Partial level density of n-quasiparticle excitations, radiative strength functions and new experimental information on the dynamics of nuclear structure change in the B n range

The most reliable at present values of the level density in the fixed spin window and the sums of radiative strength functions of cascade gamma transitions are obtained from analysis of intensities of two-step cascades excited upon thermal neutron capture for approximately 40 nuclei in the mass range 40 ≤ A ≤ 200. The maximal reliability of these data is provided by the experimental conditions—minimum possible propagation error coefficients and practically unique solution of the problem of determination of gamma decay parameters from measured spectra. The experimental data are approximated by the sum of partial level densities corresponding to excitation of n quasiparticles. Steplike structures in the level density at excitation energies smaller than 3–4 MeV are described with good accuracy as the superposition of two-quasiparticle (three-quasiparticle in odd A nuclei) and vibrational excitations with the coefficient of collective density enhancement K _coll ≈ 10?20. They correspond to excitation-energy-correlated maximum enhancement of the radiative strength functions of primary gamma transitions. The level density at larger excitation energies is well reproduced if the breakup of at least two more Cooper pairs of nucleons is taken into account. The increase in the number of excited quasiparticles in the nucleus corresponds to unconditional reduction of the radiative strength functions of primary gamma transitions of the compound state decay. However, the maximum possible value of partial widths of primary transitions increases regularly with decreasing energy. Some ambiguity in the results of approximation and divergence from existing theoretical ideas of the energy dependence of nucleon correlation functions in an excited nucleus point to the possibility of direct extraction from experiment of fundamentally new information on the structure of excited nuclear levels in the range of the neutron binding energy. These are, first of all, the parameters of dependence of nucleon correlation functions on the excitation energy of the nucleus.     

Estimations of level densities and radiative strength functions from experimental data and probable change in the properties of nuclei at E exc ⋍ 3–4 MeV

Investigations of two-step γ cascades following thermal-neutron capture by heavy nuclei reveal that the density of excited levels is significantly smaller than that which is predicted by an exponential extrapolation like that of the back-shifted Fermi gas model. Data on two-step cascades allow one to determine in a model-independent way the most probable energy dependences of the level density and radiative strength functions, virtually over the whole excitation-energy interval below the neutron binding energy B _n . Data for more than 30 heavy nuclei cannot be understood without assuming a considerable change in the nuclear properties at E _exc ? 3–4 MeV.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

Radiative strength functions for nuclei in which the number of protons is close to the magic number of Z=28

The distribution of the radiative strength in nuclei where the number of nucleons of one type is nearly magic (Z=28±1) and where there are a few valence nucleons of the other type is investigated. It is shown that the statistical approach that is based on Fermi liquid theory and which takes into account temperature and the shell structure of nuclei leads to good agreement with experimental data on radiative strength functions below the neutron binding energy in such nuclei. Only for the ⁵⁹Co and ⁶⁵Cu nuclei, which have the largest number of valence neutrons among the cobalt and copper isotopes being investigated, is the energy dependence of the radiative strength compatible with a Lorentz distribution as well.     

Dependence of 14 MeV radiative neutron capture on mass number

The 14 MeV neutron radiative capture cross section has been measured for six nuclei in the mass range from A = 155 to A = 238. The integrated radiative cross sections are found to have a value near 1 mb. These results are at variance with the results obtained by the activation technique. Detailed captude γ-ray spectra have been measured for one closed-shell and two deformed nuclei to illustrate their similarity in shape and magnitude.     

Basic parameters of the gamma-decay process and properties of the <Superscript>174</Superscript>Yb nucleus that manifest themselves in radiative resonance-and thermal-neutron capture

An independent analysis of available data on the intensities of primary gamma rays from the capture of ≈2-keV neutrons by a ¹⁷³Yb nucleus is performed. The distribution of the scatter of these intensities around the average value is approximated in various intervals of energies of primary gamma transitions. An extrapolation of the distributions obtained in this way to zero detection threshold for the intensity of a primary gamma transition makes it possible to estimate, independently of other experimental procedures, the expected number of levels of both parities for spins in the range J = 1–4 and the total possible sum of partial widths with respect to electric and magnetic dipole gamma transitions to levels whose excitation energies extend up to about 4 MeV. The results obtained in this way for the level density and the sum of radiative strength functions confirm the characteristic features of analogous data extracted from the intensities of two-step gamma-ray cascades initiated by radiative thermal-neutron capture by 40 ≤ A ≤ 200 nuclei and also make it possible to assess the sign and magnitude of their systematic uncertainty associated with a very strong dependence of radiative strength functions for cascade gamma transitions on the structure of the excited level, at least for excitation energies below half the neutron binding energy. A comparison with model concepts of the level density reveals that the ¹⁷⁴Yb nucleus is in a superfluid states for the bulk of excited levels, at least below 3.5 to 4 MeV.     

