Gamow-Teller Strength Functions Research Articles

Validity of Brink-Axel Hypothesis for calculations of allowed stellar weak rates of heavy nuclei

The knowledge of beta-decay transitional probabilities and Gamow-Teller (GT) strength functions from highly excited states of nuclides is of particular importance for applications to astrophysical network calculations of nucleosynthesis in explosive stellar events. These quantities are challenging to achieve from measurements or computations using various nuclear models. Due to unavailability of feasible alternatives, many theoretical studies often rely on the Brink-Axel (BA) hypothesis, that is, the response of strength functions depends merely on the transition energy of the parent nuclear ground state and is independent of the underlying details of the parent state, for the calculation of stellar rates. BA hypothesis has been used in many applications from nuclear structure determination to nucleosynthesis yield in the astrophysical matter. We explore here the the validity of BA hypothesis in the calculation of stellar beta-decay (BD) and electron capture (EC) weak rates of fp- and fpg-shell nuclides for GT transitions. Strength functions have been computed employing the fully microscopic proton-neutron QRPA (quasi-particle random-phase approximation) within a broad density, ρY e = (10-1011) [g cm−3], and temperature, T = (1−30) [GK], grid relevant to the pre-collapse astrophysical environment. Our work provides evidence that the use of the approximation based on the BA hypothesis does not lead to reliable calculations of excited states strength functions under extreme temperature-density conditions characteristic of presupernova and supernova evolution of massive stars. Weak rates obtained by incorporating the BA hypothesis in the calculation of strength functions substantially deviate from the rates based on the state-by-state microscopically calculated strength functions. Deviation in the two calculations becomes significant as early as neon burning phases of massive stars. The deviation in the calculation of BD rates is even more pronounced, reaching up to three orders of magnitude.

Strength of the isoscalar pairing interaction determined by a relation between double-charge change and double-pair transfer for double- β decay

A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double charge change and the double transfer of like-particle pair, and a constraint is derived to the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, detail of this method is explained thoroughly, and applications are made to nuclei of several instances of the double-$\beta$ decays. The systematics of the strengths determined for those nuclei is understood in terms of a midshell effect. The effect of the new interaction strength is examined in two examples of the Gamow-Teller strength function with comparisons with the experimental data. The nuclear matrix elements of the neutrinoless double-$\beta$ decay are also calculated.

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.

Configuration splitting of the Gamow-Teller resonance in antimony isotopes: Is this a real or a virtual effect?

The Gamow-Teller strength functions for a number of antimony isotopes were calculated within a semimicroscopic approach based on the continuum version of the charge-exchange quasiparticle random-phase approximation and on phenomenologically taking into account the fragmentation effect. The structural effect of splitting of the main maximum of the Gamow-Teller resonance in these isotopes was confirmed. Experimental data on the excitation of this resonance in a direct and a resonance reaction for the 118Sn parent nucleus were analyzed with allowance for this effect.

Neutrinoless ββ decay nuclear matrix elements in an isotopic chain

We analyze nuclear matrix elements (NME) of neutrinoless double beta decay calculated for the cadmium isotopes. Energy density functional methods including beyond mean field effects such as symmetry restoration and shape mixing are used. Strong shell effects are found associated to the underlying nuclear structure of the initial and final nuclei. Furthermore, we show that NME for two-neutrino double beta decay evaluated in the closure approximation, Mcl2ν, display a constant proportionality with respect to the Gamow–Teller part of the neutrinoless NME, MGT0ν. This opens the possibility of determining the MGT0ν matrix elements from β∓ Gamow–Teller strength functions. Finally, the interconnected role of deformation, pairing, configuration mixing and shell effects in the NMEs is discussed.

Nickel isotopes in stellar matter

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.

Ground and excited states Gamow-Teller strength distributions of iron isotopes and associated capture rates for core-collapse simulations

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 54,55,56Fe. 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 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, 54,55,56Fe, 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 54Fe 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.

Tensor Effects on Spin-Dependent Charge-Exchange transitions

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model. The Gamow-Teller (GT) and Spin-Dipole (SD) strength functions of 208Pb are calculated with and without the tensor terms. The main GT peak is moved downwards by about 2 MeV and about 10 % of the total strength is shifted to the excitation energy region above 30 MeV by the RPA tensor correlation. The SD 0 − peaks are moved upward while the 1 − peaks are moved downward dramatically, by the RPA tensor correlation. An qualitative understanding of these effects are given by using a separable tensor force.

