3.10 Tesis magíster

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Self-assembly of submonolayer-coverage organic films
(2009) Corrales Iturriaga, Tomás Patricio; Volkmann, Ulrich; Pontificia Universidad Católica de Chile. Instituto de Física
In this work we present a study of self assembled submonolayer coverage organic films. The types of molecules studied here are n-alkane chains, mainly n-dotriacontane (n-C32H66), that are deposited on silicon substrates with a thin native silicon oxide layer (∼15Å). In this research we have developed a velocity controlled dip-coating device to prepare submonolayer films. We have identified the parameters that affect the coverage, morphology and structures that arise in the preparation of the film. The techniques used to characterize these films are Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS). Fur- thermore, this is the first work that demonstrates that SEM is a plausible technique to study thin films of n-alkanes. The future importance of this research is related to the possibility of micro-structuring energetically homogenous surfaces with nanometer thick films using relatively simple techniques, such as velocity controlled dip-coating. Micro-structured patterns, such as the stripes reported here, could be applied as optical diffraction grids or as templates for other materials.In this work we present a study of self assembled submonolayer coverage organic films. The types of molecules studied here are n-alkane chains, mainly n-dotriacontane (n-C32H66), that are deposited on silicon substrates with a thin native silicon oxide layer (∼15Å). In this research we have developed a velocity controlled dip-coating device to prepare submonolayer films. We have identified the parameters that affect the coverage, morphology and structures that arise in the preparation of the film. The techniques used to characterize these films are Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS). Fur- thermore, this is the first work that demonstrates that SEM is a plausible technique to study thin films of n-alkanes. The future importance of this research is related to the possibility of micro-structuring energetically homogenous surfaces with nanometer thick films using relatively simple techniques, such as velocity controlled dip-coating. Micro-structured patterns, such as the stripes reported here, could be applied as optical diffraction grids or as templates for other materials.
Wetting properties of n-alkane thin films to understand the adherence mechanism of artificial membranes on silicon substrates
(2017) Díaz Díaz, Diego Ignacio; Volkmann, Ulrich; Pontificia Universidad Católica de Chile. Facultad de Física
In this work we present a study of the wetting properties of silicon samples coated with a single layer of n-alkane molecules that self-assemble perpendicular to the surface.The types of molecules studied here are n-alkane chains, mainly n-dotriacontane (n-C32 H66), that were deposited on silicon substrates with a thin native silicon oxidelayer (15˚A). The thin films were prepared by Dip-Coating technique in a C32 H66/n-heptane solution. The techniques used to characterize these films are Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). In this research a contact angle setup was developed to measure wettability of submonolayer films. An influence of morphology and coverage on the contact angle was found. Moreover, alkane molecules migrate much like a reverse coffee-ring effect after drop evaporation, forming complex tail-like morphologies.This research is relevant to understand alkane adhesion on silicon substrates, which is related with artificial membrane fabrication, which are used for biosensors applications. Micro-structured pattern like stripes could be applied as templates for other materials, especially considering the possibility of creating homogeneous surfaces with nanometer thick films.
Individual breast dosimetry for mammographic exams : a back-projection approach
(2017) Rioseco Mora, Camila Belén; Sánchez Nieto, Beatriz; Dörner Yaksic, Edgardo Andrés; Häring, Peter; Pontificia Universidad Católica de Chile. Facultad de Física
The aim of this project is to propose and validate a procedure for estimating a dose at the axial plane of the breast in patients under mammographic exposure by means of electronic portal imaging device (EPID) dosimetry. In vivo transit dosimetry consists of measuring the transmitted radiation through the breast with an EPID, and then back-projecting the fluence through the same volume in order to reconstruct the dose at a certain plane. The methodology relies on the fact that from individual beam attenuation information, is possible to estimate dose deposition in the mammary gland. Beam attenuation was calculated from the exit and entrance fluence. Monte Carlo simulation of the entrance fluence was computed for three beam qualities. Exit fluence is calculated for each case, by deconvolution of the EPID image with previously determined composite kernel. A complete model (i.e., X-ray tube, breast compression paddle, different breast thickness and detector) of the GE Senograph Essential with Tomosynthesis device, was simulated with EGSnrc. Specific codes as BEAMnrc and DOSXYZnrc were used for beam and detector simulations, respectively. Three different beam qualities were simulated (only for 2D conventional mammography image acquisition) and additionally, and in-house graphical user interphase MATLAB1 program “BreDose” was designed to estimate doses at an axial mid-plane of the breast from the EPID images.
