Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.

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Summary Most of the nitrous oxide (N2O) in the atmosphere, thought to be involved in global warming, is emitted from soil. Although the main factors controlling the production of N2O in soil are well known, we need more quantitative data on the interactions of soil and the environment in the soil that affect the emission. We therefore studied the effects of irrigation, cropping (fallow, barley with grass undersown) and N fertilization (unfertilized, 103 kg N ha−1) on the composition of soil air and direct N2O emission from soil (using the closed chamber method) in a factorial field experiment on a well‐structured loamy clay soil during 1 June−22 October 1993. The measurements were made weekly during the growing season and three times after harvesting. The composition of the soil air did not indicate severe anoxia in any treatment or combination of treatments, but the accumulation of N2O in the soil air indicated that hypoxia was common. At the start of the irrigation the emissions were small, even though there was much ammonium and nitrate in the soil and therefore a potential for emission of N2O produced by both nitrification and denitrification. Larger emissions occurred later. The largest emissions were found when 60–90% of the soil pore space was filled with water. Irrigation and fertilization with N both roughly doubled the cumulative N2O emission. Growing a crop decreased it by a factor of 3–7. Most N2O was lost from the irrigated fertilized soil under fallow (3.5 kg N ha−1), and least from the unirrigated unfertilized soil under barley (0.1 kg N ha−1).

Elastic constants c11, c12, and c44 of degenerately doped silicon are studied experimentally as a function of the doping level and temperature. First-and second-order temperature coefficients of the elastic constants are extracted from measured resonance frequencies of a set of MEMS resonators fabricated on seven different wafers doped with phosphorus (carrier concentrations 4.1, 4.7, and 7.5 x 10(19) cm(-3)), arsenic (1.7 and 2.5 x 10(19) cm(-3)), or boron (0.6 and 3 × 10(19) cm(-3)). Measurements cover a temperature range from -40°C to +85°C. It is found that the linear temperature coefficient of the shear elastic parameter c11 - c12 is zero at n-type doping level of n ~ 2 x 10(19) cm(-3), and that it increases to more than 40 ppm/K with increasing doping. This observation implies that the frequency of many types of resonance modes, including extensional bulk modes and flexural modes, can be temperature compensated to first order. The second-order temperature coefficient of c11 - c12 is found to decrease by 40% in magnitude when n-type doping is increased from 4.1 to 7.5 × 10(19) cm(-3). Results of this study enable calculation of the frequency drift of an arbitrary silicon resonator design with an accuracy of ±25 ppm between the calculated and real(ized) values over T = -40°C to +85°C at the doping levels covered in this work. Absolute frequency can be estimated with an accuracy of ±1000 ppm.

A field experiment was established in 1978 on a loam soil (pH in CaCl2 7.1) to monitor gradual changes in the soil P status as response to different P fertilization regimes. For 18 years, cereals or grass were cultivated without P fertilization (P0) or with annual P application of 35 kg ha-1 (P1) or 70-79 kg P ha-1 and 71-83 kg K ha-1 (P2K). The effects of the treatments on the crop yield varied yearly. The Chang and Jackson fractionation analysis revealed that fertilizer P not taken up by the plant crops was mostly in the NH4F extract and to a lesser extent in the NaOH extract. The NH4F-extractable P proved also to be the main P source for plants. However, the changes in the reserves of inorganic and organic P did not agree very well with the calculated P balance in soil (applied P minus plant P uptake). This disproportion was partly explained by the soil movement from plots to the neighbouring ones during the experiment. Phosphorus extractable in acid ammonium acetate or water decreased gradually when no P was applied and increased with increasing P accumulation. The changes in the inorganic P reserves due to different P fertilization history were reflected a little more sensitively in the water extraction test than in the acid acetate test.

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