Experimentally constrained $(p,\gamma ){}^{89}\mathrm{Y}$ and $(n,\gamma ){}^{89}\mathrm{Y}$ reaction rates relevant to $p$-process nucleosynthesis

The nuclear level density and the $\gamma$-ray strength function have been extracted for ${}^{89}\mathrm{Y}$ by using the Oslo method on ${}^{89}\mathrm{Y}(p,p^{\prime }\gamma ){}^{89}\mathrm{Y}$ coincidence data. The $\gamma$-ray strength function displays a low-energy enhancement consistent with previous observations in this mass region $\left({}^{93\text{–}98}\mathrm{Mo}\right)$. Shell-model calculations support the conclusion that the observed enhancement is due to strong, low-energy $M1$ transitions at high excitation energies. The data were further used as input for calculations of the ${}^{88}\mathrm{Sr}(p,\gamma ){}^{89}\mathrm{Y}$ and ${}^{88}\mathrm{Y}(n,\gamma ){}^{89}\mathrm{Y}$ cross sections with the talys reaction code. Comparison with cross-section data, where available, as well as with values from the BRUSLIB library, shows a satisfying agreement.

Figure 1

$\mathrm{\Delta }E\text{−}E$ plot for ${}^{89}\mathrm{Y}+p$ (a), with the deposited energy in the thick $E$ detector versus the thin $\mathrm{\Delta }E$ detector for $\theta ={132}^{\circ }\pm 1^{\circ }$, and (b) the sum of the deposited energy in the thin and thick detector for the same angle. The labeled peaks are the ground state (0), the first excited 909 keV level (1), the second excited 1507 keV level (2), and the third excited 1744 keV level (3).

Figure 2

(a) Raw NaI spectra and (b) unfolded, primary $\gamma$ spectra for each initial excitation-energy bin for ${}^{89}\mathrm{Y}(p,p^{\prime }\gamma ){}^{89}\mathrm{Y}$; the area within the dashed lines are used in the further analysis, i.e., the data for $E_{\gamma }>2.00$ MeV, $5.43<E_x<10.98$ MeV are selected. (c) Projection of the primary $\gamma$ spectra for the range of excitation energies between the lines.

Figure 3

Spin distributions for ${}^{89}\mathrm{Y}$ at the neutron-separation energy $S_n=11.482$ MeV for the three different normalization approaches. For FG09 and FG05, Eq. (6) is used with their respective spin-cutoff parameters in Eqs. (4) and (5). The $\text{HFB}+\text{c}$ calculations assume no specific shape of the spin distribution but happens to be very similar to FG05 in this case.

Figure 4

Level densities at $S_n$ in the Y mass region with global systematics of (a), (b) Ref. [26] (FG05) and (c), (d) Ref. [27] (FG09) (see Table 1). The unknown level density for ${}^{89}\mathrm{Y}$ is shown as a purple diamond. The global-systematics predictions are scaled with a factor of 0.31 and 0.34 for the FG05 and FG09 approaches, respectively. The error bands show the upper-limit scaling of (a), (b) 0.40 for FG05 and (c), (d) the lower limit of 0.27 for FG09.

Figure 5

The extracted level density of ${}^{89}\mathrm{Y}$. The black points give the $\text{HFB}+\text{c}$ normalization, the lower and upper limits are shown as azure lines. The inset shows a zoom of the high-$E_x$ part.

Figure 6

Normalized $\gamma \mathrm{SF}$ of ${}^{89}\mathrm{Y}$ compared to ${}^{89}\mathrm{Y}(\gamma ,n)+{}^{89}\mathrm{Y}(\gamma ,np)$ data from Refs. [36, 37], and evaluated data from Ref. [38]. The black points are obtained with the $\text{HFB}+\text{c}$ normalization, and the azure lines show the lower and upper limits.

Figure 7

The $\gamma \mathrm{SF}$ of ${}^{89}\mathrm{Y}$ together with photonuclear data [36, 37] and evaluated $\left(\gamma ,n\right)$ data from Ref. [38] compared with models for the dipole strength.

Figure 8

Same as Fig. 7 but with the QRPA $E1$ strength (see text).

Figure 9

(a) Input $\gamma \mathrm{SFs}$ of ${}^{89}\mathrm{Y}$, note that the talys default is for $E_n=1$ MeV, corresponding to an initial excitation energy of 12.48 MeV in the GLo model, and that the GLo model is by default normalized to a radiative width $\langle {\mathrm{\Gamma }}_{\gamma }\rangle =170$ meV taken from an interpolation routine in talys; (b) the resulting ${}^{88}\mathrm{Y}(n,\gamma ){}^{89}\mathrm{Y}$ cross sections, (c) and the corresponding astrophysical reaction rates compared to the BRUSLIB (dashed magenta line, Ref. [50]) and the JINA REACLIB (green solid line, Ref. [53]). The minimum and maximum predictions from the models implemented in talys are also shown (thick, black lines).

Figure 10

(a) Calculated ${}^{88}\mathrm{Sr}(p,\gamma ){}^{89}\mathrm{Y}$ cross sections shown as a blue-shaded band compared to data from Ref. [61], and (b) the corresponding astrophysical reaction rates compared to the BRUSLIB (dashed magenta line, Ref. [50]) and the JINA REACLIB (green solid line, Ref. [53]). The minimum and maximum predictions from the models implemented in talys are also shown (thick, black lines), as well as the result using default input parameters (black crosses).