Numerical simulations of wire array Z-pinches under variations of global magnetic fields
(2017) Donoso Tapia, Luis Alberto; Veloso Espinosa, Felipe Eduardo; Pontificia Universidad Católica de Chile. Facultad de Física
During the last five years a lot of work has been done with the computational code GORGON [1,2] to simulate the dynamics of transient plasmas. The main work has been focused on studying plasmas in different configurations of wire arrays.These configurations include conical arrays [3,4,5], asymmetrical cylindrical arrays [6].This thesis focuses on two primary areas. First, how does spatial resolution affect the reliability of observed simulation results? This was studied by simulating conical wire array Z-pinches with varying resolutions. Second, the dynamics of Z pinch plasmas generated by asymmetrical wire arrays are examined. This causes the magnetic field topology to become asymmetrical, this causing the plasma to move away from the geometrical center [6]. Regarding the conical arrays studied in this work, a low electronic density region was initially observed, which was located between two high density regions, similar to what has been observed in stellar phenomena like the Herbig-Haro objects [7]. However, subsequent simulations, with resolution increased by a factor of 2,5,have disproved this supposition.The second main aspect of this work shows how undermassed aluminium wire configurations can be used for accurate control of plasma dynamics, by modifying the governing magnetic field topology of the system. This leads to an acceptable method for controlling the direction and velocity of the plasma precursor within a time period similar to the associated pulsed power generator rise time [6,8,9].
Optical surface monitoring and pillow positioning configuration for complex system's set-up
(2017) Loreto Javiera Godoy Solís; Häring, Peter, 1965-; Sánchez Nieto, Beatriz; Pontificia Universidad Católica de Chile. Facultad de Física
Optical Surface Monitoring and Pillow Positioning Configuration for Complex System’s Set-Up: Aligning the patient’s target volume, isocenter and OARs with the linac’s isocenter can be done using certain immobilization device and imaging to adapt therapy if any variation of the tumor or patient’s body has occurred. In this investigation, a configuration of 10 pillows and Vision RT were employed to positioning the patient while it was checked by CBCT. The results show that for non-coplanar fields, Vision RT is accurate enough, with shifts less than 1º and 1mm. 4 pillows in a wedge under the head show an accurate position in the rotational axis (lessthan 1º) comparing with Vision RT and the off-set values given by the CBCT, although more pillows should be necessary for thorax and pelvis plans, since the differences between both methods are in average of 5 mm and 10º. Since the image registration was made manually, there are difference between 2 CBCTs of 6 mm and 5º in average in each plan, around the same magnitude than the difference between the two methods, so the differences might be due to the fact that Vision RT matches surfaces and CBCT matches the target volume, and because the manual image registration is involved with a human error
Caracterización de propiedades clásicas y cuánticas de pulsos de femtosegundos
(2017) Rojas Aedo, Ricardo; Seifert, Birger; Pontificia Universidad Católica de Chile. Facultad de Física
Este informe de tesis versa sobre propuestas hacia la caracterización de las propiedades clásicas y cuánticas de pulsos de femtosegundos, que en principio pueden ser expandidas a pocos pico segundosy a atto segundos, al menos en su sentido conceptual. El texto principalmente analizará en detalle el método de caracterización de propiedades clásicas de pulsos, basado en la mezcla no lineal de diferentes trenes pulsados, llamado FROG, reinterpretando el campo mezcla, desde una perspectiva clásica, donde se desarrolla una nueva técnica de caracterización analítica y no interferométrica llamada “VAMPIRE analítico” , y otra perspectiva cuántica, donde surge una propuesta para el análisis de las propiedades cuánticas internas de pulsos haciendo uso de esquemas tipo FROG . Por completitud en la última línea, además se comentará como generar estados cuánticos interesantes (no-coherentes), y los resultados obtenidos experimentalmente en el laboratorio, con pulsos de femtosegundos utilizando fibras ópticas.