Description of the two-neutrino ββ decay of 100Mo by pnMAVA

The microscopic anharmonic vibrator approach (MAVA) is a scheme where the one- and two-phonon states of an even–even nucleus are treated consistently by using a realistic microscopic nuclear Hamiltonian. This model has recently been extended to describe odd–odd nuclei by adding proton–neutron phonons in a scheme called the proton–neutron MAVA (pnMAVA). In this paper, we apply pnMAVA to compute the nuclear matrix elements corresponding to the two-neutrino double beta (2νββ) decay of 100Mo to the ground state and the first excited 0+ state of 100Ru in a realistic single-particle space. We also compute the GT− and GT+ Gamow–Teller strength functions and compare them with the plain pnQRPA (proton–neutron QRPA) and available data. The redistribution of strength to four-quasiparticle degrees of freedom can be clearly seen in the GT+ function. The more striking effect is seen in the 2νββ matrix element corresponding to the ground-state transition where the incoherence of individual contributions is stronger for the pnMAVA than for the pnQRPA, and a 15% reduction in the magnitude of the matrix element is obtained for the pnMAVA. The 2νββ transition rate to the excited 0+ state is zero in a pnQRPA calculation, whereas the pnMAVA result is not far from the measured decay rate.

E1transitions between spin-dipole and Gamow-Teller giant resonances

The branching ratios for E1 transitions between the spin-dipole (SD) and Gamow-Teller (GT) giant resonances in ${}^{90}\mathrm{Nb}$ and ${}^{208}\mathrm{Pb}$ are evaluated. Assuming the main GT state has a wave function close to that for the ``ideal'' GT state, we reduced the problem to calculate the SD and GT strength functions. These strength functions are evaluated within an extended continuum-random phase approximation approach.

Half-lives and presupernova weak interaction rates for nuclei away from the stability line

A detailed model for the calculation of -decay rates of the fp shell nuclei for situations prevailing in presupernova and collapse phases of evolution of the core of massive stars leading to supernova explosion has been extended for electron-capture rates. It can also be used to determine the half-lives of neutron-rich nuclei in the fp/fpg shell. The model uses an averaged Gamow-Teller (GT) strength function, but it can also use the experimental log ft values and GT strength function from (n, p) reaction studies wherever available. The calculated rate includes contributions from each of the low-lying excited states of the mother including some specific resonant states (`back resonance') having large GT matrix elements.

Shell-model study of partial muon-capture rates in light nuclei

The nuclear shell model is used to study ordinary muon capture of light nuclei in the p, sd and p-sd shell-model spaces. Several well-established two-body interactions are applied to calculate the involved nuclear matrix elements and the emerging results are compared with each other. The resulting theoretical partial muon-capture rates are compared with experimental data and their stability against different model spaces and interactions studied. The effects of the induced-pseudoscalar strength, C p, on the capture rates is discussed. The relation between the allowed partial muon capture rates and the Gamow-Teller strength function is stressed.

β-decay of 40Ti

The β-decay of 40Ti was studied. The Fermi and Gamow-Teller strength function was deduced from the observed β-delayed emission of protons and γ-rays and from the measured half-life of 55(2) ms. The results are compared to shell-model predictions and are used to estimate the neutrino-capture rate of the solar-neutrino detector ICARUS.

Nuclear Weak Processes in Presupernova Stars

The structure and the size of the core of massive presupernova stars are determined by the electron fraction and entropy of the core during its late stages of evolution; these in turn affect the subsequent evolution during gravitational collapse and supernova explosion phases. Beta decay and electron capture on a number of neutron rich nuclei can contribute substantially towards the reduction of the entropy and possibly the electron fraction in the core. Methods for calculating the weak transition rates for a number of nuclei for which no reliable rates exist (particularly for A > 60) are outlined. The calculations are particularly suited for presupernova matter density (p = 107 - 109 g/cc) and temperature (T = 2 - 6 × 109 °K). We include besides the contributions from the ground state and the known excited states, the Gamow-Teller (GT) resonance states (e.g. for beta decay rates, the GT+ states) in the mother nucleus which are populated thermally. For the GT strength function for transitions from the ground state (as well as excited states) we use a sum rule calculated by the spectral distribution method where the centroid of the distribution is obtained from experimental data on (p,n) reactions. The contribution of the excited levels and GT+ resonances turn out to be important at high temperatures which may prevail in presupernova stellar cores.

