In 1978, physicists bombarded a target with a beam of ions and measured how quickly they slowed down in matter. Using the Doppler shift of gamma rays, they calculated the lifetimes of excited nuclear states. For iron-58, they obtained a value that did not agree with shell-model calculations.
Now, in a Coulomb excitation experiment, beams of iron-56 and iron-58 nuclei passed near a heavy target. The target's electric field gently jostled the nuclei, lifting them to higher energy states. By measuring the gamma radiation emitted as they returned to the ground state, physicists determined the transition probability between levels. For iron-56, the result matched previous data, but for iron-58 it was noticeably lower.
Re-evaluating the old data with modern stopping values resolves the discrepancy. The iron-58 nucleus, which seemed like a capricious exception, now follows the predictions of the nuclear shell model precisely. This is reminiscent of a situation where an old recipe had a mistake in the amount of salt, making the dish taste off — once corrected, everything falls into place.
as written by the authors arXiv:2603.17414
The low-excitation states of atomic nuclei in the region around the $$N = Z = 28$$ shell closure are generally well described by the shell model. Most experimental observables in the iron isotopes $$^{56}$$Fe, $$^{58}$$Fe, and $$^{60}$$Fe ($$Z = 26$$; $$N=30$$, $$32$$, $$34$$) support a shell-model description. However, the lifetimes of the $$4_1^+$$ state in $$^{58}$$Fe in the literature result in a reduced transition strength that deviates markedly from shell-model predictions. There are three independent measurements, all in agreement and all based on the Doppler Shift Attenuation Method (DSAM) or Doppler-Broadened Line Shape method (DBLS). In this work, Coulomb-excitation measurements were performed on $$^{56}$$Fe and $$^{58}$$Fe beams to determine the ratios $$B(E2; 4_1^+ \to 2_1^+)/B(E2; 2_1^+ \to 0_1^+)$$. Thus, $$B(E2; 4_1^+ \to 2_1^+)$$ is determined relative to the known $$B(E2; 2_1^+ \to 0_1^+)$$ values. For $$^{56}$$Fe, $$B(E2; 4_1^+ \to 2_1^+) = 23(4)$$ W.u., agreeing with the adopted value. However, for $$^{58}$$Fe, the $$B(E2; 4_1^+ \to 2_1^+)$$ values obtained (for the various combinations of matrix element signs that could not be firmly established) are all significantly lower than the value derived from the previous lifetime measurements, and are in accord with shell-model calculations. The 1978 DSAM measurement of Bolotin et al., Nucl. Phys. A 311, 75 (1978), has been re-examined. The discrepancy between that measurement and the Coulomb-excitation measurement can be ascribed to the Lindhard-Scharff-Schi{\o}tt (LSS) electronic stopping powers adopted for the DSAM analysis, which considerably overestimate contemporary values. Evidently, lifetime measurements from that era that are based on LSS stopping powers should be used with caution. The revised lifetime data, incorporating current stopping powers, are compared with shell-model calculations.
The stopping power of matter for ions depends on their velocity somewhat like air resistance for a car: at low speeds the loss is linear, and at high speeds it's quadratic, but for ions the picture is more complex due to charge exchange.