Precision measurements of transitions between singlet ($S=0$) Rydberg states of H${}_2$ belonging to series converging on the ${\mathrm{X}}^{+}{}^2{\Sigma }_g^{+}(v^{+}=0,N^{+}=0)$ state of H${}_2^{+}$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were observed for the principal numbers 50 and 70, at fields below 50 mV/cm, with linewidths below 500 kHz. The energy-level structure was calculated using a matrix-diagonalisation approach, in which the zero-field positions of the $\ell \le 3$ Rydberg states were obtained either from multichannel-quantum-defect-theory calculations or experiment, and those of the $\ell \ge 4$ Rydberg states from a long-range core-polarisation model. This approach offers the advantage of including rovibronic channel interactions through the MQDT treatment while retaining the advantages of a spherical basis for the determination of the off-diagonal elements of the Stark operator. Comparison of experimental and calculated transition frequencies enabled the quantitative description of the Stark manifolds, with residuals typically below 50 kHz. We demonstrate how the procedure leads to quantum defects and binding energies of high Rydberg states with unprecedented accuracy, opening up new prospects for the determination of ionisation energies in molecules.

单线态之间转换的精确测量（$\mathrm{小号}=0$) H 的里德堡态${}_2$属于系列收敛于${\mathrm{X}}^{+}{}^2{\Sigma }_G^{+}(v^{+}=0,{ñ}^{+}=0)$H状态${}_2^{+}$已经通过毫米波光谱在无场条件下和弱静电场存在下进行。斯塔克效应混合了具有不同轨道角动量量子数值的状态$\ell$并导致低的二次斯塔克位移$\ell$状态和线性斯塔克位移的几乎退化流形的高$\ell$状态。主要数字 50 和 70 在低于 50 mV/cm 的场中观察到向斯塔克流形的转变，线宽低于 500 kHz。使用矩阵对角化方法计算能级结构，其中$\ell \le 3$里德堡态是从多通道量子缺陷理论计算或实验中获得的，而那些$\ell \ge 4$里德堡从远程核心极化模型中陈述。这种方法提供了通过 MQDT 处理包括 rovibronic 通道相互作用的优点，同时保留了用于确定 Stark 算子的非对角元素的球形基础的优点。实验和计算的过渡频率的比较使斯塔克流形的定量描述成为可能，残差通常低于 50 kHz。我们展示了该过程如何以前所未有的准确度导致量子缺陷和高里德堡态的结合能，为确定分子中的电离能开辟了新的前景。