Because the attenuation coefficient descibes the interaction and the energy absorption (with some corrections) the response of the detectors strongly depends.
Because the attenuation coefficient descibes the interaction and the energy absorption (with some corrections) the response of the detectors strongly depends.
To elaborate further: there are several different mass attenuation coefficients in a counting room. First, there is the mass attenuation coefficient of the sample, then the mass attenuation coefficient of air (which, in x-ays, can be significant) and finally the mass attenuation coefficient of the detector.
The detector's mass attenuation coefficient is often accounted for by measuring the detector's efficiency by a set of standard calibration sources.
The mass attenuation coefficient of the air can be calculated. It also can be measured by using the same set of sources.
The last one, the measurement or estimation of the mass attenuation coefficient of the sample, can be complex. For homogeneous samples with a uniform density, the estimation/measurement is straight-forward. For heterogeneous samples with non uniform density, it is very difficult.
A transmission source through the sample of a known calibrated source is the best way to estimate the attenuation coefficient. If the sample is very large, it is common practice to rotate the sample, thus producing a line geometry.
The PANDA (Passive Nondestructive Assay of Nuclear Materials) book by Reilly, Ensslin et al. has excellent descriptions of how to perform these measurements.
In addition to Hanno's answer, the mass attenuation coefficient is energy dependent. The detector's response to different energies will be different. The response of the detector will depend upon its size and shape. Further, the electronic configuration of the detector will alter the response.
The attenuation coefficient enters in different ways into the detector response function. Firstly, it influences the efficiency of the detector, i.e. the capability of the detector to stop radiation inside. A detector with a higher attenuation coeff. will be more efficient to detect radiation of that energy. Secondly, you have to consider the components of the attenuation coefficient (i.e., if we are talking about x.rays photons, for example, the photoelectric effect, and Compton and Rayleigh scattering are these components) which determine the possible mechanisms to escape from the deector. It is the escape that characterizes the energy distribution of the detector response. For more details, perhaps you can look inside the following article "Simulation of the detector response function with the code MCSHAPE", Radiation Physics and Chemistry 78 (2009) 882–887.