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Recently, the total absorption gamma spectroscopy technique was used to determine the Gamow–Teller (GT) distribution of β-decay of 186Hg. It was concluded that the best description of the measured data was obtained with dominantly prolate components for both parent 186Hg and daughter 186Au. Motivated by the recent findings, we investigate the effect of nuclear deformation on the energy distribution of the GT strength of the decay of 186Hg into 186Au within the framework of proton–neutron quasiparticle random phase approximation (pn-QRPA) based on the deformed Nilsson potential. To do the needful, we first calculate the energy levels and shape prediction of 186Hg within the interacting boson model. The computed GT strength distribution satisfied the model-independent Ikeda sum rule 100% (99.98%) for the prolate (oblate) case. Based on the strength distributions, the deformed pn-QRPA model with separable interaction prefers a prolate shape for the ground state of 186Hg and supports the shape coexistence for this nucleus.

Calculating weak decay rates under stellar conditions for studying presupernova evolution of massive stars is a challenging task. Here, we show the importance of odd-A nuclei for presupernova simulations. In order to calculate the required nuclear matrix elements, we apply the pn-QRPA model in a deformed basis. Nuclear deformation, thought to play an integral role in calculation of associated weak decay rates, is taken into account in our model. We calculate Gamow–Teller (GT) strength distributions, $$\beta ^-$$ emission and positron capture rates for selected odd-A nuclei. Our model does not employ the Brink–Axel hypothesis as used in previous calculations of weak decay rates, and we perform a state-by-state microscopic calculation of GT strength distributions from all parent excited states. Our calculated $$\beta ^-$$ decay rates are in good agreement with large-scale shell model calculations.

It is known that the calculated values of log(ft) and the half-life of beta decay are less than the measured values when a single-particle approach is used to calculate these quantities. In this article, we discuss the importance of taking into account the spectroscopic factor in the calculation of the half-life and log(ft) beta decay of nuclei containing one nucleon in the outermost shell. We also emphasize the dominant role of the asymptotic normalization coefficient, which takes into account the many-particle effect and allows us to obtain the spectroscopic factor necessary to describe the reaction 13N → 13C + β+ + νe . We find the asymptotic normalization coefficients using the experimental data of the elastic scattering phase-shift of the proton and neutron on 12C. Using overlap functions instead of single-particle functions, we obtain a better comparison with the experimental data. The overlap function is represented as the product of the single-particle function and the root of the corresponding spectroscopic factor.

In this work, we explore the role of deformation parameter (β) on the calculated Gamow-Teller (GT) strength distributions and electron capture cross-sections (ECC) for 46,48,50Cr isotopes within the formalism of the proton neutron-quasi-particle random phase approximation (pn-QRPA). Three different β parameters were used in the present study. Two of them were calculated by using the interacting boson model (IBM) and the macroscopic-microscopic (Mac-mic) models. The third one is the experimental β values obtained by employing its relation with the experimental B(E2)↑ values. The GT strength distributions were widely dispersed among all the daughter states of the given isotopes. They were found to have an inverse relation with the β parameter i.e decreasing with increasing the β value. The ECC was computed as a function of the β parameter and the results suggest that the calculated ECC decreased with decreasing value of the β for the selected cases.

The total cross-section, astrophysical S-factor, and rate of radiative capture reaction 12C(p, γ)13N are calculated using the potential model. In this work, we take into account the capture of protons through s1/2 → p1/2 and d3/2 → p1/2 single-particle transitions, fine-tune the values of the depth and nuclear radius of the Woods-Saxon potential to achieve better comparison with the measured data. The results for the elastic scattering phase shift, astrophysical S-factor, and rates are compared with the previously reported results of the calculations and experimental data.

Neutron imaging is a nondestructive inspection technique that has a wide range of applications. One of the important aspects of neutron imaging is achieving a micrometer-scale spatial resolution. The development of a high-resolution neutron detector is a challenging task. As one potential solution to this task, we investigate whether neutron detectors based on fine-grained nuclear emulsions are suitable for high-resolution neutron imaging applications. High track density is necessary to improve the quality of neutron imaging. However, the available track analysis methods are difficult to apply under high track density conditions. Simulated images are used to determine the required track density for neutron imaging. A track density of the order of [Formula: see text] tracks per [Formula: see text] is sufficient to utilize neutron detectors for imaging applications. Contrast resolution was also investigated for image datasets with various track densities and neutron transmission rates. Moreover, experiments were performed for the neutron imaging of gadolinium-based gratings with known geometries. The grating structures were successfully resolved. The calculated [Formula: see text] 10%–90% edge response using the grayscale optical images of the grating slit with a periodic structure of 9 [Formula: see text]m was [Formula: see text] [Formula: see text]m.

