Microscopic cluster model for the description of new experimental results on the ${}^{13}\mathrm{C}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{15}\mathrm{C}$ two-neutron transfer at 84 MeV incident energy

The ${}^{13}\mathrm{C}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{15}\mathrm{C}$ reaction is studied at 84 MeV incident energy. Excitation energy spectra and absolute cross-section angular distributions for the strongest transitions are measured with good energy and angular resolutions. Strong selectivity for two-neutron configurations in the states of the residual nucleus is found. The measured cross-section angular distributions are analyzed by exact finite-range coupled reaction channel calculations. The two-particle wave functions are extracted using the extreme cluster and the independent coordinate scheme with shell-model derived coupling strengths. A new approach also is introduced, the microscopic cluster, in which the spectroscopic amplitudes in the center-of-mass reference frame are derived from shell-model calculations using the Moshinsky transformation brackets. This new model is able to describe well the experimental cross section and to highlight cluster configurations in the involved wave functions.

Figure 1

Excitation energy spectrum of the ${}^{13}\mathrm{C}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{15}\mathrm{C}$ reaction at 84 MeV incident energy and ${11}^{\circ }<{\theta }_{\mathrm{lab}}<{12}^{\circ }$. The red-hatched area corresponds to the background that comes from ${}^{12}\mathrm{C}$ impurities in the target. Lines corresponding to the one- $\left(S_n\right)$ and two-neutron $\left(S_{2n}\right)$ separation energies also are indicated.

Figure 2

Experimental cross-section angular distributions for the transitions to the ground state and states at 0.74 and 3.103 MeV in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): extreme cluster calculations (red lines), independent coordinate calculations using the ZBM (green dashed lines) and ps-d-mod (blue dashed-dotted lines) interactions, and two-step sequential DWBA calculations using the ZBM (orange dashed-double-dotted lines) and ps-d-mod (magenta dotted lines) interactions.

Figure 3

Experimental cross-section angular distributions for the transitions to the 4.22 and 4.66 MeV states in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): extreme cluster calculations (red lines), independent coordinate calculations using the ZBM (green dashed lines) and ps-d-mod (blue dashed-dotted lines) interactions, and two-step sequential DWBA calculations using the ZBM (orange dashed-double-dotted lines) and ps-d-mod (magenta dotted lines) interactions.

Figure 4

Experimental cross-section angular distributions for the transitions to the 6.84 and 7.35 MeV states in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): extreme cluster calculations (red lines), independent coordinate calculations using the ZBM (green dashed lines) and ps-d-mod (blue dashed-dotted lines) interactions, and two-step sequential DWBA calculations using the ZBM (orange dashed-double-dotted lines) and ps-d-mod (magenta dotted lines) interactions. (a) Calculations performed assuming $J^{\pi }=7/2^{-}$ for the 6.84 MeV state and $J^{\pi }=9/2^{-}$ for the 7.35 MeV state. (b) $J^{\pi }=9/2^{-}$ for the 6.84 MeV state and $J^{\pi }=7/2^{-}$ for the 7.35 MeV state.

Figure 5

Coupling scheme for (a) direct two-neutron transfer and (b) and (c) sequential two-neutron transfer with the ZBM and ps-d-mod interactions, respectively.

Figure 6

Experimental cross-section angular distributions for the transitions to the ground state and states at 0.74 and 3.103 MeV in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): $1s$ microscopic cluster calculations using the ZBM (green dotted lines) and ps-d-mod (blue dashed-dotted lines) interactions and $1s+1p$ microscopic cluster calculations using the ZBM (red lines) and ps-d-mod (orange dashed lines) interactions.

Figure 7

Experimental cross-section angular distributions for the transitions to the 4.22 and 4.66 MeV states in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): $1s$ microscopic cluster calculations using the ZBM (green dotted lines) and ps-d-mod (blue dashed-dotted lines) interactions and $1s+1p$ microscopic cluster calculations using the ZBM (red lines) and ps-d-mod (orange dashed lines) interactions.

Figure 8

Experimental cross-section angular distributions for the transitions to the 6.84 and 7.35 MeV states in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): $1s$ microscopic cluster calculations using the ZBM (green dotted lines) and ps-d-mod (blue dashed-dotted lines) interactions and $1s+1p$ microscopic cluster calculations using the ZBM (red lines) and ps-d-mod (orange dashed lines) interactions. Left panel: calculations performed assuming $J^{\pi }=7/2^{-}$ for the 6.84 MeV state and $J^{\pi }=9/2^{-}$ for the 7.35 MeV state. Right panel: $J^{\pi }=9/2^{-}$ for the 6.84 MeV state and $J^{\pi }=7/2^{-}$ for the 7.35 MeV state.

Figure 9

Experimental cross-section angular distributions for the transitions to the ground state in ${}^{15}\mathrm{C}$. Theoretical calculations (see the text): (a) coherent sum (red line) of the sequential DWBA calculations (pink dotted-dashed line) and the IC calculation (blue dashed line) using the ZBM interaction; (b) coherent sum (red line) of the DWBA calculation (orange dashed-dotted line) and the $1s+1p$ microscopic cluster calculation (blue dashed line) using the ZBM interaction.