# Image reconstruction techniques applied to nuclear mass models

Abstract: A new procedure is presented that combines well-known nuclear models with image reconstruction techniques A color-coded image is built by taking the differences between measured masses and the predictions given by the different theoretical models This image is viewed as part of a larger array in the ($N,Z$) plane, where unknown nuclear masses are hidden, covered by a ``mask'' We apply a suitably adapted deconvolution algorithm, used in astronomical observations, to ``open the window'' and see the rest of the pattern We show that it is possible to improve significantly mass predictions in regions not too far from measured nuclear masses

## Summary (2 min read)

### Introduction

- A new procedure is presented that combines well-known nuclear models with image reconstruction techniques.
- The authors apply a suitably adapted deconvolution algorithm, used in astronomical observations, to “open the window” and see the rest of the pattern.
- Reliable theoretical models and methodologies that can predict the mass and other properties of these “exotic” nuclei are still missing [3].
- Instead, simplified approaches to model the atomic nucleus have been devised.

### II. SYSTEMATIC PATTERNS

- For each model, the authors observe a residual systematic pattern related to the physics and that is not included in the model.
- The basic idea is to consider that the more than 2000 differences between the different models and the known nuclear masses represent partial views of a larger image array in the (N,Z) plane, and that all other mass differences (perhaps around 7000 in number) that exist between the neutron and proton drip lines remain hidden, covered by a “mask.”.
- The problem is narrowed down to obtaining the function M(kN, kZ), from which m(N,Z) can be recovered by applying an inverse Fourier transform.
- A new version of the corrupted spectrum is calculated eliminating the removed component and the effects produced on it by the mask.

### IV. MASS PREDICTIONS

- Once this extrapolated pattern is obtained, it is then possible to predict the nuclear masses by adding the mass predicted by the model: m(N,Z) = mextrapolated(N,Z) + mth(N,Z). (12).
- Table I shows a comparison of the rms deviations for the AME95-03 test, and those obtained with the CLEAN method for each model.
- Figure 3 shows S2n in the N ∼ 78–128 region of the AME95-03 test, obtained with the LDMM [isotopic lines in Fig. 3(a)], and the results obtained after applying the reconstruction algorithm [isotopic lines in Fig. 3(b)].
- In order to test this the authors have calculated the rms deviation between the masses extrapolated by Audi et al. and the predictions of the DZ model with and without CLEAN.

### V. THE ACCURACY OF CLEAN

- The rms deviations obtained in the previous tests show that the CLEAN method improves the mass predictions of the models used as input.
- For the border test this definition of distance is not useful because all nuclei in the prediction are as close as possible to the known region.
- Table III show a comparison of the results obtained for each model in the AME95-03 test.
- Because it is known that different models can have wildly different predictions, even when they apply to masses close to the experimentally known region [22], it is important to discuss the uncertainties due to the use of different models.
- If the predictions of the CLEAN algorithm using different models are consistent with each other then the difference between the models must be reduced after using CLEAN.

### VI. CONCLUSIONS

- A method to improve predictions of arbitrary nuclear mass models was presented, based on the detection and extrapolation of regularities in the pattern of differences between experimental and theoretical nuclear masses.
- The CLEAN image reconstruction technique was applied to improve the theoretical predictions given by three different models each having a different degree of accuracy in their predictions.
- (a) a macroscopic LDM, (b) a macroscopic LDM with the inclusion of shellcorrection terms (LDMM), and (c) the Duflo-Zuker model, also known as The models analyzed are.
- The authors believe that the CLEAN method presented here is a relatively simple method that improves predictions by nuclear mass models and that can be constantly improved by the incorporation of new measurements.
- Some of these questions are currently under investigation.

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