Fluorescent nuclear track detectors (FNTDs) based on Al${_2}$O${_3}$:C,Mg crystals are luminescent detectors that can be used for dosimetry and detection of charged particles and neutrons. These detectors can be utilised for imaging applications where a reasonably high track density, approximately of the order of 1 $\times$ $10^4$ tracks in an area of 100 $\times$ 100 $\mu$m$^2$, is required. To investigate the reusability of FNTDs for imaging applications, we present an approach to perform optical bleaching under the required track density conditions. The reusability was assessed through seven irradiation-bleaching cycles. For the irradiation, the studied FNTD was exposed to alpha-particles from an $^{241}$Am radioactive source. The optical bleaching was performed by means of ultraviolet laser light with a wavelength of 355 nm. Three dedicated regions on a single FNTD with different accumulated track densities and bleaching conditions were investigated. After every irradiation-bleaching cycle, signal-to-noise ratio was calculated to evaluate FNTD performance. It is concluded that FNTDs can be reused at least seven times for applications where accumulation of a high track density is required.

This project aims to investigate the most important weak interaction nuclei in the presupernova evolution of massive stars. To achieve this goal, an ensemble containing 728 nuclei in the mass range of A = 1–100 was considered. We computed the mass fractions of these nuclei using Saha’s equation for predetermined values of T, ρ, and Y e and assuming nuclear statistical equilibrium. The nuclear partition functions were obtained using a newly introduced recipe where excited states, up to 10 MeV, were treated as discrete. The weak interaction rates (electron capture (ec) and β-decay (bd)) were calculated in a totally microscopic fashion using the proton–neutron quasiparticle random phase approximation model and without assuming the Brink–Axel hypothesis. The calculated rates were coupled with the computed mass fractions to investigate the time rate of change of lepton to baryon fraction of the stellar matter. We compare our results with the previous calculations reported in the literature. Noticeable differences up to orders of magnitude are reported with previous calculations. These differences may influence the evolution of the star in the later stages of presupernova. We present a list of the top 50 ec and bd nuclei, which have the largest effect on Y e for conditions after silicon core burning. The competition between the ec and bd rates in the stellar core was investigated and it was found that Y e = 0.424–0.455 is the interval where the bd results are bigger than the ec rates.

Within the framework of the modified potential model, we computed the astrophysical S-factor of the proton radiative capture p + 11C → 12N + γ. At energies bearing astrophysical importance, radiative capture is a key process in the spectroscopic study of 12N. In this work, we consider the radiative capture cross-section for the proton capture by 11C within the framework of the potential model. For the possible electric and magnetic dipole transitions, we computed the partial components of the astrophysical S-factor within the energy range E = (0.01–0.8) MeV. The computed value of the S-factor at zero energy shows satisfactory agreement with the reported results. Furthermore, we computed the radiative capture rates for the selected reaction, which shows a better comparison with the reported data.

We explore the effectiveness of the Brink–Axel hypothesis (BAH) for the computation of stellar electron capture (EC) and β-decay (BD) rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow–Teller (GT) strength distributions for a selection of sd-shell nuclides, using two different microscopic models, namely the proton–neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into weak-interaction mediated rates in stellar matter, specifically EC and BD rates, for a range of densities 10 g cm−3 ⩽ ρ ⩽ 1011 g cm−3 and range of temperatures 1 GK ⩽ T ⩽ 30 GK. When transitions from excited states were approximated using the BAH, augmented by so-called ‘back-resonance’ transitions, the rates were affected by up to three orders of magnitude or more at high temperatures and densities. Thus the BAH is not a reliable approximation for the calculation of stellar rates, especially in high temperature–density environments.

In this paper, we present the &beta, decay half-lives calculation for selected even-even nuclei that decay through electron emission. The kinematical portion of the half-life calculation was performed using a recently introduced technique for computation of phase space factors (PSFs). The dynamical portion of our calculation was performed within the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. Six nuclei ( 20 O, 24 Ne, 34 Si, 54 Ti, 62 Fe and 98 Zr) were selected for the present calculation. We compare the calculated PSFs for these cases against the traditionally used recipe. In our new approach, the Dirac equation was numerically solved by employing a Coulomb potential. This potential was adopted from a more realistic proton distribution of the daughter nucleus. Thus, the finite size of the nucleus and the diffuse nuclear surface corrections are taken into account. Moreover, a screened Coulomb potential was constructed to account for the effect of atomic screening. The power series technique was used for the numerical solution. The calculated values of half-lives, employing the recently developed method for computation of PSFs, were in good agreement with the experimental data.

