Role of dynamical deformation in pre-scission neutron multiplicity

The light-particle emission probability from an excited compound nucleus depends explicitly on the time-evolution of the system as the available internal excitation energy and, consequently, the particle decay widths depend on the instantaneous deformation of the nucleus. The Langevin dynamical model for fission is employed to extract this deformation dependence in pre-scission particle multiplicities by following the propagation of fissioning trajectories up to scission. The variation of particle decay widths with nuclear deformation is accounted more precisely in comparison to the existing calculations. The number of neutrons emitted from different configurations of the compound nucleus are calculated for a detailed analysis. The deformation dependence of particle emission widths is found to be relevant for highly fissile systems where the dynamics is primarily governed by the saddle to scission motion. This dynamical effect essentially predicts the nuclear shape evolution through evaporated light particles and, for a heavy compound system, simultaneous measurement of neutron multiplicities for fission and evaporation residue events can reveal its intricate nature.

Figure 1

Relative variation of neutron (solid line), proton (dashed line), and $\alpha$-particle (dash-dotted line) binding energies with respect to the value at spherical shape ($c=1$).

Figure 2

Upper panel: $n_{\mathrm{pre}}^{-}$ (solid line) and $n_{\mathrm{pre}}^{+}$ (dashed line) calculated with deformation independent ${\mathrm{\Gamma }}_n(\ell ,c=1)$ and deformation dependent ${\mathrm{\Gamma }}_n(\ell ,c)$, respectively. Experimental values (solid circles) of $n_{\mathrm{pre}}$ is taken from [7]. Lower panel: $n_{\mathrm{pre}}^{>-}$ (solid line) and $n_{\mathrm{pre}}^{>+}$ (dashed line) calculated for $\ell \ge {\ell }_{\mathrm{crit}}$ (see text).

Figure 3

Upper panel: Contours of ${\mathrm{\Gamma }}_n(E^{*},c)$ as a function of excitation energy and deformation for fixed $\ell =0$. The $E^{*}(\ell ,c)$ corresponding to $E_{\mathrm{c}.\mathrm{m}.}=120$ MeV is shown for $\ell =0$ (thick-solid line) and $\ell =72\hslash$ (thick-dashed line). Lower panel: Distributions of $n_{\mathrm{pre}}^{-}$ (solid line) and $n_{\mathrm{pre}}^{+}$ (dashed line) in log scale (left scale) and distributions of $n_{\mathrm{pre}}^{>-}$ (dotted dashed line) and $n_{\mathrm{pre}}^{>+}$ (double dotted-dashed-line) in linear scale (right scale) as functions of deformation $c$. The shaded belongs to the deformation larger than saddle-point deformation.

Figure 4

Pre-scission particle multiplicities for different target-projectile combinations calculated with (dashed lines) and without (solid lines) deformation dependence. Inset of top panel: $n_{\mathrm{frac}}$ (see text) as a function of excitation energy for these systems.

Figure 5

Upper panel: $n_{\mathrm{pre}}$ as a function of excitation energy for deformation dependent (solid lines) and independent (dashed lines) neutron decay widths calculated for $\beta =1.0$, 1.5, 2.0, 2.5, 3.0, and 3.5 (with $n_{\mathrm{pre}}$ smaller to larger). Experimental data points (solid circles) are from Ref. [48]. Lower panel: The excitation energy dependence of $\beta$ for deformation dependent (solid line) and independent (dashed line) neutron decay widths.

Figure 6

Upper panel: $n_{\mathrm{pre}}^{+}$ (dashed line) and $n_{\mathrm{pre}}^{-}$ (solid line) for different systems as indicated along with experimental data points (solid circles). Lower panel: Associated saddle to scission neutron multiplicity ($n_{\mathrm{sad}-\mathrm{sci}}$).