Neutron-rich rare-isotope production from projectile fission of heavy nuclei near 20 MeV/nucleon beam energy

We investigate the possibilities of producing neutron-rich nuclides in projectile fission of heavy beams in the energy range of 20 MeV/nucleon expected from low-energy facilities. We report our efforts to theoretically describe the reaction mechanism of projectile fission following a multinucleon transfer collision at this energy range. Our calculations are mainly based on a two-step approach: The dynamical stage of the collision is described with either the phenomenological deep-inelastic transfer model (DIT) or with the microscopic constrained molecular dynamics model (CoMD). The de-excitation or fission of the hot heavy projectile fragments is performed with the statistical multifragmentation model (SMM). We compared our model calculations with our previous experimental projectile-fission data of ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$ and ${}^{197}\mathrm{Au}$ (20 MeV/nucleon) + ${}^{197}\mathrm{Au}$ and found an overall reasonable agreement. Our study suggests that projectile fission following peripheral heavy-ion collisions at this energy range offers an effective route to access very neutron-rich rare isotopes toward and beyond the astrophysical r-process path.

Figure 1

Isobaric yield distributions (cross sections) of projectile fission fragments from the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$. Closed points, measured cross sections; open points, total cross sections extracted after correction for the angular acceptance of the spectrometer [42]. Solid (red) lines: DIT/SMM calculations. Dotted (blue) lines CoMD/SMM calculations. The upper set of lines gives total cross sections. The lower set of lines is after filtering with the acceptance of the spectrometer (see text). The dashed (green) line gives the total cross sections from the CoMD calculation of the full dynamics (1000 events, $t=15000$ fm/c).

Figure 2

Average $Z/A$ vs $A$ of projectile fission fragments from the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$. The experimental data for U+Pb are given by the closed points [42]. The full (red) lines are calculations with DIT/SMM. The dotted (blue) lines are calculations with CoMD/SMM. The upper set of curves are the final (cold) fission fragments. The lower set of curves are the hot fission fragments (after the SMM binary partition, but before deexcitation). The dashed (green) line is the full CoMD calculation (1000 events, $t=15000$ fm/c) with $t_{\mathrm{decay}}=5000\mathrm{fm}/\mathrm{c}$ (see text). The open circles are data from ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{27}\mathrm{Al}$ [42, 43]. The open triangles, squares, and inverted triangles are the GSI data from the reaction ${}^{238}\mathrm{U}$ (750 MeV/nucleon) + ${}^{208}\mathrm{Pb}$ for low-energy fission, high-energy fission and fragmentation products, respectively [74, 75, 76]. The dashed (black) line represents the radiochemical data of $p$ (24 MeV) + ${}^{238}\mathrm{U}$ [77] The continuous (black) line gives the line of $\beta$ stability.

Figure 3

Comparison of calculated mass distributions (lines) of projectile fission fragments from the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$ with the experimental data (closed points) of Ref. [42]. The calculations are with DIT/SMM [solid (red) line] and with CoMD/SMM [dotted (blue) line]. The dashed (green) lines for $Z=54$, 40 are for hot fission fragments from DIT/SMM. The open circles are data from ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{27}\mathrm{Al}$ [42, 43]. The open right triangles and inverted triangles are the GSI data from the reaction ${}^{238}\mathrm{U}$ (750 MeV/nucleon) + ${}^{208}\mathrm{Pb}$ for projectile fission and fragmentation (abrasion-ablation) products, respectively [74, 75, 76].

Figure 4

Comparison of calculated mass distributions (lines) of projectile fission fragments from the reaction ${}^{197}\mathrm{Au}$ (20 MeV/nucleon) + ${}^{197}\mathrm{Au}$ with the experimental data (closed points) of Ref. [45]. The calculations are with DIT/SMM [solid (red) line] and with CoMD/SMM [dotted (blue) line]. The dashed (green) lines for $Z=54$, 40 are for hot fission fragments from DIT/SMM.

Figure 5

(a) DIT/SMM calculated mass-resolved angular distibutions of projectile fission fragments from the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$. The successive contours (starting from the innermost) represent a drop in the yield by a factor of two. The horizontal lines represent the polar angular acceptance of the A1200 spectrometer setup [42] (lower solid lines) and the KOBRA spectrometer [78] (upper dashed lines) (see text). The arrow indicates the grazing angle of the U+Pb reaction (in the laboratory system). (b) As in panel (a), but for the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{64}\mathrm{Ni}$ (see text).

Figure 6

Representation of DIT/SMM calculated cross sections of projectile fission fragments from the reaction ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{64}\mathrm{Ni}$ on the $Z-N$ plane. The cross-sectional ranges are shown by open circles according to the key. Panel (a) shows the hot fission fragments (before de-excitation). Panel (b) shows the final (cold) fission fragments. The closed squares are the stable isotopes. The solid (red) line shows the astrophysical r-process path and the dotted (gray) line shows the location of the neutron drip-line according to Ref. [66].

Figure 7

Comparison of DIT/SMM calculated cross-sectional distributions of projectile fission fragments from ${}^{238}\mathrm{U}$ induced reactions. The solid (red) lines are for the 20-MeV/nucleon ${}^{238}\mathrm{U}+{}^{208}\mathrm{Pb}$ reaction and the dotted (blue) lines are for the 20-MeV/nucleon ${}^{238}\mathrm{U}+{}^{64}\mathrm{Ni}$ reaction. The dashed (green) lines are for the ${}^{238}\mathrm{U}+{}^{64}\mathrm{Ni}$ reaction at 10 MeV/nucleon.

Figure 8

DIT calculated properties of quasiprojectiles. (a) Average excitation energy per nucleon $E^{*}/A$ vs mass $A$ of quasiprojectiles from the reactions ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{208}\mathrm{Pb}$ [solid (red) line] and ${}^{238}\mathrm{U}$ (20 MeV/nucleon) + ${}^{64}\mathrm{Ni}$ [dotted (blue) line]. (b) Average $Z/A$ vs $A$ of quasiprojectiles. Lines are as in panel (a). The horizontal dashed line indicates the $Z/A$ of the ${}^{238}\mathrm{U}$ projectile. The lower and upper arrows indicate the $Z/A$ values corresponding to full $N/Z$ equilibration for the U+Pb and U+Ni systems, respectively. (c) Average angular momentum $J$ of quasiprojectiles versus the impact parameter of the collision. Lines are as in panel (a).

Figure 9

Representation of DIT calculated cross sections of quasiprojectiles from the 20-MeV/nucleon reactions ${}^{238}\mathrm{U}+{}^{208}\mathrm{Pb}$ (a) and ${}^{238}\mathrm{U}+{}^{64}\mathrm{Ni}$ (b) on the $Z-A$ plane. The cross-sectional ranges are shown by open circles according to the key. The lines indicate the location of the projectile nucleus ${}^{238}\mathrm{U}$.