Error analysis of nuclear mass fits

We discuss the least-squares and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models’ parameters and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number-dependent weights on uncertainties of liquid-drop global parameters.

Figure 1

Areas of nuclear mass chart where the shell energy polynomials of Eq. (24) are defined. The black dots mark lines of semimagic nuclei for which the shell energy polynomials of adjacent rectangles are constrained to have the same values. The numbers in the rectangles show how many nuclei in the given area was used in the fit. Semimagic and magic nuclei belong always to the rectangle to the right and up.

Figure 2

The rms deviations of the least-squares fits (8) as functions of the standard deviation of the Gaussian noise σ added to the metadata.

Figure 3

Distributions of fit residuals for three different polynomial fits to metadata. Bin widths are 0.1 MeV.

Figure 4

Singular values of the fit matrix $J$ of Eq. (10) when three different polynomial orders are used in the least-squares fit.

Figure 5

The rms deviations (8) of the least-squares fits to metadata, calculated for the models of Eqs. (23) and (24), as functions of number of singular values kept for matrix $J$, Eq. (14).

Figure 6

Values of the LD parameters obtained from fits with weight factors of Eq. (25), as functions of parameter $\alpha$.

Figure 7

Same as in Fig. 6 but for the error estimates, Eq. (19), of the LD parameters.

Figure 8

Confidence intervals ($99\%$ confidence level) of binding energies of the model defined in Eqs. (23) and (24), calculated in lead isotopes using Eq. (22).

Figure 9

Same as in Fig. 8 but for the binding-energy residuals, Eq. (26).