Brink-Axel Hypothesis Research Articles

Continuing influence of shell effects at high-excitation energies

Empirical drops in ground-state nuclear polarizabilities indicate deviations from the effect of giant dipole resonances and may reveal the presence of shell effects in semi-magic nuclei with neutron magic numbers N=50, 82 and 126. Similar drops of polarizability in the quasi-continuum of nuclei with, or close to, magic numbers N=28, 50 and 82, could reflect the continuing influence of shell closures up to the nucleon separation energy. These findings open a new avenue to investigating magic numbers at high-excitation energies and strongly support recent large-scale shell-model calculations in the quasi-continuum region, which describe the origin of the low-energy enhancement of the photon strength function as induced paramagnetism. The nuclear-structure dependence of the photon-strength function asserts the generalized Brink-Axel hypothesis as more universal than originally expected.

How do we infer shell effects at high-excitation energies? A new spectroscopic probe to search for magic numbers

The nuclear dipole polarizability is mainly governed by the dynamics of the giant dipole resonance and, assuming validity of the brink-Axel hypothesis, has been investigated along with the effects of the low-energy enhancement of the photon strength function for nuclides in medium- and heavy-mass nuclei. Cubic-polynomial fitsto both data sets extrapolated down to a gamma-ray energy of 0.1 MeV show a significantreduction of the nuclear dipole polarizability for semi-magic nuclei, with magic numbers N =28, 50 and 82, which supports shell effects at high-excitation energies in the the quasi-continuum region. This work assigns σ-2 values as sensitive measures of long-range correlations of the nuclear force and provides a new spectroscopic probe to search for “old” and “new” magic numbers at high-excitation energies.

The concept of nuclear photon strength functions: A model-independent approach via ([formula omitted]) reactions

Most theoretical approaches used in nuclear astrophysics to model the nucleosynthesis of heavy elements incorporate the so-called statistical model in order to describe the excitation and decay properties of atomic nuclei. One of the basic assumptions of this model is the validity of the Brink–Axel hypothesis and the related concept of so-called photon strength functions to describe γ-ray transition probabilities. We present a novel experimental approach that allows for the first time to experimentally determine the photon strength function simultaneously in two independent ways by a unique combination of quasi-monochromatic photon beams and a newly implemented γ–γ coincidence setup. This technique does not assume a priori the validity of the Brink–Axel hypothesis and sets a benchmark in terms of the detection sensitivity for measuring decay properties of photo-excited states below the neutron separation energy. The data for the spherical off-shell nucleus 128Te were obtained for γ-ray beam-energy settings between 3 MeV and 9 MeV in steps of 130 keV for the lower beam energies and in steps of up to 280 keV for the highest beam settings. We present a quantitative analysis on the consistency of the derived photon strength function with the Brink–Axel hypothesis. The data clearly demonstrate a discrepancy of up to a factor of two between the photon strength functions extracted from the photoabsorption and photon emission process, respectively. In addition, we observe that the photon strength functions are not independent of the excitation energy, as usually assumed. Thus, we conclude, that the Brink–Axel hypothesis is not strictly fulfilled in the excitation-energy region below the neutron separation threshold (Sn=8.78MeV) for the studied case of 128Te.

Role of exact pairing in the description of nuclear level density and radiative strength function

An approach utilizing the microscopic pairing Hamiltonian is proposed to simultaneously describe the nuclear level density and radiative strength function, taking into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for 170,171,172Yb isotopes demonstrates the importance of exact thermal pairing in the description of nuclear level densities at low and intermediate excitation energies and invalidates the assumption based on the Brink-Axel hypothesis in the description of the radiative strength functions.

