Gamow-Teller Research Articles

Study of Gamow–Teller strength and associated weak-rates on odd-A nuclei in stellar matter

In a recent study by Cole et al. [A. L. Cole et al., Phys. Rev. C 86 (2012) 015809], it was concluded that quasi-particle random phase approximation (QRPA) calculations show larger deviations and overestimate the total experimental Gamow–Teller (GT) strength. It was also concluded that QRPA calculated electron capture rates exhibit larger deviation than those derived from the measured GT strength distributions. The main purpose of this study is to probe the findings of the Cole et al. paper. This study gives useful information on the performance of QRPA-based nuclear models. As per simulation results, the capturing of electrons that occur on medium heavy isotopes have a significant role in decreasing the ratio of electron-to-baryon content of the stellar interior during the late stages of core evolution. We report the calculation of allowed charge-changing transitions strength for odd-[Formula: see text] [Formula: see text]-shell nuclei ([Formula: see text]Sc and [Formula: see text]Mn) by employing the deformed pn-QRPA approach. The computed GT transition strength is compared with previous theoretical calculations and measured data. For stellar applications, the corresponding electron capture rates are computed and compared with rates using previously calculated and measured GT values. Our finding shows that our calculated results are in decent accordance with measured data. At higher stellar temperature, our calculated electron capture rates are larger than those calculated by independent particle model (IPM) and shell model. It was further concluded that at low temperature and high density regions, the positron emission weak-rates from [Formula: see text]Sc and [Formula: see text]Mn may be neglected in simulation codes.

Quantum Monte Carlo calculations of weak transitions in A=6–10 nuclei

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, i.e., the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.

Beyond mean-field description of Gamow-Teller resonances and β-decay

β-decay half-lives set the time scale of the rapid neutron capture process, and are therefore essential for understanding the origin of heavy elements in the universe. The random-phase approximation (RPA) based on Skyrme energy density functionals is widely used to calculate the properties of Gamow-Teller (GT) transitions, which play a dominant role in β-decay half-lives. However, the RPA model has its limitations in reproducing the resonance width and often overestimates β-decay half-lives. To overcome these problems, effects beyond mean-field can be included on top of the RPA model. In particular, this can be obtained by taking into account the particle-vibration coupling (PVC). Within the RPA+PVC model, we successfully reproduce the experimental GT resonance width and β-decay half-lives in magic nuclei. We then extend the formalism to superfluid nuclei and apply it to the GT resonance in 120Sn, obtaining a good reproduction of the experimental strength distribution. The effect of isoscalar pairing is also discussed.

Analogous Gamow-Teller and M1 Transitions in Tz = ±½ Mirror Nuclei and in Tz = ±1, 0 Triplet Nuclei relevant to Low-energy Super GT state

Nuclei have spin- and isospin-degrees of freedom. Therefore, Gamow-Teller (GT) transitions caused by the στ operator (spin-isospin operator) are unique tools for the studies of nuclear structure as well as nuclear interactions. They can be studied in β decays as well as charge-exchange (CE) reactions. Similarly, M1 γ decays are mainly caused by the στ operator. Combined studies of these transitions caused by Weak, Strong, and Electro-Magnetic interactions provide us a deeper understanding of nuclear spin-isospin-type transitions. We first compare the strengths of analogous GT and M1 transitions in the A = 27, Tz = ±½ mirror nuclei 27Al and 27Si. The comparison is extended to the Tz = ±1, 0 nuclei. The strength of GT transition from the ground state (g.s.) of 42Ca to the 0.611 MeV first Jπ = 1+ state in 42Sc is compared with that of the analogous M1 transition from the 0.611 MeV state to the T = 1, 0+ g.s. (isobaric analog state: IAS) in 42Sc. The 0.611 MeV state has the property of Low-energy Super GT (LeSGT) state, because it carries the main part of the GT strength of all available transitions from the g.s. of 42Ca (and 42Ti) to the Jπ = 1+ GT states in 42Sc.

Investigation of Gamow Teller transition properties in [formula omitted]Ni isotopes using QRPA methods

Weak rates in nickel isotopes play an integral role in the dynamics of supernovae. Electron capture and β-decay of nickel isotopes, dictated by Gamow–Teller transitions, significantly alter the lepton fraction of the stellar matter. In this paper we calculate Gamow–Teller (GT) transitions for isotopes of nickel, Ni56–64, using QRPA methods. The GT strength distributions were calculated using four different QRPA models. Our results are also compared with previous theoretical calculations and measured strength distributions wherever available. Our investigation concluded that amongst all RPA models, the pn-QRPA(C) model best described the measured GT distributions (including total GT strength and centroid placement). It is hoped that the current investigation of GT properties would prove handy and may lead to a better understanding of the presupernova evolution of massive stars.

