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Purpose Radiation therapy with ion beams provides a better conformation and effectiveness of the dose delivered to the tumor with respect to photon beams. This implies that a small uncertainty or variation in the crossed tissue shape and density may lead to a more important underdosage of the tumor and/or an overdosage of the surrounding healthy tissue. Although the online control of beam fluence and transverse position is well managed by an appropriate beam delivery system, the online measurement of the longitudinal position of the Bragg peak inside the patient is still an open issue. In this paper we propose a proof‐of‐concept study of a technique that would allow the online verification of the patient thickness along the beam direction, which could permit detecting a subset of possible range error causes, such as morphological variations. Methods The nuclei 12C and 4He have the same magnetic rigidity: the two species could be accelerated together in an accelerator and a mixed particle beam delivered to the patient. In the same medium and with the same energy per nucleon, the range of 4He2+ is about three times the 12C6+ one. It is, thus, conceivable to achieve a dual goal with a single mixed beam: carbon, stopping into the tumor, is appointed to cure, while helium, emerging from the patient, to control: by detecting and measuring the residual range and position of He, it would be possible to determine the integrated relative stopping power of the patient and prove that it is the expected one. For the detection of helium particles, a plastic scintillator and an optical sensor are proposed. Being helium ions not available at CNAO, the detection system has been characterized using a proton beam. Nevertheless, since the light emitted by a proton is less than the one produced by a helium ion, the helium signal is expected to be more pronounced than the proton one (for the same number of particles). To predict the magnitude of the light signal measured by the sensor, two Monte Carlo models have been setup and validated by measuring the photons per pixel impinging on the sensor. To deal with the many optical issues and to reliably describe the physical process, some corrections have been included into the models. Results The predictions of both the models are in good agreement with the measurements (within the 20% in terms of absolute photons per pixel). The proposed detection system is able to measure the range of a proton beam with sub‐millimetrical precision also in the presence of the background produced by carbon ion fragments and discrepancies in the expected range were detected with a resolution better than 1 mm. Conclusions Although many technical issues have still to be addressed for a real implementation in a clinical environment, the preliminary results of this study suggest that a surrogate of real‐time verification of the beam range inside the patient during a treatment with carbon ions is possible by adding a small fraction of helium ions to the primary beam.

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and nextnearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1 > 1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T = 0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and nonmagnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.

The recent advances in angle resolved photoemission techniques allowed the unambiguous experimental confirmation of spin charge decoupling in quasi one dimensional (1D) Mott insulators. This opportunity stimulates a quantitative analysis of the spectral function A(k, ω) of prototypical one dimensional correlated models. Here we combine Bethe Ansatz results, Lanczos diagonalizations and field theoretical approaches to obtain A(k, ω) for the 1D Hubbard model as a function of the interaction strength. By introducing a single spinon approximation, an analytic expression is obtained, which shows the location of the singularities and allows, when supplemented by numerical calculations, to obtain an accurate estimate of the spectral weight distribution in the (k, ω) plane. Several experimental puzzles on the observed intensities and line-shapes in quasi 1D compounds, like SrCuO2, find a natural explanation in this theoretical framework.