Gamma Strength Functions and Level Densities from High-Resolution Proton Scattering under 0°

Inelastic proton scattering at energies of a few 100 MeV and forward angles including 0° provides a novel method to measure gamma strength functions (GSF) in nuclei in an energy range of about 5 – 20 MeV. The experiments provide not only the E1 but also the M1 part of the GSF. The latter is poorly known in heavy nuclei. Comparison with gamma decay data (e.g. from the Oslo method) allows to test the generalised Brink-Axel (BA) hypothesis in the energy region of the pygmy dipole resonance (PDR) crucial for the modelling of (n,γ) and (γ,n) reactions in astrophysical reaction networks. From the two test cases studied, 208Pb remains inconclusive in the energy region of the PDR because of large Porter-Thomas fluctuations due to the small level density (LD), while the BA hypothesis seems to hold in case of 96Mo. A fluctuation analysis of the high-resolution data also provides a direct measure of the LD in the energy region of the isovector giant dipole resonance (IVGDR) well above the neutron threshold, where hardly any experimental information is available. This permits an independent test of the decomposition of GSF and LD in Oslo-type experiments.

Study of photon strength functions via (γ→, γ′, γ″) reactions at the γ3-setup

One of the basic ingredients for the modelling of the nucleosynthesis of heavy elements are so-called photon strength functions and the assumption of the Brink-Axel hypothesis. This hypothesis has been studied for many years by numerous experiments using different and complementary reactions. The present manuscript aims to introduce a model-independent approach to study photon strength functions via γ-γ coincidence spectroscopy of photoexcited states in 128Te. The experimental results provide evidence that the photon strength function extracted from photoabsorption cross sections is not in an overall agreement with the one determined from direct transitions to low-lying excited states.

Neutrino Spectra from Nuclear Weak Interactions in sd-Shell Nuclei under Astrophysical Conditions

Abstract We present shell model calculations of nuclear neutrino energy spectra for 70 sd-shell nuclei over the mass number range A = 21–35. Our calculations include nuclear excited states as appropriate for the hot and dense conditions characteristic of pre-collapse massive stars. We consider neutrinos produced by charged lepton captures and decays, and for the first time in tabular form, neutral current nuclear deexcitation, providing neutrino energy spectra on the Fuller–Fowler–Newman temperature–density grid for these interaction channels for each nucleus. We use the full sd-shell model space to compute initial nuclear states up to 20 MeV excitation with transitions to final states up to 35–40 MeV, employing a modification of the Brink-Axel hypothesis to handle high-temperature population factors and the nuclear partition functions.

Test of the Brink-Axel Hypothesis for the Pygmy Dipole Resonance.

The gamma strength function and level density of 1^{-} states in ^{96}Mo have been extracted from a high-resolution study of the (p[over →], p[over →]^{'}) reaction at 295MeV and extreme forward angles. By comparison with compound nucleus γ decay experiments, this allows a test of the generalized Brink-Axel hypothesis in the energy region of the pygmy dipole resonance. The Brink-Axel hypothesis is commonly assumed in astrophysical reaction network calculations and states that the gamma strength function in nuclei is independent of the structure of the initial and final state. The present results validate the Brink-Axel hypothesis for ^{96}Mo and provide independent confirmation of the methods used to separate gamma strength function and level density in γ decay experiments.

Low-energy enhancement and fluctuations of γ-ray strength functions in 56,57Fe: test of the Brink–Axel hypothesis

Nuclear level densities and γ-ray strength functions of 56,57Fe have been extracted from proton-γ coincidences. A low-energy enhancement in the γ-ray strength functions up to a factor of 30 over common theoretical E1 models is confirmed. Angular distributions of the low-energy enhancement in 57Fe indicate its dipole nature, in agreement with findings for 56Fe. The high statistics and the excellent energy resolution of the large-volume LaBr3(Ce) detectors allowed for a thorough analysis of γ strength as function of excitation energy. Taking into account the presence of strong Porter–Thomas fluctuations, there is no indication of any significant excitation energy dependence in the γ-ray strength function, in support of the generalized Brink–Axel hypothesis.

Simultaneous Microscopic Description of Nuclear Level Density and Radiative Strength Function.

The nuclear level density (NLD) and radiative strength function (RSF) are simultaneously described within a microscopic approach, which takes into account the thermal effects of the exact pairing as well as the giant resonances within the phonon-damping model. The good agreement between the results of calculations and experimental data extracted by the Oslo group for ^{170,171,172}Yb isotopes shows the importance of exact thermal pairing in the description of NLD at low and intermediate excitation energies. It also invalidates the assumption based on the Brink-Axel hypothesis in the description of the RSF.