Gamow-Teller strength in the β-decay of 36Ca

The β-decay of 36Ca has been studied at the projectile fragment separator at GSI Darmstadt. The measured Gamow-Teller strength function B (GT), deduced from the observed β-delayed proton- and γ-emission and from the measured half-life of 102(2) ms, is compared to results obtained from large-scale sd-shell model calculations. A systematic underestimation of the measured strength by the theory is found.

Effect of inclusion of 1g orbits on the Gamow-Teller strengths for the capture rates of solar neutrinos in Ga detectors

Neutrino capture rates for Ga detectors are calculated using a simple model for the Gamow-Teller strength distribution in an extended shell model space consisting of (1f2p1g) orbits and compared to the values obtained in the (1f2p) model space. It is seen that though the Gamow-Teller strength functions for the two model spaces differ at energies greater than the neutron emission threshold of 71Ge, the difference is small below this energy. This results in a vanishingly small change in the neutrino capture cross section and consequently the actual capture rate.

Missing and quenched Gamow-Teller strength.

Gamow-Teller strength functions in full $(pf)^{8}$ spaces are calculated with sufficient accuracy to ensure that all the states in the resonance region have been populated. Many of the resulting peaks are weak enough to become unobservable. The quenching factor necessary to bring into agreement the low lying observed states with shell model predictions is shown to be due to nuclear correlations. To within experimental uncertainties it is the same that is found in one particle transfer and (e,e') reactions. Perfect consistency between the observed $^{48}Ca(p,n)^{48}Sc$ peaks and the calculation is achieved by assuming an observation threshold of 0.75\% of the total strength, a value that seems typical in several experiments

Gamow-Teller strength functions of superfluid odd- A nuclei and neutrino capture reactions

The charge-exchange excitations of superfluid odd- A nuclei are studied within the framework of the self-consistent finite Fermi-system theory. The pairing blocking effects due to the odd quasiparticle, the effective NN-interactions both in the particle-hole (ph) and particle-particle (pp) channel, and also the ph-continuum are taken into account. Gamow-Teller strength functions of 71Ga, 115In and 19F nuclei are calculated and compared with those extracted from experimental spectra of (p,n) reactions. The total capture cross sections of the reactor electron antineutrinos are calculated (assuming complete ν e → ν e conversion), as well as the solar-neutrino capture rates for the 71Ga and 115In+ 19F detectors. Uncertainties regarding nuclear-structure information involved in these calculations are discussed.

Full pf shell model study of A=48 nuclei.

Exact diagonalizations with a minimally modified realistic force lead to detailed agreement with measured level schemes and electromagnetic transitions in $^{48}\mathrm{Ca}$, $^{48}\mathrm{Sc}$, $^{48}\mathrm{Ti}$, $^{48}\mathrm{V}$, $^{48}\mathrm{Cr}$, and $^{48}\mathrm{Mn}$. Gamow-Teller strength functions are systematically calculated and reproduce the data to within the standard quenching factor. Their fine structure indicates that fragmentation makes much strength unobservable. As a by-product, the calculations suggest a microscopic description of the onset of rotational motion. The spectroscopic quality of the results provides strong arguments in favor of the general validity of monopole corrected realistic forces, which is discussed.

Shell-model calculations of Gamow-Teller strength in 51V, 54Fe, and 59Co.

The Gamow-Teller (GT) strength functions of $^{51}\mathrm{V}$, $^{54}\mathrm{Fe}$, and $^{59}\mathrm{Co}$ measured by recent charge-exchange experiments have been studied using shell-model calculations employing two model spaces. The shell model is fairly successful at reproducing GT strength in the (p,n) direction, but the agreement is not as good in the (n,p) direction. It is found that both directions can be fit consistently by shifting single particle energies in a systematic manner. It is found that roughly 75% of the sum-rule strength can be seen in the experiments for both $^{51}\mathrm{V}$ and $^{54}\mathrm{Fe}$. It is also found that roughly 35% of the GT strength predicted by the shell model is seen in the (n,p) direction for all three nuclei, but that the quenching in the (p,n) direction varies with nucleus. The consequences of these findings for improving the calculation of weak interaction rates are discussed.