Level density and thermodynamics in the hot rotating ${}^{96}\mathrm{Tc}$ nucleus

Evaporated neutron energy spectra have been measured in coincidence with low-energy discrete $\gamma$ rays in the reaction ${}^4\mathrm{He}+{}^{93}\mathrm{Nb}$ at $E\left({}^4\mathrm{He}\right)=28$ MeV. The low-energy light-ion beam provides the scope of extracting the experimental nuclear level density (NLD) in the compound nuclear reaction. Angular-momentum gated NLDs have been extracted in the excitation energy range of $E^{*}\sim 5–15$ MeV from the measured neutron energy spectra. The extracted NLDs have been compared with different theoretical calculations such as the exact pairing plus independent particle model at finite temperature (EP+IPM), Hartree-Fock plus BCS (HFBCS), and Hartree-Fock-Bogoliubov plus combinatorial method (HFBC). Interestingly, the experimental NLDs are in good agreement with the results of the EP+IPM, whereas the HFBCS and HFBC fail to describe these data. Consequently, the thermodynamic properties of ${}^{96}\mathrm{Tc}$ at finite angular momentum have been extracted using the EP+IPM NLDs. Through the analysis of the calculated thermodynamic quantities, it is shown that no pronounced bump is seen in the heat capacity of ${}^{96}\mathrm{Tc}$, in opposition with the earlier results of ${}^{96}\mathrm{Mo}$, which showed a prominent bump at $T\sim 0.7–1$ MeV. This difference is understandable since pairing in the even-even system (${}^{96}\mathrm{Mo}$) is always stronger than that in the odd-odd one (${}^{96}\mathrm{Tc}$).

Figure 1

(a) Time-of-flight and (b) pulse shape discrimination (bottom panel) spectra in the reaction of ${}^4\mathrm{He}+{}^{93}\mathrm{Nb}$ at ${\mathrm{E}}_{\mathrm{lab}}\left({}^4\mathrm{He}\right)=28\mathrm{MeV}$. ${\mathrm{Q}}_L$ and ${\mathrm{Q}}_S$ are the charge integrated over the long ($2\mu \mathrm{s}$) and short integration (50 ns) gate widths, respectively.

Figure 2

(a) Experimental fold distribution along with the geant4 simulation. (b) Angular momentum distribution for different folds ($F$) for the ${}^4\mathrm{He}+{}^{93}\mathrm{Nb}$ reaction at 28 MeV incident energy.

Figure 3

Evaporated neutron energy spectra (filled circles) along with results of the statistical model calculations (continuous line) for different folds ($F$).

Figure 4

Neutron contribution (cascade) from different channels along with experimental data for fold $F=2$.

Figure 5

Neutron and proton pairing gaps for ${}^{96}\mathrm{Tc}$ as functions of temperature. The thick and thin lines denote the exact and BCS results, respectively.

Figure 6

The value of $k, J$ and $T$ for different folds. The dotted and dashed lines represent the $k$ value according to CGCM [40] and EGSM [41], respectively, as discussed later in the text.

Figure 7

Angular momentum gated NLD (filled cirlces) along with the results of different theoretical calculations. Open circles are taken from RIPL-3 [45] weighted over our $J$ distribution and filled triangle is from Hille et al. [52].

Figure 8

Excitation energy-dependent spin cutoff factor (filled symbols) along with different theoretical calculations. The dotted lines are taken from Ref. [53], the dashed lines are taken from Ref. [54]. The continuous and double dot-dashed lines represent the ${\sigma }_{\perp }$ and ${\sigma }_{\parallel }$, respectively, used in the EP+IPM calculation.

Figure 9

Angular momentum gated thermodynamic quantities as functions of temperature obtained using EP+IPM level densities.