Gamma strength functions and level densities from high-resolution inelastic proton scattering at very forward angles

Inelastic proton scattering at energies of a few 100 MeV and forward angles including 0∘ provides a novel method to measure gamma strength functions (GSF) in nuclei in an energy range of about 5–23 MeV. The experiments provide not only the E1 but also the M1 part of the GSF. The latter is poorly known in heavy nuclei. A case study of 208 Pb indicates that the systematics proposed for the M1-GSF in RIPL-3 needs to be substantially revised. Comparison with gamma decay data (e.g. from the Oslo method) allows to test the generalised Brink-Axel (BA) hypothesis in the energy region of the pygmy dipole resonance (PDR) crucial for the modelling of (n,γ) and (γ,n) reactions in astrophysical reaction networks. A fluctuation analysis of the high-resolution data also provides a direct measure of level densities in the energy region well above the neutron threshold, where hardly any experimental information is available.

γ strength function and level density of Pb208 from forward-angle proton scattering at 295 MeV

Gamma strength functions (GSFs) and level densities (LDs) are essential ingredients of statistical nuclear reaction theory with many applications in astrophysics, reactor design, and waste transmutation. The aim of the present work is a test of systematic parametrizations of the GSF recommended by the RIPL-3 data base for the case of $^{208}$Pb. The upward GSF and LD in $^{208}$Pb are compared to gamma decay data from an Oslo-type experiment to examine the validity of the Brink-Axel (BA) hypothesis. The E1 and M1 parts of the total GSF are determined from high-resolution forward angle inelastic proton scattering data taken at 295 MeV at RCNP, Osaka, Japan. The total LD in $^{208}$Pb is derived from the $1^-$ LD extracted with a fluctuation analysis in the energy region of the isovector giant dipole resonance. The E1 GSF is compared to parametrizations recommended by the RIPL-3 data base showing systematic deficiencies of all models in the energy region around neutron threshold. The new data for the poorly known spinflip M1 resonance call for a substantial revision of the model suggested in RIPL-3. The total GSF derived from the present data is larger in the PDR energy region than the Oslo data but the strong fluctuations due to the low LD resulting from the double shell closure of $^{208}$Pb prevent a conclusion on a possible violation of the BA hypothesis. Using the parameters suggested by RIPL-3 for a description of the LD in $^{208}$Pb with the back-shifted Fermi gas model, remarkable agreement between the two experiments spanning a wide excitation energy range is obtained. Systematic parametrizations of the E1 and M1 GSF parts need to be reconsidered at low excitation energies. The good agreement of LD provides an independent confirmation of the approach underlying the decomposition of GSF and LDs in Oslo-type experiments.

Validity of the Generalized Brink-Axel Hypothesis in (238)Np.

We analyze primary γ-ray spectra of the odd-odd (238)Np nucleus extracted from (237)Np(d,pγ)(238)Np coincidence data measured at the Oslo Cyclotron Laboratory. The primary γ spectra cover an excitation-energy region of 0≤E(I)≤5.4 MeV, and allow us to perform a detailed study of the γ-ray strength as a function of excitation energy. Hence, we can test the validity of the generalized Brink-Axel hypothesis, which, in its strictest form, claims no excitation-energy dependence on the γ strength. In this work, using the available high-quality (238)Np data, we show that the γ-ray strength function is to a very large extent independent of the initial and final states. Thus, for the first time, the generalized Brink-Axel hypothesis is experimentally verified for γ transitions between states in the quasicontinuum region, not only for specific collective resonances, but also for the full strength below the neutron separation energy. Based on our findings, the necessary criteria for the generalized Brink-Axel hypothesis to be fulfilled are outlined.

Systematics of strength function sum rules

Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).

