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Global calculations of gamma-ray strength functions with the Skyrmefinite amplitude method
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Radiative strength functions from the energy-localized Brink-Axel hypothesis
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Recent Investigations and Findings about the 2d- and 3d- Neutron Strength Functions and the p-wave Scattering Radius
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Anisotropic Relaxation Functions and Strength of Oriented Solids Technical Report No. 106
Anisotropic relaxation functions and strength of oriented solids
Extraction of neutron-capture cross sections on 92 Zr using the charge-exchange Oslo method
The 93 Nb (𝑡, 3 He ) reaction at 115 MeV/nucleon was studied to demonstrate that nuclear level densities and 𝛾-ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in 93 Zr, reconstructed from the (𝑡, 3 He ) reaction, versus the energy of 𝛾 rays emitted by the excited 93 Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETINA 𝛾 -ray detector. The extracted level density and 𝛾 -ray strength function obtained by applying the Oslo method to this matrix were used to estimate the 92 Zr(𝑛,𝛾) 93 Zr cross section by combining the new results with other experimental data and theoretical calculations for 𝐸1 and 𝑀1 strength functions at higher energies. Good agreement with direct measurements of the 92 Zr(𝑛,𝛾) 93 Zr cross section was found. The contribution from the upbend in the extracted 𝛾-ray strength function was important to achieve the consistency, as the neutron-capture cross section without this contribution is significantly below the direct measurements otherwise. Since charge-exchange reactions at intermediate energies have long been used for extracting Gamow-Teller strengths, the successful demonstration of the charge-exchange Oslo method enables experiments in which (𝑛,𝛾) cross sections and Gamow-Teller strengths can be measured simultaneously, which is of benefit for astrophysical studies.
Modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions
Weak interaction charged current transition strengths from highly excited nuclear states are fundamental ingredients for accurate modeling of compact object composition and dynamics, but are difficult to obtain either from experiment or theory. For lack of alternatives, calculations have often fallen back upon a generalized Brink-Axel hypothesis, that is, assuming the strength function (transition probability) is independent of the initial nuclear state but depends only upon the transition energy and the weak interaction properties of the parent nucleus ground state. Here we present numerical evidence for a modified “local” Brink-Axel hypothesis for Gamow-Teller transitions for pf-shell nuclei relevant to astrophysical applications. Specifically, while the original Brink-Axel hypothesis does not hold globally, strength functions from initial states nearby in energy are similar within statistical fluctuations. This agrees with previous work on strength function moments. Using this modified hypothesis, we can tackle strength functions at previously intractable initial energies, using semiconverged initial states at arbitrary excitation energy. Our work provides a well-founded method for computing accurate thermal weak transition rates for medium-mass nuclei at temperatures occurring in stellar cores near collapse. We finish by comparing results to previous calculations of astrophysical rates.
The TDHF code Sky3D version 1.2
The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code.
Nuclear level density and γ -decay strength of Sr 93
This work presents the first experimentally determined nuclear level density and γ-ray strength function of the short-lived fission product 93 Sr, accomplished using the β-Oslo method. Direct measurement of the 92 Sr(n, γ) 93 Sr cross section is not currently possible, as the half-life of 2.66 hours is too short; instead, 93 Sr was formed through β decay of 93 Rb to excitation energies around the neutron separation energy. The γ-ray spectra were measured using a total absorption spectrometer at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU). The statistical properties of the 93 Sr nucleus were experimentally determined, including the γ-ray strength function and nuclear level density. At low energies, the γ-ray strength function exhibits a constant γ-decay strength, rather than a slightly increasing strength with decreasing γ-ray energy as had been previously observed for several nuclei in this mid-mass region. Finally, these statistical properties were then implemented in the reaction code TALYS1.95 to calculate the 92 Sr(n, γ) 93 Sr cross section.
