Isospin effect in statistical sequential decay

Isospin effect of the statistical emission fragments from the equilibrated source is investigated in the frame of statistical binary decay implemented into the GEMINI code, isoscaling behavior is observed and the dependences of isoscaling parameters α and β on emission fragment size, source size, source isospin asymmetry and excitation energies are studied. Results show that α and β neither depends on light fragment size nor on source size. A good linear dependence of α and β on the inverse of temperature $T$ is manifested and the relationship of $\alpha =4C_{\mathrm{sym}}[(Z_s/A_s){}_1^2-(Z_s/A_s){}_2^2]/T$ and $\beta =4C_{\mathrm{sym}}[(N_s/A_s){}_1^2-(N_s/A_s){}_2^2]/T$ from different isospin asymmetry sources is satisfied. The symmetry energy coefficient $C_{\mathrm{sym}}$ extracted from simulation results is ∼ 23 MeV which includes both the volume and surface term contributions, of which the surface effect seems to play a significant role in the symmetry energy.

Figure 1

Isoscaling parameters α (positive values) and β (negative values) as a function of the fragment proton number $Z$ or neutron number $N$ from source pair ($Z_s=50$, $A_s=100$) and ($Z_s=50$, $A_s=105$) at various excitation energies: $E_{\mathit{ex}}=1.0$ (open squares), 1.4 (solid squares), 2.0 (open circles), 2.4 (solid circles), 3.0 (open up triangles) MeV/nucleon.

Figure 2

Isoscaling parameters α (positive values) and β (negative values) as a function of the fragment proton number $Z$ or neutron number $N$ from source pairs with the fixed proton number $Z_s=50$ at excitation energies $E_{\mathit{ex}}=2$ MeV/nucleon. Symbols in the figure correspond to $Y_{A_s=115}/Y_{A_s=110}$ (solid squares), $Y_{A_s=110}/Y_{A_s=105}$ (open squares), $Y_{A_s=105}/Y_{A_s=100}$ (solid circles), $Y_{A_s=115}/Y_{A_s=105}$ (open circles), $Y_{A_s=110}/Y_{A_s=100}$ (solid up triangles).

Figure 3

Same as Fig. 2, but for source pairs with the fixed proton number $Z_s=30$ at excitation energies $E_{\mathit{ex}}=2$ MeV/nucleon. Symbols in the figure correspond to $Y_{A_s=69}/Y_{A_s=66}$ (solid squares), $Y_{A_s=66}/Y_{A_s=63}$ (open squares), $Y_{A_s=63}/Y_{A_s=60}$ (solid circles), $Y_{A_s=69}/Y_{A_s=63}$ (open circles), $Y_{A_s=66}/Y_{A_s=60}$ (solid up triangles).

Figure 4

Dependence of isoscaling parameters α and $\left|\beta \right|$ on excitation energy (left panel) and the inverse temperature $1/T$ (right panel) for various source pairs with same proton number $Z_s=30$. Symbols in the figure are α (solid symbols) or $\left|\beta \right|$ (open symbols) from source pair $Y_{A_s=63}/Y_{A_s=60}$ (squares), $Y_{A_s=66}/Y_{A_s=63}$ (circles), $Y_{A_s=69}/Y_{A_s=66}$ (up-triangles), $Y_{A_s=66}/Y_{A_s=60}$ (down-triangles), and $Y_{A_s=69}/Y_{A_s=63}$ (diamonds).

Figure 5

Same as Fig. 4, but for various source pairs with $Z_s=50$. Symbols in the figure are α (solid symbols) or $\left|\beta \right|$ (open symbols) from source pair $Y_{A_s=105}/Y_{A_s=100}$ (squares), $Y_{A_s=110}/Y_{A_s=105}$ (circles), $Y_{A_s=115}/Y_{A_s=110}$ (up-triangles), $Y_{A_s=110}/Y_{A_s=100}$ (down-triangles), and $Y_{A_s=115}/Y_{A_s=105}$ (diamonds).

Figure 6

$\alpha ·T$ (positive parts) and $\beta ·T$ (negative parts) as a function of $(Z_s/A_s){}_1^2-(Z_s/A_s){}_2^2$ or $(N_s/A_s){}_1^2-(N_s/A_s){}_2^2$ of the sources for various source pairs with atomic number $Z_s=50$ which is illustrated in the figure at different excitation energies.

Figure 7

Same as Fig. 6, but for various source pairs with $Z_s=30$ which is illustrated in the figure at different excitation energies.

Figure 8

Top panel: mass excess calculated from Eq. (12) as a function of nuclear mass number, curves from left to right correspond to the atomic number $Z$ of isotopes series from $Z=5$ to $Z=60$ in order. Bottom panel: numerically calculated derivative of symmetry energy $E_{\mathrm{sym}}$ (MeV/nucleon) with respect to neutron number $N$ in Eq. (12) as a function of $(Z/A){}^2$ (solid marks) and the linear fit of the numerical calculation, fitted result is printed in the figure.