Modelling incomplete fusion dynamics of complex nuclei at Coulomb energies

The incomplete fusion dynamics of ${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}$ collisions at energies above the Coulomb barrier are investigated using a novel semiclassical dynamical model, which combines a classical trajectory model with stochastic breakup, as implemented in the platypus code, with a dynamical fragmentation theory treatment of two-body clusterization and decay of a projectile. A finite-difference method solution to the time-independent Schrödinger equation in the charge asymmetry coordinate is employed by way of diagonalizing a tridiagonal Hamiltonian matrix with periodic boundary conditions. Results are compared with published experimental values to indicate the success of this new model, and next steps for its development are detailed.

Figure 1

A diagram representing ICF of a complex projectile (undergoing fragmentation in the charge asymmetry coordinate) and an inert target.

Figure 2

Schematic diagram representing the overlap between intranuclear nucleon-distribution tails of the two fragments (the neck) of a dinuclear system.

Figure 3

Inertia coefficient ($\times$) / potential ($+$) plot for the fragmentation of ${}_{10}{}^{20}\mathrm{Ne}$ in the charge asymmetry coordinate, with the potential energy of the compound nucleus $U0=0$ MeV. Markers denote values calculated, whilst intermediate values can be interpolated.

Figure 4

Normalized PDF representing the fragmentation for the first three energy eigenvalues of ${}_{10}{}^{20}\mathrm{Ne}$ in the charge asymmetry coordinate, with the potential energy and inertia coefficients of Fig. 3: (a) $-5.38$ MeV, (b) $-5.34$ MeV, and (c) $-4.76$ MeV. The inertia coefficients and potentials of Fig. 3 have been interpolated here using $\mathrm{\Delta }{\eta }_Z=0.001$.

Figure 5

Normalized total PDF representing the fragmentation for all 34 eigenvalues that lie within a 5 MeV excitation energy range of ${}_{10}{}^{20}\mathrm{Ne}$ in the charge asymmetry coordinate, with the potential energy and inertia coefficients of Fig. 3. The inertia coefficients and potentials of Fig. 3 have been interpolated here using $\mathrm{\Delta }{\eta }_Z=0.001$.

Figure 6

Angular distributions for the transfer reaction of ${}_2{}^4\mathrm{He}$ (${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}\to {}_{84}{}^{212}\mathrm{Po}+{}_8{}^{16}\mathrm{O}$) for projectile incident energies of 105 MeV ($+$) and 115 MeV ($\times$): (a) from experiment [64], (b) from the present model calculations for a projectile with an excitation energy range ($E_{\max }^{*}-E_{\min }^{*}$) of 1 keV.

Figure 7

Combined angular distributions for the transfer reactions of ${}_2{}^4\mathrm{He}$ (${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}\to {}_{84}{}^{212}\mathrm{Po}+{}_8{}^{16}\mathrm{O}$) and ${}_4{}^8\mathrm{Be}$ (${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}\to {}_{86}{}^{216}\mathrm{Rn}+{}_6{}^{12}\mathrm{C}$) for projectile incident energies of 105 MeV ($+$) and 115 MeV ($\times$): (a) from experiment [64], (b) from the present model calculations for a projectile with an excitation energy range ($E_{\max }^{*}-E_{\min }^{*}$) of 5 MeV.

Figure 8

ICF cross sections for ICF channels 1 ($+$), 2 ($\times$) and both combined ($*$) for the reaction ${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}$ for a projectile with an excitation energy range ($E_{\max }^{*}-E_{\min }^{*}$) of 5 MeV, for a range of projectile incident energies ($E_0$). ICF channel 1 refers to the production of ${}_{90}{}^{224}\mathrm{Th}$ and ${}_{88}{}^{220}\mathrm{Ra}$, while ICF channel 2 refers to the production of ${}_{84}{}^{212}\mathrm{Po}$ and ${}_{86}{}^{216}\mathrm{Rn}$.

Figure 9

Inclusive angular distributions of ICF products ($+$) and associated survival fragments ($\times$) for the reaction ${}_{10}{}^{20}\mathrm{Ne}+{}_{82}{}^{208}\mathrm{Pb}$ for a projectile with an excitation energy range ($E_{\max }^{*}-E_{\min }^{*}$) of 5 MeV, for a projectile incident energy ($E_0$) of 160 MeV: (a) ICF channel 1 (${}_{90}{}^{224}\mathrm{Th}$ and ${}_{88}{}^{220}\mathrm{Ra}$), (b) ICF channel 2 (${}_{84}{}^{212}\mathrm{Po}$ and ${}_{86}{}^{216}\mathrm{Rn}$).

Figure 10

Angular momentum distributions of the inclusive ICF products (the sum of all the ICF channels) for the same reaction as in Fig. 9, using two different representations, namely in terms of the angular momentum brought by the ICF fragments into the target ($+$) and the ${}_{10}{}^{20}\mathrm{Ne}$ orbital angular momentum ($\times$).

Figure 11

Excitation energy distribution of the primary ICF products for ICF channels 1 ($+$) and 2 ($\times$) for the same reaction as in Fig. 9. ICF channel 1 refers to the production of ${}_{90}{}^{224}\mathrm{Th}$ and ${}_{88}{}^{220}\mathrm{Ra}$, while ICF channel 2 refers to the production of ${}_{84}{}^{212}\mathrm{Po}$ and ${}_{86}{}^{216}\mathrm{Rn}$.

Figure 12

Asymptotic angular distribution of the ICF products and the surviving breakup fragments for ICF channels 1 ($+$) and 2 ($\times$) for the same reaction as in Fig. 9. ICF channel 1 refers to the production of ${}_{90}{}^{224}\mathrm{Th}$ and ${}_{88}{}^{220}\mathrm{Ra}$, while ICF channel 2 refers to the production of ${}_{84}{}^{212}\mathrm{Po}$ and ${}_{86}{}^{216}\mathrm{Rn}$.