Analysis of the ${}^{16}\mathrm{C}(d,p){}^{17}\mathrm{C}$ reaction from microscopic ${}^{17}\mathrm{C}$ wave functions

We present a semimicroscopic study of the ${}^{16}\mathrm{C}{(d,p)}^{17}\mathrm{C}$ transfer reaction. The ${}^{17}\mathrm{C}$ overlap integrals and spectroscopic factors are obtained from a microscopic cluster model, involving many ${}^{16}\mathrm{C}+n$ configurations. This microscopic model provides a fair description of the ${}^{17}\mathrm{C}$ bound-state energies. The ${}^{16}\mathrm{C}+d$ scattering wave functions are defined in the continuum discretized coupled channel (CDCC) method, where the deuteron breakup is simulated by pseudostates. The transfer cross sections are in good agreement with recent data. We confirm the ${}^{16}\mathrm{C}\left(2^{+}\right)+n$ structure of the ground state, and show that deuteron breakup effects have a significant influence on the cross sections. We study the ${}^{17}\mathrm{C}{(p,d)}^{16}\mathrm{C}$ reverse reaction and suggest that the cross section to the $2^{+}$ state should be large. A measurement of the ground-state cross section would provide a strong test of the microscopic wave functions.

Figure 1

Overlap integrals of the ${}^{17}\mathrm{C}$ bound states with spin $I_1$. The solid and dashed lines correspond to the ${}^{16}\mathrm{C}\left(0^{+}\right)+n$ and ${}^{16}\mathrm{C}\left(2^{+}\right)+n$ configurations, respectively. The labels refer to the $\left(I\ell \right)$ values (see also Table 1).

Figure 2

Elastic ${}^{16}\mathrm{C}+d$ cross section (divided by the Rutherford cross section) with the CDCC wave functions (solid lines) and with the single-channel approximation (dashed lines). The black and red lines correspond to the KD and CH ${}^{16}\mathrm{C}+\text{nucleon}$ optical potentials, respectively. Experimental data are taken from Ref. [34].

Figure 3

${}^{16}\mathrm{C}{(d,p)}^{17}\mathrm{C}$ cross sections to the $1/2^{+}$ (a) and $5/2^{+}$ (b) states. The solid and dashed lines correspond to the full CDCC calculation and to the no-breakup approximation, respectively. Results with the KD and CH ${}^{16}\mathrm{C}+\text{nucleon}$ optical potentials are shown in black and red, respectively. The experimental data are taken from Ref. [19] and transformed from the laboratory frame to the c.m. frame.

Figure 4

Ground-state ($\times 20$) and total ${}^{16}\mathrm{C}{(d,p)}^{17}\mathrm{C}$ cross sections with the KD potential (the CH results are very similar). See caption of Fig. 3.

Figure 5

${}^{17}\mathrm{C}{(p,d)}^{16}\mathrm{C}$ cross sections to the $0^{+}$ and $2^{+}$ states of ${}^{16}\mathrm{C}$ at $E_{\mathrm{c}.\mathrm{m}.}=29.1$ MeV (see text). The black and red lines correspond to the KD and CH ${}^{16}\mathrm{C}+\text{nucleon}$ optical potentials.