Comparison of statistical model calculations for stable isotope neutron capture

It is a well-observed result that different nuclear input models sensitively affect Hauser-Feshbach (HF) cross-section calculations. Less well-known, however, are the effects on calculations originating from nonmodel aspects, such as experimental data truncation and transmission function energy binning, as well as code-dependent aspects, such as the definition of level-density matching energy and the inclusion of shell correction terms in the level-density parameter. To investigate these aspects, Maxwellian-averaged neutron capture cross sections (MACS) at 30 keV have been calculated using the well-established statistical Hauser-Feshbach model codes talys and non-smoker for approximately 340 nuclei. For the same nuclei, MACS predictions have also been obtained using two new HF codes, cigar and sapphire. Details of these two codes, which have been developed to contain an overlapping set of identically implemented nuclear physics input models, are presented. It is generally accepted that HF calculations are valid to within a factor of 3. It was found that this factor is dependent on both model and nonmodel details, such as the coarseness of the transmission function energy binning and data truncation, as well as variances in details regarding the implementation of level-density parameter, backshift, matching energy, and giant dipole strength function parameters.

Figure 1

$E1$ ${}^{107}\mathrm{Ag}$ strength function for three commonly used models, GLO [42], SLO [40, 41], and DLO [43]. For the depicted GLO curve the initial excitation energy was 7.27 MeV.

Figure 2

Red and blue points correspond to the percentage difference of $kT=30$ keV MACS, calculated with sapphire and cigar, respectively, to the KADoNiS database. Calculations were performed using the $\gamma$-strength function from Ref. [42], the $\mathrm{CT}+\mathrm{BSFG}$ level density with parameters from Ref. [8], and the optical model from Ref. [58].

Figure 3

MACS calculated with sapphire obtained using truncated $J^{\pi }$ data, compared to identical calculations performed using nontruncated $J^{\pi }$ data. The level data are from RIPL-3 [45].

Figure 4

Percentage difference of $kT=30$ keV MACS calculated with talys, compared to the KADoNiS database. For solid circles, calculations have been performed using the $\gamma$-strength function from Ref. [42], the $\mathrm{CT}+\mathrm{BSFG}$ level density with parameters from Ref. [17], and the optical model from Ref. [58]. Open circles represent identical calculations; however, the talys default to use experimental level-density data has been adopted.

Figure 5

Left axis: Ratio of CT $T$ calculated by talys to those calculated by cigar/sapphire using Eq. (15). Right axis: Ratio of cigar MACS using talys $T$ to base cigar calculations.

Figure 6

Left axis: Ratio of matching energies $E_m$ calculated by talys to those calculated by cigar/sapphire using Eq. (16). Right axis: Ratio of cigar MACS using talys $E_m$ to base cigar calculations.

Figure 7

Left axis: Backshift as calculated in cigar(sapphire) using Eq. (17) (solid blue circles), and talys using Eq. (18) (solid red circles). Right axis: Ratio of cigar MACS to KADoNiS values. Open blue circles were obtained using Eq. (17); open red circles were obtained using Eq. (18).

Figure 8

Left axis: Ratio of level-density parameter $a$ at $S_n$ calculated by talys to those calculated by cigar/sapphire using Eq. (17). Right axis: Red points show ratio of cigar MACS using talys $a$ to base cigar calculations.

Figure 9

Left axis: Ratio of the spin cutoff parameter $\sigma$ calculated by talys to those calculated by cigar/sapphire using Eq. (8). Right axis: Red points show ratio of cigar MACS using talys ${\sigma }^2$ to base cigar calculations.

Figure 10

Percentage difference of $kT=30$ keV MACS calculated with cigar, compared to the KADoNiS database. Solid blue circles have been calculated with GDR parameters from the theoretical compilation of Ref. [45]; open blue circles are identical calculations obtained using the experimental GDR parameters from Ref. [45].

Figure 11

Percentage difference of $kT=30$ keV MACSs calculated by non-smoker. Rate data taken from Ref. [65].