Gamow-Teller resonance in hot nuclei and astrophysical applications

A formalism based on thermo field dynamics is described. It allows the effect of the temperature on the strength distribution of charge-exchange transitions in hot nuclei to be taken into account. Numerical calculations with the pair correlations in the BCS approximation and the schematic στ interaction are carried out for Gamow-Teller transitions in the ⁵⁶Fe nucleus. The electron capture and β^? decay rates are calculated for this nucleus at temperatures and densities corresponding to the advanced stage of the evolution of massive stars.     

Weak-interaction-mediated rates on iron isotopes for presupernova evolution of massive stars

During the presupernova evolution of massive stars, the isotopes of iron, ^{54, 55, 56}Fe , are advocated to play a key role inside the cores primarily decreasing the electron-to-baryon ratio (Y_e) mainly via electron capture processes thereby reducing the pressure support. Electron decay and positron capture on ⁵⁵Fe , on the other hand, also have a consequential role in increasing the lepton ratio during the silicon burning phases of massive stars. The neutrinos and antineutrinos produced, as a result of these weak-interaction reactions, are transparent to the stellar matter and assist in cooling the core thereby reducing the entropy. The structure of the presupernova star is altered both by the changes in Y_e and the entropy of the core material. The aim of this paper is to report the improved microscopic calculation of Gamow-Teller (GT_±) strength distributions of these key isotopes of iron using the pn-QRPA theory. The main improvement comes from the incorporation of experimental deformation values for these nuclei. Additionally six different weak-interaction rates, namely electron and positron capture, electron and positron decay, and, neutrino and antineutrino cooling rates, were also calculated in presupernova matter. The calculated electron capture and neutrino cooling rates due to isotopes of iron are in good agreement with the large-scale shell model (LSSM) results. The calculated beta decay rates, however, are suppressed by three to five orders of magnitude.     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Fine-grid calculations for stellar electron and positron capture rates on Fe isotopes

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 corematerial. 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 ^54–56Fe, are considered to be key players in controlling Y _e ratio via electron capture on these nuclides. 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 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 ^54–56Fe. The sensitivity of the pn-QRPA calculated capture rates to the deformation parameter is also studied in this work. Core-collapse simulators may find this calculation suitable for interpolation purposes and for necessary incorporation in the stellar evolution codes.     

In-trap decay spectroscopy for 2�ͦ¦� decay experiments

Knowledge of 2??|? nuclear matrix elements is essential to probe the theoretical framework of 0??|? decays. At TITAN, TRIUMF??s Ion Trap for Atomic and Nuclear science, a novel technique has been developed to measure electron capture branches of virtual intermediate nuclei in ?|? decays. During two experiments with radioactive ^{124, 126}Cs isotopes the feasibility of this new method was proven.     

Deep processes in nuclei and in-medium dressing of the nucleons and mesons

K⁺ scattering and quasielastic electron scattering from nuclei are expected to provide information about the nucleons and mesons in the inner regions of nuclei. The K⁺- nucleus cross sections and the quasielastic electron-nucleus response functions have been calculated taking into account the same in-medium dressing of the nucleons and the same coupling of the σ and ω mesons to the polarization of nuclear matter. We obtain a good agreement with experimental data for the two processes.     

Determination of theK-shell electron capture probabilityP K in the decay of139Ce

A new coincidence procedure for the determination of theK-shell electron capture probability in simpleEC decays is described. By measuringγ-rays andK-shell conversion electrons separately and in coincidence with theK X-rays theK capture probability can be deduced only from counting rates. The method has been applied to¹³⁹Ce. The result ofP _K = 0.726±0.010 is in fairly good agreement with other experimental values reported previously.     

Excited collective states of heavy even-even nuclei

Quadrupole-type collective excitations of even-even nuclei are analyzed. In this analysis, transverse γ vibrations of the nuclear surface are taken into account effectively, while longitudinal beta vibrations remain free. A potential energy of the exponential form is used for free surface longitudinal beta vibrations. The behavior of the energy levels of excited states in the ground-state, β, and γ bands of heavy nuclei is studied, and the predictive potential of the model used is demonstrated for transfermium nuclei.     

