Role of direct mechanism in two-nucleon $T=0$ transfer reactions in light nuclei using the $({}^6\mathrm{Li},\alpha )$ probe

Background: Two-nucleon transfer reactions provide a unique tool to understand the correlation between nucleon pairs. Two-nucleon $(pp,$ $nn$, and $np)$ transfer reactions can occur via isoscalar $(T=0,$ $S=1)$ or isovector $(T=1,$ $S=0)$ processes. In particular, the isoscalar pair transfer can be induced by the $(\alpha ,d)$ or $({}^6\mathrm{Li},\alpha )$ probes. In the past, most of the isoscalar $np$-transfer studies were performed with the $(\alpha ,d)$ reaction, but this probe is strongly momentum mismatched with respect to other two-nucleon transfer reactions.

Purpose: We aim to investigate the interplay between direct and sequential reaction mechanisms from the analysis of experimental $({}^6\mathrm{Li},\alpha )$ angular distributions in light targets.

Method: Differential cross sections of $({}^6\mathrm{Li},\alpha )$ reactions at a beam energy of 20 MeV were measured with ${}^{12}\mathrm{C}$ and ${}^{19}\mathrm{F}$ targets. The interplay between direct and sequential transfer mechanisms in the experimental angular distributions was investigated with coupled-reaction-channels calculations.

Results: The experimental angular distributions of isoscalar $np$ transfer were compared with theoretical calculations assuming a direct or a sequential reaction mechanism. Direct $np$-transfer calculations describe successfully most of the angular distributions. The sequential transfer mechanism is about two orders of magnitude smaller than the direct process.

Conclusions: The present results suggest a significant $np$ correlation in the ${}^{12}\mathrm{C}({}^6\mathrm{Li},\alpha ){}^{14}\mathrm{N}^{*}$ and ${}^{19}\mathrm{F}({}^6\mathrm{Li},\alpha ){}^{21}\mathrm{Ne}^{*}$ reactions. Despite the relatively low cross section for the reactions with the asymmetric ${}^{19}\mathrm{F}$ target, the direct transfer mechanism remains dominant over the sequential process. Further studies including measurements with other asymmetric $sd$-shell nuclei will be required to fully understand the isoscalar and isovector $np$-transfer mechanism in this nuclear region.

Figure 1

(a) Particle identification spectrum for the ${}^6\mathrm{Li}+{}^{12}\mathrm{C}$ collision obtained from a telescope detector at ${27}^{\circ }$ in the laboratory system. $E_{\text{T}}$ corresponds to the total energy deposited in the telescope detector, which is given by $\mathrm{\Delta }E+E_R$. (b) The projected energy of the $\alpha$ particles in the excitation energy of the ${}^{14}\mathrm{N}$ residual nucleus.

Figure 2

Single-channel calculations for the ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{12}\mathrm{C}$ reaction at 20 MeV incident energy. (i) the elastic-scattering data of the present work. (ii) the elastic-scattering data from Ref. [22]. (a) and (b) are the same figure but plotted with different ranges.

Figure 3

Single-channel calculations for the ${}^{19}\mathrm{F}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{19}\mathrm{F}$ reaction at 20 MeV incident energy. (a) and (b) are the same figure but plotted with different ranges.

Figure 4

Coupling scheme considered for the projectile and target overlaps in the ${}^{12}\mathrm{C}({}^6\mathrm{Li},\alpha ){}^{14}\mathrm{N}$ reaction.

Figure 5

Elastic-scattering angular distribution, for the ${}^6\mathrm{Li}+{}^{12}\mathrm{C}$ collision, obtained from CRC calculations (a). The inelastic-scattering angular distribution for the projectile excitation to the first $3^{+}$ (2.19 MeV) state was obtained from the CRC calculations (b). The inelastic scattering data were extracted from Ref. [22].

Figure 6

Experimental angular distributions of the ${}^{12}\mathrm{C}({}^6\mathrm{Li},\alpha ){}^{14}\mathrm{N}$ reaction for several bound states in ${}^{14}\mathrm{N}$. The curves are the prediction from CRC calculations. See text for details.

Figure 7

The contribution of the intrinsic $s$ and $np$ wave functions of the deuteron valence for the transfer differential cross section of the ${}^4\mathrm{He}_{\mathrm{g}.\mathrm{s}.}\left(0^{+}\right)+{}^{14}\mathrm{N}_{4.92}\left(0^{-}\right)$ channel. See text for details.

Figure 8

Experimental angular distributions of the ${}^{12}\mathrm{C}({}^6\mathrm{Li},\alpha ){}^{14}\mathrm{N}$ reaction for several unbound states in ${}^{14}\mathrm{N}$ (above the proton separation energy, $S_p=7.55$ MeV). The curves are the prediction from CRC calculations. Other components (o.c.) such as the $4^{-}$ (12.41 MeV), $4^{-}$ (12.42 MeV), and $3^{-}$ (12.70 MeV) unbound states were included in the angular distribution at 12.5 MeV (f). See text for details.

Figure 9

Elastic-scattering angular distribution, for the ${}^6\mathrm{Li}+{}^{19}\mathrm{F}$ collision, obtained from CRC calculations.

Figure 10

Coupling scheme considered for the projectile and target overlaps in the ${}^{19}\mathrm{F}({}^6\mathrm{Li},\alpha ){}^{21}\mathrm{Ne}$ reaction.

Figure 11

Experimental angular distributions of the ${}^{19}\mathrm{F}({}^6\mathrm{Li},\alpha ){}^{21}\mathrm{Ne}$ reaction populating a few states in ${}^{21}\mathrm{Ne}$. The curves are the prediction from CRC calculations. Note that the lower angular distributions at 2.7 (c) and 4.5 MeV (e) were scaled by factors of 20 and 3, respectively. Other components (o.c.) such as the $11/2^{+}$ (4.43 MeV) and the $3/2^{-}$ (4.72 MeV) excited ${}^{21}\mathrm{Ne}$ states around 4.5 MeV were included in the calculation (e). See text for details.

Figure 12

Comparison between the direct and sequential $np$-transfer mechanisms of the $np$-cluster angular distribution for the ${}^{19}\mathrm{F}({}^6\mathrm{Li},{}^4\mathrm{He}_{\mathrm{g}.\mathrm{s}.}){}^{21}\mathrm{Ne}_{\mathrm{g}.\mathrm{s}.}$ (a) and ${}^{12}\mathrm{C}({}^6\mathrm{Li},{}^4\mathrm{He}_{\mathrm{g}.\mathrm{s}.}){}^{14}\mathrm{N}_{\mathrm{g}.\mathrm{s}.}$ (b) reactions.

Figure 13

Comparison of $np$-transfer probes. The height of the histogram bars corresponds to the ratio between the angular-integrated cross section of the excited state and the ground state. The $({}^3\mathrm{He},p)$ data (a) were extracted from Ref. [47], and the $(\alpha ,d)$ data (b) from Ref. [48].

Figure 14

Comparison of states populated in the mirror nuclei ${}^{21}\mathrm{Na}$ (a) and ${}^{21}\mathrm{Ne}$ (b) via $nn$-transfer and $np$-transfer reactions, respectively. The height of the histogram bars corresponds to the ratio between the angular-integrated cross section of the excited state and the ground state. The ${}^{23}\mathrm{Na}(p,t){}^{21}\mathrm{Na}$ data was extracted from Ref. [51].