Influence of angular momentum and Coulomb interaction of colliding nuclei on their multifragmentation

Theoretical calculations are performed to investigate the angular momentum and Coulomb effects on fragmentation and multifragmentation in peripheral heavy-ion collisions at Fermi energies. Inhomogeneous distributions of hot fragments in the freeze-out volume are taken into account by microcanonical Markov chain calculations within the statistical multifragmentation model. Including an angular momentum and a long-range Coulomb interaction between projectile and target residues leads to new features in the statistical fragmentation picture. In this case, one can obtain specific correlations of the sizes of emitted fragments with their velocities and an emission in the reaction plane. In addition, one may see a significant influence of these effects on isotope production both in the midrapidity and in the kinematic regions of the projectile/target. The relation of this approach to the simulations of such collisions with dynamical models is also discussed.

Figure 1

Total charge yield of primary hot fragments, in cases without (filled circles) and with (open circles; $L=80\hslash$) angular momentum, after multifragmentation of the projectile ${}^{84}\mathrm{Kr}$ source at excitation energy $E_x=5$ MeV/nucleon. This source is assumed to be formed in the peripheral ${}^{84}\mathrm{Kr}+{}^{84}\mathrm{Kr}$ collision at 35 MeV/nucleon, and its disintegration is affected by the Coulomb field of the target source. Results at freeze-out densities $\rho ={\rho }_0/2$ (top) and $\rho ={\rho }_0/6$ (bottom). For comparison, the results of multifragmentation of a single isolated ${}^{84}\mathrm{Kr}$ source, at the same excitation energy but without the external Coulomb field and without angular momentum, are also shown.

Figure 2

Charge yield of the first, second, and third largest hot fragments ($Z_{\max 1},Z_{\max 2}$, and $Z_{\max 3}$) after multifragmentation of the ${}^{84}\mathrm{Kr}$ source (as in Fig. 1). Results without angular momentum (top panels) and with angular momentum ($L=80\hslash$) (bottom panels).

Figure 3

Mean neutron-to-proton ratios $\langle N\rangle /Z$ of hot primary fragments produced at the freeze-out density $\rho ={\rho }_0/2$ (top) and $\rho ={\rho }_0/6$ (bottom). Other notation is as in Fig. 1.

Figure 4

$V_X$ and $V_Y$ velocity distributions of the first, second, and third largest fragments in multifragmentation of ${}^{84}\mathrm{Kr}$ with angular momentum $L=80\hslash$ and at freeze-out density $\rho ={\rho }_0/2$, in the source frame.

Figure 5

Relative yields of specific fragments coming from the disintegration of a ${}^{84}\mathrm{Kr}$ projectile source at the excitation energy of 5 MeV/nucleon as a function of the velocity $V_Y$ in the source frame. Calculations were performed with (open circles; $L=80\hslash$), and without (filled circles) angular momentum at freeze-out density $\rho ={\rho }_0/2$.

Figure 6

Mean neutron-to-proton ratios $\langle N\rangle /Z$ as a function of $V_Y$ shown in Fig. 5 (notation is the same).

Figure 7

Mean charge $Z$ (top panels) and $\langle N\rangle /Z$ (bottom panels) distributions of the first, second, and third largest hot fragments ($Z_{\max 1},Z_{\max 2}$, and $Z_{\max 3}$) after multifragmentation of a ${}^{84}\mathrm{Kr}$ projectile source at $E_x=5$ MeV/nucleon versus $V_Y$ in the source frame. The freeze-out density is $\rho ={\rho }_0/2$. Left panels represent results without angular momentum; right panels, with angular momentum ($L=80\hslash$).

Figure 8

Total charge yield (top) and mean neutron-to-proton ratios $\langle N\rangle /Z$ (bottom) of all primary fragments produced at freeze-out density $\rho ={\rho }_0/2$ and at different distances between the sources (see notations in the figure).

Figure 9

Yield distribution (top) and mean neutron-to-proton ratios $\langle N\rangle /Z$ (bottom) of primary fragments with $Z=6$ as a function of their velocity $V_Y$ in the source frame, at different distances between the sources (see notations in the figure). The freeze-out density is $\rho ={\rho }_0/2$.

Figure 10

The same as Fig. 9, however, for the distance $R_Y=-10.6$ fm between the sources and with the presence of the neck-like fragment ($A=12$, $Z=6$) at midrapidity between the sources. Calculations without (filled circles) and with (open circles) angular momentum $L=80\hslash$ are shown.