Gamow-Teller transitions and proton-neutron pair correlation in N=Z odd-odd p -shell nuclei

We have studied the Gamow-Teller (GT) transitions from $N=Z+2$ neighbors to $N=Z=$ odd nuclei in $p$-shell region by using isospin-projected and $\beta\gamma$-constraint antisymmetrized molecular dynamics combined with generator coordinate method. The calculated GT transition strengths from $0^+1$ states to $1^+0$ states such as ${}^{6} \textrm{He}(0_1^+1)\rightarrow{}^{6} \textrm{Li}(1_1^+0)$, ${}^{10} \textrm{Be}(0_1^+1)\rightarrow{}^{10} \textrm{B}(1_1^+0)$, and ${}^{14} \textrm{C}(0_1^+1)\rightarrow{}^{14} \textrm{N}(1_2^+0)$ exhaust more than 50\% of the sum rule. These $N=Z+2$ initial states and $N=Z=$ odd final states are found to dominantly have $S=0,T=1$ $nn$ pairs and $S=1,T=0$ $pn$ pairs, respectively. Based on two-nucleon ($NN$) pair picture, we can understand the concentration of the GT strengths as the spin-isospin-flip transition $nn(S=0,T=1)\rightarrow pn(S=1,T=0)$ in $LS$-coupling scheme. The GT transition can be a good probe to identify the spin-isospin partner states with $nn$ pairs and $pn$ pairs of $N=Z+2$ and $N=Z=$ odd nuclei, respectively.

Allowed and unique first-forbidden stellar electron emission rates of neutron-rich copper isotopes

The allowed charge-changing transitions are the most common weak interaction processes of spin-isospin form that play a crucial role in several nuclear/astrophysical processes. The first-forbidden (FF) transition becomes important, in the circumstances where allowed Gamow-Teller (GT) transitions are unfavored, specifically for neutron-rich nuclei due to phase space considerations. In this paper deformed proton-neutron quasi-particle random phase approximation (pn-QRPA) model is applied, for the first time, for the estimation of allowed GT and unique first-forbidden (U1F) transitions ( $|\Delta J| = 2$ ) of neutron rich copper isotopes in mass range $72 \leq A \leq 82$ under stellar conditions. We compared our computed terrestrial $\beta$ -decay half-life values with previous calculations and experimental results. It was concluded that the pn-QRPA calculation is in good accordance with measured data. Our study suggests that the addition of rank (0 and 1) operators in FF transitions can further improve the comparison which remain unattended at this stage. The deformed pn-QRPA model was employed for the estimation of GT and U1F stellar electron emission ( $\beta^{-}$ -decay) rates over wide range of stellar temperature (0.01 GK–30 GK) and density ( $10\mbox{--}10^{11}\mbox{ g}/\mbox{cm}^{3}$ ) domains for astrophysical applications. Our study shows that, in high density and low temperature regions, the contribution of U1F rates to total electron emission rates of neutron-rich copper nuclei is negligible.

Nuclear structure properties and stellar weak rates for 76Se: Unblocking of the Gamow Teller strength

At finite temperatures (≥ 107K), 76Se is abundant in the core of massive stars and electron capture on 76Se has a consequential role to play in the dynamics of core-collapse. The present work may be classified into two main categories. In the first phase we study the nuclear structure properties of 76Se using the interacting boson model-1 (IBM-1). The IBM-1 investigations include the energy levels, B(E2) values and the prediction of the geometry. We performed the extended consistent-Q formalism (ECQF) calculation and later the triaxial formalism calculation (constructed by adding the cubic term to the ECQF). The geometry of 76Se can be envisioned within the formalism of the potential energy surface based on the classical limit of IBM-1 model. In the second phase, we reconfirm the unblocking of the Gamow–Teller (GT) strength in 76Se (a test case for nuclei having N>40 and Z<40). Using the deformed pn-QRPA model we calculate GT transitions, stellar electron capture cross section (within the limit of low momentum transfer) and stellar weak rates for 76Se. The distinguishing feature of our calculation is a state-by-state evaluation of stellar weak rates in a fully microscopic fashion. Results are compared with experimental data and previous calculations. The calculated GT distribution fulfills the Ikeda sum rule. Rates for β-delayed neutrons and emission probabilities are also calculated. Our study suggests that at high stellar temperatures and low densities, the β+-decay on 76Se should not be neglected and needs to be taken into consideration along with electron capture rates for simulation of presupernova evolution of massive stars.

