Structure of chlorine isotopes populated by heavy ion transfer reactions

Neutron-rich chlorine isotopes were populated in the ${}^{40}$Ar+${}^{208}$Pb multiple transfer reaction via the $-1p$ channels in a fragment-$\gamma$ coincident measurement employing the Prisma-Clara setup. New $\gamma$ transitions have been identified and, together with already available data, level schemes have been revised and compared with the results of large-scale $sd-pf$ shell-model calculations. The evolution of the energy splitting between the $s_{1/2}$ and $d_{3/2}$ orbitals and the increased mixing of different proton configurations in the populated Cl isotopic chain have been deduced by inspecting the shell-model wave functions.

Figure 1

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

Figure 2

Doppler corrected $\gamma$-ray spectra for ${}^{37,39,41}$Cl populated in ${}^{40}$Ar+${}^{208}$Pb by detecting the $-1p-2n$, $-1p$, and $-1p+1n$ channels in Prisma and the coincident $\gamma$ rays in Clara. The strongest transitions are labeled with $E_{\gamma }$; see Ref. [38] and Table . Strong $\gamma$ transitions, not labeled in the lower energy part of the spectra, belong to the wrongly Doppler corrected $\gamma$ rays of the heavy partners. The inset displays the enlarged energy region in vicinity of $\sim$3100 keV of ${}^{37}$Cl.

Figure 3

Doppler corrected $\gamma$-ray spectra for ${}^{38,40,42}$Cl populated in ${}^{40}$Ar+${}^{208}$Pb by detecting the $-1p-1n$, $-1p+1n$, and $-1p+3n$ channels in Prisma and the coincident $\gamma$ rays in Clara. The strongest transitions are labeled with $E_{\gamma }$; see Ref. [38] and Table . Strong $\gamma$ transitions, not labeled in the lower energy part of the spectra, belong to the wrongly Doppler corrected $\gamma$ rays of the heavy partners. The insets display the higher energy regions in ${}^{38}$Cl and ${}^{40}$Cl.

Figure 4

The experimental negative and positive parity (left) and SM calculated (PSDPF interaction) negative and positive parity (right) level schemes of ${}^{37}$Cl, populated via the $-1p-2n$ channel. Relative $\gamma$-ray intensities (left) are indicated by the widths of the arrows (see text for dashed lines). Only the states populated 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. [38]. SM calculations (using PSDPF interaction) with energies up to $\sim$5.6 MeV for the positive and up to $\sim$6 MeV for the negative parities are plotted (right).

Figure 5

Experimental negative and positive parity (left) and SM calculated (right) level scheme of ${}^{39}$Cl, populated via the $-1p$ channel. SM calculations have been done by using the SDPF-U interaction in the $0\hslash \omega$ space, therefore only the positive parity states are described and they are plotted with energies up to $\sim 3600$ keV (right). Relative $\gamma$-ray intensities (left) are indicated by the widths of the arrows. Only the states populated in our measurement are plotted (solid lines). The energy, spin and parity of levels, their branching ratios (with tabulated $\gamma$ intensity $I_{\gamma }\ge 10$), and energy of transitions, where known, are as in Ref. [38]. Some of the weaker intensity $\gamma$ rays were not observed in our measurement with sufficient statistical accuracy, thus they are plotted as dashed lines. The state at 2572 keV is tabulated as ${(5/2,7/2,9/2)}^{-}$, where we have preference for $J^{\pi }=9/2^{-}$, the $9/2^{-}$ being a yrast state. The $\gamma$ ray with $E_{\gamma }=1176.4$ keV has been attributed to the $(11/2^{-})\to (7/2^{-})$ transition.

Figure 6

Proton (left panels) and neutron (right panels) occupation probabilities for different orbitals in ${}^{39}$Cl (shaded bars) from the SM (SDPF-U) calculations. The states to which these probabilities correspond are labeled at the far right. Empty bars correspond to the $\pi {\left(d_{5/2}\right)}^6{\left(s_{1/2}\right)}^2{\left(d_{3/2}\right)}^1\otimes \nu {\left(f_{7/2}\right)}^2$ pure configuration.

Figure 7

Experimental negative and positive parity (left) and SM calculated (right) level scheme of ${}^{41}$Cl, populated via the $-1p+2n$ channel. Relative $\gamma$-ray intensities (left) are indicated by the widths of the arrows. Only the levels populated in our measurement are plotted. The energy, spin and parity of levels, their branching ratios (with tabulated $\gamma$ intensity $I_{\gamma }\ge 10$), and energy of transitions, where known, are as in Ref. [38]. SM calculations have been done by using the SDPF-U interaction in the $0\hslash \omega$ space, therefore only the positive parity states are described and they are plotted with energies up to 3000 keV (right).

Figure 8

Experimental (left) and SM calculated (right) level scheme of ${}^{38}$Cl, populated via the $-1p-1n$ channel. Relative $\gamma$-ray intensities (left) are indicated by the widths of the arrows (see text for dashed line). Only the levels populated in our measurement are plotted. The energy, spin and parity of levels, their branching ratios (with tabulated $\gamma$ intensity $I_{\gamma }\ge 10$), and energy of transitions, where known, are as in Ref. [38]. SM calculations have been done by using the SDPF-U interaction in the $0\hslash \omega$ space, therefore only the negative parity states are described and they are plotted with energies up to $\sim 2000$ keV (right).

Figure 9

Experimental [separated in two bands for clarity's sake] (left), and SM calculated (right) level scheme of ${}^{40}$Cl, populated via the $-1p+1n$ channel. Relative $\gamma$-ray intensities (left) are indicated by the widths of the arrows. Only the states observed in our measurement are plotted. The energy, spin and parity of levels, their branching ratios (with tabulated $\gamma$ intensity $I_{\gamma }\ge 10$), and energy of transitions, where known, are as in Ref. [38]. Some of the weaker intensity $\gamma$ rays were not observed in our measurement with sufficient statistical accuracy, thus they are plotted as dashed lines. SM calculations have been done by using the SDPF-U interaction in the $0\hslash \omega$ space, therefore only the negative parity states are described and they are plotted with energies up to $\sim$2800 keV (right).

Figure 10

Experimental (left) and SM calculated (right) level scheme of ${}^{42}$Cl, populated via the $-1p+3n$ channel. SM calculations have been done by using the SDPF-U interaction in the $0\hslash \omega$ space, therefore only the negative parity states are described and they are plotted with energies up to $\sim$1200 keV (right).

Figure 11

Energy splitting, as a funcion of neutron number, between the lowest $1/2^{+}$ and $3/2^{+}$ states in the odd-even chlorine isotopes. The experimental values are denoted with black circles while SM calculated ones are denoted with red squares.

Figure 12

Absolute energy difference between the lowest $1/2^{+}$ and $3/2^{+}$ states in the odd-even chlorine isotopes (filled squares, violet) and excitation energies of the $5/2^{+}$ states (filled circles, black), compared with the energies of the $2^{+}$ states in S isotopes (empty squares, red), as a function of the neutron number.