Short timescale behavior of colliding heavy nuclei at intermediate energies

Noncentral collisions of ${}^{114}\mathrm{Cd}$ projectiles with ${}^{92}\mathrm{Mo}$ target nuclei at $E/A=50$ MeV are explored with an antisymmetrized molecular dynamics model. These collisions are found to be essentially binary in character with formation of an excited projectile-like fragment (PLF${}^{*}$) and targetlike fragment (TLF${}^{*}$). The average excitation energy deduced for the PLF${}^{*}$ and TLF${}^{*}$ saturates for midcentral collisions, $3.5\le b\le 6$ fm, with its magnitude depending on the cluster recognition time. For short cluster recognition times $(t=150\mathrm{fm}/c)$, an average excitation energy as high as ≈6 MeV is determined, indicating a short statistical lifetime for the fragments produced. Evidence for such a rapid deexcitation is observed in the present calculations.

Figure 1

Contour diagram depicting the nucleon density distribution in spatial coordinates as a function of time for the reaction ${}^{114}\mathrm{Cd}$+${}^{92}\mathrm{Mo}$ at $E/A=50$ MeV. The positive $z$ direction corresponds to the direction of the projectile. The columns correspond to different impact parameters, $b=7.79$ fm (left) and $b=5.15$ fm (right).

Figure 2

Two dimensional diagram of the correlation between the atomic number and parallel velocity of particles at $t=300$ fm/$c$ for different impact parameters. The arrows correspond to the projectile and target velocities. The color scale indicates the yield on a logarithmic scale.

Figure 3

Dependence of the primary (solid) and secondary (dashed) $Z$ distributions on impact parameter. The differential yield $\mathrm{dN}/\mathit{dZ}$ has been normalized by the total number of events for each impact parameter interval.

Figure 4

Dependence of the $\langle Z\rangle ,\langle V\rangle$, and $E^{*}/A$ of the PLF${}^{*}$ and TLF${}^{*}$ on impact parameter. Error bars indicate the standard deviation of the distribution. In the bottom panels the solid symbols denote the 〈($E^{*}/A){}_{{\mathrm{XLF}}^{*}}\rangle$ as a function of $b$.

Figure 5

Dependence of the $\langle Z\rangle$ and $\langle E^{*}/A\rangle$ of the PLF${}^{*}$ on impact parameter for different cluster recognition times.

Figure 6

Dependence of the $\langle \mathcal{Z}\rangle ,\langle \mathcal{V}\rangle$, and $\langle E^{*}/A\rangle$ of the PLF${}^{*}$ on cluster recognition time for different impact parameters. The dashed line represents the projectile atomic number (velocity) in the top (middle) panel.

Figure 7

(Top panel) Dependence of the $\langle N/Z\rangle$ of the PLF${}^{*}$ and TLF${}^{*}$ on impact parameter. Dashed lines indicate the initial $N/Z$ of projectile and target nuclei. (Bottom panel) Fraction, $f$, of nucleons found in the PLF${}^{*}$ (solid symbols) or TLF${}^{*}$ (open symbols) that originate from the projectile.

Figure 8

Dependence of the $\langle E^{*}/A\rangle$ on $A$ for $t=150$ fm/$c$ (upper panel) and $t=300$ fm/$c$ (lower panel).

Figure 9

Multiplicity of fragments as a function of impact parameter. (a) Average multiplicity of $Z\ge$ 3 at $t=300$ fm/$c$ (solid circles), after secondary decay (solid triangles) and for QMD (open crosses). The QMD results are extracted from Ref. 54. (b) Multiplicity of $Z=3\text{−}10$. (c) Average multiplicity of $Z=3\text{−}10$ for different cluster recognition times.

Figure 10

Multiplicity of neutrons and light charged particles as a function of impact parameter for different cluster recognition times. The multiplicities in the right column have been scaled by the factors indicated. Error bars indicate the standard deviation of the distribution.

Figure 11

Invariant cross-section for IMFs $(3\le Z\le 10)$ in the COM frame. The arrows indicate the average parallel velocity of the PLF${}^{*}$ and TLF${}^{*}$. The color scale indicates the yield on a logarithmic scale. The vertical scale in the bottom two panels has been scaled by a factor of two as compared to the other panels.

Figure 12

(Left column) Parallel velocity distributions for the PLF${}^{*}$ and TLF${}^{*}$ (shaded), as well as IMFs (solid histogram) as a function of impact parameter. The dashed histograms correspond to a two gaussian fit as described in the text. (Right column) Parallel velocity distributions of the PLF, TLF, and IMFs following Coulomb propagation and decay. The IMFs distributions have been normalized to the number of events. The PLF${}^{*}$, TLF${}^{*}$, PLF, and TLF distributions have been scaled relative to the IMFs distributions. The arrows indicate the projectile and target velocities.

Figure 13

Invariant cross section for α particles in the COM frame. The arrows indicate the average parallel velocity of the PLF${}^{*}$ and TLF${}^{*}$. The color scale indicates the yield on a logarithmic scale. In the left column the vertical scale of the bottom panel is scaled by a factor of six as compared to the upper panels. The right column is scaled by a factor of three with respect to the left column.

Figure 14

Angular distribution for α particles on the PLF${}^{*}$ Coulomb ridge ($V_{\alpha }^{*}<$ 3.5 cm/ns). All angles are in the PLF${}^{*}$ frame.