This study employs the post-form distorted wave Born approximation (DWBA) within a fully quantum mechanical framework to probe the Coulomb breakup dynamics of one-neutron halo nuclei interacting with heavy targets. A novel first-order perturbative Fourier transform method is developed in momentum space to evaluate the transition amplitude, enabling efficient computation of exclusive and inclusive observables for light and deformed medium-mass systems, such as ${}^{11}\mathrm{Be}$ and ${}^{31}\mathrm{Ne}$, respectively. Validated against the full-order Coulomb wave Born approximation, which captures higher-order effects at low energies, the Fourier transform method demonstrates robust accuracy across high beam energies. This analytic approach bridges perturbative simplifications with exact dynamics, and may offer a versatile tool for extracting electromagnetic response and astrophysical capture rates from exotic beam facilities.

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• Breakup reactions
• Coulomb dissociation
• Direct reactions
• Nuclear reactions
• Unstable nuclei induced nuclear reactions