Neutron capture cross section measurements in time-of-flight facilities are usually performed by detecting the prompt ¿-rays emitted in the capture reactions. One of the difficulties to be addressed in these measurements is that the emitted ¿-rays may change with the neutron energy, and therefore also the detection efficiency. To deal with this situation, many measurements use the so called Total Energy Detection (TED) technique, usually in combination with the Pulse Height Weighting Technique (PHWT). With it, it is sought that the detection efficiency depends only on the total energy of the ¿-ray cascade, which does not vary much with the neutron energy. This technique was developed in the 1960s and has been used in many neutron capture experiments to date. One of the requirements of the technique is that ¿-ray detectors have a low efficiency. This has meant that the PHWT has been used with experimental setups with low detection efficiencies. However, this condition does not have to be fulfilled by the experimental system as a whole. The main goal of this work is to show that it is possible to measure with a high efficiency detection system that uses the PHWT, and how to analyze the measured data