U. Agvaanluvsan

Breaking of nucleon Cooper pairs at finite temperature in {sup 93-98}Mo

The S shape of the canonical heat-capacity curve is known as a signature of the pairing transition, and along an isotopic chain it is significantly more pronounced for nuclei with an even number of neutrons than for those with an odd number. Although the heat capacities extracted from experimental level densities in {sup 93-98}Mo exhibit a clear S shape, they do not show such an odd-even staggering. To understand the underlying physics, we analyze thermal quantities evaluated from the partition function calculated using the static-path plus random-phase approximation (SPA+RPA) in a monopole pairing model with number-parity projection. The calculated level densities reproduce very well the experimental data, and they also agree with estimates made using the back-shifted Fermi-gas model. We clarify the reason why the heat capacities for Mo isotopes do not show odd-even staggering of the S shape. We also discuss thermal odd-even mass differences in {sup 94-97}Mo that were calculated using the three-, four-, and five-point formulas. These thermal mass differences are regarded as indicators of pairing correlations at finite temperature.

Test of the statistical model in {sup 96}Mo with the BaF{sub 2}{gamma} calorimeter DANCE array

The {gamma}-ray cascades following the {sup 95}Mo(n,{gamma}){sup 96}Mo reaction were studied with the {gamma} calorimeter DANCE (Detector for Advanced Neutron Capture Experiments) consisting of 160 BaF{sub 2} scintillation detectors at the Los Alamos Neutron Science Center. The {gamma}-ray energy spectra for different multiplicities were measured for s- and p-wave resonances below 2 keV. The shapes of these spectra were found to be in very good agreement with simulations using the DICEBOX statistical model code. The relevant model parameters used for the level density and photon strength functions were identical with those that provided the best fit of the data from a recent measurement of the thermal {sup 95}Mo(n,{gamma}){sup 96}Mo reaction with the two-step-cascade method. The reported results strongly suggest that the extreme statistical model works very well in the mass region near A=100.

Neutron capture cross section of {sup 241}Am

The neutron capture cross section of {sup 241}Am for incident neutrons from 0.02 eV to 320 keV has been measured with the detector for advanced neutron capture experiments (DANCE) at the Los Alamos Neutron Science Center. The thermal neutron capture cross section was determined to be 665{+-}33 b. Our result is in good agreement with other recent measurements. Resonance parameters for E{sub n}<12 eV were obtained using an R-matrix fit to the measured cross section. The results are compared with values from the ENDF/B-VII.0, Mughabghab, JENDL-3.3, and JEFF-3.1 evaluations. {gamma}{sub n} neutron widths for the first three resonances are systematically larger by 5-15% than the ENDF/B-VII.0 values. The resonance integral above 0.5 eV was determined to be 1553{+-}7 b. Cross sections in the resolved and unresolved energy regions above 12 eV were calculated using the Hauser-Feshbach theory incorporating the width-fluctuation correction of Moldauer. The calculated results agree well with the measured data, and the extracted averaged resonance parameters in the unresolved resonance region are consistent with those for the resolved resonances.

Bulk properties of iron isotopes

Nuclear level densities and radiative strength functions (RSFs) in 56Fe and 57Fe were measured using the 57Fe(3He, αγ) and 57Fe(3He, 3He′γ) reactions, respectively, at the Oslo Cyclotron Laboratory. A low-energy enhancement in the RSF below 4-MeV energy was observed. This finding cannot be explained by common theoretical models. In a second experiment, two-step cascade intensities with soft primary transitions from the 56Fe(n, 2γ) reaction were measured. The agreement between the two experiments confirms the low-energy enhancement in the RSFs. In a third experiment, the neutron evaporation spectrum from the 55Mn(d, n)56Fe reaction was measured at 7-MeV deuteron energy at the John Edwards Accelerator Laboratory at Ohio University. Comparison of the level density of 56Fe obtained from the first and third experiments gives an overall good agreement. Furthermore, observed enhancement for soft γ rays is strengthened by the last experiment.

