We formulate the Jost function formalism based on the Hartree-Fock-Bogoliubov (HFB) theory which has been used to represent the nature of the superfluidity of nucleus. The Jost function based on the HFB can give the analytic representation of the S-matrix for the nucleon elastic scattering targeting on the open-shell nucleus taking into account the pairing effect. By adopting the Woods-Saxon potential, we show the numerical results of S-matrix poles and their trajectories with varying the pairing strength in two cases of Fermi energies: λ = −8.0 and −1.0 MeV. The total cross sections in each cases for neutron elastic scattering are also analyzed, and we confirmed some staggering shapes or sharp resonances originated from the effect of pairing can be seen in the cross section.

By focusing on the asymmetric shape of cross section, we analyze the pairing effect on the partial wave components of cross section for neutron elastic scattering off stable and unstable nuclei within the Hartree-Fock-Bogoliubov (HFB) framework. Explicit expressions for Fano parameters q lj and ǫ lj have been derived and the pairing effects have been analyzed in term of these parameters, and the Fano effect was found on the neutron elastic scattering off the stable nucleus in terms of the pairing correlation. Fano effect was appeared as the asymmetric line-shape of the cross section caused by the small absolute value of q lj due to the small pairing effect on the deep-lying hole state of the stable nucleus. In the case of the unstable nuclei, the large q lj value is expected because of the small absolute value of the Fermi energy. The quasiparticle resonance with the large q lj forms the Breit-Wigner type shape in the elastic scattering cross section.

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This study reports the [Formula: see text]-decay half-lives of 39 transfermium isotopes with [Formula: see text], most of which have not been observed. The half-lives were calculated using micro–macroscopic approaches and semi-empirical formulae, applying current [Formula: see text]-decay Q-values from the latest mass database, AME2016. These results were compared to predicted values in previous works to evaluate the efficiency of and difference between various calculation methods. We found that the [Formula: see text]-resonance approach used in a previous study is not appropriate to predict though most other approaches are mutually consistent. An uncertainty of 70% was observed in the present theoretical calculations, similar to that observed in measurements. A Q-value uncertainty of 10% can lead to a large variation of 3 orders of magnitude in predicted [Formula: see text]-decay half-life. We also found that the dominance of either [Formula: see text] decay or spontaneous fission is unclear for the isotopes with [Formula: see text]–[Formula: see text], whereas most of the nuclei of [Formula: see text]–[Formula: see text] can be clearly identified as [Formula: see text] emitters. Finally, we provide the updated [Formula: see text]-decay half-lives for the isotopes of interest, including their uncertainties and corresponding decay modes.

Abstract. Fermions in the model of electroweak-scale right-handed neutrinos (EWRH) with masses of the order of 300 GeV or more could result in dynamical electroweak symmetry breaking by forming condensates through the exchange of a fundamental Higgs scalar doublet or triplet. These condensates are dynamically studied within the framework of the SchwingerDyson equation. With the electroweak symmetry broken by condensates, the fully worked-out model of EWRH in which there are two doublets and two triplets, one of which is composite and the others being the original fundamental scalar doublet and triplet could be suitable for recent LHC discovery of the 125 GeV scalar particle. IntroductionThe SM has been established for a long time and has shown its abilities to address many problems in High Energy Physics. Nevertherless, some problems can not be explained by SM. One of which is SM Higgs mechanism where spontaneous symmetry breaking (SSB) is put in by hand. With Higgs potential V (φ) = µ 2 φ + φ + λ(φ + φ) 2 , this mechanism does not explain why µ 2 is negative when it could, a priori, have been positive. µ 2 and hence m 2 H = −2µ 2 = 2λv 2 are unstable to large radiative corrections from much higher enery scales (gauge hierarchy problem, fine-tuning needed to keep Higgs light, etc.). Moreover, the SM Yukawa mechanism for generating fermion masses, with m f = y f v/ √ 2, does not give insight into these masses, since it just puts in the value of Yukawa couplings y f by hand, and some y f 's range down to 10 −5 with no explanation. Might it be a possible way to give a dymanical reason for fermion masses? Consider two major previous cases of superconductivity and Gell-Mann Levy σ model for spontaneous chiral symmetry breaking (SχSB) where the fundamental scalar fields were used to model SSB. For these cases, the actual underlying physics did not involve fundamental scalar fields but instead a bilinear fermion condensate. For instance, the physical properties of superconductor materials can be explained by dynamically forming a condensate state of Cooper pairs (ee) in BCS theory; since these are charged, they give mass to photon, resulting in Meissener effect. In the second case, the actual origin of SχSB in QCD is the dynamical formation of a (qq) condensate. These previous models of symmetry breaking, therefore, bring about the underlying physics responsible for this symmetry breaking may well be a dynamically induced fermion condensate. The condition for condensation mentioned in [1] is that the Yukawa couplings are larger than critical Yukawa couplings α c . For instance, when the energy scale is of the order of O(1TeV), the Yukawa coupling of a heavy fourth generation in [2] is large enough, exceeding α c , to form

In this paper, we applied the method developed by Santhosh and Safoora in [Phys. Rev. C  94 (2016) 024623; 95 (2017) 064611] to theoretically investigate the fusion, evaporation-residue (ER) and fission cross-sections of the synthesis of the unknown superheavy [Formula: see text]126 nuclei produced by using the [Formula: see text]Ni + [Formula: see text]Cf and [Formula: see text]Zn + [Formula: see text]Cm combinations. The charge asymmetry, mass asymmetry and fissility of the DiNuclear System (DNS) in the synthesis of the mentioned combinations are also estimated. The calculated results show that the ER cross-sections for the synthesis of the [Formula: see text]126 nuclei are predicted to be much less than 1.0[Formula: see text]fb. In particular, it has been found that there may exist a valley of the ER cross-sections in the synthesis of a superheavy [Formula: see text] element, which produces the [Formula: see text]126 isotope. Subsequently, a model for the mass dependence of the ER cross-section in the synthesis of the [Formula: see text]126 isotopes has been proposed for the first time. On the other hand, the quasi-fission process strongly dominates over the fusion in the two concerned interacting systems. The present results, together with those reported in the previous studies, indicate that the investigated projectile–target combinations are not capable for the synthesis of the [Formula: see text]126 isotopes due to tiny fusion cross-sections (about 2–3[Formula: see text]zb), which go beyond the limitations of available facilities. Further studies are thus recommended to search for alternative interacting systems. In conclusion, this work provides useful information for the synthesis of the gap isotopes [Formula: see text]126, which have not been well studied up to date.