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.     

A study of the giant dipole resonance of vibrational nuclei in the 103 ≦ A ≦ 133 mass region

This paper presents a set of experimental data concerning the giant dipole resonance of nuclei (GDR) in the 103 ≦ A ≦ 133 mass region. The cross sections σ(γ,n) and σ(γ, 2n) were obtained in the energy region 8–30 MeV by means of a monochromatic photon beam produced by annihilation in flight of positons. This paper attempts also to give an interpretation of the experimental behaviour of the GDR for vibrational nuclei in the 103 ≦ A ≦ 133 mass region in terms of the simple dynamic collective model. In particular it is shown that the width of the GDR increases as β increases and as E₂₊ decreases and that the theoretically predicted spreading of the dipole strength is confirmed by our experimental results. As to the characteristic behaviour of the GDR above its peak value at E₀, we come to the conclusion that the actual state of the art in (γ, xn) research does not allow one to make an unambiguous choice between isospin splitting or electric quadrupole absorption. Finally the numerical evaluations of the different sum rules are given and some empirical results concerning the average energy of the GDR as a function of A are also presented.     

A measurement of the 50Ti(γ, n) and 50Ti(γ, n0) cross sections

Measurements of the ⁵⁰Ti(γ, n) and ⁵⁰Ti(γ, n₀) cross sections have been made in the energy range of the giant dipole resonance (GDR). Assuming the GDR is split into two isospin components, approximated as Lorentzians, a calculation based on statistical decay of the GDR states is consistent with the experimental results.     

Radiative strength functions in odd-A spherical nuclei

The radiative strength functions for the partial γ-transitions from neutron resonances to the ground and low-lying states of odd-A spherical nuclei are calculated within the quasiparticle-phonon nuclear model. The fragmentation of one-quasiparticle and quasiparticle-plus-phonon states is calculated. This allowed one to calculate γ-transitions between the one-quasi-particle components (valence transitions) and γ-transitions between the quasiparticle-plus-phonon and one-quasiparticle components of the wave functions. The energy dependence of the strength functions $\text{C}$(E1, η) and $\text{C}$(M1, η) is calculated near the neutron binding energy B_n for ⁵⁵Fe and ^{59, 61}Ni. The corresponding experimental data are described qualitatively. The contribution of the valence E1 transitions to the strength function is shown to be from 20% to 90%, and M1 transitions about 1%. The influence of the M1 giant resonance is important for M1 transition probabilities.     

(γ, p) cross sections and isospin splitting of the giant dipole resonance in N = 50 nuclei

The differential (e, e'p) cross sections of ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr and ⁹²Mo have been measured at θ = 90°. The results are used to obtain the (γ, p) cross sections by correcting with the angular distribution data. The (γ, p) cross sections are compared with the (γ, n) cross sections. A resonance corresponding to the T_< GDR is found and another resonance is separated by fitting a Lorentz line with a width equal to that of the (γ, n) GDR. The ratios σ(γ, p)/σ(γ, n) and σ(γ, p₀)/σ(γ, p) show differences between the two resonances. The two GDR resonances are studied from the isospin splitting point of view. The sum rule and splitting energy of the (γ, p) GDR agree well with theory. However, when the sum of the (γ, p) and (γ, n) experimental data is taken, the results are too large to be explained by the T_> GDR.     

High-spin levels in137,139Ce and139,141Nd evidence for hole-core coupling

Excited states of the¹³⁷Ce,¹³⁹Ce,¹³⁹Nd and¹⁴¹Nd nuclei have been studied using the¹³⁸Ba(α, 5nγ)¹³⁷Ce,¹³⁸Ba(³He, 4nγ)¹³⁷Ce,¹³⁸Ba(α, 3nγ)¹³⁹Ce,¹⁴⁰Ce(α, 5nγ)¹³⁹Nd,¹⁴⁰Ce(³He,4nγ)¹³⁹Nd,¹⁴⁰Ce(α, 3nγ)¹⁴¹Nd and¹⁴²Ce(α, 5nγ)¹⁴¹Nd reactions. Singlesγ-ray spectra,γ —γ coincidence spectra, angular distributions and time distributions ofγ-rays with respect to beam pulses have been measured. Gamma transitions between excited states with spin values up to 21/2, 23/2 or 25/2 have been observed. Isomeric states with T_1/2=70 ns have been observed in¹³⁹Ce at 2631.5 keV (19/2) and in¹⁴¹Nd probably at 2952.0 keV (19/2). The level structure observed in the nuclei studied can be explained if the neutron-holes are coupled to the doubly even core excitations. The coupling of theh _11/2 neutron-hole with the 2⁺, 4⁺ and 3^? collective excitations are calculated in terms of the weak and intermediate coupling models. The intermediate coupling results seem to be in better agreement with the experimental data. The energies of theree-particle states, being the result of the coupling of theh _11/2 neutron-hole with the two-proton excitations in the core, are well reproduced in the calculations when empirical values of the two-body interaction matrix elements were used.     

