Low-energy Enhancement Research Articles

Magnetic dipole γ-ray strength functions of heavy nuclei in the configuration-interaction shell model

A low-energy enhancement (LEE) has been observed in the deexcitation γ-ray strength function (γSF) of compound nuclei. The LEE has been a subject of intense experimental and theoretical interest since its discovery, and, if the LEE persists in heavy neutron-rich nuclei, it would have significant effects on calculations of r-process nucleosynthesis. Standard configuration-interaction (CI) shell-model calculations in medium-mass nuclei have attributed the LEE to the magnetic dipole γSF but such calculations are computationally intractable in heavy nuclei. We review a combination of beyond-mean-field many-body methods within the framework of the CI shell model that enables the calculation of γSF in heavy nuclei, and discuss the recent theoretical identification of a LEE in the magnetic dipole γSF of lanthanide isotopes.

Radiative neutron capture reaction rates for nucleosynthesis: The creation of the first r-process peak

About half of the elements beyond iron are synthesized in stars by rapid-neutron capture process (r-process). The stellar environment provides very high neutron flux in a short time ($\sim$ seconds) which is conducive for the creation of progressively neutron-rich nuclei till the waiting point is reached after which no further neutron capture reactions proceed. At this point such extremely neutron-rich nuclei become stable via $\beta^-$ decay. A detailed understanding of the r-process remains illusive. In the present work, we explore the radiative neutron-capture (n,$\gamma$) cross sections and reaction rates around the r-process peak near mass number eighty. The inherent uncertainties remain large in some cases, particularly in case of neutron-rich nuclei. When the low-energy enhancement exists, it results in significant increase in the reaction rate for neutron-capture.

Nuclear level density and γ -ray strength function of Ni63

The nuclear level density (NLD) and $\gamma$-ray strength function ($\gamma$SF) of $^{63}\mathrm{Ni}$ have been investigated using the Oslo method. The extracted NLD is compared with previous measurements using particle evaporation and those found from neutron resonance spacing. The $\gamma$SF was found to feature a strong low energy enhancement that could be explained as M1 strength based on large scale shell model calculations. Comparison of $\gamma$SFs measured with the Oslo method for various $\mathrm{Ni}$ isotopes reveals systematic changes to the strength below $5$ MeV with increasing mass.

Evolution of the γ -ray strength function in neodymium isotopes

The experimental gamma-ray strength functions (gamma-SFs) of 142,144-151Nd have been studied for gamma-ray energies up to the neutron separation energy. The results represent a unique set of gamma-SFs for an isotopic chain with increasing nuclear deformation. The data reveal how the low-energy enhancement, the scissors mode and the pygmy dipole resonance evolve with nuclear deformation and mass number. The data indicate that the mechanisms behind the low-energy enhancement and the scissors mode are decoupled from each other.

Evolution of low-lying M1 modes in germanium isotopes

Magnetic dipole strength functions are determined for the series of germanium isotopes from $N=Z=32$ to $N$ = 48 on the basis of a large number of transition strengths calculated within the shell model. The evolution of the strength with increasing neutron number in the $1{g}_{9/2}$ orbital is analyzed. A bimodal structure comprising an enhancement toward low transition energy and a resonance in the region of the scissors mode is identified. The low-energy enhancement is strongest near closed shells, in particular at the almost completely filled $1{g}_{9/2}$ orbital, while the scissorslike resonance is most pronounced in the middle of the open shell, which correlates with the magnitude of the also deduced electric quadrupole transition strengths. The results are consistent with previous findings for the shorter series of iron isotopes and prove the occurrence and correlation of the two low-lying magnetic dipole modes as a global structural feature.

Low-energy magnetic dipole strength in cadmium isotopes

Magnetic-dipole strength functions have been deduced from averages of large numbers of $M1$ transition strengths calculated within the shell model for the nuclides $^{105}\mathrm{Cd}$, $^{106}\mathrm{Cd}$, $^{111}\mathrm{Cd}$, and $^{112}\mathrm{Cd}$. Enhancements of the $M1$ strengths toward low transition energy have been found for all nuclides considered. These properties are compared with those of experimental photon strength functions obtained from $^{3}\mathrm{He}$-induced reactions, which seem to indicate a disappearance of the low-energy enhancement in the heavier isotopes.

Nonresonant Density of States Enhancement at Low Energies for Three or Four Neutrons.

The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated four-neutron ejection events observed experimentally in a nuclear reaction by Kisamori etal. [Phys. Rev. Lett. 116, 052501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.052501].