Experimental constraints on the γ-ray strength function in 90Zr using partial cross sections of the [formula omitted] reaction

Partial cross sections of the Y89(p,γ)Zr90 reaction have been measured to investigate the γ-ray strength function in the neutron–magic nucleus 90Zr. For five proton energies between Ep=3.65 MeV and Ep=4.70 MeV, partial cross sections for the population of seven discrete states in 90Zr have been determined by means of in-beam γ-ray spectroscopy. Since these γ-ray transitions are dominantly of E1 character, the present measurement allows an access to the low-lying dipole strength in 90Zr. A γ-ray strength function based on the experimental data could be extracted, which is used to describe the total and partial cross sections of this reaction by Hauser–Feshbach calculations successfully. Significant differences with respect to previously measured strength functions from photoabsorption data point towards deviations from the Brink–Axel hypothesis relating the photo-excitation and de-excitation strength functions.

Modification of the Brink-Axel hypothesis for high-temperature nuclear weak interactions

We present shell model calculations of electron capture strength distributions in A=28 nuclei and computations of the corresponding capture rates in supernova core conditions. We find that in these nuclei the Brink-Axel hypothesis for the distribution of Gamow-Teller strength fails at low and moderate initial excitation energy, but may be a valid tool at high excitation. The redistribution of GT strength at high initial excitation may affect capture rates during collapse. If these trends which we have found in lighter nuclei also apply for the heavier nuclei which provide the principal channels for neutronization during stellar collapse, then there could be two implications for supernova core electron capture physics. First, a modified Brink-Axel hypothesis could be a valid approximation for use in collapse codes. Second, the electron capture strength may be moved down significantly in transition energy, which would likely have the effect of increasing the overall electron capture rate during stellar collapse.

Coulomb excitation of double giant dipole resonances

We implement the Brink–Axel hypothesis for the excitation of the double giant dipole resonance (DGDR): the background states which couple to the one-phonon giant dipole resonance are themselves capable of dipole absorption. These states (and the ones which couple to the two-phonon resonance) are described in terms of the gaussian orthogonal ensemble of random matrices. We use second-order time-dependent perturbation theory and calculate analytically the ensemble-averaged cross section for excitation of the DGDR. Numerical calculations illuminate the mechanism and the dependence of the cross section on the various parameters of the theory, and are specifically performed for the reaction 208Pb + 208Pb at a projectile energy of 640 MeV /nucleon. We show that the contribution of the background states to the excitation of the DGDR is significant. We find that the width of the DGDR, the energy-integrated cross section and the ratio of this quantity over the energy-integrated cross section for the single giant dipole resonance, all agree with experiment within experimental errors. We compare our approach with that of Carlson et al. who have used a similar physical picture.

Model calculations of the radiative capture process and the Brink–Axel hypothesis

Using the consistent Direct–SemiDirect (DSD) and the improved Preequilibrium (PEQ) exciton model we analyzed the excitation functions for the neutron radiative capture transitions to the isolated single-particle states in 141 Ce and 209 Pb in order to study the energy positions of the peaks belonging to the Brink–Axel Giant Resonances (BA GDR) built on single-particle states. The PEQ calculations of γ transitions to discrete levels have been performed for the first time. The PEQ model peaks appear at energies lower than those of the BA GDRs for about 0.2 MeV for low-spin states, and for about 0.4 MeV for high-spin ones. The DSD model energies are higher than the BA GDR ones for about 0.3 MeV (1 MeV for high-spin states). Both models reproduce the available experimental peak energies within about 0.25 MeV.

Gamma emission in precompound reactions. I. Statistical model and collective gamma decay.

We extend the theory of particle-induced precompound reactions by including gamma decay. We use the Brink-Axel hypothesis and consider the gamma emission of giant-dipole resonances built on the ground state and on the excited states of the composite system. The latter are modeled as multiparticle multihole excitations. In this way, we combine the statistical ansatz and the chaining hypothesis typical for precompound reaction theories, with the collective aspects of gamma decay. Formulas for average S matrix and average cross section are derived in this framework.

Pre-equilibrium γ rays from single-particle radiative transitions in the hybrid model

A formulation is developed for γ ray emission via single-particle radiative transitions in the hybrid model. Pre-equilibrium γ emission rates, derived using the Brink-Axel hypothesis and detailed balance, are influenced little by the dipole effective charge and are consistent with the established equilibrium limit. The model can explain a considerable part of the γ rays in the giant resonance range observed in nuclear reactions.