Asirunaka: Generador de Potencia Pulsada de Doble Pulso Dedicado a Plasmas de Explosión de Alambres y Formación de Nanopartículas
(2017) Masoliver Aguirre, Pavel; Bhuyan, Heman; Pontificia Universidad Católica de Chile. Facultad de Física
Force spectroscopy of a saxitoxin bindingaptamer
(2017) Figueroa Leigh, Nataniel; Maze Ríos, Jerónimo; Pontificia Universidad Católica de Chile. Facultad de Física
Over the last decades optical tweezers have enabled the exploration of pico-Newton forces involved in several single-molecule mechanisms relevant in important biological systems (ie. DNA-folding and molecular motors). This has lead to a new understanding of the mechanical nature of the interactions occuring between biologicaly-relevant molecules. Here, in this thesis we used optical tweezers to study the folding/unfolding dynamics of the Handy-aptamer, a single-stranded-DNA molecule with high affinity for saxitoxin, a potent neurotoxin that is present in red tide algal blooms. This is the cause of substantial economic damage to the shellfish industry. To perform the pulling experiments, we developed a method to chemically attach the Handy-aptamerin between two double-stranded-DNA handles, which themselves were attached tomicron-sized polystyrene beads that were manipulated using the optical tweezers and a micropipette. From the pulling experiments we observed sharp folding/unfolding transitions. None the less, the transition between these states was observed to be erraticand time-dependent, exhibiting changes in sharpness and rate of occurence. Weattempted to stabilize the structure of the aptamer by adding Mg+2 and saxitoxin, both giving similar results; making the rip (sudden transition in extension) force histograms narrower and less abudant at higher forces; implying structure stabilization.These results have been the first steps towards characterizing the folding properties of the Handy-aptamer and identifying the properties that make it bind to saxitoxin.This would prove useful to develop better saxitoxin identifiers and sensors that would have lower toxin surveying costs and prevent deaths.
A dynamic nonlinear coupled differential equations model of tumor growth and response to radiotherapy
(2018) Ortiz Guzmán, Valentina; Gago Arias, Araceli; Espinoza Bornscheuer, Ignacio Guillermo; Karger, Christian; Pontificia Universidad Católica de Chile. Facultad de Física
Evaluación dosimétrica de tratamientos con Leksell gamma knife en presencia de inhomogeneidades
(2018) Elgueda Farías, Susan Pamela; Caprile Etchart, Paola F.; Pontificia Universidad Católica de Chile. Facultad de Física
Desarrollo e implementación de un sistema de auditoría para dosimetría absoluta con alanina y TLD en centros de radioterapia chilenos
(2018) Faúndez Cifuentes, Daniel; Gago Arias, Araceli; Pontificia Universidad Católica de Chile. Facultad de Física
Contrasting neutron star heating mechanisms with Hubble Space Telescope observations
(2018) Rodríguez Tapia, Luis; Reisenegger, Andreas; Pontificia Universidad Católica de Chile. Instituto de Física
Si las estrellas de neutrones se enfriaran pasivamente, se esperaría que se vuelvan indetectables en un tiempo menor a 107 años, al alcanzar bajas temperaturas T < 104 K. Sin embargo, radiación del tipo ultravioleta, que implica temperaturas superficiales T ∼ 105 K, fue detectada desde los pulsares de Giga años PSR J0437- 4715 y PSR J2124-3358 y también desde el pulsar B0950+08 cuya edad es ∼ 107 años. Esta discrepancia puede ser explicada por un grupo de mecanismos de calentamiento propuestos en la literatura. Usando el código de Petrovich y Reisenegger se calcularon curvas de evolución térmica considerando diferentes mecanismos de calentamiento. Estas fueron contrastadas con las temperaturas inferidas a partir de las observaciones de los pulsares para determinar cuál es la principal fuente de emisión térmica de las estrellas de neutrones. Encontramos que el calentamiento rotoquímico, reacciones nucleares en las capas profundas de la corteza y el calor liberado por la fricción de vórtices superfluidos pueden mantener la estrella lo suficientemente caliente más allá del tiempo estándar de enfriamiento pasivo y explicar las observaciones.Si las estrellas de neutrones se enfriaran pasivamente, se esperaría que se vuelvan indetectables en un tiempo menor a 107 años, al alcanzar bajas temperaturas T < 104 K. Sin embargo, radiación del tipo ultravioleta, que implica temperaturas superficiales T ∼ 105 K, fue detectada desde los pulsares de Giga años PSR J0437- 4715 y PSR J2124-3358 y también desde el pulsar B0950+08 cuya edad es ∼ 107 años. Esta discrepancia puede ser explicada por un grupo de mecanismos de calentamiento propuestos en la literatura. Usando el código de Petrovich y Reisenegger se calcularon curvas de evolución térmica considerando diferentes mecanismos de calentamiento. Estas fueron contrastadas con las temperaturas inferidas a partir de las observaciones de los pulsares para determinar cuál es la principal fuente de emisión térmica de las estrellas de neutrones. Encontramos que el calentamiento rotoquímico, reacciones nucleares en las capas profundas de la corteza y el calor liberado por la fricción de vórtices superfluidos pueden mantener la estrella lo suficientemente caliente más allá del tiempo estándar de enfriamiento pasivo y explicar las observaciones.