Gamow-Teller strength and lepton captures rates on 66−71Ni in stellar matter

Charge-changing transitions play a significant role in stellar weak-decay processes. The fate of the massive stars is decided by these weak-decay rates including lepton (positron and electron) captures rates, which play a consequential role in the dynamics of core collapse. As per previous simulation results, weak interaction rates on nickel (Ni) isotopes have significant influence on the stellar core vis-à-vis controlling the lepton content of stellar matter throughout the silicon shell burning phases of high mass stars up to the presupernova stages. In this paper, we perform a microscopic calculation of Gamow–Teller (GT) charge-changing transitions, in the [Formula: see text]-decay and electron capture (EC) directions, for neutron-rich Ni isotopes ([Formula: see text]Ni). We further compute the associated weak-decay rates for these selected Ni isotopes in stellar environment. The computations are accomplished by employing the deformed proton–neutron quasiparticle random phase approximation (pn-QRPA) model. A recent study showed that the deformed pn-QRPA theory is well suited for the estimation of GT transitions. The astral weak-decay rates are determined over densities in the range of 10–10[Formula: see text][Formula: see text]g/cm3and temperatures in the range of 0.01[Formula: see text]–30[Formula: see text][Formula: see text]K. The calculated lepton capture rates are compared with the previous calculation of Pruet and Fuller (PF). The overall comparison demonstrates that, at low stellar densities and high temperatures, our EC rates are bigger by as much as two orders of magnitude. Our results show that, at higher temperatures, the lepton capture rates are the dominant mode for the stellar weak rates and the corresponding lepton emission rates may be neglected.

βdecay ofSi38,40(Tz=+5,+6) to low-lying core excited states in odd-oddP38,40isotopes

Low-lying excited states in $^{38,40}\mathrm{P}$ have been identified in the $\ensuremath{\beta}$ decay of ${T}_{z}=+5,\phantom{\rule{0.16em}{0ex}}+6, ^{38,40}\mathrm{Si}$. Based on the allowed nature of the Gamow-Teller (GT) decay observed, these states are assigned spin and parity of ${1}^{+}$ and are core-excited 1p1h intruder states with a parity opposite to the ground state. The occurrence of intruder states at low energies highlights the importance of pairing and quadrupole correlation energies in lowering the intruder states despite the $N=20$ shell gap. Configuration interaction shell model calculations with the state-of-art SDPF-MU effective interaction were performed to understand the structure of these 1p1h states in the even-$A$ phosphorus isotopes. States in $^{40}\mathrm{P}$ with $N=25$ were found to have very complex configurations involving all the $fp$ orbitals leading to deformed states as seen in neutron-rich nuclei with $N\ensuremath{\approx}28$. The calculated GT matrix elements for the $\ensuremath{\beta}$ decay highlight the dominance of the decay of the core neutrons rather than the valence neutrons.

A study of Gamow-Teller transitions for N = Z nuclei, 24Mg, 28Si, and 32S, by a deformed QRPA

We investigated Gamow-Teller (GT) transitions and strength distributions of s-d shell N = Z nuclei, 24Mg, 28Si, and 32S, by a deformed quasi-particle random phase approximation (DQRPA). In the DQRPA, we included particle model space up to p-f shell and considered explicitly the deformation as well as the like- and unlike-pairing correlations. Shell evolution by deformation and attractive force by unlike-pairing correlations turned out to play vital roles to reproduce the experimental GT data. Correlations between the deformation and the pairing correlations are also discussed with the comparison to the experimental data shape.

