Pyatov Method Research Articles

BAZI TEK ÇEKİRDEKLİ GERMANYUM İZOTOBU İÇİN DEFORME VE KÜRESEL ÇEKİRDEKLERİN LOG(FT) DEĞERLERİ

The log(ft) values of the allowed 𝛽± decay between odd-A spherical and deformed nuclei are studied for germanium isotopes in this paper. The Pyatov Method (PM) and the Schematic Model (SM)) are used to the GT strength distributions, including the schematic residual spin-isospin interaction between nucleons in the particle-hole and particle-particle channels. Particle-hole and particle-particle interaction parameters are calculated respectively with X_ph^GT= 5.2 A^(0.7 ) MeV and X_pp^GT= 0.58 A^(0.7 ) MeV. Deformed Woods-Saxon potential is used in calculations of single-particle energies and wave functions. The results are also compared with previous experiment values wherever available.

Beta decay logft values for zinc isotopes by using pn-QRPA

Allowed Fermi (F), Gamow-Teller (GT), and first forbidden (FF) transitions were simulated using Pyatov Method (PM) and Schematic Model (SM) for even-even neutron rich isotopes of Zinc. The Fermi beta-decay calculations were obtained by the pure the Pyatov Method without introducing effective values of coupling constants using the proton-neutron quasi-particle random phase approximation (pn-QRPA). The pn-QRPA was utilized in the particle-hole (ph) and particle-particle (pp) channels in the PM and SM for the GT transitions. For FF transitions, only the corresponding ph channel in the SM was considered in the calculations. We solved the secular equations of Fermi, Gamow-Teller, and first forbidden transitions for eigenvalues and eigenfunctions of corresponding Hamiltonians. A spherical shape was assigned for each Zn nuclei throughout all simulations. Compared to the experimental studies, in general, the calculated logft values of the allowed F and GT transitions of PM and SM simulations were found to be closer to the experimental values. Alongside logft values, simulated half-lives obtained in this work are also in excellent agreement with experimental counterparts for the FF excitations.

Several QRPA method calculations of the Gamow–Teller strength distributions in $$^{62{-}72}$$Ge

Studies of exotic nuclei are currently one of the most prolific in nuclear physics. Weak rates in germanium isotopes have a fundamental role in the dynamics of supernovae. Electron capture and beta-decay of germanium isotopes, specified by Gamow–Teller transitions, importantly modify the lepton fraction of the stellar matter. In this study, Gamow–Teller Transitions (GT) for $$^{62{-}72}$$ Ge are calculated using QRPA methods. The GT strength distributions are calculated using eight different QRPA models. QRPA models, namely single quasi-particle (sqp), Pyatov method (PM) and the schematic model (SM), are further divided into four subcategories. Using these models, Gamow–Teller distribution, total GT strengths along electron capture direction ( $$\sum $$ B(GT) $$_+$$ ) and Ikeda sum rule are calculated. The results of sqp, PM, and SM are also compared with previous theoretical calculations and measured strength distributions wherever available. It is expected that this study of GT properties would gain favor and may help to a better understanding of the presupernova evolution of massive stars.

Effect of deformation, particle-hole and particle-particle interaction on Gamow-Teller transitions of 76Ge

Gamow-Teller (GT) transitions for 76Ge using QRPA methods in this article are calculated, which play an essential role in the supernovae. Three different QRPA models are used to the GT strength distributions. QRPA models namely single quasi-particle (sqp), Pyatov Method (PM) and the Schematic Model (SM). Gamow-Teller distribution, ΣB(GT)-, the centroid of energy, the width of energy and ISR are calculated by using these models. The effect of particle-particle interaction on spherical nuclei and deformed nuclei on Gamow-Teller transitions is wanted to show. Deformed Woods-Saxon potential is used in calculations of Single-particle energies and wave functions. The results are also compared with previous theoretical calculations and measured strength distributions wherever available. It is expected that the current study of GT features would be helpful and may guide to a better knowledge of the presupernova progression of massive stars.

Spin-isospin transitions in chromium isotopes within the quasiparticle random phase approximation

Beta decay and electron capture on isotopes of chromium are advocated to play a key role in the stellar evolution process. In this paper we endeavor to study charge-changing transitions for 24 isotopes of chromium (42–65Cr). These include neutron-rich and neutron-deficient isotopes of chromium. Three different models from the QRPA genre, namely the pn-QRPA, the Pyatov method (PM) and the Schematic model (SM), were selected to calculate and study the Gamow–Teller (GT) transitions in chromium isotopes. The SM was employed separately in the particle–particle (pp) and pp+particle-hole (ph) channels. To study the effect of deformation, the SM was first used assuming the nuclei to be spherical and later to be deformed. The PM was used both in pp and pp + ph channels but only for the case of spherical nuclei. The pn-QRPA calculation was done by considering both pp and ph forces and taking deformation of nucleus into consideration. A recent study proved this version of pn-QRPA to be the best for calculation of GT strength distributions amongst the QRPA models. The pn-QRPA model calculated GT distributions had low-lying centroids and small widths as compared to other QRPA models. Our calculation results were also compared with other theoretical models and measurements wherever available. Our results are in decent agreement with previous measurements and shell model calculations.

Investigation of isospin forbidden 0+ → 0+ Fermi beta decays with Pyatov method

Abstract In the present work, the matrix elements, isospin impurities and log ft values of the isospin forbidden 0+ → 0+ beta decays have been investigated. The calculated results have been compared with available experimental and another theoretical data. The isotopic invariance of the Hamiltonian has been restored by Pyatov method. Within the quasi-particle random phase approximation (QRPA), the computations have been performed both in presence and absence of the pairing interactions.

Study of Gamow–Teller transitions in isotopes of titanium within the quasi particle random phase approximation

The Gamow-Teller (GT) transition is inarguably one of the most important nuclear weak transitions of the spin-isosopin $\sigma\tau$ type. It has many applications in nuclear and astrophysics. These include, but are not limited to, r-process $\beta$-decays, stellar electron captures, neutrino cooling rates, neutrino absorption and inelastic scattering on nuclei. The quasiparticle random phase approximation (QRPA) is an efficient way to generate GT strength distribution. In order to better understand both theoretical systematics and uncertainties, we compare the GT strength distributions, centroid and width calculations for $^{40-60}$Ti isotopes, using the pn-QRPA, Pyatov method (PM) and the Schematic model (SM). The pn-QRPA and SM are further sub-divided into three categories in order to highlight the role of particle-particle (pp) force and deformation of the nucleus in the GT strength calculations. In PM, we study only the influence of the pp force in the calculation. We also compare with experimental results and other calculations where available. We found that the inclusion of pp force and deformation significantly improves the performance of SM and pn-QRPA models. Incorporation of pp force leads to pinning down the centroid value in the PM. The calculated GT strength functions using the pn-QRPA (C) and SM (C) models are in reasonable agreement with measured data.

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.

Gamow-Teller 1+ states in 112–124Sb isotopes

The violated supersymmetry property of the pairing interaction between nucleons were restored using the Pyatov method [Pyatov and Salamov, Nucleonica22, 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 investigation of the 2νββ 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.

Beta-transition properties for neutron-rich Sn and Te isotopes by Pyatov method

Based on Pyatov’s method, the low-lying Gamow-Teller (GT) 1+ state energies and log(ft) values for 128,130,132Sb and 132,134,136I isotopes have been calculated. In this method, the strength parameter of the effective spin-isospin interaction is found by providing the commutativity of the GT operator with the central part of the nuclear Hamiltonian. The problem has been solved within the framework of RPA. The calculation results have been compared with the corresponding experimental data.