Statistical $\gamma$-decay properties of ${}^{64}\mathrm{Ni}$ and deduced ($n,\gamma$) cross section of the $s$-process branch-point nucleus ${}^{63}\mathrm{Ni}$

Particle-$\gamma$ coincidence data have been analyzed to obtain the nuclear level density and the $\gamma$-strength function of ${}^{64}\mathrm{Ni}$ by means of the Oslo method. The level density found in this work is in very good agreement with known energy levels at low excitation energies as well as with data deduced from particle-evaporation measurements at excitation energies above $E_x\approx 5.5$ MeV. The experimental $\gamma$-strength function presents an enhancement at $\gamma$ energies below $E_{\gamma }\approx 3$ MeV and possibly a resonancelike structure centered at $E_{\gamma }\approx 9.2$ MeV. The obtained nuclear level density and $\gamma$-strength function have been used to estimate the $(n,\gamma )$ cross section for the $s$-process branch-point nucleus ${}^{63}\mathrm{Ni}$, of particular interest for astrophysical calculations of elemental abundances.

Figure 1

Original (a), unfolded (b), and first-generation (c) coincidence matrices for ${}^{64}\mathrm{Ni}$ from the ${}^{64}\mathrm{Ni}(p,p^{\prime }\gamma ){}^{64}\mathrm{Ni}$ reaction. The $x$ axis represents the $\gamma$ energy, while the $y$ axis gives the excitation energy of ${}^{64}\mathrm{Ni}$. The number of counts is represented by the color scale.

Figure 2

Level density for ${}^{64}\mathrm{Ni}$ as obtained in two different normalizations. Normalization 1 (see text) corresponds to a spin cutoff parameter $\sigma$ within the model of Ref. [43], while in normalization 2 the model of Ref. [44] has been applied. For both normalizations, discrete energy levels have been used at low energies and a value of $\rho \left(S_n\right)$ has been obtained corresponding to the considered model for $\sigma$. The constant temperature model has been used for interpolation between the experimental data and the point $\rho \left(S_n\right)$ in each case. The bin width is 124 keV.

Figure 3

The $\gamma$-ray-strength function of ${}^{64}\mathrm{Ni}$ (black squares), together with its upper and lower limits (solid green lines). The GDR datasets for ${}^{60}\mathrm{Ni}$ [51] and ${}^{66}\mathrm{Zn}$ [52] used for normalization are also shown. The estimated GDR strength for the ${}^{64}\mathrm{Ni}$ data has been included, together with the models used to reproduce the resonancelike structures. The estimated total strength for the ${}^{64}\mathrm{Ni}$ data is depicted as a red dashed line. Data on the GDR for ${}^{68}\mathrm{Ni}$ are also shown [54].

Figure 4

Experimental nuclear level density for ${}^{64}\mathrm{Ni}$ from the present work (as obtained in normalization 1) compared to the level density from Ref. [55].

Figure 5

The $\gamma$-strength function of ${}^{64}\mathrm{Ni}$ obtained in the present work compared to the $\gamma$ strength of ${}^{56}\mathrm{Fe}$ [13], ${}^{76}\mathrm{Ge}$ [56], and ${}^{94}\mathrm{Mo}$ [12]. All these nuclei present a low-energy enhancement or upbend in the $\gamma$-strength function. In addition, the upper and lower limits for the $\gamma$-strength function estimated in this work have been depicted as green solid lines.

Figure 6

The ${}^{63}\mathrm{Ni}(n,\gamma ){}^{64}\mathrm{Ni}$ cross section from Refs. [29] and [28] compared to the one calculated with talys using the level density and $\gamma$-strength function obtained in this work. The lower and upper limits for the estimated cross section associated with the systematic errors are depicted as solid lines. For the cases in which the ${}^{64}\mathrm{Ni}\gamma$ strength presents a resonancelike structure at $E_{\gamma }\approx 9.2$ MeV, the calculations have been performed assuming a resonance of purely $M1$ character (black) and purely $E1$ character (red).

Figure 7

MACS obtained with talys using the level density and $\gamma$-strength function from this work. The results are presented as a function of $K_{B}T$, where $T$ is the temperature and $K_B$ is the Boltzmann constant. Theoretical values from Ref. [63] and estimates based on measurements from Ref. [30] and [28] are included for comparison. The lower and upper limits estimated in this work are depicted as solid lines. For the cases in which the ${}^{64}\mathrm{Ni}\gamma$ strength presents a resonancelike structure at $E_{\gamma }\approx 9.2$ MeV, the calculations have been performed assuming a resonance of purely $M1$ character (black) and purely $E1$ character (red).

Figure 8

The ${}^{63}\mathrm{Ni}(n,\gamma ){}^{64}\mathrm{Ni}$ reaction rate obtained with talys as a function of temperature $T$, where $K_B$ is the Boltzmann constant. The results from this work have been compared to theoretical values from Ref. [63] and estimates based on measurements from Ref. [28]. The lower and upper limits from this work are depicted as solid lines. For the cases in which the ${}^{64}\mathrm{Ni}\gamma$ strength presents a resonancelike structure at $E_{\gamma }\approx 9.2$ MeV, the calculations have been performed assuming a resonance of purely $M1$ character (black) and purely $E1$ character (red).