Level densities in ${}^{56,57}\mathrm{Fe}$ and ${}^{96,97}\mathrm{Mo}$

Level densities up close to the neutron binding energy have been extracted from primary $\gamma$ spectra for ${}^{56,57}\mathrm{Fe}$ and ${}^{96,97}\mathrm{Mo}$ nuclei using $\left({}^3\mathrm{He},\alpha \gamma \right)$ and $({}^3\mathrm{He},{}^3\mathrm{He}\prime \gamma )$ reactions on ${}^{57}\mathrm{Fe}$ and ${}^{97}\mathrm{Mo}$ targets. It is shown that statistical spectroscopy provides a useful tool in this mass region. Apparent step structures in the level-density curves are tentatively explained by a schematic microscopic model comprising single-particle level spacings and seniority-conserving and seniority-nonconserving interactions.

Figure 1

Singles $\alpha$ spectrum (upper panel) and $\alpha \text{−}\gamma$ coincidence spectrum (lower panel) for the ${}^{97}\mathrm{Mo}\left({}^{\mathrm{3}}\mathrm{He},\alpha \right){}^{96}\mathrm{Mo}$ reaction. At the neutron binding energy $B_n$, the coincidence spectrum shows a rapid decrease reflecting the lower $\gamma$ multiplicity in the decay from low-lying states in ${}^{95}\mathrm{Mo}$ which are populated by neutron emission. The transfer peaks to the first three states are well known from the $(p,d)$ reaction [15]. The strong transfer peak at $5.3\text{MeV}$ has not been observed previously, and presumably indicates the opening of the $g_{9∕2}$ shell at this energy.

Figure 2

Raw, unfolded, and primary $\gamma$ spectra from the ${}^{57}\mathrm{Fe}\left({}^{\mathrm{3}}\mathrm{He},\alpha \gamma \right){}^{56}\mathrm{Fe}$ reaction at $5-\text{MeV}$ excitation energy (upper panels) and from the ${}^{57}\mathrm{Fe}\left({}^{\mathrm{3}}\mathrm{He},{}^3\mathrm{He}^{\prime }\gamma \right){}^{57}\mathrm{Fe}$ reaction at $6.2\text{−}\text{MeV}$ excitation energy (lower panels).

Figure 3

Experimental primary $\gamma$ spectra (data points with error bars) at two different initial excitation energies (indicated in the figure) compared to the least-${\chi }^2$ fit (solid lines) for the ${}^{97}\mathrm{Mo}\left({}^{\mathrm{3}}\mathrm{He},{}^3\mathrm{He}^{\prime }\gamma \right){}^{97}\mathrm{Mo}$ reaction. The fit is performed simultaneously to the entire primary $\gamma$ matrix of which the two displayed spectra are only a small fraction. The first-generation spectra are normalized to one at each excitation energy bin.

Figure 4

Experimental level densities for the four nuclei under study (full and open symbols represent even and odd nuclei, respectively). Wherever available, level-density data from neutron resonance spacings have been added (triangles). The square represents level-density data from a particle evaporation study [26]. The smooth solid curves are the renormalized level-density parametrizations according to von Egidy et al. [24]. The jagged solid lines are level-density information from counting of discrete levels as given in the Table of Isotopes [23]. Apparent step structures in the level densities are marked by arrows. In the level density of ${}^{56}\mathrm{Fe}$, the bump and the plateau at $0.8\text{MeV}$ and $2.0\text{MeV}$, respectively, are due to the first and second excited states.

Figure 5

Level density as a function of excitation energy. Model calculation (dotted line) using the Hamiltonian of Eq. (3) with $ϵ=0.25\text{MeV}$, $G=0.5\text{MeV}$, and $\kappa \approx 0\text{MeV}$ . Adding a random two-body interaction with the strength $\kappa =0.14\text{MeV}$ (solid line) results in a step structure similar to what is seen in the experimental level-density curve of the iron nuclei.