Evaluación de algoritmos comerciales de cálculo de dosis absorbida de fotones en regiones fuera del campo de tratamiento
(2018) Medina Ascanio, Karem Nathalie; Sánchez Nieto, Beatriz; Pontificia Universidad Católica de Chile. Facultad de Física
Los algoritmos presentes en los Sistemas de Planificación están optimizados para entregar una dosis veraz y precisa dentro de los límites del campo de tratamiento. Fuera de este, se ha demostrado una inexactitud que depende del algoritmo particular. Este estudio analiza, por medio de medidas experimentales, la exactitud de la dosis fuera del campo de dos algoritmos semianalíticos, Pencil Beam Convolution y Collapsed Cone Convolution, implementados en dos Sistemas de Planificación comerciales EclipseTM (Varian Medical System) y Monaco® (Elekta) respectivamente, así como también, el algoritmo de cálculo de dosis basado en métodos de Monte Carlo implementado en Monaco®. Tanto los cálculos con los Sistemas de Planificación, como las determinaciones experimentales de las dosis se realizaron en medios homogéneos (agua) para diferentes configuraciones de campos convencionales y para una distribución de dosis de un plan real de IMRT de próstata. Las determinaciones experimentales se llevaron a cabo con TLDs-100, películas radiocrómicas EBT3 ycámara de ionización Semiflex. Los resultados obtenidos al comparar perfiles dedosis laterales de campos abiertos calculados por los algoritmos respecto a los medidos experimentalmente muestran que, a partir del 9% de la dosis los cálculos realizados por el algoritmo Pencil Beam subestiman la dosis real en un promedio de 53%. Mientras que, se obtuvo un buen acuerdo con los cálculos realizados por el algoritmo Collapsed Cone, con una desviación local promedio de aproximadamente 2,5%. En el caso del algoritmo Monte Carlo, de los resultados obtenidos no se puede inferir ninguna conclusión ya que cálculos de este tipo (conformados) donde se logra la dosis deseada con una incertidumbre de 1% en un punto (generalmente el isocentro), emplean pocas partículas para lograr dicha incertidumbre y, por lo tanto, el ruido estadístico se hace significativo. Con respecto al desempeño de los algoritmos Pencil Beam y Monte Carlo en el caso de un plan clínico de irradiación de próstata en relación a la medida experimental con EBT3, al hacer un análisis gamma local (3% - 3 mm) ambos algoritmos fallaron en regiones de dosis bajas (> 5%), siendo el algoritmo MC el que obtuvo la mayor cantidad de puntos que no pasaron el criterio gamma, mientras que, Pencil Beam fue el que arrojo mayor imprecisión en regiones de dosis altas (para lo cual es análisis gamma fue global, respecto al máximo).
Predictors for radiation-induced xerostomia and their reliability considering random setup errors and parotid gland migration
(2018) Astaburuaga García, Rosario; Bangert, Mark; Pontificia Universidad Católica de Chile. Facultad de Física
Feasibility study : use of cine-MRI in MR-guided particle therapy
(2018) Sepúlveda Muñoz, César; Pfaffenberger, Asja; Sánchez Nieto, Beatriz; Pontificia Universidad Católica de Chile. Facultad de Física
Cinematic Magnetic Resonance Imaging (cine-MRI) are fast time-resolved 2D MRI sequences that allow online visualization of organ motion without exposing patients to ionizing radiation. In this study, the potential of cine-MRI for the definition of animage-based gating criterion in particle therapy of pancreatic cancer is investigated. Transversal cine-MRI are employed to segment the pancreas, since they can provide information on tissue changes in the beam-path during delivery. Volunteer data were acquired on 10 different acquisition days. An image-based gating window was defined based on the breathing-curve (BC) of the first day (end-exhale breathing phase ±30%). The superposition of the pancreas segmentations in this window was calculated. For other days of data acquisition, the agreement with this initial superposition contour was evaluated by using different segmentation image similarity metrics. Additionally, a motion analysis of the pancreas was performed. From the metrics comparisons, a gating criterion was defined to establish when irradiation can be allowed. An evaluation of the dosimetric differences due to differences in the segmentations achieving the criterion and the spatial location of the organs was carried out for a proton treatment. Although the method applied was subjected to several limitations, it was proved to be feasible.