Spin-multipole nuclear matrix elements in thepnquasiparticle random-phase approximation: Implications forβandββhalf-lives

Half-lives for 148 potentially measurable 2nd-, 3rd-, 4th-, 5th-, 6th-, and 7th-forbidden unique beta transitions are predicted. To achieve this, the ratio of the nuclear matrix elements (NMEs), calculated by the proton-neutron quasiparticle random-phase approximation (pnQRPA), ${M}_{\mathrm{pnQRPA}}$, and a two-quasiparticle (two-qp) model, ${M}_{\mathrm{qp}}$, is studied and compared with earlier calculations for the allowed Gamow-Teller (GT) ${1}^{+}$ and first-forbidden spin-dipole (SD) ${2}^{\ensuremath{-}}$ transitions. The present calculations are done using realistic single-particle model spaces and $G$-matrix based microscopic two-body interactions. In terms of the ratio $k={M}_{\mathrm{pnQRPA}}/{M}_{\mathrm{qp}}$ the studied decays fall into two groups: for GROUP 1, which consists of transitions involving non-magic nuclei, the ratio turns out to be $k=0.29\ifmmode\pm\else\textpm\fi{}0.15$. For GROUP 2, consisting of transitions involving semimagic nuclei, the ratio is 0.5--0.8 for half of the decays and less than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for the other half. The magnitudes of the NMEs for several nuclei of GROUP 2 depend sensitively on the size of the used single-particle space and the energies of few key single-particle orbitals used in the pnQRPA calculation, while no such dependence is found for the transitions involving nuclei of GROUP 1. Comparing the NME ratios $k$ of GROUP 1 with those of the earlier GT and SD calculations, where also experimental data are available, the expected ``experimental'' half-lives for the decays between the ${0}^{+}$ ground state of the even-even reference nuclei and the ${J}^{\ensuremath{\pi}}={3}^{+},{4}^{\ensuremath{-}},{5}^{+},{6}^{\ensuremath{-}},{7}^{+},{8}^{\ensuremath{-}}$ states of the neighboring odd-odd nuclei are derived for possible experimental verification. The present results could also shed light to the magnitudes of the NMEs corresponding to the high-forbidden unique ${0}^{+}\ensuremath{\rightarrow}{J}^{\ensuremath{\pi}}={3}^{+},{4}^{\ensuremath{-}},{5}^{+},{6}^{\ensuremath{-}},{7}^{+},{8}^{\ensuremath{-}}$ virtual transitions taking part in the neutrinoless double beta decays.

Beta decay rates for 50,52Fe isotopes by Pyatov-Salamov method

Abstract . The Pyatov-Salamov Method (PM) has been used to study the Gamow-Teller (GT) transitions for chosen iron isotopes. The eigenvalues and eigenfunctions of the restored Hamiltonian have been solved within the framework of proton-neutron quasiparticle random phase approximation (pn-QRPA). The allowed GT beta decay half-life values have been calculated for the nuclei under consideration. The results have been compared with the schematic model (SM) calculations and corresponding experimental data. Keywords: Pyatov-Salamov method, pn-QRPA approximation, Gamow-Teller

Effects of deformation and neutron-proton pairing on the Gamow-Teller transitions forMg24,26in a deformed quasiparticle random-phase approximation

We investigate effects of neutron-proton ($np$) pairing correlations on the Gamow-Teller (GT) transition of $^{24,26}\mathrm{Mg}$ by explicitly taking into account deformation effects. Our calculation is performed by a deformed quasiparticle random phase approximation (DQRPA) which includes the deformation at the Bardeen-Cooper-Schrieffer and RPA stage. In this paper, we include the $np$ pairing as well as neutron-neutron ($nn$) and proton-proton ($pp$) paring correlations to the DQRPA. Our new formalism is applied to the GT transition of well-known deformed Mg isotopes. The $np$ pairing effect is found to affect more or less the GT distribution of $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$. But the deformation effect turns out to be much larger than the $np$ paring effect because the Fermi surfaces smear more widely by the deformation rather than the $np$ pairing correlations. Correlations between the deformation and the $np$ pairing effects and their ambiguities are also discussed with the comparison to experimental GT strength data by triton and $^{3}\mathrm{He}$ beams.

Spin dipole nuclear matrix elements for double beta decay nuclei by charge-exchange reactions

Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied experimentally for the first time by using measured cross sections of (3He, t) charge-exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) for low-lying 2− states were derived from the experimental SD strengths by referring to the experimental α = GT (Gamow–Teller) and α = F (Fermi) strengths. They are consistent with the empirical NMEs based on the quasi-particle model with the empirical effective SD coupling constant. The CERs are used to evaluate the SD NME, which is associated with one of the major components of the neutrino-less DBD NME.

Tritiumβdecay in chiral effective field theory

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $\beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($\chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $\chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.