Level density and radiative strength functions from (n th,2γ) reactions and basic properties of the 96Mo nucleus

Published data on the intensities of two-step cascades to 12 final-state levels of the ⁹⁶Mo nucleus are approximated by using a set of possible random dependences of the level density and radiative strength functions for primary E1 and M1 transitions. The average values of these parameters of gamma decay for any excitation energies and for gamma transitions agree well with basic dependences revealed to date from similar experiments for 42 nuclei in the mass-number range 40 ≤ A ≤ 200, but they are inconsistent with the generally accepted ideas of the parameters of the cascade gamma decay of compound states of nuclei having high level densities.     

Fundamentals of a modified model of the distribution of neutron-resonance widths and results of its application in the mass-number range of 35 ≤ A ≤ 249

A modified model is developed for describing the distribution of random resonance width for any nuclei. The model assumes the coexistence in a nucleus of one or several partial radiative and neutron amplitudes for respective resonance widths, these amplitudes differing in their parameters. Also, it is assumed that amplitude can be described by a Gaussian curve characterized by a nonzero mean value and a variance not equal to unity and that their most probable values can be obtained with the highest reliability from approximations of cumulative sums of respective widths. An analysis of data for 157 sets of neutron widths for 0 ≤ l ≤ 3 and for 56 sets of total radiative widths has been performed to date. The basic result of this analysis is the following: both for neutron and for total radiative widths, the experimental set of resonance width can be represented with a rather high probability in the form of a superposition of k ≤ 4 types differing in mean amplitude parameters.     

Search for neutron resonances in the $$^{178m_2 } Hf$$ isomer and their investigation

Experiments aimed at detecting and investigating neutron resonances in the \(^{178m_2 } Hf\) isomer are described, and the results obtained in these experiments are presented. The investigations in question are of great interest since the structure of this isomer—it is interpreted as the (π7/2⁺, π9/2⁺, ν7/2⁺, ν9/2⁺) configuration—and its high spin of J=16 differ significantly from the structure and spin of nuclei studied previously. The experiments performed at the Kurchatov Institute employed a neutron source based on the FAKEL linear electron accelerator and a multisection detector from NaI(Tl) crystals that was able to ensure a 4π coverage. This equipment made it possible to study gamma-ray cascades in radiative neutron capture versus neutron energy. Despite an extremely small number of isomer nuclei, a low content of the isomer in the target used, and its high radioactivity, resonances were discovered that arise upon neutron capture by a high-spin \(^{178m_2 } Hf\) nucleus. The parameters of these resonances were found. The mean spacing between the revealed resonances is about 1 eV, which is consistent with calculations based on the Fermi gas model. This indicates that the Fermi gas model describes well the density of both low-and high-spin levels. At the same time, the above agreement suggests that, upon the formation of a compound nucleus, the structure of the isomeric state is destroyed completely. On the other hand, glaring discrepancies between experimental data and the predictions of the statistical model were found: gamma transitions from high-spin resonances (J=31/2⁺, 33/2⁺) populate predominantly the low-spin ground state (J=9/2⁺) rather than the high-spin state of the \(^{178m_2 } Hf\) isomer (J=25/2^?); the radiative width is approximately one-third as great as that which is predicted by the statistical model; and the properties of gamma cascades are different for different resonances, this difference being beyond statistical fluctuations. The results of the present investigation make it possible to reveal special features in the behavior of the quantum number K at high excitation energies.     

Average neutron resonance parameters and radiative capture cross sectins for the isotopes of molybdenum

The neutron capture cross sections of the stable molybdenum isotopes have been measured with high energy resolution (ΔE/E ? 0.2 %), between 3 and 90 keV neutron energy, at the 40 m station of ORELA. Average resonance parameters are extracted for s- and p-wave resonances. The s-wave neutron strength function is close to 0.5 × 10^?4 for all isotopes, but the p-wave strength function exhibits a well defined peak near At~ 95.Both s- and p-wave radiative widths decrease markedly as further neutrons are added to the closed shell. The p-wave radiative widths are generally greater than the s-wave widths showing the presence of non-statistical γ-decay mechanisms.Valence neutron theory fails to explain the magnitude of the p- to s-wave radiative width disparity and doorway state processes are invoked. In particular, the data for ⁹⁸Mo appear to violate the usual valence theory, since the correlations between radiative and neutron strengths are small. Further, the radiative widths are smaller than can be explained on the valence model. An explanation for the loss of valence strength is advanced.Interpolated resonance parameters allow an estimate for the unknown cross section for ⁹⁹Mo(n, γ).     

