Fitting nuclear spectra

The term fitting ideally means that Eq. (9.79) will produce the expected value of N(f,) for any value of the independent variable f,. (See Sect. 9.6 on fitting nuclear spectra.) Note that the expression spectrum point is used here in the same sense as in Sect. 9.6. See in contrast one of the comments after Eq. (9.1). 

The spectrum fitting is done by the least-squares method by using an appropriate model function S, e.g., a linear combination of Lorentzians. (See also Sect. 9.3.6 on Fitting nuclear spectra in Chap. 9, Vol. 1, on Stochastics and Nuclear Measurements. ) In this procedure, the sum... 

The above expression is an example of a model function, which fits the nuclear spectrum consisting of the spectrum points... 

The JV(0, 1) random numbers simulated according to the above remark can be used, e.g., for the simulation of nuclear spectra. Nuclear spectrum points (see in O Sect. 9.6) have N pi, pi) distribution. If the p values are calculated from the fitting function and Rj is an N 0, 1) random number, then the formula Y) = Pj + y/plRi defines a random number with N pi, Pi) distribution as required. 

An example for a nuclear spectrum. The main graph shows a single-peak Mossbauer spectrum "measured" at transmission geometry. Such a spectrum can be fitted with a Lorentzian curve blue line), whose shape is identical with the density function of a Cauchy distribution. Due to standardization, the tick distance on the horizontal axis is half of the full width at half maximum (FWHM) of the Lorentzian (y). As mentioned in remark ( 66), FWHM/2 = y gives the natural line width r provided that the absorber is ideally thin. On the other hand, the vertical scattering of the counts red dots) is characterized by the normal distribution. The colored graph on the left, e.g., shows the normal density function belonging to the baseline (/ ,) The color code is explained byO Fig. 9.2. On the vertical axis the distance between the ticks equals to [Pg.442]

H = di(Z—iy di are the potential parameters I is the orbital quantum number 3 characterizes the spin direction Z is the nuclear charge). Our experience has show / that such a model potential is convenient to use for calculating physical characteristics of metals with a well know electronic structure. In this case, by fitting the parameters di, one reconstructs the electron spectrum estimated ab initio with is used for further calculations. 

A critical point in the retrieving of the number of nuclear reactions in laser-solid experiments is that there is no control on the spectrum of the electrons accelerated in the interaction, as well as the acceleration mechanism is uncertain and difficult to fit in a predictable scheme. In most cases, the electron energy distribution is assumed to be Boltzmann-like and deconvolutions are performed starting from this assumption. 

The analysis of a full tilt series of 2H NMR spectra not only allows the determination of the unique bond angle for a deuteriated methyl group, but also provides an internal check for the consistency of the spectral interpretation. In particular, simulations provide a means for the analysis of line-broadening effects, which arise from the sample mosaic spread as well as the intrinsic line width of the nuclear transition and instrumental factors. When line shapes are fitted to a full tilt series of spectra in a concerted manner and are also compared with the powder spectrum of an unoriented sample, the different contributions can be discerned. In that way an intrinsic line width of around 2 kHz is found for the spectra shown here, together with a mosaic spread between 8° and 10° for the three samples. 

An example of this situation are plutonium isotopes, Pu and Pu. They are used for estimation of a burn up of nuclear fuel. As the energy difference of these alpha emitters is only 10 keV, the alpha particle spectrum is observed as an overlapped single peak. However, when a Si detector is used, which has an energy resolution of less than 10 keV (FWHM), the overlapped peaks can be analyzed by the least squares fitting technique. 

---