22Ne(a,n)25Mg reaction in CONe mantle of massive stars at high temperatures

The effectiveness of²²Ne (a, n)²⁵Mg reaction as a neutron source is examined at high temperatures 0.8?T ₉?3.0 (T ₉ is the temperature in units of 10⁹ K). An assembly consisting of¹²C,¹⁶O, and²²Ne is considered at the end of helium burning in some massive stars. Alpha particles necessary for this neutron producing reaction are assumed to be due to reactions involving¹²C and¹⁶O nuclei. Assuming²²Ne as the only neutron absorber, the number density of neutrons is calculated. The mantles outside the cores of massive stars are possibly the physical sites for these reactions.     

Microscopic calculations of weak interaction rates of nuclei in stellar environment for A = 18 to 100

We report here the microscopic calculation of weak interaction rates in stellar matter for 709 nuclei with A = 18 to 100 using a generalized form of proton-neutron quasiparticle RPA model with separable Gamow-Teller forces. This is the first ever extensive microscopic calculation of weak rates calculated over a wide temperature-density grid which includes 10⁷≤ T(K) ≤ 30 × 10⁹ and 10 ≤ρ Y_e (gcm⁻³) ≤ 10¹¹, and over a larger mass range. Particle emission processes from excited states, previously ignored, are taken into account, and are found to significantly affect some β decay rates. The calculated capture and decay rates take into consideration the latest experimental energy levels and ft value compilations. Our calculation of electron capture and β-decay rates, in the fp-shell, show considerable differences with a recently reported shell model diagonalization approach calculation. Received: 16 April 1999     

Nuclear-matter incompressibility from fits of generalized Skyrme force to breathing-mode energies

In an attempt to extend the range of values of K_v, the incompressibility of symmetric nuclear matter, for which fits to the measured breathing-mode energies are possible, we investigate generalized Skyrme-type forces with a term that is both density- and momentum-dependent. Acceptable fits are found to be possible only for values of K_v in the range 215±15 MeV. For higher values fits are impossible, while for lower values fits are achieved only by introducing an unphysical collapse of nuclear matter. Thus our generalization of the Skyrme force does not permit a significantly wider range of values of K_v than that already given by force SkM¹. However, with a view to having a more reliable estimate of the compressional properties of the highly neutron-rich nuclear matter that comprises the core of collapsed stars, we present a new version of this latter force giving a much better fit to the masses of neutron-rich nuclei. Comparison with force SkM¹ also shows that the value of K_v extracted from the breathing-mode energies is essentially independent of the choice of effective mass. By providing a counter-example, we show that K_v cannot be extracted from masses and charge distributions alone. As for the third-order coefficient K′, we cannot be more precise than to say that it lies in the interval 700 ± 500 MeV.     

Second-forbidden beta-decay and the effect of (V+A)- andS-interaction admixtures:36Cl

The shapefactor, the logft-value, the electron longitudinal polarization and the distribution of electrons emitted from oriented nuclei of³⁶Cl have been calculated by applying two different nuclear models. Firstly a pure 1d_3/2→1d_3/2 transition has been considered. Secondly a more refined shell model of thes-d shell configuration space has been taken into account. It is shown that there is no great influence of the shell model version to the observables, that the observables depend strongly on the relativistic nuclear matrix elements, that the so-called “two parameter equation” for the shapefactor cannot be used in the case of³⁶Cl and that there is no larger sensitivity of (V+A) admixtures to the electron longitudinal polarization than normally found in allowed decays. Comparisons with the existing experimental data are made.     

Exchange current corrections for partial capture rates of muons in nuclei

A calculation is made of exchange current corrections for partial capture rates of muons in¹²C,¹⁶O,³²S and⁴⁰Ca nuclei. One-pion exchange is taken into account. Adler-Dothan's results are used to obtain the weak pion production amplitude. The nuclear states are described in the Tamm-Dancoff approximation. It is found that the corrections are very erratic and state dependent. A large effect is found for the 0⁺→0^? transitions due to the size of the time part of the axial exchange current.     

The isospin mixing and the superallowed Fermi beta decay

In the present work, the isospin admixtures in the nuclear ground states of the parent nuclei and isospin structure of the isobar analog resonance (IAR) states have been investigated by studying the 0^?+???0^?+? superallowed Fermi ?? decays using Pyatov??s restoration method. Within the random phase approximation (RPA), in this method, the effect of isospin breaking due to the Coulomb forces has been evaluated, taking into account the effect of pairing correlations between nucleons.     

