The investigation of 0<Superscript>+</Superscript> ↔ 0<Superscript>−</Superscript><Emphasis Type="Italic">β</Emphasis> decay in some spherical nuclei

The 0⁺ ↔ 0⁻ first-forbidden β decay transitions have been investigated for some spherical nuclei. The theoretical framework is based on a proton-neutron quasiparticle random phase approximation (pnQRPA). The Woods-Saxon potential basis has been used in our calculations. The transition probabilities have been calculated within the ξ approximation. The relativistic β moment matrix element has been calculated both directly without any assumption and assuming that it is proportional to the non-relativistic one.     

The homotopy analysis method to solve the modified equal width wave equation

In this article, to solve the modified equal width wave (MEW) equation, the homotopy analysis method (HAM) is proposed. The initial approximation can be freely chosen with possible unknown constant, which can be determined by using the boundary and initial conditions. The HAM contains the auxiliary parameter ?, which provides us to adjust and control the convergence region of solution series with a simple way. Three conservative quantities are reported. Numerical results show that this method is a promising and powerful tool to solve the MEW equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

The investigation of the 2<Emphasis Type="Italic">νββ</Emphasis> decay by Pyatov method within quasiparticle random phase approximation formalism

The violated commutation condition between the total shell model Hamiltonian and Gamow-Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by h ₀(restoration term). The influence of the h ₀ effective interaction on the 2νββ decay of ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ^128,130Te and ¹³⁶Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the 2νββ decay nuclear matrix elements is analysed.      

Gamow-Teller 1<Superscript>+</Superscript> states in <Superscript>112–124</Superscript>Sb isotopes

The violated supersymmetry property of the pairing interaction between nucleons were restored using the Pyatov method [Pyatov and Salamov, Nucleonica 22, 127 (1977)]. The eigenvalues and eigenfunctions of the restored Hamiltonian with the separable residual Gamow-Teller effective interactions in the particle-hole and particle-particle channels were solved within the framework of proton-neutron quasirandom phase approximation (pnQRPA). The Gamow-Teller resonance energies for ^112–124Sb isotopes and the differential cross-sections for Sn(³He, t)Sb reactions at E(³He) = 200 MeV occurring by the excitation of the Gamow-Teller resonance state were calculated. The calculated values were compared with other calculations and the corresponding experimental data.     

The influence of pairing correlations on the isospin symmetry breaking corrections of superallowed Fermi beta decays

Within the framework of quasi-particle random phase approximation, the isospin breaking correction of superallowed 0⁺ → 0⁺ beta decay and unitarity of Cabibbo-Kobayashi-Maskawa mixing matrix have been investigated. The broken isotopic symmetry of nuclear part of Hamiltonian has been restored by Pyatov’s method. The isospin symmetry breaking correction with pairing correlations has been compared with the previous results without pairing. The effect of pairing interactions has been examined for nine superallowed Fermi beta decays; their parent nuclei are ²⁶Al, ³⁴Cl, ³⁸K, ⁴²Sc, ⁴⁶V, ⁵⁰Mn, ⁵⁴Co, ⁶²Ga, ⁷⁴Rb.     

Deformation effects on isospin mixing and isobar analogue resonance for 74−80Kr isotopes

Pyatov’s method has been applied to investigate Fermi beta transitions in deformed ^74–80Kr isotopes. This self-consistent method, which was used to study the isobar analogue states in the spherical odd-odd nuclei, has to date not been applied for the isobar analogue states in deformed nuclei. The nucleon-nucleon residual interaction has been included so that the broken isospin symmetry in the mean field approximation has been restored and the strength parameter of the effective interaction has been taken out to be a free parameter. The energies and wave functions of the isobaric analogue excitations in ^74–80Rb isotopes have been obtained within the framework of the pnQRPA method. The probability of the isospin mixing in the ground states and the centroid energies of the isobar analogue resonance have been presented and the deformation effects on these quantities have been quantified.     

Low-lying Gamow-Teller transitions in spherical nuclei

The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 ⩽ A ⩽ 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying β decay log(ft) values have been calculated for the nuclei under consideration.