## 2 Materials and Methods
### The Numerical Calculations
#### 2.4.1 Generation of the Folding Potential  
To determine the interaction potential microscopically, the folded potential \(V_{F}\) is obtained using the nucleon density of the target nucleus, \(\rho_{1}(\stackrel{{\rightarrow}}{{r}}_{1})\), and the NN interaction potential, \(V_{NN}(\stackrel{{\rightarrow}}{{s}})\). This process is defined by the integral Equation (7).  
Figure 3: Example input file used in TALYS 1.96 simulations for (n,el) reactions on tungsten isotopes. Calculation for \(n+^{182}W\) reaction at 1.5 MeV neutron incident energy.  
2.4.2. Incorporation of the OMP into the Schrodinger Equation  
The folded potential \(V_{F}\) is used within the Schrodinger equation to obtain the wave function \(\varphi(\overrightarrow{r})\):  
\[\left[\frac{\hbar^{2}}{2\mu}\
abla^{2}+V\left(\overrightarrow{r}\right) \right]\varphi\left(\overrightarrow{r}\right)=E\varphi(\overrightarrow{r}) \tag{12}\]  
Here, \(\mu\) is the reduced mass of the system and \(E\) represents the energy eigenvalue.  
2.4.3. Calculation of the Cross Section via Partial Wave Expansion  
Using the asymptotic solution of the wave function, the scattering amplitude \(f(\theta)\) calculated, and this amplitude is converted into the differential cross section as:  
\[\frac{d\sigma}{d\Omega}=|f(\theta)|^{2} \tag{13}\]  
2.4.4. Use of TALYS 1.96 Software  
The TALYS 1.96 software, when provided with folded potentials (in this study obtained via the SHF-WS + SF approach) as input, solves the Schrodinger equation and automatically generates differential cross sections by utilizing angular distribution functions expressed through Legendre expansions.  
[PERSON] [47] provided a detailed mathematical formulation of the OM theory and scattering functions. Furthermore, the study by [PERSON] et al. [48] experimentally demonstrated how OM parameters relate to nuclear matter radii and scattering data.  
2.4.5. Neutron Densities and Folded Potential for W Isotopes  
In this study, neutron densities for tungsten isotopes were calculated using the SHF-WS theoretical method. These density distributions represent the spatial arrangement of nucleons within the nucleus and form the fundamental input for the folding potential.  
The interaction potential between the tungsten nucleus and the neutron is obtained via the SF integral using these densities and the NN interaction (M3Y-Reid). This potential is Equation (9). The NN interaction potential used is Equation (11). The folded potential is then adapted as an OMP using a WS form. The imaginary part is taken in WS form:  
\[U\left(\overrightarrow{r}\right)=V\left(\overrightarrow{r}\right)+iW( \overrightarrow{r}). \tag{14}\]  
For this potential, the parameters \(r_{v}\) and \(a_{v}\) were employed, and the value \(V_{0}\) was obtained.  
2.4.6. Calculation and Comparison of Results  
The Schrodinger equation is solved numerically using the potential described above. The TALYS 1.96 software was employed for the numerical solution. The scattering amplitude \(f(\theta)\) obtained from this solution is then used to calculate the differential cross section \(d\sigma/d\Omega\) as a function of angle. These calculations are performed for various scattering angles, and the resulting data are compared with experimental measurements.