and parity of levels, the branching ratios, and the energy of transitions, when known, are as in Ref.[19]. For the new levels we propose the following assignments: $(9/2^{-})$ and $(11/2^{-})$. SM calculations for all negative parity states with the energy up to 2119 keV are plotted (right). Positive parity states could not be generated in the chosen 0$\hslash \omega$ valence space.

Figure 6

The experimental and SM calculated level scheme of ${}^{43}$Ar, populated via $+3n$ channel for negative parity states (left and middle) (being the absolute position of the $7/2^{-}$ unknown, only relative position is indicated) and calculated in SM (right) are plotted. Relative $\gamma$-ray intensities (left and middle) are indicated by the width of the arrows. Only $\gamma$ transitions observed in our measurement are plotted. SM calculations for all negative parity states with the energy up to 2000 keV are plotted (right).

Figure 7

The strength functions SF${}^{\mathit{SM}}$(E) calculated in the SM framework. They are displayed as percents of the strength function sum rule integrals in each panel. The top panels display the strength functions of the creation of a neutron in $p_{1/2}$, $p_{3/2}$, $f_{5/2}$, and $f_{7/2}$ on the $0^{+}$ ground state of ${}^{40}$Ar (left) and ${}^{42}$Ar (right). The bottom panels show the strength functions of a neutron in $f_{7/2}$ coupled to the $2^{+}$ state of ${}^{40}$Ar (left) and ${}^{42}$Ar (right) for the states $5/2^{-}$, $7/2^{-}$, and $11/2^{-}$.

Figure 8

Energies of the $2^{+}$ and $11/2^{-}$ states of argon isotopes with $N=$ 20–28. Solid circles are SM calculated energies, open squares are the adopted levels, whereas open triangles correspond to the energies of $11/2^{-}$ in ${}^{41}$Ar and ${}^{43}$Ar from the present work. In the most recent compilation of the ${}^{45}$Ar level properties[31], a level at 1911(5) keV is reported to decay by 100$\%$ to the $7/2^{-}$ ground state. This level is a good candidate for the $11/2^{-}$ state in this nucleus[32, 33], and was added (cross symbol) for completeness. Curves are here only to guide eyes.