Abstract: A review is presented of the Hall-Post inequalities that give lower-bounds to the ground-state energy of quantum systems in terms of energies of smaller systems. New applications are given for systems experiencing both a static source and inner interactions, as well as for hydrogen-like molecules and for tetraquarks in some quark models. In the latter case, the Hall-Post inequalities constrain the possibility of deeply-bound exotic mesons below the threshold for dissociation into two quark-antiquark mesons. We also emphasize the usefulness of the Hall-Post bounds in terms of 3-body energies when some 2-body subsystems are ill defined or do not support any bound state.

Abstract: Treatment of small skin lesions using HDR brachytherapy applicators is a widely used technique. The shielded applicators currently available in clinical practice are based on a tungsten-alloy cup that collimates the source-emitted radiation into a small region, hence protecting nearby tissues. The goal of this manuscript is to evaluate the correction factors required for dose measurements with a plane-parallel ionization chamber typically used in clinical brachytherapy for the 'Valencia' and 'large field Valencia' shielded applicators. Monte Carlo simulations have been performed using the PENELOPE-2014 system to determine the absorbed dose deposited in a water phantom and in the chamber active volume with a Type A uncertainty of the order of 0.1%. The average energies of the photon spectra arriving at the surface of the water phantom differ by approximately 10%, being 384 keV for the 'Valencia' and 343 keV for the 'large field Valencia'. The ionization chamber correction factors have been obtained for both applicators using three methods, their values depending on the applicator being considered. Using a depth-independent global chamber perturbation correction factor and no shift of the effective point of measurement yields depth-dose differences of up to 1% for the 'Valencia' applicator. Calculations using a depth-dependent global perturbation factor, or a shift of the effective point of measurement combined with a constant partial perturbation factor, result in differences of about 0.1% for both applicators. The results emphasize the relevance of carrying out detailed Monte Carlo studies for each shielded brachytherapy applicator and ionization chamber.

Abstract: Intraoperative radiotherapy using mobile linear accelerators is used for a wide variety of malignancies. However, when large fields are used in combination with high energies, a deterioration of the flatness dose profile is measured with respect to smaller fields and lower energies. Indeed, for the LIAC HWL of Sordina, this deterioration is observed for the 12 MeV beam combined with 10 cm (or larger) diameter applicator. Aimed to solve this problem, a flattening filter has been designed and validated evaluating the feasibility of its usage at the upper part of the applicator. The design of the filter was based on Monte Carlo simulations because of its accuracy in modeling components of clinical devices, among other purposes. The LIAC 10 cm diameter applicator was modeled and simulated independently by two different research groups using two different MC codes, reproducing the heterogeneity of the 12 MeV energy beam. Then, an iterative process of filter design was carried out. Finally, the MC designed conical filter with the optimal size and height to obtain the desired flattened beam was built in-house using a 3D printer. During the experimental validation of the applicator-filter, percentage depth dose, beam profiles, absolute and peripheral dose measurements were performed to demonstrate the effectiveness of the filter addition in the applicator. These measurements conclude that the beam has been flattened, from 5.9% with the standard configuration to 1.6% for the configuration with the filter, without significant increase of the peripheral dose. Consequently, the new filter-applicator LIAC configuration can be used also in a conventional surgery room. A reduction of 16% of the output dose and a reduction of 1.1 mm in the D50 of the percentage depth dose was measured with respect to the original configuration. This work is a proof-of-concept that demonstrates that it is possible to add a filter able to flatten the beam delivered by the Sordina LIAC HWL. Future studies will focus on more refined technical solutions fully compatible with the integrity of the applicator, including its sterilization, to be safely introduced in the clinical practice.