Effect of synchrotron radiation on nuclear beta decay

The stimulation of the endothermic beta decay of stable nuclei by the field of synchrotron radiation has been analyzed theoretically in the framework of the photobeta decay mechanism. In contrast to works devoted to the effect of laser fields on beta decay, the action of the field directly on a nucleus rather than on a beta electron is considered (a sufficiently intense flux of hard photons whose energies exceed 60 keV allows this action). The rates of such a beta decay are calculated for a number of “parent nucleus-daughter nucleus” pairs for the relativistic case including Coulomb effects. For the most intense available sources of synchrotron radiation, the rate of stimulated beta decay for most nuclei under investigation appears to be characteristic of third-forbidden β^? transitions. The effect of synchrotron radiation on highly forbidden natural nuclear β^? decays is also analyzed. In particular, irradiation increases the rate of the β^? decay of the ₃₇ ⁸⁷ Rb and ₄₉ ¹¹⁵ In nuclei by 2% and by almost two orders of magnitude, respectively.     

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

A comprehensive representation is presented of a generalized form of the proton-neutron quasiparticle RPA model, originally introduced by Halbleib and Sorensen almost thirty years ago. The model uses separable Gamow-Teller forces, including, in addition to the particle-hole force of the former model, the particle-particle force, which is of decisive importance for β⁺ decay andββ decay. The above model has further been extended to the treatment of odd-odd nuclei. An extension is also made to transitions from nuclear excited states. This is essential for calculations of nuclear weak transition rates in the high-temperature interior of massive stars. Complementing the discussion of Halbleib and Sorensen on the particle-hole force, the structure of the RPA dispersion relation is discussed with emphasis on effects of the particle-particle force.     

Strong interaction physics from hadronic atoms

Hadronic atoms provide a unique laboratory for studying strong interactions and nuclear medium effects at zero kinetic energy. Previous results from analyses of strong-interaction data consisting of level shifts, widths and yields in π⁻, K⁻, p̄ and ∑⁻ atoms are reviewed. Recent results from fits to comprehensive sets of data in terms of density-dependent optical potentials that respect the low-density limit, where the interaction tends to the free hadron nucleon value, are discussed. The importance of using realistic nuclear density distributions is highlighted. The introduction of density dependence in most cases significantly improves the fit to the data and leads to some novel results. For K⁻ atoms, a substantial attraction of order 200 MeV in nuclear matter is suggested, with interesting repercussions for K̄ condensation and the evolution of strangeness in high-density stars. For p̄ atoms it is found that a reasonable p-wave strength can be accommodated in the fitted optical potential, in agreement with the energy dependence observed for some low-energy p̄N reactions. For ∑⁻ atoms, the fitted potential becomes repulsive inside the nucleus, implying that Σ hyperons generally do not bind in nuclei in agreement with recent measurements. This repulsion significantly affects calculated masses of neutron stars.     

Equations for O+ states in deformed nuclei

The quasiparticle-phonon nuclear model equations are derived for describing theKπ=O⁺ states in doubly even deformed nuclei taking account of particle-hole and particle-particle interactions between quasiparticles. Inclusion of particle-particle interactions complicates the RPA equations. Equations for the functions of monopole and quadrupole pairing are derived from the condition of eliminating spurious RPA solutions. In the QPNM, inclusion of a particle-particle interaction does not lead to very complicated calculations. The obtained equations can serve as a basis for calculating characteristics of the O⁺ excited states of doubly even deformed nuclei.     

Majorana neutrinos in rare meson decays

The rare meson decays K ⁺ → π ^??⁺?′⁺ and D ⁺ → K ^??⁺?′⁺ (?, ?′ = e, μ), which are induced by Majorana neutrino exchange and which are accompanied by lepton-number nonconservation, are considered. The effects of the meson structure are taken into account on the basis of the Gaussian model for the respective Bethe-Salpeter amplitudes. It is shown that existing direct experimental constraints on the decay branching ratios are overly lenient and therefore give no way to set realistic limits on effective Majorana masses. On the basis of the constraints on the lepton-mixing parameters and neutrino masses from precision measurements of electroweak processes, neutrino-oscillation experiments, searches for neutrinoless double-beta decay of nuclei, and cosmological data, indirect constraints on the branching ratios for the decays in question are obtained and found to be much more stringent than the above direct constraints.