The allowed Gamow-Teller (GT) strengths and associated weak interaction rates on fp-shell nuclides are the most familiar processes of spin-isospin (στ) type. These rates play a crucial role in several astrophysical processes, particularly in nuclear synthesis and supernova-explosions. As per simulation consequences, the electron capture cross-section on medium-heavy nuclei has a key impact on decreasing the ratio of electron-to-baryon of the stellar matter during the late stages of stars formation. Stellar model based on the theoretical approaches should be tested against the available measured data. In the current work we present calculated Gamow-Teller strength distributions by pn-QRPA model for selected fp-shell nuclei (42Ti, 46Cr, 50Fe and 54Ni) and compare our results with available measured data. The Gamow-Teller strength distributions are well fragmented over the energy range 0-12 MeV and have a good comparison with experimental data. We calculate the electron capture cross-section for selected nuclei at temperature 0.5 MeV, 1.0 MeV and 1.5 MeV that shows the temperature dependence of calculated electron capture cross-section for astrophysical applications.

We investigate even-even nuclei in the $A\sim70$ mass region within the framework of the proton-neutron quasi-particle random phase approximation (\mbox{pn-QRPA}) and the interacting boson model-1 (\mbox{IBM-1}). Our work includes calculation of the energy spectra and the potential energy surfaces $V(\beta,\gamma)$ of Zn, Ge, Se, Kr and Sr nuclei with the same proton and neutron number, $N = Z$. The parametrization of the \mbox{IBM-1} Hamiltonian was performed for the calculation of the energy levels in the ground state bands. Geometric shape of the nuclei was predicted by plotting the potential energy surfaces $V(\beta,\gamma)$ obtained from the \mbox{IBM-1} Hamiltonian in the classical limit. The \mbox{pn-QRPA} model was later used to compute half-lives of the neutron-deficient nuclei which were found to be in very good agreement with the measured ones. The \mbox{pn-QRPA} model was also used to calculate the Gamow-Teller strength distributions and was found to be in decent agreement with the measured data. We further calculate the electron capture and positron decay rates for these $N$ = $Z$ waiting point (WP) nuclei in the stellar environment employing the \mbox{pn-QRPA} model. For the $rp$-process conditions, our total weak rates are within a factor two compared with the Skyrme HF+BCS+QRPA calculation. All calculated electron capture rates are comparable to the competing positron decay rates under $rp$-process conditions. Our study confirms the finding that electron capture rates form an integral part of the weak rates under $rp$-process conditions and should not be neglected in the nuclear network calculations., Comment: 25 pages, 13 figures, 5 tables

Rates for (anti-)neutrino energy loss on nickel isotopes, due to interactions involving weak decays (β±-decay and lepton captures) are regarded as having fundamental importance during late evolutionary stages of massive stars. These rates substantially affect the leptonic ratio (Ye) of stellar interior. For the densities less than 1011 g/cm3, weak processes produce (anti-)neutrinos which cause reduction in the stellar core’s entropy. In this paper, rates for neutrino and anti-neutrino energy loss on nickel neutron-rich isotopes (66-71Ni) have been presented. Rates for energy loss have been determined by applying the deformed pn-QRPA model. The ranges for temperature and density, have been used to determine the rates, are from 0.01 to 30 (109 K) and 101 to 1011 (g/cm3), respectively. Our computed rates for energy loss, at higher temperature regions, are enhanced in comparison with previously reported rates of Pruet and Fuller (PF).

Radiative capture p + 13C → 14N + γ at energies of astrophysical interest is one of the important process in the CNO cycle. We focus the reader’s attention on the possibility of describing this reaction within the framework of a single-particle potential model even when the reaction has a resonant characteristic. The partial components of the astrophysical S-factor are calculated for electric dipole transition. The calculated value of S-factor is in good agreement with experimental data both at low and high energy from the resonance position.

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 ($^{42-65}$Cr). 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., Comment: 32 pages, 12 figures, 6 tables

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $\mathrm{\ensuremath{\Delta}}$ method, is proved and developed. This method was proposed by Ram\'{\i}rez Su\'arez and Sparenberg (arXiv:1602.04082.) but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function ${K}_{l}({k}^{2})$ is actually defined by the Coulomb term. One of the resulting effects is a wrong description of the energy behavior of the elastic scattering phase shift ${\ensuremath{\delta}}_{l}$ reproduced from the fitted total effective-range function ${K}_{l}({k}^{2})$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $\mathrm{\ensuremath{\Delta}}$ method to calculate the pole position values and the ANC. We apply it to the vertices $^{4}\mathrm{He}+^{12}\mathrm{C}\ensuremath{\leftrightarrow}^{16}\mathrm{O}$ and $^{3}\mathrm{He}+^{4}\mathrm{He}\ensuremath{\leftrightarrow}^{7}\mathrm{Be}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\mathrm{O}$ bound final states as well as to the $^{7}\mathrm{Be}$.

