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The mutual dipole-dipole interaction of atoms in a trap can affect their fluorescence. Extremely large effects were reported for double jumps between different intensity periods in experiments with two and three Ba ϩ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg ϩ at 15 wavelengths. In this theoretical paper we study this question for configurations with three and four levels, which model those of Hg ϩ and Ba ϩ , respectively. For two systems in the Hg ϩ configuration we find cooperative effects of up to 30% for distances around one or two wavelengths, about 5% around ten wavelengths, and, for larger distances in agreement with experiments, practically none. This is similar for two V systems. However, for two four-level configurations, which model two Ba ϩ ions, cooperative effects are practically absent, and this latter result is at odds with the experimental findings for Ba ϩ .

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Abstract. We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally valid. Differences that may occur are consequences of Doppler and momentum-transfer effects. Ways to minimize these are discussed.

We investigate the effect of the dipole-dipole interaction on the quantum jump statistics of three atoms. This is done for three-level systems in a V configuration and in what may be called a D configuration. The transition rates between the four different intensity periods are calculated in closed form. Cooperative effects are shown to increase by a factor of 2 compared to two of either three-level systems. This results in transition rates that are, for distances of about one wavelength of the strong transition, up to 100% higher than for independent systems. In addition the double and triple jump rates are calculated from the transition rates. In this case cooperative effects of up to 170% for distances of about one wavelength and still up to 15% around 10 wavelengths are found. Nevertheless, for the parameters of an experiment with Hg+ ions the effects are negligible, in agreement with the experimental data. For three Ba+ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.Comment: 9 pages, 9 figures. Revised version, to be published in PR

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A simplified scheme for the investigation of cooperative effects in the quantum jump statistics of small numbers of fluorescing atoms and ions in a trap is presented. It allows the analytic treatment of three dipole-dipole interacting four-level systems which model the relevant level scheme of Ba + ions. For the latter, a huge rate of double and triple jumps was reported in a former experiment and the huge rate was attributed to the dipoledipole interaction. Our theoretical results show that the effect of the dipole-dipole interaction on these rates is at most 5% and that for the parameter values of the experiment there is practically no effect. Consequently it seems that the dipole-dipole interaction can be ruled out as a possible explanation for the huge rates reported in the experiment.

In PNAS, Priyadarshi et al. (1) reported the detection of unusual levels of atmospheric 35 S in California related to releases from the Fukushima nuclear plant. The authors stated that the 35 S was generated by "leaking neutrons," activating the chlorine in the seawater that was used to cool the Fukushima reactors via the nuclear reaction 35 Cl(n,p) 35 S. The authors calculated "that 4e11 neutrons per m 2 were released," of which "2e8 neutrons per m 2 reacted with 35 Cl."Although we acknowledge it as probable that the detected 35 S originated from Fukushima, we have doubts about the proposed creation and release path. First, there are several possible alternative sources of 35 S:The primary coolant of light water reactors contains veritable amounts of 35 S, typically 0.07-2 MBq/m 3 (or, in other terms, about 7e11 to 2e13 atoms/m 3 ) (2). A typical concentration of Cl in the coolant is about 0.1 ppm, (i.e., 5 decades less than in seawater). However, a reactor at power level generates 1e18 neutrons/m 2 each second, 6 decades more than the calculated "neutron leakage." Hence, the 35 S content in the primary coolant alone could explain the calculated releases. Irradiated fuel itself also contains even more 35 S generated from Cl impurities of the fuel, about 1e19 atoms per ton. This is a huge reservoir of 35 S that might be released if coolant (whether primary or seawater) comes into contact with damaged fuel rods. Finally, the seawater contains dissolved atmospheric 35 S, which will be released immediately once the seawater has evaporated.Additionally, a calculation of the activation of the seawater used for cooling strongly depends on a number of unknown parameters that determine the "irradiation geometry" and reaction rate, most prominently the fuel and core geometry (i.e., the degree of fuel degradation), the water flow rate, moderation, and (self-)shielding effects. Also, the spent fuel pools have to be considered as possible origins, further complicating the analysis. Without any estimation of the size of these uncertainties, probably several orders of magnitude, the results are of little value. Furthermore, the term "neutron leakage" is misleading because its use is not in accordance with common understanding. As far as we understand it, the number given is a neutron fluence (i.e., the neutron flux integrated over the duration of the activation process). In any case, such a number does not provide any new insight as long as it is not compared with any typical value.To conclude, the attempt to gain insights into the accident at Fukushima from airborne radioactivity measurements is very interesting. However, given the uncertainties stated above, we doubt that meaningful quantitative statements are possible from such an analysis. The Fukushima accident is anything but a "well-defined 35 S source." The evidence appears to be too weak to gain "previously undescribed insight" into environmental transformational rates, simultaneously estimating the depositional time scale, oxidation time scale, and a neutron fluen...