Analysis of uncertainties in $\alpha$-particle optical-potential assessment below the Coulomb barrier

Background: Recent high-precision measurements of $\alpha$-induced reaction data below the Coulomb barrier have pointed out questions about the $\alpha$-particle optical-model potential (OMP) which are still unanswered within various mass ranges.

Purpose: The applicability of previous optical potential and eventual uncertainties and/or systematic errors of the OMP assessment at low energies can be further considered on this basis.

Method: Nuclear model parameters based on the analysis of recent independent data, particularly $\gamma$-ray strength functions, have been involved within statistical model calculation of the $(\alpha ,x)$ reaction cross sections.

Results: The above-mentioned potential provides a consistent description of the recent $\alpha$-induced reaction data with no empirical rescaling factors of the $\gamma$ and/or nucleon widths.

Conclusions: A suitable assessment of $\alpha$-particle optical potential below the Coulomb barrier should involve the statistical-model parameters beyond this potential on the basis of a former analysis of independent data.

Figure 1

Comparison of the measured $(p,n)$ and $(p,\gamma )$ reaction cross sections for ${}^{63,65}\mathrm{Cu}$ target nuclei [26] and calculated values using the proton OMP parameters of either the local set for ${}^{63}\mathrm{Cu}$ of Ref. [24] (dashed curves) or finally adopted [46] (solid curves), with addition in the latter case of the results for the $(p,\gamma )$ reaction corresponding also to the SLO (dash-dot-dotted curves) and GLO (dash-dotted curves) RSF models for $E1$ radiations.

Figure 2

Comparison of the sum of calculated $\gamma$-ray strength functions of the $E1$ and $M1$ radiations for ${}^{64}\mathrm{Zn}$ and ${}^{68}\mathrm{Zn}$ nuclei, using to the SLO (dash-dot-dotted curves), GLO (dash-dotted curves), and EGLO (solid curves) models for $E1$ radiations and the SLO model for $M1$ radiations. Also shown are the measured dipole $\gamma$-ray strength functions for ${}^{61,62,63,64,65}\mathrm{Cu}$, ${}^{64,66}\mathrm{Zn}$, ${}^{69}\mathrm{Ga}$, and ${}^{76}\mathrm{Ge}$ nuclei [27, 28, 29, 30, 31, 32, 33].

Figure 3

As Fig. 2 but for ${}^{105,106,111,112}\mathrm{Cd}$ [34] and ${}^{116-119,121,122}\mathrm{Sn}$ [35] nuclei.

Figure 4

Comparison of the measured $\alpha$-induced reaction cross sections for ${}^{58,60-62,64}\mathrm{Ni}$ target nuclei [1, 26] and calculated values using the $\alpha$-particle global OMPs of either Ref. [17] (dashed curves) or Ref. [7] (solid curves), and with the alternate involvements for the latter OMP of either the GLO (dash-dotted curves) and SLO (dash-dot-dotted curves) RSF models, or the nucleon OMPs [24] (short-dotted curves), vs laboratory energy of $\alpha$ particles (bottom) and corresponding ratio of the center-of-mass energy and the Coulomb barrier $B$ [52] (top).

Figure 5

As Fig. 4 but for ${}^{107}\mathrm{Ag}$ [2, 26, 53].

Figure 6

As Fig. 4 but for ${}^{106}\mathrm{Cd}$ [26].

Figure 7

As Fig. 4 but for ${}^{112}\mathrm{Sn}$ [4, 26] and the partial $(\alpha ,\gamma )$ reaction cross sections for the decay of the entry state to the ground state and the first and the third excited states of the residual nucleus ${}^{116}\mathrm{Te}$.

Figure 8

Comparison of recently measured $(\alpha ,n)$ reaction cross sections for ${}^{164,166}\mathrm{Er}$ [5, 57] with the calculated values using the $\alpha$-particle OMPs of Refs. [17] (dashed curves) and [7] with (solid curves) as well as without (dash-dotted curves) the energy-dependent radius for the lower-energy surface imaginary potential of the well-deformed nuclei.

Figure 9

As Fig. 8 but for ${}^{187}\mathrm{Re}$ [6] (left), and the OMPs I–III of Ref. [16] (short dotted, short dash-dotted, and short dashed curves, respectively) (right).