Gamma ray heating rates are thought to play a crucial role during the pre-supernova stage of high mass stars. Gamma ray heating rates, due to β±-decay and electron (positron) capture on chromium isotopes, are calculated using proton-neutron quasiparticle random phase approximation theory. The electron capture significantly affects the lepton fraction (Ye) and accelerates the core contraction. The gamma rays emitted as a result of weak processes heat the core and tend to hinder the cooling and contraction due to electron capture and neutrino emission. The emitted gamma rays tend to produce enormous entropy and set the convection to play its role at this stage. The gamma heating rates, on 50-60Cr, are calculated for the density range 10 < ρ (g.cm-3) < 1011 and temperature range 107 < T (K) < 3.0×1010.

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., Comment: 24 pages, 5 figures and 5 tables

The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration., Comment: 8 pages, 2 figures with 3 eps graphs

We revisit the computation of the phase space factors (PSF) involved in the positron decay and EC processes for a large number of nuclei of experimental interest. To obtain the electron/positron wave functions, we develop a code for solving accurately the Dirac equation with a nuclear potential derived from a realistic proton density distribution in the nucleus. The finite nuclear size (FNS) and screening effects are included through recipes which differ from those used in previous calculations. Comparing our results with previous calculations, performed with the same Q-values, we find a close agreement for positron decays, while, for the EC process, there are relevant differences. For the EC process, we also find that the screening effect has a notable influence on the computed PSF values especially for light nuclei. Further, we recomputed the same PSF values but using the most recent Q-values reported in literature. In several cases, the new Q-values differ significantly from the older ones, leading to large differences in the PSF values as compared with previous results. Our new PSF values can contribute to more reliable calculations of the beta-decay rates, used in the study of nuclei far from the stability line and stellar evolution.

First-forbidden (FF) charge-changing transitions become relatively important for nuclei as their proton number increases. This is because the strength of allowed Gamow-Teller (GT) transitions decreases with increasing Z. The FF transitions play an important role in reducing the half-lives as against those calculated from taking the GT transitions alone into account. In this paper we calculate allowed GT as well as $0^{+} \rightarrow 0^{-}$ and $0^{+} \rightarrow 2^{-}$ transitions for neutron-rich Zn and Ge isotopes. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and FF transitions. Half-lives calculated after inclusion of FF transitions were in excellent agreement with the experimental data. Our calculations were also compared to previous QRPA calculations and were found to be in better agreement with measured data. Stellar $\beta$-decay rates were calculated for these nuclei including allowed GT and unique FF transitions for astrophysical applications. $^{86,88}$Ge has a sizeable contribution to the total stellar rate from unique FF transitions., Comment: 21 pages, 8 figures, 2 tables. arXiv admin note: text overlap with arXiv:1211.6968

Gamow-Teller transitions in isotopes of chromium play a consequential role in the presupernova evolution of massive stars. $\beta$-decay and electron capture rates on chromium isotopes significantly affect the time rate of change of lepton fraction ($\dot{Y_{e}}$). Fine-tuning of this parameter is one of the key for simulating a successful supernova explosion. The (anti)neutrinos produced as a result of electron capture and $\beta$-decay are transparent to stellar matter during presupernova phases. They carry away energy and this result in cooling the stellar core. In this paper we present the calculations of Gamow-Teller strength distributions and (anti)neutrino energy loss rates due to weak interactions on chromium isotopes of astrophysical importance. We compare our results with measured data and previous calculations wherever available., Comment: 22 pages, 12 figures, 5 tables. arXiv admin note: text overlap with arXiv:1602.06134

First-forbidden (FF) transitions can play an important role in decreasing the calculated half-lives specially in environments where allowed Gamow-Teller (GT) transitions are unfavored. Of special mention is the case of neutron-rich nuclei where, due to phase-space amplification, FF transitions are much favored. We calculate the allowed GT transitions in various pn-QRPA models for even-even neutron-rich isotopes of nickel. Here we also study the effect of deformation on the calculated GT strengths. The FF transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nuclei to be spherical. Later we take into account deformation of nuclei and calculate GT + unique FF transitions, stellar $\beta$-decay rates, energy rate of $\beta$-delayed neutrons and probability of $\beta$-delayed neutron emissions. The calculated half-lives are in excellent agreement with measured ones and might contribute in speeding-up of the $r$-matter flow., Comment: 22 pages, 10 figures, 7 tables. arXiv admin note: text overlap with arXiv:1301.5225 by other authors

