$M1$ $\gamma$ Strength for Zirconium Nuclei in the Photoneutron Channel

Photoneutron cross sections were measured for ${}^{91}\mathrm{Zr}$, ${}^{92}\mathrm{Zr}$, and ${}^{94}\mathrm{Zr}$ near the neutron separation energy with quasimonochromatic $\gamma$ rays. The data exhibit some extra components around the neutron threshold. A coherent analysis of the photoneutron data for ${}^{92}\mathrm{Zr}$ together with the neutron capture on ${}^{91}\mathrm{Zr}$ based on the microscopic Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation model for the $E1$ strength has revealed the presence of an $M1$ resonance at 9 MeV. The microscopic approach systematically shows the same $M1$ strength in the photoneutron cross section for ${}^{91}\mathrm{Zr}$ and ${}^{94}\mathrm{Zr}$. The total $M1$ strength is about 75% larger than the strength predicted by the systematics, being qualitatively consistent with the giant $M1$ resonance observed in the inelastic proton scattering.

Figure 1

Comparison of experimental and theoretical photoneutron cross sections. The theoretical estimates are based on different $E1$ $\gamma$-ray strengths, as described in the text, but they all consider the same standard $M1$ strength from systematics. The dash-dotted line shows the expected threshold behavior $\sigma (E_{\gamma })\propto (E_{\gamma }-S_n{)}^{\ell +1/2}$ with $\ell =1$.

Figure 2

Comparison of experimental [26, 27, 28] and theoretical radiative neutron capture cross section ${}^{91}\mathrm{Zr}(n,\gamma ){}^{92}\mathrm{Zr}$. The dotted line corresponds to the calculation based on the $E1$ and $M1$ Lorentzian model recommended in Ref. 19 and shown in Fig. 1. The solid (dashed) line corresponds to the calculation using the $\mathrm{HFB}+\mathrm{QRPA}$ $E1$ strength with (without) an additional $M1$ contribution as explained in the text.

Figure 3

Comparison of experimental and theoretical photoneutron capture cross section. In all panels, the solid line corresponds to the calculation with an $M1$ strength renormalized as explained in the text, and the dashed line without any contribution of the $M1$. In all cases, the $E1$ strength from the $\mathrm{HFB}+\mathrm{QRPA}$ calculation of 4 is adopted.