To develop a method of (a) calculating the dose rate of voxels within a proton field delivered using pencil beam scanning (PBS), and (b) reporting a representative dose rate for the PBS treatment field that enables correspondence between multiple treatment modalities. This method takes into account the unique spatiotemporal delivery patterns of PBS FLASH radiotherapy. Methods: The dose rate at each voxel of a PBS radiation field is approximately the quotient of the voxel's dose and "effective" irradiation time. Each voxel's "effective" irradiation time starts when the cumulative dose rises above a chosen threshold value, and stops when its cumulative dose reaches its total dose minus the same threshold value. The above calculation yields a distribution of dose rates for the voxels within a PBS treatment field. To report a representative dose rate for the PBS field, we propose a user-selectable parameter of pth percentile of the dose rate distribution, such that (100 − p) % of the field is above the corresponding dose rate. To demonstrate the method described above, we design FLASH transmission fields using 250 MeV protons and calculate the PBS dose rate distributions in both two-dimensional (2D) and three-dimensional (3D) models. To further evaluate the formalism, we provide an example of a clinical PBS treatment field. Results: With the 2D PBS transmission field, it is demonstrated that the time to accumulate the total dose at a voxel is limited to a fraction of the delivery time of the entire field. In addition, the spatial distributions of dose and dose rate are quite different within the field. For the 10 × 10 cm 2 PBS field irradiating a 3D water phantom, the prescribed dose of 10 Gy at 10 cm depth is delivered in 1.0 s. The dose rate decreases in the irradiated volume with increasing depth (until the Bragg peak) due to increase of beam spot size by Coulomb scattering. For example, 95% of the irradiated volume between 0 and 10 cm depth receive >40 Gy/s, whereas between 0-20 cm and 0-30 cm depth, 95% of the irradiated volume received >36 Gy/s and >24 Gy/s, respectively. For the clinical PBS treatment field, the scanning pattern conforms to the PTV. PBS dose rate data are presented for the PTV and adjacent normal organs. Conclusion: We have developed a method of calculating the dose rate distribution of a PBS proton field and have recommended nomenclature for reporting PBS treatment dose rate. We believe that standardizing the method for calculating and reporting PBS treatment dose rates, in a manner that corresponds with other treatment modalities, will advance the research and potential application of PBS FLASH radiotherapy.

Formation and subsequent decay of very highly charged states of CO molecular ions has been studied in 97 MeV collisions between F8+ and CO using a crossed beams apparatus by measuring the energy distributions of carbon and oxygen ions. The kinetic energies released (KER) upon dissociation of COq+ (q=2-10) ions have been investigated by means of large scale, ab initio configuration interaction molecular orbital calculations. Results indicate that dissociation via non-Coulombic potential energy curves of COq+ ions yields lower values of KER than would be expected from purely Coulombic considerations due to the significance of electronic charge density distributions in the internuclear region.

Potential-energy curves of various electronic states of CO + and CO+ are computed using allelectron ab initio molecular-orbital methods. Configuration-interaction eR'ects are treated by perturbative techniques (using Moiler-Plesset perturbation theory to fourth order) and by variational methods (using the coupled-cluster approach). In the case of CO +, calculations indicate that the lowest-energy II and E+ states are nearly degenerate in the Franck-Condon region but that only the latter is likely to be metastable; the former is expected to predissociate rapidly due to a curve crossing with a purely repulsive E state. Experimental measurements have been carried out on the kinetic energy released when metastable CO + ions dissociate by a tunneling mechanism, using an ion-translational-energy spectrometer. The kinetic-energy spectra are measured of fragment ions produced when CO + dissociates via an intermediate highly excited (dissociative) CO+' state populated in an electron-capture reaction in collision with He. The experimental results remain di%cult to interpret within the framework of the computed potential-energy curves.PACS number(s): 31.20.Ej, 34.50.Gb, 35.20.Gs

The ratio of ionization - excitation to single ionization of hydrogen molecules caused by fast proton impact was measured over a wide velocity range (v = 6 - 24 au) using the coincidence time-of-flight technique. This ratio, %, is independent of the collision velocity at high velocities. It differs from the ratio of total to production mostly due to a large contribution from the dissociation of the electronic ground state of the molecular ion. The dissociation fraction of was measured and compares well with our calculations using the Franck - Condon approximation.

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