Gamow-Teller (GT) transitions play a preeminent role in the collapse of stellar core in the stages leading to a Type-II supernova. The B(GT) strength distributions for ground and excited states of $^{57}$Zn are calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. No experimental insertions were made (as usually made in other pn-QRPA calculations of B(GT) strength function) to check the performance of the model for proton-rich nuclei. The calculated ground-state B(GT) strength distribution is in good agreement with measurements and shows differences with the earlier reported shell model calculation. The pn-QRPA model reproduced the measured low-lying strength for $^{57}$Zn better in comparison to the KB3G interaction used in the large-scale shell model calculation. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{57}$Cu. The primary mechanism for producing such nuclei is the rp-process and is believed to be important in the dynamics of the collapsing supermassive stars. Small changes in the binding and excitation energies can lead to significant modifications of the predictions for the synthesis of proton rich isotopes. The $\beta^{+}$-decay and electron capture (EC) rates on $^{57}$Zn are compared to the seminal work of Fuller, Fowler and Newman (FFN). The pn-QRPA calculated $\beta^{+}$-decay rates are generally in good agreement with the FFN calculation. However at high stellar temperatures the calculated $\beta^{+}$-decay rates are almost half of FFN rates. On the other hand, for rp-process conditions, the calculated electron capture ($\beta^{+}$-decay) rates are bigger than FFN rates by more than a factor 2 (1.5) and may have interesting astrophysical consequences., Comment: 9 pages, 5 figures, 1 table

$\beta$-decay and positron decay are believed to play a consequential role during the late phases of stellar evolution of a massive star culminating in a supernova explosion. Recently the microscopic calculation of weak-interaction mediated rates on key isotopes of iron was introduced using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory with improved model parameters. Here I discuss in detail the improved calculation of $\beta^{\pm}$ decay rates for iron isotopes ($^{54,55,56}$Fe) in stellar environment. The pn-QRPA theory allows a microscopic "state-by-state" calculation of stellar rates as explained later in text. Excited state Gamow-Teller distributions are much different from ground state and a microscopic calculation of decay rates from these excited states greatly increases the reliability of the total decay rate calculation specially during the late stages of stellar evolution. The reported decay rates are also compared with earlier calculations. The positron decay rates are in reasonable agreement with the large-scale shell model calculation. The main finding of this work includes that the stellar $\beta$-decay rates of $^{54,55,56}$Fe are around 3 -- 5 orders of magnitude smaller than previously assumed and hence irrelevant for the determination of the evolution of $Y_{e}$ during the presupernova phase of massive stars. The current work discourages the inclusion of $^{55,56}$Fe in the list of key stellar $\beta$-decay nuclei as suggested by former simulation results., Comment: 35 pages, 15 figures

Weak interaction rates on titanium isotopes are important during the late phases of evolution of massive stars. A search was made for key titanium isotopes from available literature and a microscopic calculation of weak rates of these nuclei were performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. Earlier the author presented the stellar electron capture rates on titanium isotopes. In this paper I present the neutrino and antineutrino energy loss rates due to capture and decay rates on isotopes of titanium in stellar environment. Accurate estimate of neutrino energy loss rates are needed for the study of the late stages of the stellar evolution, in particular for cooling of neutron stars and white dwarfs. The results are also compared against previous calculations. At high stellar temperatures the calculated neutrino and antineutrino energy loss rates are bigger by more than two orders of magnitude as compared to the large scale shell model results and favor stellar cores with lower entropies. This study can prove useful for core-collapse simulators., Comment: 16 pages, 7 figures

In this work, superconducting pellets without lead (Pb) as well as with different concentrations of lead are prepared by solid state reaction. The prepared samples are then characterized using X-ray powder diffraction (XRD), scanning electron microscope (SEM), and energy-dispersive X-ray spectroscopy (EDX). The superconducting properties are examined using electrical resistivity and transport critical current density J c . Our results show that the sample prepared with calcination of 48 hours with intermediate grinding has the ideal value of the superconducting transition temperature T c and transport critical current density J c .

The Gamow-Teller strength distribution function, B(GT), for the odd Z parent $^{51}$V, $N-Z$ =5, up to 30 MeV of excitation energy in the daughter $^{51}$Ti is calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. The pn-QRPA results are compared against other theoretical calculations, (n, p) and high resolution (d, $^{2}$He) reaction experiments. For the case of (d, $^{2}$He) reaction the calibration was performed for $0\leq E_{j} \leq 5.0$ MeV, where the authors stressed that within this excitation energy range the $\Delta L = 0$ transition strength can be extracted with high accuracy for $^{51}$V. Within this energy range the current pn-QRPA total B(GT) strength 0.75 is in good agreement with the (d, $^{2}$He) experiment's total strength of 0.9 $\pm$ 0.1. The pn-QRPA calculated Gamow-Teller centroid at 4.20 MeV in daughter $^{51}$Ti is also in good agreement with high resolution (d, $^{2}$He) experiment which placed the Gamow-Teller centroid at 4.1 $\pm$ 0.4 MeV in daughter $^{51}$Ti. The low energy detailed Gamow-Teller structure and Gamow-Teller centroid play a sumptuous role in associated weak decay rates and consequently affect the stellar dynamics. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{51}$Ti. The calculated electron capture rates on $^{51}$V in stellar matter are also in good agreement with the large scale shell model rates., Comment: 13 pages, 4 figures and 1 table. arXiv admin note: text overlap with arXiv:1203.4669

