Time-dependent isospin composition of particles emitted in fission events following ${}^{40}\mathrm{Ar}+{}^{197}\mathrm{Au}$ at 35 MeV/u

Fission fragments resulting from the fission of target-like nuclei produced in the ${}^{40}\mathrm{Ar}+{}^{197}\mathrm{Au}$ reaction at 35 MeV/u are measured in coincidence with the emitted light charged particles (LCPs). Comparison of the $N/Z$ composition of the LCPs at middle and large angles in the laboratory frame shows that particles emitted at smaller angles, which contain a larger contribution from dynamical emission, are more neutron rich. A moving-source model is used to fit the energy spectra of the hydrogen isotopes. A hierarchy from proton to deuteron and triton is observed in the multiplicity ratio between the intermediate velocity source and the compound nucleus source. This ratio is sensitive to the dynamical emission at early stages of the reaction and to statistical emission lasting up to the scission point. Calculations with the improved quantum molecular dynamics (ImQMD) transport-model qualitatively support the picture that more free and bound neutrons are emitted during the early stage, showing a clear dependence of $N/Z$ on the parametrization of the symmetry energy. The time-dependent isospin composition of the emitted particles thus may be used to probe the symmetry energy at subsaturation densities.

Figure 1

Schematic of detector setup. The beam goes from the lower left to the upper right. The concentric hodoscope is the Si-BGO array. The six large squares are the PPACs, while the six single cylinders represent the LCP telescopes.

Figure 2

Azimuthal-angle correlation of two fission fragments detected in coincidence.

Figure 3

(a) The mass asymmetry and (b) the relative velocity as a function of compound-nucleus velocity. The black solid curves in the two plots represent the variance of $\eta$ and the mean value of ${\mathbf{v}}_{\mathrm{rel}}$, respectively.

Figure 4

(a) The distribution of the mass asymmetry and (b) the relative velocity of the two fission fragments firing the PPACs. The vertical lines indicate the window cuts used in the moving-source analysis.

Figure 5

The double yield ratio of LCPs and proton $Y_{\mathrm{A}}/Y_{\mathrm{p}}$ between the telescopes 4 (80${}^{\circ }$) and 1 (158${}^{\circ }$) as a function of particle $N/Z$ for hydrogen and helium isotopes.

Figure 6

The energy spectra of hydrogen isotopes at 158${}^{\circ }$ (upper panels) and 80${}^{\circ }$ (lower panels) with the moving-source fit in three mass asymmetry windows. For clarity the counts are offset by factors of ten. The total fitting curves are superimposed on all spectra, while the curves of all three moving sources are plotted only for the spectra in the lowest mass asymmetry window, ${\eta }_0$, for a clear display.

Figure 7

The ${\chi }_{\min }^2$ distribution of the moving-source fits to the spectra of hydrogen isotopes in three mass asymmetry gates. Each value on the contour is obtained by searching the minimum ${\chi }^2$ in a wide space of $T$ and $E_{\mathrm{c}}$ while keeping the two multiplicity ratios fixed. The solid stars indicate the lowest ${\chi }_{\min }^2$ locations.

Figure 8

The upper panel shows the multiplicity from the intermediate velocity (int) source and the lower panel shows that from the fission fragment (ff) source, both normalized to the multiplicity from the compound -nucleus (cn) source.

Figure 9

The energy spectra with the moving source fitting for hydrogen isotopes in three LMT gates. For clarity the counts with LMT1 and LMT2 are offset by 10 and 100, respectively. The legends are the same as those in Fig. 6.

Figure 10

Same as Fig. 8; the ordinate is the velocity of the compound nucleus reconstructed from the two fragments.

Figure 11

The average $\langle N/Z\rangle$ summed for the light particles with $Z\le 3$ as a function of time with $\gamma =0.5$ (soft, open circles) and $\gamma =2$ (stiff, solid circles) in ImQMD simulation for (left panel) the inclusive events and (right panel) the selected fission events. The vertical arrows show the contact time of the projectile and the target.