Photon strength and the low-energy enhancement
Several measurements in medium mass nuclei have reported a low-energy enhancement in the photon strength function. Although, much effort has been invested in unraveling the mysteries of this effect, its physical origin is still not conclusively understood. Here, a completely model-independent experimental approach to investigate the existence of this enhancement is presented. The experiment was designed to study statistical feeding from the quasi-continuum (below the neutron separation energy) to individual low-lying discrete levels in {sup 95}Mo produced in the (d, p) reaction. A key aspect to successfully study gamma decay from the region of high-level density is the detection and extraction of correlated particle-gamma-gamma events which was accomplished using an array of Clover HPGe detectors and large area annular silicon detectors. The entrance channel excitation energy into the residual nucleus produced in the reaction was inferred from the detected proton energies in the silicon detectors. Gating on gamma-transitions originating from low-lying discrete levels specifies the state fed by statistical gamma-rays. Any particle-gamma-gamma event in combination with specific energy sum requirements ensures a clean and unambiguous determination of the initial and final state of the observed gamma rays. With these requirements the statistical feeding to individual discrete levels is extracted on an event-by-event basis. The results are presented and compared to {sup 95}Mo photon strength function data measured at the University of Oslo.
Constraining calculations of Pu 239 ( n , γ ) cross sections with multistep cascade γ -ray spectra measured at the DANCE facility
Measurements of multistep cascade gamma-ray spectra from several low-lying 1 + resonances in the Pu 239 ( n , γ ) reaction were made using the DANCE detector. The measured spectra are compared to spectra simulated using several models for the photon strength function and the nuclear level density, representing the first analysis of this nature on a fissile nucleus. In general, models of the photon strength function that included a strong M 1 “scissors mode” contribution coupled with a Gilbert-Cameron nuclear level density provided a reasonable description of the spectra. Simulations using photon strength functions and nuclear level densities specifically for Pu 240 , extracted by the Oslo method, resulted in a very good representation of the measured spectra. Neutron-capture cross section calculations that included the scissors mode provided a good estimate of the previously measured values, without additional normalization. However, the scissors-mode energy that produced the best description of the multistep cascade spectra was different from the value that best reproduced the capture cross section. In addition, the 〈 Γ γ 〉 inferred from the multistep cascade calculations was somewhat less than the tabulated value, which was determined from resonance analysis. Published by the American Physical Society 2025
Gamma-Ray Emission Spectra as a Constraint on Calculations of 234,236,238 U Neutron-Capture Cross Sections
Neutron capture cross sections in the “continuum” region (>≈1 keV) and gamma-emission spectra are of importance to basic science and many applied fields. Careful measurements have been made on most common stable nuclides, but physicists must rely on calculations (or “surrogate” reactions) for rare or unstable nuclides. Calculations must be benchmarked against measurements (cross sections, gamma-ray spectra, and <Γ γ >). Gamma-ray spectrum measurements from resolved resonances were made with 1 - 2 mg/cm 2 thick targets; cross sections at >1 keV were measured using thicker targets. The results show that the shape of capture cross section vs neutron energy is not sensitive to the form of the strength function (although the magnitude is); the generalized Lorentzian E1 strength function is not sufficient to describe the shape of observed gamma-ray spectra; MGLO + “Oslo M1” parameters produces quantitative agreement with the measured 238 U(n,γ) cross section; additional strength at low energies (~ 3 MeV) -- likely M1-- is required; and careful study of complementary results on low-lying giant resonance strength is needed to consistently describe observations.
Probabilities of delayed processes for nuclei involved in the r-process
Delayed fission, along with induced and spontaneous fission, is responsible for the suppression of the production of superheavy elements both during the r-process and after its completion. Beta-decay strength functions are required for calculating delayed fission. In the present study, respective strength functions are calculated by relying on the theory of finite Fermi systems and by predominantly employing nuclear masses and fission barriers predicted by a generalized Thomas-Fermi model. The probabilities for delayed fission and for the emission of delayed neutrons are calculated for a number of isotopes. On the basis of calculations performed in order to determine the probabilities for delayed processes, it is shown that some of the delayed-fission probabilities calculated thus far were substantially overestimated. The application of these new results to calculating the r-process may change substantially both the r-process path and the yields of superheavy nuclei.