Accurate estimate of the neutrino cooling rates is required in order to study the various stages of stellar evolution of massive stars. Neutrino losses from proto-neutron stars play a crucial role in deciding whether these stars would be crushed into black holes or explode as supernovae. Both pure leptonic and weak-interaction processes contribute to the neutrino energy losses in stellar matter. At low temperatures and densities, characteristic of the early phase of presupernova evolution, cooling through neutrinos produced via the weak-interaction is important. Proton-neutron quasi-particle random phase approximation (pn-QRPA) theory has recently being used for calculation of stellar weak-interaction rates of $fp$-shell nuclide with success. The lepton-to-baryon ratio ($Y_{e}$) during early phases of stellar evolution of massive stars changes substantially alone due to electron captures on $^{56}$Ni. The stellar matter is transparent to the neutrinos produced during the presupernova evolution of massive stars. These neutrinos escape the site and assist the stellar core in maintaining a lower entropy. Here I present the expanded calculation of weak-interaction mediated neutrino and antineutrino cooling rates due to $^{56}$Ni in stellar matter using the pn-QRPA theory. This detailed scale is appropriate for interpolation purposes and of greater utility for simulation codes. The calculated rates are compared against earlier calculations. During the relevant temperature and density regions of stellar matter the reported rates show little differences with the shell model rates and might contribute in fine-tuning of the lepton-to-baryon ratio during the presupernova phases of stellar evolution of massive stars., Comment: 20 pages, 6 figures and 1 table. arXiv admin note: text overlap with arXiv:1108.1010, arXiv:1203.4344

The Gamow-Teller (GT) transitions within massive stars play sumptuous role in the dynamics of core collapse supernovae. GT strength distributions and electron capture rates have been calculated for odd-A nucleus $^{59}$Co within the proton-neutron quasiparticles random phase approximation (pn-QRPA) formalism. The pn-QRPA results are compared with other model calculations and (n, p) reaction experiment carried out at TRIUMF charge-exchange facility. The pn-QRPA calculated a total $B(GT_{+})$ strength of 3.3 for $^{59}$Co to be compared with the shell model value of 2.5 and the 1.9 $\pm$ 0.1 in the (n, p) charge-exchange reaction. Aufderheide et. al. \cite{Aufderheide93} extracted total strength equaling 2.4 $\pm$ 0.3. The placement of GT centroid at 5.6 MeV by the pn-QRPA model is in reasonable agreement with the shell model centroid at 5.1 MeV whereas the measured GT centroid was placed at 4.4 $\pm$ 0.3 MeV in the (n, p) experiment. Fuller, Fowler and Newman (FFN) \cite{FFN80, FFN82, FFN82b}, placed the GT centroid at too low excitation energy of 2.0 MeV in the daughter nucleus $^{59}$Fe, and this misplacement led to the enhancement of FFN rates. The suppressed pn-QRPA and shell model electron capture rates are in good agreement with each other. The rates are suggestive of higher value of $Y_{e}$ (electron-to-baryon ratio) and may contribute to a more massive homologously collapsing core resulting in a more energetic shock. It might be interesting for the simulators to check the effect of these suppressed rates on the fine-tuning of the time rate of $Y_{e}$, the concomitant heavy element nucleosynthesis, and, on the energetics of the subsequent shock wave., Comment: 11 pages, 3 figures and 1 table. arXiv admin note: text overlap with arXiv:1408.4529

