Transfer reactions of exotic nuclei including core deformations: ${}^{11}\mathrm{Be}$ and ${}^{17}\mathrm{C}$

Background: Reactions with halo nuclei from deformed regions exhibit important deviations from the inert core $+$ valence picture. Structure and reaction formalisms have recently been extended or adapted to explore the possibility of exciting the underlying core.

Purpose: We will study up to what extent transfer reactions involving halo nuclei ${}^{11}\mathrm{Be}$ and ${}^{17}\mathrm{C}$ can be reproduced with two different models that have previously shown a good success reproducing the role of the core in light halo nuclei.

Methods: We focus on the structure of ${}^{11}\mathrm{Be}$ and ${}^{17}\mathrm{C}$ with two core $+$ valence models: Nilsson and a semimicroscopic particle-rotor model using antisymmetrized molecular dynamic calculations of the cores. These models are later used to study ${}^{16}\mathrm{C}(d,p){}^{17}\mathrm{C}$ and ${}^{11}\mathrm{Be}(p,d){}^{10}\mathrm{Be}$ transfer reactions within the adiabatic distorted wave approximation. Results are compared with three different experimental data sets.

Results: A good reproduction of both the structure and transfer reactions of ${}^{11}\mathrm{Be}$ and ${}^{17}\mathrm{C}$ is found. The Nilsson model provides an overall better agreement for the spectrum and reactions involving ${}^{17}\mathrm{C}$ while the semimicroscopic model is more adequate for ${}^{11}\mathrm{Be}$, as expected, since the ${}^{17}\mathrm{C}$ core is closer to an ideal rotor.

Conclusions: Both models show promising results for the study of transfer reactions with halo nuclei. We expect that including microscopic information in the Nilsson model, following the spirit of the semimicroscopic model, can provide a useful, yet simple framework for studying newly discovered halo nuclei.

Figure 1

Nilsson diagram obtained for ${}^{17}\mathrm{C}$ by diagonalization in the THO basis using the parameters from [5]. Solid lines represent positive-parity levels, while negative-parity levels are represented by dashed lines.

Figure 2

Experimental and calculated energy levels of ${}^{17}\mathrm{C}$. Starting from the left, the second column is the Nilsson model and the third is the PAMD. Experimental values are from Refs. [29, 30].

Figure 3

Radial parts of the wave function obtained for the ground state of ${}^{17}\mathrm{C}$. The panel (a) shows the most relevant components in the Nilsson model according to their quantum numbers $\ell$, $j$, and $\mathrm{\Omega }$. The panel (b) shows the components, both for the Nilsson (solid lines) and PAMD (dashed lines) models, according to $\ell$, $j$, and $I$. Core radius for these two models are indicated with arrows.

Figure 4

Radial part of the wave function obtained for the first-excited state of ${}^{17}\mathrm{C}$. The results of the Nilsson (solid lines) and PAMD (dashed lines) models are compared, the arrows indicate the core radius for each model.

Figure 5

Spectrum obtained for ${}^{11}\mathrm{Be}$ with the Nilsson and the PAMD models calculations compared with the experimental one [33, 34].

Figure 6

Radial parts of the ground-state wave function of ${}^{11}\mathrm{Be}$. Solid and dashed lines correspond, respectively, to the Nilsson and PAMD models. Core radii are marked with arrows.

Figure 7

Radial parts of the continuum wave function for the first ${}^{11}\mathrm{Be}$ resonance. The Nilsson wave function (solid lines) corresponds to an energy of 0.77 MeV above the ${}^{10}\mathrm{Be}\left(0^{+}\right)+n$ threshold, while the result of the PAMD model (dashed lines) is for 1.14 MeV. For both models the core radius is indicated with an arrow.

Figure 8

Angular distribution of the ${}^{16}\mathrm{C}(d,p){}^{17}\mathrm{C}$ reaction at 17.2 MeV/nucleon when the ${}^{17}\mathrm{C}$ first-excited state $1/2_1^{+}$ (a), and second-excited state $5/2_1^{+}$ (b) are populated. The results using the Nilsson and PAMD models are compared with the experimental data [10].

Figure 9

Differential cross section of ${}^{16}\mathrm{C}(d,p){}^{17}\mathrm{C}$ for transfer to all bound states at 17.2 MeV/nucleon. For both models, the sum of the results for all bound states are shown and they are compared with the experimental data [10].

Figure 10

Angular distribution of the ${}^{11}\mathrm{Be}(p,d){}^{10}\mathrm{Be}$ cross section at 26.9 MeV/nucleon when ${}^{10}\mathrm{Be}$ ground state $0^{+}$ (a), and first-excited state $2^{+}$ (b) are populated. The solid lines represent the results applying the different models and they are compared with the experimental data [38].

Figure 11

Differential cross section for the ${}^{11}\mathrm{Be}(p,d){}^{10}\mathrm{Be}$ transfer reaction to ${}^{10}\mathrm{Be}\left(0^{+}\right)$ (a) and ${}^{10}\mathrm{Be}\left(2^{+}\right)$ (b). The calculations for 35.3 MeV/nucleon are compared with the experimental data from GANIL [40].