Least-squares fitting applied to nuclear mass formulas. Solution by the Gauss–Seidel method

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

Top condensation model: a step towards the correct prediction of the Higgs mass

A realization of the composite Higgs scenario in the context of the effective model with the $$SU(2)_L\times U(1)_R$$ S U ( 2 ) L × U ( 1 ) R symmetric four-Fermi interactions proposed by Miransky, Tanabashi and Yamawaki is studied. The model implements Nambu’s mechanism of dynamical electroweak symmetry breaking leading to the formation of $${{\bar{t}}}t$$ t ¯ t and $${{\bar{b}}}b$$ b ¯ b quark condensates. We explore the vacuum structure and spectrum of the model by using the Schwinger proper-time method. As a direct consequence of this mechanism, the Higgs acquires a mass in accord with its experimental value. The present prediction essentially differs from the known overestimated value, $$m_\chi = 2m_t$$ m χ = 2 m t , making more favourable the top condensation scenario presented here. The mass formulas for the members of the second Higgs doublet are also obtained. The Nambu sum rule is discussed. It is shown that the anomalous $$U(1)_A$$ U ( 1 ) A symmetry breaking modifies this rule at next to leading order in $$1/N_c$$ 1 / N c .

Self-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq

In this paper, we establish a mass formula for Euclidean and Hermitian self-orthogonal codes over the finite ring Fq + uFq, where Fq is the finite field of order q and u2 = 0. We also establish a mass formula for Euclidean self-orthogonal codes over the finite ring Fq + uFq + u2Fq, with u3 = 0 and characteristic of Fq is odd. These mass formulas are used to give a classification of Euclidean and Hermitian self-orthogonal codes over F2 + uF2 and F3 + uF3 of small lengths.

Dilaton mass formulas in a hairy binary black hole model

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein–Maxwell–dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.

COLLECTIVE POTENTIAL FOR HEAVY ION NUCLEAR REACTIONS

It is shown that the nuclear charge polarisation during heavy ion nuclear reactions enhances the secondary maximum of the collective energy surface and produces a secondary minimum in the deformation energy near R ~ Rmin + 2fm. The potential energy and mass formulas are given as a function of A and Z. It has been shown that charge polarisation without shape deformation and indeed of the prolate type does not produce any secondary minimum. It is also seen that the relativity effect consists in shifting the secondary minimum towards higher rest excentricities. For deformation of the oblate type the collective potential has a similar form like that in the spherical case. Entry and exit channel collective potentials are also given for the case of strong nucléon transfer. The mass for the two-body interacting system has been calculated and for large distances it tends to the corresponding reduced mass. The present theory is based on a particular form of the single particle potential following from the scalar π-meson classical field theory.

New global atomic mass formulas

We illustrate the improved empirical methods of estimating atomic masses using Garvey–Kelson like local relations and global equations using generic point functions.