Few white dwarfs, located in binary systems, may acquire sufficiently high mass accretion rates resulting in the burning of carbon and oxygen under nondegenerate conditions forming a O+Ne+Mg core. These O+Ne+Mg cores are gravitationally less bound than more massive progenitor stars and can release more energy due to the nuclear burning. They are also amongst the probable candidates for low entropy r-process sites. Recent observations of subluminous Type II-P supernovae (e.g., 2005cs, 2003gd, 1999br, 1997D) were able to rekindle the interest in 8 -- 10 M$_{\odot}$ which develop O+Ne+Mg cores. Microscopic calculations of capture rates on $^{24}$Mg, which may contribute significantly to the collapse of O+Ne+Mg cores, using shell model and proton-neutron quasiparticle random phase approximation (pn-QRPA) theory, were performed earlier and comparisons made. Simulators, however, may require these capture rates on a fine scale. For the first time a detailed microscopic calculation of the electron and positron capture rates on $^{24}$Mg on an extensive temperature-density scale is presented here. This type of scale is more appropriate for interpolation purposes and of greater utility for simulation codes. The calculations are done using the pn-QRPA theory using a separable interaction. The deformation parameter, believed to be a key parameter in QRPA calculations, is adopted from experimental data to further increase the reliability of the QRPA results. The resulting calculated rates are up to a factor of 14 or more enhanced as compared to shell model rates and may lead to some interesting scenario for core collapse simulators., Comment: 20 pages, 6 figures and 1 table. arXiv admin note: substantial text overlap with arXiv:1108.0511, arXiv:1108.0826

Using expansion of the three-body wave function of the $pep$ system in the initial state on hyperharmonic functions, the rate of the $p+p+e^{-} \rightarrow d+\nu_e$ reaction in the Sun is calculated. The results of calculation of the flux at 1 AU are compared with the results of a measurement made by the Borexino collaboration and Bahcall \textit{et al.} theoretical predictions.

The acquisition of precise and reliable nuclear data is a prerequisite to success for stellar evolution and nucleosynthesis studies. Core-collapse simulators find it challenging to generate an explosion from the collapse of the core of massive stars. It is believed that a better understanding of the microphysics of core-collapse can lead to successful results. The weak interaction processes are able to trigger the collapse and control the lepton-to-baryon ratio ($Y_{e}$) of the core material. It is suggested that the temporal variation of $Y_{e}$ within the core of a massive star has a pivotal role to play in the stellar evolution and a fine-tuning of this parameter at various stages of presupernova evolution is the key to generate an explosion. During the presupernova evolution of massive stars, isotopes of iron, mainly $^{54,55,56}$Fe, are considered to be key players in controlling $Y_{e}$ ratio via electron capture on these nuclide. Recently an improved microscopic calculation of weak interaction mediated rates for iron isotopes was introduced using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic \textit{state-by-state} calculation of stellar capture rates which greatly increases the reliability of calculated rates. The results were suggestive of some fine-tuning of the $Y_{e}$ ratio during various phases of stellar evolution. Here we present for the first time the fine-grid calculation of the electron and positron capture rates on $^{54,55,56}$Fe. Core-collapse simulators may find this calculation suitable for interpolation purposes and for necessary incorporation in the stellar evolution codes., 21 pages, 6 ps figures and 2 tables

In astrophysical environments, allowed Gamow-Teller (GT) transitions are important, particularly for $\beta$-decay rates in presupernova evolution of massive stars, since they contribute to the fine-tuning of the lepton-to-baryon content of the stellar matter prior to and during the collapse of a heavy star. In environments where GT transitions are unfavored, first-forbidden transitions become important especially in medium heavy and heavy nuclei. Particularly in case of neutron-rich nuclei, first-forbidden transitions are favored primarily due to the phase-space amplification for these transitions. In this work the total $\beta$-decay half-lives and the unique first-forbidden(U1F) $\beta$-decay rates for a number of neutron-rich nickel isotopes, $^{72-78}$Ni, are calculated using the proton-neutron quasi-particle random phase approximation (pn-QRPA) theory in stellar environment for the first time. For the calculation of the $\beta$-decay half-lives both allowed and unique first-forbidden transitions were considered. Comparison of the total half-lives is made with measurements and other theoretical calculations where it was found that the pn-QRPA results are in better agreement with experiments and at the same time are suggestive of inclusion of rank 0 and rank 1 operators in first-forbidden rates for still better results., Comment: (16 pages, 10 figures, 2 tables)

Isotopes of nickel play a key role during the silicon burning phase up to the presupernova phase of massive stars. Electron capture rates on these nickel isotopes are also important during the phase of core contraction. I present here the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions for key nickel isotopes. The calculation is performed within the frame-work of pn-QRPA model. A judicious choice of model parameters, specially of the Gamow-Teller strength parameters and the deformation parameter, resulted in a much improved calculation of GT strength functions. The excited state GT distributions are much different from the corresponding ground-state distributions resulting in a failure of the Brink's hypothesis. The electron capture and positron decay rates on nickel isotopes are also calculated within the framework of pn-QRPA model relevant to the presupernova evolution of massive stars. The electron capture rates on odd-A isotopes of nickel are shown to have dominant contributions from parent excited states during as early as silicon burning phases. Comparison is being made with the large scale shell model calculation. During the silicon burning phases of massive stars the electron capture rates on $^{57,59}$Ni are around an order of magnitude bigger than shell model rates and can bear consequences for core-collapse simulators., Comment: 11 pages, 6 figures and 8 tables

