In this thesis, experiments with negative ions performed at the DESIREE facility are presented. DESIREE consists of two electrostatic storage rings operated at 13 K. The low temperature in combination with a low pressure allows for storage times of the negative ion beams to be up to several hours. This unique feature is to advantage in the development of a new method for high-precision measurements of electron affinities and binding energies of excited states of negative ions. In this method, ions are stored in the one of the two storage rings of DESIREE, and a high-power laser is applied to photodetach ions in the excited state. These excited states are often very long-lived for negative ions and the photodetachment signal from these states are a major source of background, which dominates the uncertainties, in threshold spectroscopy experiments. By removing the ions in the excited state, threshold photodetachment spectroscopy can be performed with almost no background below the photodetachment threshold. This allows the threshold energy to be determined with a very high precision.

The new method is demonstrated by performing measurements of the electron affinities of ¹⁶O and ¹⁸O. The obtained uncertainty in the electron affinity of ¹⁶O is a tenfold improvement in accuracy compared to previous measurements and the resulting electron affinity is the most accurately measured electron affinity of any element to date. In addition to the electron affinity, the fine-structure splitting of the ground state is also measured for both isotopes. From the measured electron affinities, the isotope shift in the ¹⁸O and ¹⁶O electron affinity is determined with a high accuracy. This shift is a quantity not only relevant in atomic physics but also of great interest in nuclear physics.

In addition to the high-precision electron affinity measurements, the possibility to store ions for a long time is utilized to perform measurements of lifetimes of excited states in negative ions. Measurements are presented where excited states in Ir^-, Bi^-, and CH^- are studied. Lifetimes ranging from 100 ms up to 5000 s are observed.