Elastic scattering and boron, lithium, and $\alpha$-particle production in the ${}^9\mathrm{Be} + {}^{51}\mathrm{V}$ reaction

Background: Experimental and theoretical investigation of breakup coupling effects due to different cluster structures (${}^8\mathrm{Be}+n$ and ${}^5\mathrm{He}+\alpha$), relative importance of neutron or ${}^5\mathrm{He}/\alpha$ transfer, and their contribution to $\alpha$ production are important to understand reaction mechanism in a weakly bound projectile (${}^9\mathrm{Be}$) near the Coulomb barrier.

Purpose: Breakup coupling effect on elastic scattering and measurement of angular distributions and energy spectra of $\alpha$ particles produced through breakup, transfer, and complete fusion processes to disentangle their relative contributions and to investigate the relative importance of breakup followed by fusion (breakup-fusion) are compared to transfer.

Methods: Elastic scattering, inclusive $\alpha$ production, lithium, and boron production cross sections have been measured for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system above Coulomb barrier energies. Continuum-discretized-coupled-channels (CDCC) breakup coupling effect using ${}^8\mathrm{Be}+n$ and ${}^5\mathrm{He}+\alpha$ cluster configurations have been investigated. Coupled reaction channels (CRC) calculations for $1\mathit{p}, 1\mathit{d}$, and $1\mathit{n}$ stripping and $1\mathit{p}, 1\mathit{d}$ pickup leading to ${}^8\mathrm{Li}+{}^{52}\mathrm{Cr}, {}^7\mathrm{Li}+{}^{53}\mathrm{Cr}, {}^8\mathrm{Be}+{}^{52}\mathrm{V}$, and ${}^{10}\mathrm{B}+{}^{50}\mathrm{Ti}, {}^{11}\mathrm{B}+{}^{49}\mathrm{Ti}$, respectively, were performed and compared with the experimental data. Theoretical calculations for the estimation of various reaction channels contributing to $\alpha$ production have been performed with CDCC and CRC methods using the fresco code.

Results: Global optical model parameters for the ${}^9\mathrm{Be}$ projectile describe the elastic scattering data very well and the optical model fit improves the ${\chi }^2$ slightly. CRC calculations show a major contribution in the production of lithium through $1\mathit{p}, 1\mathit{d}$ stripping and boron through $1\mathit{p}, 1\mathit{d}$ pickup reactions. $\alpha$ production angular and energy distributions are obtained, and direct $\alpha$ production is described with contributions from noncapture breakup, breakup-fusion, and transfer reactions.

Conclusions: Breakup coupling for ${}^5\mathrm{He}+\alpha$ and ${}^8\mathrm{Be}+n$ cluster structures shows a repulsive and attractive coupling effect on elastic scattering, respectively. The ${}^8\mathrm{Be}+n$ cluster structure also shows a dipole polarization effect by suppressing the Coulomb rainbow compared to the ${}^5\mathrm{He}+\alpha$ cluster structure. Kinematic analysis of the $\alpha$ particles energy spectra suggest that $\alpha$ production is dominated by breakup-fusion over cluster transfer. CRC calculations suggest that $1\mathit{p}, 1\mathit{d}$ stripping and pickup reactions are a major contributor to lithium and boron production cross sections.

Figure 1

The typical biparametric $\mathrm{\Delta }E-E_{\mathrm{tot}}$ plot for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system at $E_{\mathrm{lab}}=27.3$ MeV, ${\theta }_{\mathrm{lab}}={40}^{\circ }$.

Figure 2

Elastic scattering angular distribution for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system. The global optical model calculations are shown by solid lines, optical model fitted values are shown by dash-dotted lines, breakup coupling effects using CDCC for $\alpha +{}^5\mathrm{He}$ and $\mathit{n}+{}^8\mathrm{Be}$ clusters are given by dashed and dotted lines, respectively.

Figure 3

Energy spectra of $\alpha$ particles at $E_{\mathrm{lab}}=27.3$ and 25.3 MeV from ${\theta }_{\mathrm{lab}}={20}^{\circ }$ to ${65}^{\circ }$ for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system. The experimental data for total (direct $+$ compound) $\alpha$ production are presented.

Figure 4

Angular distributions of total $\alpha$ production cross-sections at $E_{\mathrm{lab}}$ = 27.3 and 25.3 MeV along with compound nuclear (dash-dotted lines), 1n-transfer (solid lines), n $+ {}^8\mathrm{Be}$ (dashed lines) non-capture breakup, $\alpha + {}^5\mathrm{He}$ (dotted lines) non-capture breakup contributions.

Figure 5

Direct $\alpha$ energy distribution at $E_{\mathrm{lab}}$ = 27.3 MeV for various measured laboratory angles. Positions of breakup, neutron transfer and $\alpha$ transfer is shown by solid, dashed and dotted lines, respectively.

Figure 6

Lithium production angular distribution for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system at (a) 27.3 MeV and (b) 25.3 MeV projectile energies. The ${}^7\mathrm{Li}, {}^8\mathrm{Li}$ production by $1\mathit{p}, 1\mathit{d}$ stripping CRC calculated values are represented by solid and dashed lines, respectively. The calculated values have a major contribution from ${}^7\mathrm{Li}$ production.

Figure 7

Boron production angular distribution for the ${}^9\mathrm{Be}+{}^{51}\mathrm{V}$ system at 27.3 MeV. The CRC calculated values for ${}^{10,11}\mathrm{B}$ production or $1\mathit{p}+1\mathit{d}$ pickup are represented by solid and dashed lines, respectively. The calculated values have a significant contribution for ${}^{10}\mathrm{B}$ production.