Accurate estimate of neutrino energy loss rates are needed for the study of the late stages of the stellar evolution, in particular for cooling of neutron stars and white dwarfs. Proton-neutron quasi-particle random phase approximation (pn-QRPA) theory has recently being used for a microscopic calculation of stellar weak interaction rates of iron isotopes with success. Here I present the detailed calculation of neutrino and antineutrino cooling rates due to key iron isotopes in stellar matter using the pn-QRPA theory. The rates are calculated on a fine grid of temperature-density scale suitable for core-collapse simulators. The calculated rates are compared against earlier calculations. The neutrino cooling rates due to isotopes of iron are in overall good agreement with the rates calculated using the large-scale shell model. During the presupernova evolution of massive stars, from oxygen shell burning till around end of convective core silicon burning phases, the calculated neutrino cooling rates due to $^{54}$Fe are three to four times larger than the corresponding shell model rates. The Brink's hypothesis used in previous calculations can at times lead to erroneous results. The Brink's hypothesis assumes that the Gamow-Teller strength distributions for all excited states are the same. It is, however, shown by the present calculation that both the centroid and total strength for excited states differ appreciably from the ground state distribution. These changes in the strength distributions of thermally populated excited states can alter the total weak interaction rates rather significantly. The calculated antineutrino cooling rates, due to positron capture and $\beta$-decay of iron isotopes, are orders of magnitude smaller than the corresponding neutrino cooling rates and can safely be neglected specially at low temperatures and high stellar densities., Comment: 25 pages, 9 figures, 6 tables

Electron capture and positron decay rates are calculated for neutron-deficient Kr and Sr waiting point nuclei in stellar matter. The calculation is performed within the framework of pn-QRPA model for rp-process conditions. Fine tuning of particle-particle, particle-hole interaction parameters and a proper choice of the deformation parameter resulted in an accurate reproduction of the measured half-lives. The same model parameters were used to calculate stellar rates. Inclusion of measured Gamow-Teller strength distributions finally led to a reliable calculation of weak rates that reproduced the measured half-lives well under limiting conditions. For the rp-process conditions, electron capture and positron decay rates on $^{72}$Kr and $^{76}$Sr are of comparable magnitude whereas electron capture rates on $^{78}$Sr and $^{74}$Kr are 1--2 orders of magnitude bigger than the corresponding positron decay rates. The pn-QRPA calculated electron capture rates on $^{74}$Kr are bigger than previously calculated. The present calculation strongly suggests that, under rp-process conditions, electron capture rates form an integral part of weak-interaction mediated rates and should not be neglected in nuclear reaction network calculations as done previously., Comment: 13 pages, 4 figures, 4 tables; Astrophysics and Space Science (2012)

This paper reports on the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions, both in the electron capture and electron decay direction, for $^{54,55,56}$Fe. The associated electron and positron capture rates for these isotopes of iron are also calculated in stellar matter. These calculations were recently introduced and this paper is a follow-up which discusses in detail the GT strength distributions and stellar capture rates of key iron isotopes. The calculations are performed within the framework of the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic \textit{state-by-state} calculation of GT strength functions and stellar capture rates which greatly increases the reliability of the results. For the first time experimental deformation of nuclei are taken into account. In the core of massive stars isotopes of iron, $^{54,55,56}$Fe, are considered to be key players in decreasing the electron-to-baryon ratio ($Y_{e}$) mainly via electron capture on these nuclide. The structure of the presupernova star is altered both by the changes in $Y_{e}$ and the entropy of the core material. Results are encouraging and are compared against measurements (where possible) and other calculations. The calculated electron capture rates are in overall good agreement with the shell model results. During the presupernova evolution of massive stars, from oxygen shell burning stages till around end of convective core silicon burning, the calculated electron capture rates on $^{54}$Fe are around three times bigger than the corresponding shell model rates. The calculated positron capture rates, however, are suppressed by two to five orders of magnitude., Comment: 18 pages, 12 figures, 10 tables

The Gamow-Teller response is astrophysically important for a number of nuclides, particularly around iron. The random phase approximation (RPA) is an efficient way to generate strength distributions. In order to better understand both theoretical systematics and uncertainties, we compare the Gamow-Teller strength distributions for a suite of nuclides and for a suite of interactions, including semi-realistic interactions in the $1p$-$0f$ space with the RPA and a separable multi-shell interaction in the quasi-particle RPA. We also compare with experimental results for GT$_-$ on ${54}$Fe., Comment: 23 pages, 2 tables, 7 figures; corrections made due to bug in program, errors in interpreting scaling factors; changes made at referee request