Systematic study of neutron-rich rare isotope production in peripheral heavy-ion collisions below the Fermi energy

Detailed calculations of the yields of projectilelike fragments (with focus on the neutron-rich isotopes) are presented for the interaction of ${}^{86}\mathrm{Kr}$ (15 MeV/nucleon) with ${}^{64}\mathrm{Ni}$, ${}^{58}\mathrm{Ni}$, and ${}^{124}\mathrm{Sn}$, ${}^{112}\mathrm{Sn}$, as well as ${}^{86}\mathrm{Kr}$ (25 MeV/nucleon) with ${}^{124}\mathrm{Sn}$ and compared with our recently published experimental data for these reactions. The calculations are based on a two-step approach: the dynamical stage of the collision was described with the microscopic constrained molecular dynamics (CoMD) model, as well as the phenomenological deep-inelastic transfer (DIT) model and its modified (DITm) version. The deexcitation of the hot projectile fragments was performed with the statistical multifragmentation model (SMM) and the binary-decay model gemini, which provided nearly similar results for the neutron-rich products from the reactions studied. An overall good agreement of the calculations with the experimental results, especially for near-projectile isotopes was observed using both the CoMD model and the DITm model for the dynamical stage. The successful description of the production of neutron-rich isotopes with the CoMD model is of particular importance, due to the predictive power of the microscopic approach that essentially does not depend on the reaction dynamics. Our studies to date suggest that peripheral heavy-ion collisions at this energy range (i.e., well above the Coulomb barrier, but below the Fermi energy), if induced by neutron-rich rare-isotope beams of adequate intensity may offer a unique route to access extremely neutron-rich rare isotopes toward the astrophysical $r$-process path and the presently uncharted neutron drip line.

Figure 1

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line], and DIT/SMM [dashed (green) line].

Figure 2

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line] and CoMD/gemini [dash-dotted (light-blue) line].

Figure 3

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=39–36$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line] and CoMD/gemini [dash-dotted (light-blue) line].

Figure 4

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=29–26$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line] and CoMD/gemini [dash-dotted (light-blue) line].

Figure 5

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{124}\mathrm{Sn}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line], and DIT/SMM [dashed (green) line].

Figure 6

Comparison calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{58}\mathrm{Ni}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line], and DIT/SMM [dashed (green) line].

Figure 7

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{112}\mathrm{Sn}$ with the experimental data (closed points) of Ref. [46]. The calculations are: CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line], and DIT/SMM [dashed (green) line].

Figure 8

Comparison of calculated mass distributions (lines) of projectilelike fragments with $Z=35–30$ from the reaction ${}^{86}\mathrm{Kr}$(25 MeV/nucleon)+${}^{124}\mathrm{Sn}$ with the experimental data (closed points) of Ref. [40]. The calculations are: CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line], and DIT/SMM [dashed (green) line].

Figure 9

Calculations of mass distributions (cross sections) with CoMD/SMM [solid (red) line], DITm/SMM [dotted (blue) line] and DIT/SMM [dashed (green) line] of projectilelike fragments with $Z=35–30$ from the radioactive-beam reaction ${}^{92}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$. For reference displayed are the experimental data (closed points) for the stable-beam reaction ${}^{86}\mathrm{Kr}$(15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ [46].

Figure 10

Representation of CoMD/SMM calculated production cross sections of projectile fragments from the radioactive-beam reaction ${}^{92}\mathrm{Kr}$ (15 MeV/nucleon)+${}^{64}\mathrm{Ni}$ on the $Z\text{−}N$ plane. The cross section ranges are shown by open circles according to the key. The closed squares show the stable isotopes. The solid (red) line shows the astrophysical $r$-process path and the dashed (green) line shows the location of the neutron drip line [61]. The horizontal and vertical dashed lines indicate, respectively, the proton and neutron number of the ${}^{92}\mathrm{Kr}$ projectile.