16 Systematic Study of Po Compound Nuclei Using Evaporation Residue …
227
from the SM calculations are in the range (0.75–0.85) for the CN
190 Pb, whereas the
K f value for
198 Pb and
192 Po are (0.65–0.70) and (1.0–1.25), respectively.
The results discussed in this section strongly indicate the significance of using
excitation energy-dependent scaling of the finite-range rotating liquid drop model
fission barrier in order to fit the experimental data for ER and fission cross-section.
16.3 Statistical Model Analysis of Neutron Multiplicity
The dissipation effect in fusion–fission process is well established. The excess in
multiplicities with respect to SM predictions indicates the presence of a dynamic
hindrance to fission. Recently, Singh et al. [29] have measured the pre-scission neutron multiplicities for
19 F +
194,196,198 Pt populating
213,215,217 Fr in the excitation
energy range of 46.6–91.8 MeV and discussed the effect of shell effect on nuclear
dissipation. In another set of measurements by Sandal et al. [30] also support the
fission hindrance due to nuclear dissipation.
In the present case, we have performed SM calculations for
210 Po populated
by
18 O +
192 Os in the excitation energy range of 65.23–91.74 MeV. Experimental
data on pre-scission neutron multiplicity is available in the literature for
210 Po [9].
In this section, we are comparing the results obtained from SM calculations with
the experimental results to see the isotopic and excitation energy dependence of
the dissipation strength. Here, SM calculations have been performed using Bohr–
Wheeler and Kramer’s formalism for
210 Po by including and excluding shell effects
in level density parameter and the fission barrier.
The fission width where effect of dissipation that is included is given by
Kramers [31]. The other ingredients used in the present calculations like Bohr–
Wheeler fission width, level density parameter, and fission barrier have been discussed in Sect. 16.2 of this chapter.
Upper panel of Fig. 16.4 shows the results of calculations for pre-scission neutron
multiplicity with no shell effects in level density parameter and barrier height for
210 Po and lower panel shows the results with inclusion of shell effects.
The comparison of calculated pre-scission neutron multiplicities with the experimental values clearly shows that the predictions using Bohr–Wheeler fission width
considerably underestimate the pre-scission neutron multiplicity at all the energies.
It is also observed that the experimental values at all the energies cannot be reproduced by a single value of β. However, the calculations which take into consideration
Kramers’ fission width are in well agreement with the experimental data.
Figure 16.5 shows the lab energy dependence of best fit β value for
210 Po where
the shaded areas represent the uncertainty in β with the experimental error in M pre .
We first note in this figure that the inclusion of shell effects in the calculation results
in higher values for best fit β.
Inclusion of shell effects affects both the particle/γ decay widths (due to change
in level density parameter) and also the fission width (due to change in both fission
barrier and level density parameter). Consequently, the relative strength of the fission
227
from the SM calculations are in the range (0.75–0.85) for the CN
190 Pb, whereas the
K f value for
198 Pb and
192 Po are (0.65–0.70) and (1.0–1.25), respectively.
The results discussed in this section strongly indicate the significance of using
excitation energy-dependent scaling of the finite-range rotating liquid drop model
fission barrier in order to fit the experimental data for ER and fission cross-section.
16.3 Statistical Model Analysis of Neutron Multiplicity
The dissipation effect in fusion–fission process is well established. The excess in
multiplicities with respect to SM predictions indicates the presence of a dynamic
hindrance to fission. Recently, Singh et al. [29] have measured the pre-scission neutron multiplicities for
19 F +
194,196,198 Pt populating
213,215,217 Fr in the excitation
energy range of 46.6–91.8 MeV and discussed the effect of shell effect on nuclear
dissipation. In another set of measurements by Sandal et al. [30] also support the
fission hindrance due to nuclear dissipation.
In the present case, we have performed SM calculations for
210 Po populated
by
18 O +
192 Os in the excitation energy range of 65.23–91.74 MeV. Experimental
data on pre-scission neutron multiplicity is available in the literature for
210 Po [9].
In this section, we are comparing the results obtained from SM calculations with
the experimental results to see the isotopic and excitation energy dependence of
the dissipation strength. Here, SM calculations have been performed using Bohr–
Wheeler and Kramer’s formalism for
210 Po by including and excluding shell effects
in level density parameter and the fission barrier.
The fission width where effect of dissipation that is included is given by
Kramers [31]. The other ingredients used in the present calculations like Bohr–
Wheeler fission width, level density parameter, and fission barrier have been discussed in Sect. 16.2 of this chapter.
Upper panel of Fig. 16.4 shows the results of calculations for pre-scission neutron
multiplicity with no shell effects in level density parameter and barrier height for
210 Po and lower panel shows the results with inclusion of shell effects.
The comparison of calculated pre-scission neutron multiplicities with the experimental values clearly shows that the predictions using Bohr–Wheeler fission width
considerably underestimate the pre-scission neutron multiplicity at all the energies.
It is also observed that the experimental values at all the energies cannot be reproduced by a single value of β. However, the calculations which take into consideration
Kramers’ fission width are in well agreement with the experimental data.
Figure 16.5 shows the lab energy dependence of best fit β value for
210 Po where
the shaded areas represent the uncertainty in β with the experimental error in M pre .
We first note in this figure that the inclusion of shell effects in the calculation results
in higher values for best fit β.
Inclusion of shell effects affects both the particle/γ decay widths (due to change
in level density parameter) and also the fission width (due to change in both fission
barrier and level density parameter). Consequently, the relative strength of the fission