Constraining nuclear properties in Mo94 via a Nb93(p,γ)Mo94 total cross section measurement

Background: The nucleosynthesis of the group of neutron-deficient $p$ nuclei remains an unsolved puzzle in nuclear astrophysics. Among these nuclei, $^{94}\mathrm{Mo}$ is one of the most abundant and is notoriously underproduced in theoretical network calculations. In these networks, the respective cross sections and reaction rates play a crucial role. Since many reactions of astrophysical relevance are not accessible in the laboratory, a global and robust theoretical framework is required to provide reliable predictions.Purpose: Extending the experimental database on the one hand and direct or indirect studies of the respective nuclear physics properties on the other hand are the key tasks of experimental nuclear astrophysics. For this purpose, total cross sections of the $^{93}\mathrm{Nb}(p,\ensuremath{\gamma})^{94}\mathrm{Mo}$ reaction have been measured at proton energies between 2.0 and 5.0 MeV.Methods: In-beam $\ensuremath{\gamma}$-ray spectroscopy has been utilized to measure total cross sections. In general, the total cross sections depend strongly on the $\ensuremath{\gamma}$-ray decay widths in $^{94}\mathrm{Mo}$, which are derived from the $\ensuremath{\gamma}$-ray strength function and the nuclear level density. In our analysis we use a Bayesian optimization analysis to disentangle the effects of the $\ensuremath{\gamma}$-ray strength function and the nuclear level density in $^{94}\mathrm{Mo}$.Results: The total cross-section results reveal a significant discrepancy with respect to formerly published values. We propose parametrizations for the nuclear level density in $^{94}\mathrm{Mo}$ based on the microscopic level densities from Hartree-Fock-Bogoliubov calculations. Moreover, we present $\ensuremath{\gamma}$-ray strength functions for the $E1$ and $M1$ mode in $^{94}\mathrm{Mo}$ that reveal a low-energy enhancement for $M1$ radiation and agree nicely with previous results.Conclusions: A model-independent approach to study $E1$ and $M1$ strength functions has been presented. In general, radiative capture cross sections are a well-suited tool to constrain the reaction rates in reaction networks but also provide insight into the statistical $\ensuremath{\gamma}$-decay behavior of atomic nuclei.

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant Nos. U1932207, 11904371, and U1732133).

Recombination of Ar14+, Ar15+, Ca16+, and Ni19+ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou, China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination (RR) and also dielectronic recombination (DR) processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semi-classical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV. However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.

Recent Shell-model Calculations of \(\gamma \)-decay Strength Functions

We present recent shell-model calculations of the gamma-decay in sd-pf and pf-shell nuclei. We focus on the M1 part of the dipole strength which was shown to exhibit interesting low-energy effects, in particular a low-energy enhancement which can have a considerable impact on the radiative neutron capture. We discuss the persistence of the shell effects in the nuclear quasi-continuum and the relation between the shape of the strength function at low energy and nuclear deformation.

Combined analysis of the low-energy enhancement of the gamma-strength function and the giant dipole resonance

The nuclear dipole polarizability is mainly governed by the dynamics of the giant dipole resonance and 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-spline interpolations to both data sets show a significant reduction of the nuclear dipole polarizability for semi-magic and doubly magic nuclei, with magic numbers N = 28, 50, 82 and 126, which supports shell effects at high-excitation energies from the quasi-continuum to the giant dipole resonance. This work expands on the data analysis of our recent publication in Ngwetsheni and Orce (Phys. Lett. B 792, 335, 2019), which reveals a new spectroscopic probe to search for “old” and “new” magic numbers at high-excitation energies. New results presented in this work suggest an even higher sensitivity of the nuclear polarizability to shell effects when extrapolating the low-energy enhancement at lower gamma-ray energies.

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.

Statistical neutron capture in the limit of low nuclear level density

A major barrier in the study of neutron-induced nuclear reactions is the impossibility of direct measurements with short-lived radioactive isotopes. For these exotic nuclei, theoretical inputs such as the photon strength function (PSF) are poorly constrained. At Los Alamos National Laboratory, the Detector for Advanced Neutron Capture Experiments (DANCE) provides direct measurements of $\ensuremath{\gamma}$-ray cascades following neutron capture reactions on stable or long-lived radioactive nuclei. While Hauser-Feshbach calculations can provide reasonable predictions for neutron capture on heavy nuclei, their application to neutron-rich light nuclei with low nuclear level densities and low neutron separation energies is questionable. In this paper, we report on the $\ensuremath{\gamma}$-ray spectra from individual neutron resonances from the $^{96}\mathrm{Zr}(n,\ensuremath{\gamma})$ reaction, with an emphasis on the sensitivity of of the $\ensuremath{\gamma}$-ray spectra to different PSF models. The comparison of the measured $\ensuremath{\gamma}$-ray spectra with predicted spectra does not support the addition of a low-energy enhancement of the size reported in many charged-particle reaction measurements, but the sensitivity of the $\ensuremath{\gamma}$-ray spectra to different PSF models is weak.

