Systematic investigation of projectile fragmentation using beams of unstable B and C isotopes

Background: Models describing nuclear fragmentation and fragmentation fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data from stable beam experiments. In the future, two-step fragmentation reactions with exotic nuclei as stepping stones are a promising tool for reaching the most neutron-rich nuclei, creating a need for models to describe also these reactions.

Purpose: We want to extend the presently available data on fragmentation reactions towards the light exotic region on the nuclear chart. Furthermore, we want to improve the understanding of projectile fragmentation especially for unstable isotopes.

Method: We have measured projectile fragments from ${}^{10,12-18}\mathrm{C}$ and ${}^{10-15}\mathrm{B}$ isotopes colliding with a carbon target. These measurements were all performed within one experiment, which gives rise to a very consistent data set. We compare our data to model calculations.

Results: One-proton removal cross sections with different final neutron numbers $\left(1pxn\right)$ for relativistic ${}^{10,12-18}\mathrm{C}$ and ${}^{10-15}\mathrm{B}$ isotopes impinging on a carbon target. Comparing model calculations to the data, we find that the epax code is not able to describe the data satisfactorily. Using abrabla07 on the other hand, we find that the average excitation energy per abraded nucleon needs to be decreased from 27 MeV to 8.1 MeV. With that decrease abrabla07 describes the data surprisingly well.

Conclusions: Extending the available data towards light unstable nuclei with a consistent set of new data has allowed a systematic investigation of the role of the excitation energy induced in projectile fragmentation. Most striking is the apparent mass dependence of the average excitation energy per abraded nucleon. Nevertheless, this parameter, which has been related to final-state interactions, requires further study.

Figure 1

Schematic view of the $\mathrm{LAND}/\mathrm{R}{}^3\mathrm{B}$ setup seen from above. The most important detectors for this work are POS, ROLU, PSP, SST, GFI, TFW, and XB. POS provides energy-loss $\left(\mathrm{\Delta }E\right)$ and time-of-flight (TOF) measurements. ROLU is an active veto detector on the incoming beam. PSP and SST are used for $\mathrm{\Delta }E$ measurements, the main purpose of the SST is to determine incoming and outgoing directions of the beam. The GFIs provide tracking of the beam behind the magnet ALADIN, and the TFW provides TOF, $\mathrm{\Delta }E$, and position information. The XB is a calorimeter for protons and $\gamma \mathrm{s}$, and is here solely used for trigger purposes. For a more detailed description of the setup see text. This schematic is not to scale.

Figure 2

Illustration of the reaction identification (ID). (a) Shows the incoming ID with charge versus mass-to-charge ratio. The ellipses indicate the $2\sigma$ selection of different isotopes. The dashed ellipse represents the selection used for the data in plots (b) and (c). (b) Presents the charge identification after the reaction target, using $\mathrm{\Delta }E$ measurements at the end of the setup versus in the first detector behind the reaction target. The ellipses indicate the $3\sigma$ selection of the unreacted beam (solid) and $1pxn$ reaction (dotted). (c) Shows the reconstructed mass from the $1pxn$ removal and the fit to the spectrum. For details see text.

Figure 3

Excerpt from the nuclear chart, illustrating the isotopes selected from the incoming secondary beams (white, thick frame). All carbon and boron isotopes with sufficient statistics were used.

Figure 4

$1pxn$ removal cross sections plotted versus the change in nucleon number for carbon and boron. The shaded area represents the statistical error bar. For boron there is a strong trend that the cross section for populating the long-lived ${}^{10}\mathrm{Be}$ is largest for all incoming isotopes. For carbon isotopes the cross section to produce the heaviest available stable isotope, ${}^{11}\mathrm{B}$ is largest, except for very neutron-rich isotopes, where instead the cross section to the semimagic ${}^{13}\mathrm{B}$ becomes largest, with the transition point located at ${}^{16}\mathrm{C}$.

Figure 5

${\chi }^2$ versus the excitation energy multiplication factor used in the abrabla07 [7] calculations. ${\chi }^2$ is determined as described in the text, summed for all experimentally determined cross sections measured in this work. Lines are used to guide the eye.

Figure 6

Comparison between abrabla07 [7] (red stars), epax [4, 28] (blue diamonds), and the experimental data (black full squares). For ${}^{12}\mathrm{C}$ experimental data from three other measurements of ${}^{12}\mathrm{C}$ on C are shown: at $600A$ MeV, Ref. [26] (orange empty square,); at $250A$ MeV, Ref. [27] (green empty circles); and at $400A$ MeV, Ref. [16] (purple bold stars).

Figure 7

Optimal excitation energy multiplication factor vs the mass number. Error bars indicate the estimated uncertainty, see text for details on the calculation. (Red) dots represent the present data, while (orange) squares indicate data from Refs. [6, 26, 29, 30, 31, 32], and (blue) bold crosses represent data from Refs. [26, 31, 33, 34] for isotopes that have a larger neutron separation energy than proton separation energy. A clear difference between lighter and heavier nuclei is visible.