β decay of Ba 141
The β-decay strength function of nuclides produced in fission is important as it dictates the distribution of decay energy between electrons, neutrinos, and γ rays and so is critical for calculating decay heat in reactors and for estimating the reactor antineutrino spectrum. Several experimental techniques are available to determine this strength function, including electron spectroscopy, γ-ray calorimetry (TAGS spectroscopy), and detailed, high-resolution spectroscopy with modern large high-purity germanium arrays. This work investigates the decay of the well-known and strongly produced fission fragment 141 Ba. A beam of 141 Cs was implanted at the target position of the Gammasphere and the subsequent decay of the daughter 141 Ba was studied. Extensive decay spectroscopy was possible up to the decay Q value of 3.197(7) MeV, including a significant extension of the level scheme and detailed angular correlation measurements for all levels with greater than 0.25% β feeding. The distribution of the β-decay strength was then inferred and compared to previous calorimetric studies. In conclusion, the agreement was excellent and provides a benchmark for comparing strength function methods and data for a more detailed understanding of the structure of 141 La.
Low-energy magnetic radiation: Deviations from GOE
A pronounced spike at low energy in the strength function for magnetic radiation (LEMAR) is found by means of Shell Model calculations, which explains the experimentally observed enhancement of the dipole strength. LEMAR originates from statistical low-energy M1-transitions between many excited complex states. Re-coupling of the proton and neutron high-j orbitals generates the strong magnetic radiation. LEMAR is closely related to Magnetic Rotation. LEMAR is predicted for nuclides participating in the r-process of element synthesis and is expected to change the reaction rates. An exponential decrease of the strength function and a power law for the size distribution of the B(M1) values are found, which strongly deviate from the ones of the GOE of random matrices, which is commonly used to represent complex compound states.
Experimentally constrained ( p , γ ) Y 89 and ( n , γ ) Y 89 reaction rates relevant to p -process nucleosynthesis
The nuclear level density and the g-ray strength function have been extracted for 89 Y, using the Oslo Method on 89 Y(p,p'γ) 89 Y coincidence data. The g-ray strength function displays a low-energy enhancement consistent with previous observations in this mass region ( 93-98 Mo). Shell-model calculations give support that the observed enhancement is due to strong, low-energy M1 transitions at high excitation energies. The data were further used as input for calculations of the 88 Sr(p,γ) 89 Y and 88 Y(n,γ) 89 Y cross sections with the TALYS reaction code. Lastly, comparison with cross-section data, where available, as well as with values from the BRUSLIB library, shows a satisfying agreement.
Evidence for the dipole nature of the low-energy γ enhancement in Fe 56
Here, the γ-ray strength function of 56 Fe has been measured from proton-γ coincidences for excitation energies up to ≈11 MeV. The low-energy enhancement in the γ-ray strength function, which was first discovered in the ( 3 He,αγ) 56 Fe reaction, is confirmed with the (p,p'γ) 56 Fe experiment reported here. Angular distributions of the γ rays give for the first time evidence that the enhancement is dominated by dipole transitions.
Breaking of axial symmetry in excited heavy nuclei as identified in giant dipole resonance data
Here, a recent theoretical prediction of a breaking of axial symmetry in quasi all heavy nuclei is confronted to a new critical analysis of photon strength functions of nuclei in the valley of stability. For the photon strength in the isovector giant dipole resonance (IVGDR) regime a parameterization of GDR shapes by the sum of three Lorentzians (TLO) is extrapolated to energies below and above the IVGDR. The impact of non-GDR modes adding to the low energy slope of photon strength is discussed including recent data on photon scattering and other radiative processes. These are shown to be concentrated in energy regions where various model calculations predict intermediate collective strength; thus they are obviously separate from the IVGDR tail. The triple Lorentzian (TLO) ansatz for giant dipole resonances is normalized in accordance to the dipole sum rule. The nuclear droplet model with surface dissipation accounts well for positions and widths without local, nuclide specific, parameters. Very few and only global parameters are needed when a breaking of axial symmetry already in the valley of stability is admitted and hence a reliable prediction for electric dipole strength functions also outside of it is expected.