Preequilibrium models for 58 Ni (n, xp) reaction in Neutrons at 8, 9, 9.4, 11 and 14.8 MeV using the EMPIRE and TALYS codes

. In this study, the calculations of proton emission spectra produced by 58 Ni (n, xp) reaction are used in the framework of preequilibrium models with the EMPIRE and TALYS codes. Exciton Model predictions combined with the Kalbach angular distributions systematics and statistical Multi-step Direct (MSD) with Multi-step Compound (MSC) processes preequilibrium models were used. Also, some necessary parameters as optical model, level density, level density a-parameter and single-particle level density parameter have been investigated for our calculations. The comparison with experimental data shows clear improvement over the Exciton and MSD with MSC models calculations.


Introduction
Nickel is a major component of austenitic steel that is widely employed in the nuclear industry and it is important structural material for nuclear applications [1]. Through an elaborate work [2], cross sections and spectra for (n, xp) and (n, xα) reactions on 58 Ni and 60 Ni at energies of 9.4 and 11 MeV and for 58 Ni at 8 MeV have been based on comparison of Hauser--Feshbach calculations with the measured spectra. On the other hand, measured and calculated differential and total yield cross-section data of 58 Ni(n, xa) and 63 Cu(n, xp) in the neutron energy range from 2.0 to 15.6 MeV [3] have been made by the STAPRE-H [4] code and compared with experimental data. According to Alvar [5], the proton energy and angular distributions from (n, p) and (n, np) reactions on 27 Al, 32 S, 59 Co and 58 Ni have been measured for 14.1 MeV neutrons, while the proton emission cross sections of Grimes et al., [6] in reactions of 15 MeV neutrons with isotopes of chromium, iron, nickel and copper were obtained using the sum of the two contributions of hybrid model calculations and the multistep Hauser--Feshbach calculations.
The main purpose of this work is to investigate the sensitivity on the input parameters from RIPL-3 [7] calculations of proton emission spectra produced by (n, xp) reaction using the EMPIRE code [8] while in the framework of TALYS code [9], we investigate some adjustable parameters of the local and global nucleon optical models of Koning and Delaroche [10] with the sensitivity on the level density a-parameter, and singleparticle level density parameter parameters. In the * Corresponding author: leilayettou448@hotmail.com framework of EMPIRE code [8], the different nuclear reaction models one component exciton model with single particle level density g, multi-step direct (MSD) model with pairing gap parameters for protons, deformation of the Nilsson Hamiltonian and spin-orbit in the harmonic oscillator used in MSD and multi-step compound (MSC) with single particle level densities in MSC model, the parameters as the level density and optical model calculations are considered. In the framework of TALYS code [9], the sensitivity of some parameters as the two-component exciton model, Fu's pairing energy correction with the parameterisation of the matrix element for the two components exciton model of the preequilibrium reaction, skip decay compound nucleus, optical model, level density with the level density a-parameter, average pairing correction, and single particle level density parameter, are considered. The plots are presented with the comparison between the results from the EMPIRE and TALYS codes [8,9] calculations and the experimental data which are retrieved from the EXFOR database [11]. The obtained results have been discussed and compared with the available experimental data [11] and found in agreement with each other.

Theoretical models' formula
In EMPIRE code [8], the phenomenological preequilibrium mechanism as defined by Griffin [12] is the exciton model. In the PCROSS code of EMPIRE code [8], the pre-equilibrium spectra in this model are given as: The PCROSS code uses the Williams formula [13], where the Pauli correction ( , ℎ) is calculated in accordance with Kalbach's method [14]: The next pre-equilibriums described in the EMPIRE code [8] are the quantum-mechanical preequilibrium models of the multi-step Direct (MSD) theory of preequilibrium direct inelastic scattering to the continuum originally proposed by Tamura, Udagawa and Lenske [15], while the multi-step Compound (MSC) model follows the approach of Nishioka et al. [16]. In TALYS code [9], the pre-equilibrium differential cross section where the factor P represents the part of the preequilibrium population that has survived emission from the previous states and passes through the ( , ℎ ,  , ℎ  ) configurations, averaged over time.

Results and discussions
The calculated double differential cross sections for 58 Ni(n, xp) nuclear reaction at 11 MeV, the proton emission spectra at 9 and 14.8 MeV for 58 Ni(n, xp) have been illustrated in Figs.1--3, while the calculated cross sections for the same nuclear reaction at 8,9,4 MeV are illustrated in the paper of Yettou et al [17]. As shown in figure 1, the results of the optical model parameters [18 ,19] chosen are close to the experimental data [11] and very fairly differences to the standard EMPIRE Koning--Delaroche potential [10] are observed. In the framework of the two-component exciton [9], we calculated the double differential cross sections and compared with the experimental data [11] as shown in Figs. 1--3 (continuous and dotted blue lines). Through the level density parameter a at the neutron separation energy in MeV −1 in 28 59 (compound nucleus) as shown in Figs. 1 (except for figure 3, the single-particle level density parameter affects strongly the calculations) and 2, the results are close to the experimental data [11]. As shown in Fig. 2, the calculated angle integrated proton particle emission spectra with Hartree--Fock--Bogoliubov (HFB) microscopic level density [20] cross sections are in good agreement with the experimental data [11] using EMPIRE code [8]. For all the figures as shown in this paper, the EMPIRE and TALYS codes' [8,9] results are close to the experimental results and the lower 2 value gives a significantly better fit when compared with the experimental result (except in Fig.3, the results affect fairly the form of the curve using TALYS code [9]).

Fig.2.
Comparison between calculated angle integrated proton particle emission spectra with Hartree--Fock--Bogoliubov (HFB) level density [20] and Fermi-Gas Model nuclear level density (continuous and dashed red lines) for 58 Ni(n, xp) using EMPIRE code [8] with those as calculated with the effect of the level density parameter-a of Back Shifted Fermi Gas Model [21] level density (continuous and dotted blue lines) using TALYS code [9] to the experimental data (open squares) [11].  [9] (The constant of the single-particle level density parameter);   =4.92469 TALYS 1.8 [9] (The default constant of the single-particle level density parameter);   =4.9431E+09

28-Ni-58(n,x) Ei1.48E+7
d/dE (b/eV) Fig.3. Comparison between calculated angle integrated proton particle emission spectra with Wilmore--Hodgson S-OMP for neutrons [18] and Perey [19] for protons, and the standard Koning--DeLaroche potential [10] using EMPIRE code [8] (continuous and dashed red lines) with those as calculated with the effect of the constant of the single-particle level density parameter (Kph keyword which set to 2.) of Back Shifted Fermi Gas Model level density [21] (continuous and dotted blue lines) using TALYS code [9] to the experimental data (open cercles) [6] from 14.8 MeV neutron induced.