Systematic description of evaporation spectra for light and heavy compound nuclei

To systematically describe evaporation spectra for light and heavy compound nuclei over a large range of excitation energies, it was necessary to consider three ingredients in the statistical model. First, transmission coefficients or barrier penetration factors for charged-particle emission are typically taken from global fits to elastic-scattering data. However, such transmission coefficients do not reproduce the barrier region of evaporation spectra and reproduction of the data requires a distributions of Coulomb barriers. This is possibly associated with large fluctuations in the compound-nucleus shape or density profile. Second, for heavy nuclei, an excitation-energy dependent level-density parameter is required to describe the slope of the exponential tails of these spectra. The level-density parameter was reduced at larger temperatures, consistent with the expected fadeout of long-range correlation, but the strong $A$ dependence of this effect is unexpected. Last, to describe the angular-momentum dependence of the level density in light nuclei at large spins, the macroscopic rotational energy of the nucleus has to be reduced from the values predicted with the finite-range liquid-drop model.

Figure 1

Center-of-mass kinetic-energy spectra of $\alpha$ particles and protons detected in coincidence with evaporation residues formed in ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ reactions. Experimental results (data points) are shown for the indicated excitation energies of the ${}^{224}\mathrm{Th}$ compound nuclei. The curves show spectra predicted with the gemini$++$ code and normalized to the same peak height as the experimental data. The solid curves (the default calculations of the code) were obtained with the excitation-dependent level-density parameter and with distributions of Coulomb barriers. The short-dashed curves indicated the results obtained using a single Coulomb barrier and the long-dashed curves are associated with an excitation-independent $\mathrm{ã}=A/7.3$ MeV${}^{-1}$ level-density parameter.

Figure 2

As in Fig. 1, but now for ${}^{200}\mathrm{Pb}$ compound nuclei formed in ${}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$ reactions.

Figure 3

As in Fig. 1 but now for ${}^{193}\mathrm{Tl}$ compound nuclei formed in ${}^{32}\mathrm{Si}+{}^{160}\mathrm{Ho}$ reactions.

Figure 4

As in Fig. 1 but now for ${}^{160}\mathrm{Yb}$ compound nuclei formed in ${}^{60}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ reactions with neutron spectra also included.

Figure 5

As in Fig. 1 but now for ${}^{156}\mathrm{Er}$ compound nuclei formed in the three indicated reactions.

Figure 6

Comparison of the experimental $\alpha$-particle evaporation spectrum (data points) measured in the ${}^{28}\mathrm{Si}+{}^{160}\mathrm{Ho}$ reaction producing ${}^{193}\mathrm{Tl}$ compound nuclei at $E^{*}=126$ MeV to gemini$++$ predictions. The solid curve was obtained with standard IWBC transmission coefficients, while the short- and long-dashed curves were obtained by increasing and decreasing the radius parameter of the nuclear potential, respectively (see text). The curves have been normalized to the same peak height as the experimental data.

Figure 7

Transmission coefficents for $\mathrm{\alpha }+{}^{193}\mathrm{Tl}$ at $\ell =0$. The dashed curves show the three transmission coefficients of different nuclear radii which are averaged in Eq. (9) and the solid curve is the result.

Figure 8

Mass dependence of level-density parameters. Experimental points from neutron-resonance counting are shown as the solid square data points. The open circles are fits obtained using Eq. (12).

Figure 9

Values of $\kappa$ in Eq. (15) obtained from fitting evaporation spectra. The solid line shows a smooth approximation used to calculate evaporation spectra and ER excitation functions. The dashed curve shows $\kappa$ values extracted from the predictions of Ref. [65].

Figure 10

Excitation-energy dependence of the smoothed level-density parameter obtained in this work for the indicated $A$ values.

Figure 11

Comparison of experimental and predicted proton multiplicities from the indicated compound nuclei. To aid in viewing, the data have been scaled by the indicated factors. The solid curves were obtained with the excitation-dependent level-density parameter and with distribution of Coulomb barriers. The dashed curves show the prediction with single Coulomb barriers and a constant ${\mathrm{ã}}_{\mathrm{eff}}=A/7.3$ MeV${}^{-1}$.

Figure 12

As for Fig. 11 but for $\alpha$-particle multiplicities.

Figure 13

Evaporation-residue excitation functions for the indicated compound nuclei. The data points are published experimental results and the short-dashed, long-dashed, and solid curves were calculated with ${\mathrm{ã}}_{\mathrm{eff}}=A/7.3$, $\mathrm{ã}=A/11$ MeV${}^{-1}$, and Eq. (15), respectively.

Figure 14

Excitation-energy dependence of (a) the nuclear temperature and (b) the entropy deduced in this work.

Figure 15

Inclusive proton and $\alpha$-particle kinetic-energy spectra in the reaction center-of-mass frame measured at angles that highlight CN emission. The data are associated with ${}^{117}\mathrm{Te}$ CN formed in (a,b) ${}^{14}\mathrm{N}+{}^{103}\mathrm{Rh}$ and (c) ${}^{40}\mathrm{Ar}+{}^{77}\mathrm{Se}$ reactions. The curves are again gemini$++$ predictions. The solid curves are the default calculations with a distribution of Coulomb barriers, the excitation-dependent level-density parameter ${\mathrm{ã}}_{\mathrm{eff}}$, and the prescription for $E_{\mathrm{yrast}}(J)$. For the short-dashed curves, a single Coulomb barrier is used and for the long-dashed curves, Sierk’s values of $E_{\mathrm{yrast}}(J)$ are employed.

Figure 16

As for Fig. 15 but for ${}^{106}\mathrm{Cd}$ compound nuclei formed in ${}^{32}\mathrm{S}+{}^{74}\mathrm{Ge}$ reactions.

Figure 17

As for Fig. 15 but for ${}^{96}\mathrm{Ru}$ compound nuclei formed in ${}^{32}\mathrm{S}+{}^{64}\mathrm{Ni}$ reactions.

Figure 18

As for Fig. 15 but for ${}^{67}\mathrm{Ga}$ compound nuclei formed in ${}^{40}\mathrm{Ar}+{}^{27}\mathrm{Al}$ and ${}^{55}\mathrm{Mn}+{}^{12}\mathrm{C}$ reactions.

Figure 19

As for Fig. 18, but now for ${}^{59}\mathrm{Cu}$ compound nuclei. For the $E^{*}=60$-MeV data, the square and circular data points represent the results measured at ${\theta }_{\mathrm{lab}}={25}^{°}$ and ${45}^{°}$, respectively, while for the 110-MeV data they correspond to ${\theta }_{\mathrm{lab}}={15}^{°}$ and ${30}^{°}$.

Figure 20

Values of $J_{*}$, the angular momentum for which the Sierk yrast energy is modified, are plotted again the mass of the first $\alpha$-daughter nucleus. The line shows a fit to these values which is used in subsequent gemini$++$ calculations.

Figure 21

Rotational-plus-deformation energies versus the nuclear angular momentum for (a) ${}^{63}\mathrm{Cu}$ and (b) ${}^{55}\mathrm{Co}$. Curves are shown for the dependence caluculated by Sierk form his macroscopioc model. These can be compared to results obtained from fitting $\alpha$-particle evaporation spectra in this work and by Huizenga et al.