Cascade γ decay of the 191Os compound state

The intensities of two-step cascades to the final levels with excitation energies below 0.82 MeV have been determined from the accumulated experimental data on the γ-γ coincidences at thermal neutron capture into ¹⁹⁰Os. These intensities made it possible to establish the decay scheme for the compound nucleus to excitation energies of about 3 MeV. The intervals of the level densities and sums of radiative strength functions of the E1 and M1 transitions, which exactly reproduce the experimental cascade intensities, have been found from the total cascade intensities. The level density is approximated by the sum of the partial densities of levels for different numbers n of quasiparticles, with the coefficient of collective increase in the density, unambiguously determined by the accepted concepts about the energy dependence of the correlation functions of the nucleons of an excited nucleus.     

Primakoff effect: Synchrotron and coulomb mechanisms of axion emission

The Primakoff effect-induced radiative emission of axions by an alternating electromagnetic field, F _a → γa, is considered for the first time. The synchrotron mechanism and the Coulomb mechanism—in the latter case, the alternating field is formed when a charge executes an infinite motion in the field of a Coulomb center—are considered as specific examples. The contributions of these effects to the axion emissivity of magnetic neutron stars and of the Sun are estimated.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Charge radii and quadrupole-deformation parameters of high-spin isomers

Experimental data on the differences of charge radii of nuclei in the ground and high-spin isomeric states are surveyed. High-resolution laser-spectroscopy methods were used for measurements. The results obtained for the differences of these radii by two methods—from measurements of isomeric shifts of the levels of atoms containing the nuclei being studied and from measurements of their quadrupole moments in both states under the assumption that the differences of the radii are determined by the difference in their quadrupole deformations—were compared. Two-particle isomers in odd—odd nuclei, isomers formed upon the break of one or several nucleon pairs, and isomers featuring the 1i _13/2 configuration of the odd neutron in mercury nuclei were considered. The observed distinctions between the aforementioned differences of charged radii are discussed for isomeric states of different nature.     

PrimaryE2 transitions observed following neutron capture for the mass region 144≦A≦180

Values or upper limits for the radiative widths of 12 primaryE2 transitions observed in thermal neutron capture for nuclei with 144≦A≦180 are presented. The results are compared with the predictions of the Axel-Brink hypothesis using the systematics of the isoscalar and isovector quadrupole resonances. The strengths are on the average lower than expected. Analysis of previously reported average resonance data results in the same conclusion.     

Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250

The parameters a and Δ for the Fermi gas model with fictive ground state are determined for about 220 nuclei from experimental level densities at low excitation energy and at the neutron binding energy. In. agreement with previous results it is found that for most nuclei the fictive ground state is back-shifted relative to the conventionally shifted ground state as determined by the pairing energy. Shell effects are evident at the mass numbers 90, 140 and 208 for both the level density parameter a and the back-shift. A comparison is given with previous results and different experimental data on level densities.     

Study of the nuclear periphery with Antiprotons

In the experiments of the PS209 collaboration at the Low Energy Antiproton Ring LEAR at CERN two methods were applied to study the nuclear periphery: first the yields of residual nuclei with mass number A — 1 were determined with radiochemical methods, and secondly the widths and shifts of the last observable transitions in antiprotonic atoms were measured with Ge detectors. The ratio of yields after annihilation for nuclei with one neutron missing to those with one proton missing from the target nucleus was found to depend strongly on the binding energy of the most loosely bound neutron of the target nucleus. The values were in astonishingly good agreement with a rather simple model for the proton and neutron density distribution devised by Gambhir et al. Furthermore the normalized yield ratio stays constant up to a relative neutron excess of about 0.15 and afterwards rises steeply. Widths for in total 62 x-ray Unes from antiprotonic atoms were compared with the results of calculations of Batty et al. The agreement is reasonable on a semiquantitative basis, but improvements are desirable. For a number of nuclei the differences between the diffuseness values for the proton and neutron distributions were determined directly from the x-ray-line intensity and width data. The root-mean-square radii for the neutron and proton distributions may be derived from these results. The experimental data for four tin isotopes are in reasonable agreement with the experiments of Krasznahorkay et al., but lower than theory predicts.