Deviations of the leptonic branching ratios of the heavy Higgs in the MSSM with broken R-parity
(2018) Méndez Leiva, Andrés; Díaz, Marco A.; Pontificia Universidad Católica de Chile. Facultad de Física
We performed a phenomenological study of the leptonic decay modes of a heavy Higgs in a supersymmetric scenario which we called the ϵλ-MSSM, in which we added ϵ-bilinear and λ-trilinear terms to break R-parity explicitly, constrained by the most recent neutrino experimental data. In particular, we explored the possibilityof decreasing the coupling associated to the τ τ mode, in order to reduce the large number of events predicted by other typical R-parity conserving (RpC) models to justify the non-observation of any heavy scalar resonance, while opening regions of the parameter space which were previously excluded. We also study the possibility of enhancing the µµ mode due to its importance in future experimental searches. We found that even with a loose cosmological bound given by the sum of the neutrino masses, the deviations for the τ τ mode are smaller than a 1%, while for the µµ mode it can be up to 50%. However, once we constrained our parameters to reproduce the most recent neutrino observables associated with neutrino oscillation, we found that the deviations attained in each mode are extremely small, leading to deviations of ∼ 0.0001% for the µµ mode and ∼ 0.0000000001% for the τ τ model, making the ϵλ-MSSM indistinguishable from the RpC-MSSM case in the leptonic channels.
Atomic force microscopy study of elastic properties of vapor-phase-deposited lipid membranes
(2018) Catalán López, Rodrigo Esteban; Volkmann, Ulrich; Pontificia Universidad Católica de Chile. Facultad de Física
In this work we present a study of phase transitions and their relation with the elastic properties of three phospholipid membranes, namely 1,2-dimyristoyl-snglycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC). Samples were generated individually by physical-vapor-deposition of the lipid molecules mentioned over acid-cleaned polished silicon chips. The thickness of the samples were measured with Very High Resolution Ellipsometry. Average thickness are 60˚Athickness on average. The molecular consistency of the lipids were characterized using Raman spectroscopy. The Young’s modulus of the lipid membranes was obtained applying the Hertz model to data acquired with Atomic Force Microscopy in Quantitative Imaging feedback mode. Finally, the individual dependence of these lipids respect to temperature changes was used to detect the main gel-to fluid phase transition.The results in the present work show an expected softening of the lipid membranes just after the main phase transition, although the values of the elastic modulus found do not match the ones reported in the literature. However, the general trends correlate well with the ones found in other works. Nevertheless,systematic investigations using similar conditions as ours are still scarce.The acquisition of information related to the elastic properties and stability of the membranes is relevant for future works on protein insertion, and to understand the lipid membranes dependance on several other environmental conditions like changes in temperature, pH-dependence or ionic strength concentration.
