High-Precision Benchmark Dataset for Hydrogenic Radial Dipole Matrix Elements: Lyman through Pfund Series

This dataset provides high-precision benchmark values of hydrogenic radial electric-dipole matrix elements for the Lyman, Balmer, Paschen, Brackett, and Pfund spectroscopic series. The calculations cover principal quantum numbers up to n=250 and are reported to 38 significant decimal digits. The matrix elements were evaluated analytically using an exact finite-sum framework and computed with arbitrary-precision arithmetic based on the GNU Multiple Precision (GMP) library. The computational engine dynamically allocates up to 32,768 bits of precision, eliminating the catastrophic cancellation and numerical instabilities that commonly arise in conventional double-precision calculations for highly excited Rydberg states. The dataset includes all electric-dipole-allowed transitions (Δl=±1) within the following spectroscopic series: Lyman Balmer Paschen Brackett Pfund All values are reported in atomic units (a_0=1) for hydrogenic systems with nuclear charge Z=1. These benchmark data are intended for applications in atomic spectroscopy, oscillator-strength calculations, Einstein transition coefficients, dynamic and static polarizabilities, Rydberg-atom physics, van der Waals (C_6) interaction calculations, quantum simulation, and precision atomic-structure computations. The accompanying PDF describes the computational methodology, dataset organization, numerical precision, and validation procedures.