<p>This study presents computational results for the proton radiative capture by triton (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^3\mathrm H\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <mi mathvariant="normal">H</mi> </mrow> </math></EquationSource> </InlineEquation>) using the Argonne V18 (AV18) potential model enhanced with three-body forces. We develop a comprehensive computational framework combining the AV18 nucleon–nucleon potential with Urbana IX three-nucleon forces to calculate the astrophysical <i>S</i>-factor, scattering length and effective range for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^3\mathrm H(p, \gamma )^4He\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <mi mathvariant="normal">H</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> <mn>4</mn> </msup> <mi>H</mi> <mi>e</mi> </mrow> </math></EquationSource> </InlineEquation> reaction. Our methodology involves solving the Schrödinger equation numerically using variational Monte Carlo (VMC) techniques with explicit treatment of three-body correlations. The results show improved agreement with the experimental data compared to the two-body potential models, particularly in the low-energy region relevant for astrophysical applications. We provide detailed comparisons with previous theoretical studies and experimental measurements, demonstrating the importance of three-body forces in accurately describing this radiative capture process.</p>