Quantum sensing using NV centers in diamond
(2018) González Brouwer, Raúl, Manuel; Maze Ríos, Jerónimo; Pontificia Universidad Católica de Chile. Facultad de Física
This thesis is focused on understanding the interaction of nitrogen vacancy (NV) defect in diamond with its environment as well as its applications in nanotechnology and biophysics. First, we study the hyperfine interaction due to nearby 13C carbon and 15N nitrogen isotopes in the vicinity of the Level Anti-Crossing (LAC), we propose an experimental method at room temperature free of microwave, in which it is possible to find the sign of the Fermi contact term, using the coupling between nuclear spins 1/2 and electronic spin 1. For this, a three-dimensional coil system was constructed to study the fluorescence close to the LAC. Second we describe an experiment in order to use the NV center as a sensor for chemical reactions, in specific to measure the pH and relate it’s macroscopic measurement with experiments like Ramsey interferometry and change in the spectrum, in order to observe changes on the charge state and T∗2 . Finally, we show a way to functionalize a nanodiamond hosting a NV defect, and use it as a biomarker for amyloid β, an Alzheimer desease related compound. We show that using this functionalized nanodiamonds might enable the development of longer experiments in biophysics due to the photostability of the NV defect compared to regular biomarkers that are widely used in biology. This works paves the way for performing unltrasensitive and reliable detection of cells involved in the pathogenesis of the Alzheimer desease.This thesis is focused on understanding the interaction of nitrogen vacancy (NV) defect in diamond with its environment as well as its applications in nanotechnology and biophysics. First, we study the hyperfine interaction due to nearby 13C carbon and 15N nitrogen isotopes in the vicinity of the Level Anti-Crossing (LAC), we propose an experimental method at room temperature free of microwave, in which it is possible to find the sign of the Fermi contact term, using the coupling between nuclear spins 1/2 and electronic spin 1. For this, a three-dimensional coil system was constructed to study the fluorescence close to the LAC. Second we describe an experiment in order to use the NV center as a sensor for chemical reactions, in specific to measure the pH and relate it’s macroscopic measurement with experiments like Ramsey interferometry and change in the spectrum, in order to observe changes on the charge state and T∗2 . Finally, we show a way to functionalize a nanodiamond hosting a NV defect, and use it as a biomarker for amyloid β, an Alzheimer desease related compound. We show that using this functionalized nanodiamonds might enable the development of longer experiments in biophysics due to the photostability of the NV defect compared to regular biomarkers that are widely used in biology. This works paves the way for performing unltrasensitive and reliable detection of cells involved in the pathogenesis of the Alzheimer desease.
Quantum sensing using NV centers in diamond
(2018) González Brouwer, Raúl, Manuel; Maze Ríos, Jerónimo; Pontificia Universidad Católica de Chile. Facultad de Física
This thesis is focused on understanding the interaction of nitrogen vacancy (NV) defect in diamond with its environment as well as its applications in nanotechnology and biophysics. First, we study the hyperfine interaction due to nearby 13C carbon and 15N nitrogen isotopes in the vicinity of the Level Anti-Crossing (LAC), we propose an experimental method at room temperature free of microwave, in which it is possible to find the sign of the Fermi contact term, using the coupling between nuclear spins 1/2 and electronic spin 1. For this, a three-dimensional coil system was constructed to study the fluorescence close to the LAC. Second we describe an experiment in order to use the NV center as a sensor for chemical reactions, in specific to measure the pH and relate it’s macroscopic measurement with experiments like Ramsey interferometry and change in the spectrum, in order to observe changes on the charge state and T2 . Finally, we show a way to functionalize a nanodiamond hosting a NV defect, and use it as a biomarker for amyloid β, an Alzheimer desease related compound. We show that using this functionalized nanodiamonds might enable the development of longer experiments in biophysics due to the photostability of the NV defect compared to regular biomarkers that are widely used in biology. This works paves the way for performing unltrasensitive and reliable detection of cells involved in the pathogenesis of the Alzheimer desease.
Correcciones magnéticas a las longitudes de scattering π-π en el modelo sigma lineal
(2018) Monje Apablaza, Leandro; Loewe Lobo, Marcelo Patricio; Pontificia Universidad Católica de Chile. Facultad de Física
En este trabajo se consideran las correcciones magnéticas a las longitudes de scattering en el marco del modelo sigma lineal. Para esto se consideraron todas las correcciones a un loop en los canales s, t y u, asociados a la inserción del propagador de Schwinger correspondiende a piones cargados, trabajando en el régimen de valores pequeños para el campo magnético. Este cálculo se basa en una expansión acorde para el propagador, resultando en que la longitud de scattering líder, t = 0 en el canal s, aumenta a medida que el campo magnético crece, en caso de isospín I = 2, mientras que el efecto opuesto se aprecia para el caso I = 0. La simetría de isospín es válida debido a que la inserción de campo magnético ocurre a través del valor absoluto de la carga eléctrica. Notamos, además que el canal I = 1 no recibe correción alguna. Además se ha de destacar que este resultado para los canales I = 0 y I = 2 es contrario respecto a las correciones térmicas para las longitudes de scattering halladas previamente en la literatura.

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