Projectilelike fragment emission angles in fragmentation reactions of light heavy ions in the energy region $<200\mathrm{MeV}∕\text{nucleon}$: Modeling and simulations

A new semiempirical model called FRANG for calculation of fragment emission angles in light and heavy ion fragmentation reactions was developed. Contributions from both central and peripheral collisions were investigated, where fragmentation occurs due to nuclear and Coulomb interaction, respectively. For central collisions the reaction was described by a two step abrasion-ablation model, where collision parameters were determined from a simple geometrical model. The fragment emission angles were calculated using a parametrization of longitudinal momentum loss and transverse momentum uptake in the collision of projectile and target atom. For peripheral collisions the Coulomb excitation of nucleon vibration resonances and subsequent decay into fragments was taken into account. Fragment emission angles were calculated from deflection in the electric field and from the amplitude of vibrations in excited nuclear states. The modeled emission angles were in accordance with the experimental values for most projectile-target systems examined and compared. It was established that the model very well reproduces the experimental results in the energy region $<200\mathrm{MeV}∕\text{nucleon}$, despite its simplicity, and can be successfully employed in several applications. The model is estimated to be valid in the energy range from a few $10\mathrm{MeV}∕\text{nucleon}$ up to few $100\mathrm{MeV}∕\text{nucleon}$.

Figure 1

Abrasion-ablation reaction scheme and corresponding momenta at different steps. The two-nucleon collision system $(P+T)$ is partitioned into three parts: projectile spectators $\left(A\right)$, target spectators $\left(B\right)$, and participant system $\left(C\right)$ according to the fireball model [20].

Figure 2

Accuracy of the nuclear radii parametrization. The full line depicts the approximation of $R=r_0{A}^{1∕3}$ type, while the symbols depict measured values [26, 27]. The inset represents the relative accuracy of the radii parametrization. Large discrepancies can be observed especially for light nuclei.

Figure 3

Calculation of the number of projectile spectator nucleons at different energies. The dotted line represents simple geometric approximation.

Figure 4

Measured Fermi momentum (open symbols) and energy (full symbols) [32]. The full and dashed lines represent the best fitted function for energy and momentum, respectively.

Figure 5

Calculated average emission angles for different fragments. The example presented here is a ${}^{12}\mathrm{C}$ projectile on an ${}^{16}\mathrm{O}$ target atom.

Figure 6

Model calculated momentum transfer distributions for different abrasion channels. Dotted lines depict weighted distributions for production of the ${}^8\mathrm{B}$ isotope through all possible abrasion channels. Each channel is labeled with the mass number of the corresponding prefragment. The sum of all channels is depicted by a full line. The example presented is the collision of a $70\mathrm{MeV}∕\text{nucleon}$ ${}^{12}\mathrm{C}$ projectile on an ${}^{16}\mathrm{O}$ target atom.

Figure 7

Model calculated momentum transfer distributions and corresponding distribution of fragment emission angles. The example presented is a collision of a $100\mathrm{MeV}∕\text{nucleon}$ ${}^{12}\mathrm{C}$ projectile on an ${}^{16}\mathrm{O}$ target atom. Momentum distributions are calculated for production of different nitrogen fragments isotopes and plotted with dotted lines. Full lines represents the momentum distribution for each isotope but weighted by an appropriate production factor. The factors are calculated with a partial reaction cross section model [35], which is an improved version of the model described in Ref. 36.

Figure 8

Peripheral collision of projectile and target in the laboratory frame. Impact parameter $b$ is larger than the sum of the radii of the two nuclei. When passing by, the projectile is slightly deflected in the electric field of the target ion. Additionally, the projectile is excited (induced proton and neutron vibrations), which can result in subsequent dissociation of the nucleus.

Figure 9

Angular distribution of vibration direction at different energies. The distribution functions at each energy are normalized so that the function integral equals 1.