Semiphenomenological approximation of the sums of experimental radiative strength functions for dipole gamma transitions of energy E γ below the neutron binding energy B n for mass numbers in the range 40 ≤ A ≤ 200

The sums of radiative strength functions for primary dipole gamma transitions, k(E1) + k(M1), are approximated to a high precision by a superposition of two functional dependences in the energy range 0.5 < E ₁ < B _n ? 0.5 MeV for the ⁴⁰K, ⁶⁰Co, ^71,74Ge, ⁸⁰Br, ¹¹⁴Cd, ¹¹⁸Sn, ^124,125Te, ¹²⁸I, ^137,138,139Ba, ¹⁴⁰La, ¹⁵⁰Sm, ^156,158Gd, ¹⁶⁰Tb, ^163,164,165Dy, ¹⁶⁶Ho, ¹⁶⁸Er, ¹⁷⁰Tm, ¹⁷⁴Yb, ^176,177Lu, ¹⁸¹Hf, ¹⁸²Ta, ^{183,184,185,187}W, ^{188,190,191,193}Os, ¹⁹²Ir, ¹⁹⁶Pt, ¹⁹⁸Au, and ²⁰⁰Hg nuclei. It is shown that, in any nuclei, radiative strength functions are a dynamical quantity and that the values of k(E1) + k(M1) for specific energies of gamma transitions and specific nuclei are determined by the structure of decaying and excited levels, at least up to the neutron binding energy B _n .     

Experimental arguments in favor of refining model ideas of the cascade gamma decay of a compound state of a complex nucleus

An analysis of the entire body of data on the intensities of two-step gamma cascades studied in thermal-neutron capture for more than 50 nuclei from the range 27 ≤ A ≤ 199 suggests that such processes should be described in terms of model concepts that are much more involved than those currently adopted by experimentalists. According to the results of this analysis, models of relevant parameters, such as the density of excited levels and radiative strength functions for dipole gamma transitions, should take into account more explicitly the coexistence and interaction of quasiparticle and phonon interactions. A direct inclusion of the idea that a second-order phase transition occurs and affects not only level densities but also radiative strength functions for dipole transitions may prove to be necessary. These conclusions concern primarily the excitation-energy region below a value of about 0.5B _n .     

On the enhancement of M1-transitions from neutron resonances in the Ba and Ce isotopes

The M1-strength functions for transitions from the ground states of ^136,138Ba and ¹⁴⁰Ce to the states lying near the neutron binding energy B_n are calculated within the quasiparticle-phonon nuclear model. The calculated M1-strength functions describe well the relevant experimental data. It is shown that a notable enhancement of the M1-transitions is caused by the proximity of the maximum of the M1-resonance to B_n. As a result the intensities of the E1 and M1-transitions appear to be close to each other.     

A study of the giant dipole resonance in doubly even tellurium and cerium isotopes

The partial photoneutron cross sections [σ(γ, n) + σ(γ, pn)] and σ (γ, 2n) of ^{124, 126, 128, 130}Te and ^{140, 142}Ce were measured in the giant dipole resonance region by means of the monochromatic photon beam installation at SACLAY. Absolute total photoneutron cross sections, Lorentz line parameters and integrated cross sections are evaluated. The experimental behaviour of the GDR for the above nuclei and in particular its spreading, is then tentatively interpreted in terms of the improved dynamic collective model using the concept of potential energy surfaces.     

Virtual excitation of the GDR mode in the subbarrier23Na(p, γ)24Mg reaction

Differential cross sections for nonresonant radiative capture of low energy protons (E _p = 1,348 keV and 1,370 keV) by²³Na nuclei exhibit features pointing to the virtual excitation of the giant dipole resonance (GDR) mode. Theoretical analysis carried out within the framework of the direct — semidirect capture model reveals an enhanced coupling of the GDR with the incident protonf-wave consistent with the microscopic structure of the GDR in thes-d shell nuclei.     

Photonuclear reactions of actinides in the giant dipole resonance region

Photonuclear reactions at energies covering the giant dipole resonance (GDR) region are analyzed with an approach based on nuclear photoabsorption followed by the process of competition between light-particle evaporation and fission for the excited nucleus. The photoabsorption cross-section at energies covering the GDR region is contributed by both the Lorentz-type GDR cross-section and the quasi-deuteron cross-section. The evaporation-fission process of the compound nucleus is simulated in a Monte Carlo framework. Photofission reaction cross-sections are analyzed in a systematic manner in the energy range of ∼ 10-20 MeV for the actinides ²³²Th , ²³⁸U and ²³⁷Np . Photonuclear cross-sections for the medium-mass nuclei ⁶³Cu and ⁶⁴Zn , for which there are no fission events, are also presented. The study reproduces satisfactorily the available experimental data of photofission cross-sections at GDR energy region and the increasing trend of nuclear fissility with the fissility parameter Z ²/A for the actinides.     

