Coherent coupled-reaction-channels analysis of existing and new $p$ + ${}^9\mathrm{Be}$ data between 1.7 and 15 MeV/nucleon

New data for the elastic scattering of ${}^9\mathrm{Be}$ from protons were obtained and analyzed together with data from the literature in a coherent coupled-reaction-channels approach. The new measurements were performed in inverse kinematics at 15, 22 and 51 MeV (1.67, 2.44, and 5.67 MeV/nucleon) by detecting the heavy ejectile in the MAGNEX spectrometer. This enabled an almost full angular distribution to be obtained, extending the results to forward angles where calculated values coincide and give the opportunity of proper normalization. Previous inconsistencies in absolute normalization between different data sets are removed. Standard collective model form factors fail to reproduce the inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$, suggesting that a more sophisticated approach based on the cluster structure of ${}^9\mathrm{Be}$ is required to describe this process.

Figure 1

Reconstructed $E\text{−}\theta$ correlation plot for ${}^9\mathrm{Be}+p$ at a ${}^9\mathrm{Be}$ projectile energy of 51 MeV. The two kinematical solutions of the reaction were obtained in two different runs with two sets of magnetic fields. The plot shows the superposition of these runs, designated by different colors. The solid black line represents the theoretical prediction which describes adequately the data, giving further support to the accuracy of the spectrum reconstruction.

Figure 2

Schematic of the coupling scheme used in the CRC calculations.

Figure 3

(a) Elastic scattering differential cross section and (b) analyzing power angular distributions for 15 MeV protons incident on ${}^9\mathrm{Be}$. The open blue squares denote the data of Ref. [13] and the filled red circles the data of Ref. [15] renormalized by a factor of 0.85. The full curves denote the result of the CRC calculation described in the text. (c) and (d) As for (a) and (b) but for the inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$. Angular distributions of the differential cross section for the ${}^9\mathrm{Be}(p,d){}^8\mathrm{Be}$ reaction leading to (e) the 0.0 MeV $0^{+}$ and (f) the 3.03 MeV $2^{+}$ states of ${}^8\mathrm{Be}$. The open red circles denote the data of Ref. [14] and the solid curves the result of the CRC calculation described in the text.

Figure 4

(a) Elastic scattering differential cross section and (b) analyzing power angular distributions for 10 MeV protons incident on ${}^9\mathrm{Be}$. (c) Angular distribution for inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$ and (d) for the ${}^9\mathrm{Be}(p,d){}^8\mathrm{Be}$ reaction leading to the 0.0 MeV $0^{+}$ state of ${}^8\mathrm{Be}$ for 10 MeV protons incident on ${}^9\mathrm{Be}$. (e)–(h) As for (a)–(d) but for 9 MeV protons. The filled red circles denote the data of Ref. [15], renormalized by a factor of 0.85, the open blue circles the data of Ref. [23], and the filled green squares the data of Ref. [24], renormalized by a factor of 0.75. The full curves denote the results of the CRC calculations described in the text.

Figure 5

(a) Elastic scattering differential cross section and (b) analyzing power angular distributions for 8 MeV protons incident on ${}^9\mathrm{Be}$. (c) Angular distribution for inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$ and (d) for the ${}^9\mathrm{Be}(p,d){}^8\mathrm{Be}$ reaction leading to the 0.0 MeV $0^{+}$ state of ${}^8\mathrm{Be}$ for 8 MeV protons incident on ${}^9\mathrm{Be}$. (e)–(h) As for (a)–(d) but for 7 MeV protons. The filled red circles denote the data of Ref. [15], renormalized by a factor of 0.85, the open blue circles the data of Ref. [23], and the filled green squares the data of Ref. [24], renormalized by a factor of 0.75. The open magenta diamonds denote the 8 MeV elastic scattering data of Blieden et al. [21] while the maroon stars denote the 7 MeV $(p,d)$ data of Yanuba et al. [25]. The full curves denote the results of the CRC calculations described in the text.

Figure 6

(a) Elastic scattering differential cross section and (b) analyzing power angular distributions for 6 MeV protons incident on ${}^9\mathrm{Be}$. (c) Angular distribution for inelastic scattering to the 2.43 MeV $5/2^{-}$ state of ${}^9\mathrm{Be}$ and (d) for the ${}^9\mathrm{Be}(p,d){}^8\mathrm{Be}$ reaction leading to the 0.0 MeV $0^{+}$ state of ${}^8\mathrm{Be}$ for 6 MeV protons incident on ${}^9\mathrm{Be}$. (e)–(h) As for (a)–(d) but for 5 MeV protons. The filled red circles denote the data of Ref. [15], renormalized by a factor of 0.8, the open blue circles the data of Ref. [23], and the filled green squares the data of Ref. [24], renormalized by a factor of 0.75. The open magenta diamonds denote the 6 MeV data of Blieden et al. [21] renormalized by a factor of 0.75 while the filled blue squares denote the 6.1 MeV data of Ishiwari [22]. The full curves denote the results of the CRC calculations described in the text.

Figure 7

Angular distributions for 3 MeV protons incident on ${}^9\mathrm{Be}$ for (a) the elastic scattering differential cross section, (b) the elastic scattering analyzing power, and (c) the differential cross section for the ${}^9\mathrm{Be}(p,d){}^8\mathrm{Be}$ reaction leading to the 0.0 MeV $0^{+}$ state of ${}^8\mathrm{Be}$. The open blue circles denote the data of Ref. [23], renormalized by a factor of 0.8 for the cross section, while the violet triangles denote the data of Morita et al. [32]. The full curves denote the results of the CRC calculations described in the text.

Figure 8

Present data denoted by the filled black circles: Angular distributions of the ${}^9\mathrm{Be}+p$ elastic scattering differential cross in inverse kinematics at equivalent incident proton energies of (a) 5.70 MeV, (b) 2.46 MeV, and (c) 1.68 MeV. The full curves denote the results of the CRC calculations described in the text.