Spin and parity assignments for {sup 94,95}Mo neutron resonances

The {gamma} rays following the {sup 94,95}Mo(n,{gamma}) reactions were measured as a function of incident neutron energy by the time-of-flight method with the DANCE (Detector for Advanced Neutron Capture Experiments) array of 160 BaF{sub 2} scintillation detectors at the Los Alamos Neutron Science Center. The targets were enriched samples: 91.59% {sup 94}Mo and 96.47% {sup 95}Mo. The {gamma}-ray multiplicities and energy spectra for different multiplicities were measured in s- and p-wave resonances up to E{sub n}=10 keV for {sup 94}Mo and up to E{sub n}=2 keV for {sup 95}Mo. Definite spins and parities were assigned in {sup 96}Mo for about 60% of the resonances, and tentative spins and parities were assigned for the remaining resonances. In {sup 95}Mo the parities were determined for the observed resonances, confirming previously known assignments.

Nuclear properties in the vicinity of closed shells

In order to learn more about the different properties of the nuclei like, e.g., collective motion, thermo‐dynamical behaviour and temperature, level density and γ‐ray strength function, it is important to study the effect of internal excitation energy. When approaching major shell gap, nuclear structure changes significantly. This makes an impact on the level densities and γ‐strength function. Around closed shells, effects from the increasing single particle energy spacing can be expected. These will also influence the entropy difference between odd‐mass and even‐even nuclei. Therefore, statistical description of the transition from closed shells to deformed nuclei is of great interest.

Nuclear thermodynamics below particle threshold

From a starting point of experimentally measured nuclear level densities, we discuss thermodynamical properties of nuclei below the particle emission threshold. Since nuclei are essentially mesoscopic systems, a straightforward generalization of macroscopic ensemble theory often yields unphysical results. A careful critique of traditional thermodynamical concepts reveals problems commonly encountered in mesoscopic systems. One of which is the fact that microcanonical and canonical ensemble theory yield different results, another concerns the introduction of temperature for small, closed systems. Finally, the concept of phase transitions is investigated for mesoscopic systems.

Improved Nuclear Level Densities via Identification of Spurious Levels

An accurate value of the nuclear resonance spacing is crucial for determination of level densities. Level densities are key input for the calculation of nuclear reaction rates and cross sections. This paper discusses various effects that can adversely impact the average level spacing, with special emphasis on the issue of quantum number assignment. The most striking property of spacings of resonances with the same quantum number is level repulsion. We investigate how a simple test based on level repulsion can be used in the identification of spin misassignment and provide new experimental verification of the proposed test. Proton resonances obtained in the 44Ca+p reaction are used as an example. In addition, s‐wave neutron resonances in the 238U+n reaction are considered.

Entropy In Hot Nuclei

The level density and the γ‐strength function have been extracted experimentally. From the level densities thermodynamical quantities such as temperature and heat capacity can be found. Structures in the micro‐canonical temperature are interpreted as the onset of new degrees of freedom by the breaking of Cooper pairs. The S‐shape in the heat capacity curves, found within the canonical ensemble, indicates the pairing‐phase transition, and a critical temperature for the quenching of pair correlations is found. The pygmy resonance at 3.3(1) MeV in 172Yb has now been established with a strength of B(M1)=6.5(15)μN2 and M1 multipolarity, the so‐called scissors mode. In addition, a strong unexpected enhancement of the radiative strength function (RSF) has been found at low γ‐ray energy in medium light Fe nuclei and also in the heavier Mo nuclei.

Level Densities from Proton Resonances

Detailed information about nuclear level densities is obtained by direct counting of individual resonances. A collection of individual resonances with the same spin and parity follows the predictions of the Gaussian Orthogonal Ensemble (GOE) version of Random Matrix Theory (RMT). RMT predictions are used to determine the corrections due to the imperfections in the measurement. We derived a general expression for the probability distribution for imperfect eigenvalue sequences. The missing level correction for the number of levels is obtained by two methods, the newly developed eigenvalue (or spacing) analysis and the more traditional reduced width analysis. Proton resonances in three nuclei are analyzed using the two methods. Improved values for the level densities are obtained, and the parity dependence of level density is considered.