A superdeformed band in131Ce

A rotational band of 16γ-rays has been found in¹³¹Ce with a high moment of inertia indicating a deformation ε₂～0.38 and extending to spin ～40?. Its intensity is ～～5% of the total in¹³¹Ce, confirming a difference in the intensity systematics for superdeformed states in Ce nuclei compared with Nd.     

New data on (γ, n), (γ, 2n), and (γ, 3n) partial photoneutron reactions

Systematic discrepancies between the results of various experiments devoted to determining cross sections for total and partial photoneutron reactions are analyzed by using objective criteria of reliability of data in terms of the transitional photoneutron-multiplicity function F _i = σ(γ, in)/σ(γ, xn), whose values for i = 1, 2, 3, ... cannot exceed by definition 1.00, 0.50, 0.33, ..., respectively. It was found that the majority of experimental data on the cross sections obtained for (γ, n), (γ, 2n), and (γ, 3n) reactions with the aid of methods of photoneutron multiplicity sorting do not meet objective criteria (in particular, F ₂ > 0.50 for a vast body of data). New data on the cross sections for partial reactions on ¹⁸¹Ta and ²⁰⁸Pb nuclei were obtained within a new experimental-theoretical method that was proposed for the evaluation of cross sections for partial reactions and in which the experimental neutron yield cross section σ ^expt(γ, xn) = σ(γ, n) + 2σ(γ, 2n) + 3σ(γ, 3n) + ..., which is free from problems associated with determining neutron multiplicities, is used simultaneously with the functions F _i ^theor calculated within a combined model of photonuclear reactions.     

Description of cross sections for photonuclear reactions in the energy range between 7 and 140 MeV

A combination of the exciton and evaporation models is used to describe photonuclear reactions induced in light, medium-mass, and heavy nuclei by photons of energy in the range 7 ≤ E _γ ≤ 140 MeV. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance at energies in the range E _γ ? 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ? 40 MeV. The density of particle-hole states, which appears in the exciton model, is calculated on the basis of the Fermi gas model. The emission of two preequilibrium particles is taken into account in describing the quasideuteron reaction channel. The effect of isospin conservation on giant-dipole-resonance decay accompanied by photonucleon emission is examined. The model in question is used to describe cross sections for photon-induced reactions on ²⁶Mg, ⁵⁴Fe, ^{112,118,119,124}Sn, and ¹⁸¹Ta nuclei.     

Temperature dependence of radiative strength functions and isomeric cross sections

The effect of a parametrization of the temperature dependence of radiative strength functions for electric dipole transitions on the cross sections for isomer excitation in (n, γ), (n, 2n), (n, p), (n, α), (γ, \g′), (γ, n), (γ, p), and (γ, 2n) reactions is investigated. It is shown that the agreement of the results of calculations with the observed isomeric cross sections can be considerably improved by using the proposed method.     

Thermal neutron captureγ-ray spectroscopy of59Ni and61Ni

Theγ-radiation emitted after thermal neutron capture in isotopically enriched⁵⁸Ni and⁶⁰Ni was measured at the ILL high flux reactor by means of Ge/NaI detectors operated in Compton suppression and pair spectrometer mode. The neutron binding energies were determined asB _n (⁵⁹Ni)=8999.15(23) keV and B_n(⁶¹Ni)=7820.07(20) keV; some 95% of the totalγ-ray fluxes through^59,61Ni were assigned. Theγ-ray strength functions of the primary transitions and the level densities are discussed.     

On the properties of charge-exchange dipole excitations and the T > component of a giant dipole resonance in spherical nuclei

Within the semimicroscopic approach based on the random-phase approximation that takes exactly into account a single-particle continuum and on a phenomenological inclusion of the fragmentation effect, it is proposed to describe the strength functions for charge-exchange giant dipole resonances and cross sections for photoabsorption and for partial “direct + semidirect” (γ, p) reactions in the vicinity of a giant E1 resonance with allowance for the isospin-splitting effect. The results of the calculations performed for some magic and semimagic nuclei without resort to free parameters are compared with available experimental data.     

New measurements of the radiative decay modes of the φ-meson

The radiative decay models of the φ-meson have been studied: e⁺e^?→φ→ηγ→3γ; e⁺e^?→φ→π^oγ→3γ. Cross sections σ_{φ→ηγ→3γ} and σ_{φ→π^oγ→3γ} have been measured at five energies in the φ-meson energy region and clearly show the φ-resonance in the ηγ → 3γ mode as well as in the π^oγ → 3γ mode. From a Breit-Wigner fit to the experimental data the values of the branching ratios are deduced: B_φ→ηγ = (1.5 ± 0.4) × 10^?2; B_φ→π^oγ = (1.4 ± 0.5) × 10^?3.