Proton, as well as other ion, beams applied by electro-magnetic deflection in pencil-beam scanning (PBS) are minimally perturbed and thus can be quantified a-priori by their fundamental interactions in medium. This a-priori quantification permits an optimal reduction of characterizing measurements on a particular PBS delivery system. The combination of a-priori quantification and measurements will then suffice to fully describe the physical interactions necessary for treatment planning purposes. We consider, for proton beams, these interactions and derive a “Golden” beam data set. The Golden beam data set quantifies the pristine Bragg peak depth dose distribution in terms of primary, multiple Coulomb scatter, and secondary, nuclear scatter, components. The set reduces the required measurements on a PBS delivery system to the measurement of energy spread and initial phase space as a function of energy. The depth doses are described in absolute units of Gy(RBE).mm2.Gp−1, where Gp equals 109 (giga) protons, thus providing a direct mapping from treatment planning parameters to integrated beam current. We used this Golden beam data on our PBS delivery systems and demonstrate that it yields absolute dosimetry well within clinical tolerance.

Measurements of the surface tension of supercooled water down to −25°C have been reported recently (Hrubýet al. J. Phys. Chem. Lett. 2014, 5, 425−428). These experiments did not show any anomalous temperature dependence of the surface tension of supercooled water reported by some earlier measurements and molecular simulations. In the present work, this finding is confirmed using a counterpressure capillary rise method (the counterpressure method) as well as through the use of the classical capillary rise method (the height method). In the counterpressure method, the liquid meniscus inside the vertical capillary tube was kept at a fixed position with an in-house developed helium distribution setup. A preset counterpressure was applied to the liquid meniscus when its temperature changed from a reference temperature (30°C) to the temperature of interest. The magnitude of the counterpressure was adjusted such that the meniscus remained at the same height, thus compensating the change of the surface tension. One advantage of the counterpressure method over the height method consists of avoiding the uncertainty due to a possible variation of the capillary diameter along its length. A second advantage is that the equilibration time due to the capillary flow of the highly viscous supercooled water can be shortened. For both the counterpressure method and the height method, the actual results are relative values of surface tension with respect to the surface tension of water at the reference temperature. The combined relative standard uncertainty of the relative surface tensions is less than or equal to 0.18%. The new data between −26 and +30°C lie close to the IAPWS correlation for the surface tension of ordinary water extrapolated below 0.01°C and do not exhibit any anomalous features. ■ INTRODUCTIONThe surface tension of supercooled liquids, in particular, water and aqueous mixtures, is an important property both in academia and in industry. It plays an essential role in atmospheric research of the nucleation and growth of water droplets 1 and ice crystals. 2 It is known that water in clouds can persist in a supercooled liquid form at temperatures down to −38°C. 3 Manka et al. 4 recently showed that liquid water nanodroplets rather than ice crystals form by homogeneous nucleation at temperatures down to −73°C. Reliable data for the surface tension of supercooled aqueous systems are also important in technical applications such as operation of wind turbines, 5 aircraft icing, 6 or design of secondary refrigeration systems operating with brine. 7 Compared to other fluids, water shows several anomalies at low temperatures, e.g., the well-known maximum in the liquid density at +4°C at atmospheric pressure. The unusual behavior of liquid water becomes more distinct in the metastable supercooled region below 0°C. For instance, the isobaric heat capacity and the isothermal compressibility seemingly diverge (or approach a sharp maximum) when extrapolated to temperatures around −45°C, i.e., below the homogeneous nuc...