Consistent optical potential for incident and emitted low-energy $\alpha$ particles

Recent measurements of $\alpha$-particle induced reactions on the ${}^{64}\mathrm{Zn}$ nucleus, below and around the Coulomb barrier, are analyzed simultaneously with $\alpha$-particle emission at similar energies in proton-induced reactions on Zn isotopes. All open reaction channels, particularly the $\gamma$ decay, are calculated using consistent input parameters. Additionally, we check a previous optical-model potential for $\alpha$ particles on nuclei within the mass number range $45\le A\le 209$ [Avrigeanu et al., Phys. Rev. C 90, 044612 (2014)] and prove its correctness in the outgoing channel at least for the present case involving ${}^{64}\mathrm{Zn}$ and nearby nuclei. The reliability of this potential for incident as well as emitted low-energy $\alpha$ particles is supported by the successful reproduction of high-precision measured data, using no empirical rescaling factor of the $\gamma$ and/or particle widths.

Figure 1

Comparison of measured [11] and calculated neutron total cross sections for Ga and ${}^{70}\mathrm{Ge}$, using either (a) the local ${}^{69}\mathrm{Ga}$ or (b) the global OMP parameters sets of Koning and Delaroche [18] (dotted curves), and additionally the energy-dependent geometry parameters mentioned in the text (solid curves).

Figure 2

Comparison of the measured [11], global predictions of the code talys [15] (short-dotted curves), and calculated $(p,n)$ reaction cross sections for the ${}^{66,67,68,70}\mathrm{Zn}$ target nuclei using either the global OMP [18] (dotted curves) or finally adopted parameters (solid curves).

Figure 3

Comparison of calculated $\gamma$-ray strength functions of the $E1$ and $M1$ radiations for the ${}^{65}\mathrm{Ga}$ and ${}^{68}\mathrm{Ge}$ nuclei, using to the SLO (dash-dot-dotted curves), GLO (dash-dotted curves), and EGLO (solid curves) models for E1 radiations, and SLO model for M1 radiations (dotted curves), as well as of the calculated $s$-wave average radiation widths ${\mathrm{\Gamma }}_{\gamma }$ (in meV) corresponding to the SLO model M1 function and each of the above-mentioned E1 model functions. There are also shown the measured dipole $\gamma$-ray strength functions for the ${}^{61,62,63,64,65}\mathrm{Cu}, {}^{64,66}\mathrm{Zn}$, and ${}^{69}\mathrm{Ga}$ nuclei [29, 30, 31, 32, 33, 34], and the ${\mathrm{\Gamma }}_{\gamma }$ values deduced for the two nuclei from systematics of the measured data [13].

Figure 4

Comparison of the measured [1, 11], global predictions of the code talys [15] (short-dotted curves), and calculated cross sections for the $(p,\gamma )$ reaction on ${}^{64,66,68}\mathrm{Zn}$ using the proton OMPs and EGLO-model RSFs given in the text, with alternate involvement of either the global OMP [18] (dotted curves) or different RSFs, namely the GLO- (dash-dotted curves) or SLO-model (dash-dot-dotted curves) RSFs.

Figure 5

As Fig. 4 but for the $\alpha$-induced reactions on ${}^{64}\mathrm{Zn}$ [9, 11], calculated using the $\alpha$-particle global OMPs of either Ref. [5] (dashed curves) or Ref. [3] (solid curves), and the alternate involvements done in the case of the latter $\alpha$-particle OMP.

Figure 6

As Fig. 5 but for the $(p,\alpha )$ reaction on ${}^{64,68,70}\mathrm{Zn}$, and the alternate use of the $\alpha$-particle OMP of Ref. [2] (short dash-dotted curves).