Experimental study of the collision ${}^{11}$Be + ${}^{64}$Zn around the Coulomb barrier

In this paper details of the experimental procedure and data analysis of the collision of ${}^{11}\mathrm{Be}{+}^{64}$Zn around the Coulomb barrier are described and discussed in the framework of different theoretical approaches. In a previous work [A. Di Pietro et al., Phys. Rev. Lett. 105, 022701 (2010).], the elastic scattering angular distribution of the collisions ${}^{9,10}\mathrm{Be}{+}^{64}$Zn as well as the angular distribution for the quasielastic scattering and transfer/breakup cross sections for the ${}^{11}\mathrm{Be}{+}^{64}$Zn reaction were briefly reported. The suppression of the quasielastic angular distribution in the Coulomb-nuclear interference angular region observed in the collision of the ${}^{11}$Be halo nucleus with respect to the other two beryllium isotopes was interpreted as being caused by a long-range absorption owing to the long decay length of the ${}^{11}$Be wave function. In this paper, new continuum-discretized coupled-channel calculations of the ${}^{11}\mathrm{Be}{+}^{64}$Zn reaction are reported in the attempt to interpret the effect of coupling with the breakup channels on the measured cross sections. The calculations show that the observed suppression of the Coulomb-nuclear interference peak is caused by a combined effect of Coulomb and nuclear couplings to the breakup channels.

Figure 1

Experimental setup used for the ${}^{10,11}\mathrm{Be}{+}^{64}$Zn experiment.

Figure 2

Elastic scattering angular distributions for the ${}^{10}\mathrm{Be}{+}^{197}$Au system multiplied by 0.1 (open circles) and ${}^{12}\mathrm{C}{+}^{197}$Au (filled circles). See text for details.

Figure 3

Elastic scattering angular distribution for the ${}^9\mathrm{Be}{+}^{64}$Zn system (filled symbols) and ${}^{10}\mathrm{Be}{+}^{64}$Zn system (open symbols). Lines represent the results of the OM analysis (see text for details).

Figure 4

Elastic scattering angular distribution for the ${}^{11}\mathrm{Be}{+}^{64}$Zn system. The solid line represents the results of the OM analysis (see text for details).

Figure 5

Real part of the WS potentials obtained from the best-fit analysis of the ${}^{10}\mathrm{Be}{+}^{64}$Zn elastic scattering data giving equivalent ${\chi }^2$ and listed in Table .

Figure 6

Modulus of the elastic $S$ matrix as a function of the angular momentum for ${}^9\mathrm{Be}{+}^{64}$Zn (dotted line), ${}^{10}\mathrm{Be}{+}^{64}$Zn (dashed line), and ${}^{11}\mathrm{Be}{+}^{64}$Zn (solid line).

Figure 7

Measured quasielastic angular distribution for ${}^{11}\mathrm{Be}{+}^{64}$Zn (symbols), compared with an OM fit of the data (solid line) and a DWBA calculation (dashed line) for the inelastic scattering to the first excited state of ${}^{11}$Be.

Figure 8

Elastic scattering angular distribution for the ${}^{11}\mathrm{Be}{+}^{64}$Zn system (symbols). The dotted line is the OM calculation performed with the bare interaction alone, and the solid line is the OM calculation adding the Coulomb DPP to the bare potential. See text for details.

Figure 9

Differential quasielastic angular distributions measured in the present experiment (symbols) and CDCC calculations. The solid line is the full CDCC calculation. The dotted line is the calculation including only the ground state and first excited state of ${}^{11}\mathrm{Be}$. The dashed (dot-dashed) line is the CDCC calculation including only nuclear (Coulomb) breakup.

Figure 10

Top: Modulus of the elastic $S$-matrix elements as a function of the total orbital angular momentum obtained from CDCC calculations. Displayed values correspond to $L=J+1/2$. Bottom: Imaginary versus real part of the elastic $S$-matrix elements for $L=J+1/2$. The values $L=18$ and $L=25$ are indicated by arrows for reference.

Figure 11

Absorption, reaction, breakup, and ${}^{11}$Be(${\frac{1}{2}}^{-}$) inelastic cross sections obtained in CDCC calculations as a function of the total angular momentum, $J$. (a) The CDCC calculation including nuclear breakup, (b) the CDCC calculation with Coulomb breakup, and (c) the full CDCC calculation.

Figure 12

$\Delta E$-$E$ scatterplot for the collision ${}^{11}\mathrm{Be}{+}^{64}$Zn at $\theta ={39}^{\circ }$.

Figure 13

Differential cross section for the angular distribution of transfer/breakup events in ${}^{11}\mathrm{Be}{+}^{64}$Zn obtained by selecting ${}^{10}$Be events in the $\Delta E$-$E$ spectrum (filled symbols). The solid line is the full CDCC calculation, whereas the dashed line is the CDCC calculation including nuclear breakup only.