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.

Consolidating the concept of low-energy magnetic dipole decay radiation

We have made a thorough study of the low-energy behaviour of the $\gamma$-ray strength function within the framework of the shell model. We have performed large-scale calculations spanning isotopic and isotonic chains over several mass regions, with the purpose of studying the systematic behavior of the low-energy enhancement (LEE) for $M1$ transitions. There are clear trends in the calculations: From being all but absent in the lowest mass region, the LEE becomes steeper and more pronounced as the mass number increases, and for a given mass region it further increases towards shell closures. Moreover, the LEE is found to be steeper in regions near doubly-magic nuclei where proton particles couple to neutron holes. These trends enable us to consolidate several previous works on the LEE into a single, consistent concept. We compare the inferred trends to the available experimental data from the Oslo method, and find suppport for the systematic behaviour. Lastly we have compared the calculations to strength functions compiled from discrete, experimental lifetimes, and find excellent agreement; the discrete data are consistent with a LEE, and indicate that the slope varies as function of mass number.

Shell-model study of the M1 dipole strength at low energy in the A>100 nuclei

A low-energy enhancement of radiative strength functions was observed in experiment in several mass regions of nuclei, and it is believed to impact considerably the calculated neutron-capture rates. In the shell-model framework it was demonstrated to be possibly due to the magnetic dipole radiation. Up to now, the M1 deexcitation strength function was described within this framework in the mid-mass nuclei from the pf and pfg shells (e.g., Sc44,Cr50,Fe56,57,60,66,68,Ni59,60,70,Mo94–96,Zr90), indicating systematically the presence of an up-bend at low energy. Therefore, the enhancement was accepted as a robust feature of the radiative decay. However, its exact magnitude and regions of emergence in the nuclear chart are still to be characterized in microscopic calculations. In this work, for the first time, the low-energy behavior of the radiative M1 strength in heavier nuclei, which can be described in the g7/2d5/2,3/2s1/2h11/2 shell, is investigated. The enhancement of the M1 deexcitation strength around N=80 is confirmed, and is similar to that found previously in lighter nuclei. In contrast, no such up-bend is present on the proton drip line, in the deformed N=Z=54Xe108 nucleus. From analysis of calculated magnetic dipole strengths the orbital nature of the observed enhancement is suggested. Photoemission and photoabsorption distributions on selected states are compared and the impact of different uncertainties in the theoretical treatment on the magnitude of M1 strengths at low photon energies is discussed.

LOW-ENERGY MAGNETIC RADIATION ENHANCEMENT WITHIN THE NUCLEAR SHELL MODEL

The γ-ray strength function, the average reduced probability of absorbing or emitting a γ-ray of a given energy, is an indispensable quantity for calculations of astrophysical interest. Experimental studies of the γSF have revealed an enhancement of this quantity in the low Eγ energy region, which cannot be described by none of the known resonances or by semiclassical models. To understand the origin of the low-energy enhancement we have calculated the M1 transition probabilities, both in the emission and absorption regions, for the 49,50Cr and 48V nuclei in the f7/2 shell-model basis. We find that the M1 strength distribution peaks at zero transition energy and falls off exponentially, independentely of the excitation energy or spin range selected. The form of this exponential is the same across all three different nuclei studied within this model space. We also show that the slope of the exponential is proportional to the strength of the T = 1 pairing matrix elements.

Examination of the low-energy enhancement of the γ -ray strength function of Fe 56

Examination of the low-energy enhancement of the γ -ray strength function of Fe 56

Examination of the low-energy enhancement of the γ -ray strength function of Fe 56

Examination of the low-energy enhancement of the γ -ray strength function of Fe 56

Electric and Magnetic Dipole Strength at Low Energy.

A low-energy enhancement of radiative strength functions was deduced from recent experiments in several mass regions of nuclei, which is believed to impact considerably the calculated neutron capture rates. In this Letter we investigate the behavior of the low-energy γ-ray strength of the ^{44}Sc isotope, for the first time taking into account both electric and magnetic dipole contributions obtained coherently in the same theoretical approach. The calculations are performed using the large-scale shell-model framework in a full 1ℏω sd-pf-gds model space. Our results corroborate previous theoretical findings for the low-energy enhancement of the M1 strength but show quite different behavior for the E1 strength.