Unique first-forbidden β-decay transitions in odd–odd and even–even heavy nuclei

The allowed Gamow–Teller (GT) transitions are the most common weak nuclear processes of spin–isospin (στ) type. These transitions play a key role in numerous processes in the domain of nuclear physics. Equally important is their contribution in astrophysics, particularly in nuclear synthesis and supernova-explosions. In situations where allowed GT transitions are not favored, first-forbidden transitions become significant, specifically in medium heavy and heavy nuclei. For neutron-rich nuclei, first-forbidden transitions are favored mainly due to the phase-space amplification for these transitions. In this work we calculate the allowed GT as well as unique first-forbidden (U1F) |ΔJ|=2 transitions strength in odd–odd and even–even nuclei in mass range 70≤A≤214. Two different pn-QRPA models were used with a schematic separable interaction to calculate GT and U1F transitions. The inclusion of U1F strength improved the overall comparison of calculated terrestrial β-decay half-lives in both models. The ft values and reduced transition probabilities for the 2−⟷0+ transitions were also calculated. We compared our calculations with the previously reported correlated RPA calculation and experimental results. Our calculations are in better agreement with measured data. For stellar applications we further calculated the allowed GT and U1F weak rates. These include β±-decay rates and electron/positron capture rates of heavy nuclei in stellar matter. Our study shows that positron and electron capture rates command the total weak rates of these heavy nuclei at high stellar temperatures.

High-resolution study of Gamow-Teller transitions in theTi48(He3,t)V48reaction

In this work we have studied ${T}_{z}=+2\ensuremath{\rightarrow}+1$, Gamow-Teller (GT) transitions in the $^{48}\mathrm{Ti}(^{3}\mathrm{He},t)^{48}\mathrm{V}$ charge-exchange reaction at 140 MeV/nucleon and ${0}^{\ensuremath{\circ}}$ at the Research Center for Nuclear Physics, Osaka. From the high-resolution facility, consisting of a high-dispersion beamline and the Grand Raiden spectrometer, the spectrum had an energy resolution of 21 keV, among the best achieved. Individual GT transitions were observed and GT strength was derived for each state populated up to an excitation energy of 12 MeV. The total sum of the $B$(GT) strength observed in discrete states was 4.0, which is 33% of the sum-rule-limit value of 12. The results were compared with the results of shell-model calculations carried out with the GXPF1J interaction. The measured $B$(GT) distribution was also compared with that obtained in the $(^{3}\mathrm{He},t)$ charge-exchange reaction on $^{47}\mathrm{Ti}$. On the assumption of isospin symmetry the $\ensuremath{\beta}$ spectrum of the ${T}_{z}=\ensuremath{-}2$ nucleus $^{48}\mathrm{Fe}$ was deduced from the observed spectrum in the $^{48}\mathrm{Ti}(^{3}\mathrm{He},t)^{48}\mathrm{V}$ reaction and this predicted spectrum was compared with the measured one.

Estimation of a 2p2h effect on Gamow-Teller transitions within the second Tamm-Dancoff approximation

Two-particle two-hole (2p2h) effect on the Gamow-Teller (GT) transition for neutron-rich nuclei is studied by the second Tamm-Dancoff approximation (STDA) with the Skyrme interaction. Unstable $^{24}\mathrm{O}$ and $^{34}\mathrm{Si}$ and stable $^{48}\mathrm{Ca}$ nuclei are chosen to study the quenching and fragmentation of the GT strengths. Correlation of the 2p2h configurations causes about $20%$ quenching and downward shift of GT giant resonances (GTGRs). The residual interaction changing relative angular momentum that appeared in the tensor force part gives a meaningful effect to the GT strength distributions. In this work, $17--26%$ of the total GT strengths are brought to high-energy region above GTGRs. In particular, the tensor force brings strengths to high energy more than 50 MeV. STDA calculation within a small model space for 2p2h configuration is also performed and experimental data of $^{48}\mathrm{Ca}$ is reproduced reasonably.

β-decay study within multireference density functional theory and beyond

Pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multi-reference density functional theory is presented. After successful test performed for 6He -> 6Li beta-decay, the model is applied to compute MEs in the sd- and pf-shell T=1/2 mirror nuclei. The calculated GT MEs and the isospin-symmetry-breaking corrections to the Fermi branch are found to be in a very good agreement with shell-model predictions in spite of fundamental differences between these models concerning model space, treatment of correlations or inclusion of a core. This result indirectly supports the two-body current based scenarios behind the quenching of axial-vector coupling constant.