The specialized knowledge and strict data security requirements in nuclear engineering limit the direct application of cloud-based, general-purpose large language models. We introduce AtomicGPT, a secure, on-premises, nuclear domain-specific language model developed through domain adaptation of small-scale (Gemma2-9B, Qwen2.5-7B) and large-scale (Exaone4-32B) base models. We curated a two-track nuclear corpus: a public foundation corpus (29.1M tokens) and an extended private corpus (84.7M tokens) incorporating internal technical reports to enhance the domain expertise of the 32B model. Furthermore, we established a comprehensive benchmark suite comprising multiple-choice, short-answer, and descriptive tasks. AtomicGPT consistently outperformed its base models in improving factual accuracy and reducing observed hallucination-like errors. AtomicGPT-Gemma2-9B improved from 23 to 40 (+73.9% relative) on the multiple-choice benchmark. Leveraging the extended private corpus, AtomicGPT-Exaone4-32B achieved scores of 56 (multiple-choice), 34.50% (short-answer), and 8.21 (descriptive), surpassing GPT-4 (48, 31.29%, and 7.70) and remaining competitive with GPT-5-class models (GPT-5:59/33.76%/8.48; GPT-5.1:58/38.66%/8.58; GPT-5.2:74/39.38%/8.68). For security-critical nuclear facilities with restricted cloud access, targeted domain adaptation of on-premises models enables strong, domain-specific performance while maintaining strict data security. This study contributes to the application of natural language processing in nuclear engineering and provides empirical evidence for the feasibility of deploying domain-adapted LLMs in heavily regulated and security-sensitive environments.