arXiv subjects
Publications and source records attributed to J. Rekstad.
In this work, we have reviewed the Oslo method, which enables the simultaneous extraction of level density and gamma-ray transmission coefficient from a set of particle-gamma coincidence data. Possible errors and uncertainties have been investigated. Typical data sets from various mass regions as well as simulated data have been tested against the assumptions behind the data analysis.
The level densities and gamma-ray strength functions of 205-208Pb have been measured with the Oslo method, utilizing the (3He, 3He' gamma) and (3He,alpha gamma) reactions on the target nuclei 206Pb and 208Pb. The extracted level densities are consistent with known discrete levels at low excitation energies. The entropies and temperatures in the micro-canonical ensemble have been deduced from the experimental level density. An average entropy difference of Delta S ~ 1.8 k_B has been observed between 205Pb and 206Pb. The gamma-ray strength functions in 205-208Pb are extracted and compared with two models; however, none of them describe the data adequately. Intermediate structures have been observed at lower gamma-ray energies in all the analyzed Pb nuclei. These structures are less pronounced while moving from the doubly-magic nucleus 208Pb to 205Pb.
Nuclear level densities for $^{56,57}$Fe have been extracted from the primary $γ$-ray spectra using ($^3$He,$^3$He$^{\prime}γ$) and ($^3$He,$αγ$) reactions. Nuclear thermodynamic properties for $^{56}$Fe and $^{57}$Fe are investigated using the experimental level densities. These properties include entropy, Helmholtz free energy, caloric curves, chemical potential, and heat capacity. In particular, the breaking of Cooper pairs and single-quasiparticle entropy are discussed and shown to be important concepts for describing nuclear level density. Microscopic model calculations are performed for level densities of $^{56,57}$Fe. The experimental and calculated level densities are compared. The average number of broken Cooper pairs and the parity distribution are extracted as a function of excitation energy for $^{56,57}$Fe from the model calculations.
The radiative strength functions of 96Mo have been reanalyzed. The enhanced gamma strength for E_gamma < 3 - 4 MeV is confirmed.
The scandium isotopes 44,45Sc have been studied with the 45Sc(3He,alpha gamma)44Sc and 45Sc(3He,3He' gamma)45Sc reactions, respectively. The nuclear level densities and gamma-ray strength functions have been extracted using the Oslo method. The experimental level densities are compared to calculated level densities obtained from a microscopic model based on BCS quasiparticles within the Nilsson level scheme. This model also gives information about the parity distribution and the number of broken Cooper pairs as a function of excitation energy. The experimental gamma-ray strength functions are compared to theoretical models of the E1, M1, and E2 strength, and to data from (gamma,n) and (gamma,p) experiments. The strength functions show an enhancement at low gamma energies that cannot be explained by the present, standard models.
The S shape of the canonical heat capacity 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 with an odd number. Although the heat capacities extracted from experimental level densities in 93-98Mo 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 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 94-97Mo using the three-, four-, and five-point formula. These thermal mass differences are regarded as indicators of pairing correlations at finite temperature.
The level densities and radiative strength functions (RSFs) of $^{50,51}$V have been extracted using the ($^3$He,$αγ$) and ($^3$He,$^3$He$^{\prime} γ$) reactions, respectively. From the level densities, microcanonical entropies are deduced. The high $γ$-energy part of the RSF is described by the giant electric dipole resonance. A significant enhancement over the predicted strength in the region of $E_γ \lesssim 3$ MeV is seen, which at present has no theoretical explanation.
The $^{55}$Mn$(d,n)^{56}$Fe differential cross section is measured at $E_d=7$ MeV\@. The $^{56}$Fe level density obtained from neutron evaporation spectra is compared to the level density extracted from the $^{57}$Fe$(^3$He,$αγ)^{56}$Fe reaction by the Oslo-type technique. Good agreement is found between the level densities determined by the two methods. With the level density function obtained from the neutron evaporation spectra, the $^{56}$Fe $γ$-strength function is also determined from the first-generation $γ$ matrix of the Oslo experiment. The good agreement between the past and present results for the $γ$-strength function supports the validity of both methods and is consistent with the low-energy enhancement of the $γ$ strength below $\sim 4$ MeV first discovered by the Oslo method in iron and molybdenum isotopes.
Level densities for 93-98Mo have been extracted using the (3He,alpha gamma) and (3He,3He' gamma) reactions. From the level densities thermodynamical quantities such as temperature and heat capacity can be deduced. Data have been analyzed by utilizing both the microcanonical and the canonical ensemble. Structures in the microcanonical temperature are consistent with the breaking of nucleon Cooper pairs. The S-shape of the heat capacity curves found within the canonical ensemble is interpreted as consistent with a pairing phase transition with a critical temperature for the quenching of pairing correlations at T_c ~ 0.7-1.0 MeV.
The two published literature values [Greenwood et al., Nucl. Phys. A252, 260 (1975) and Gelletly et al., J. Phys. G 11, 1055 (1985)] for absolute primary gamma intensities following thermal neutron capture of 171Yb differ in average by a factor of three. We have resolved this conflict in favor of Greenwood et al. by a measurement of primary versus secondary intensities.
Level densities and radiative strength functions in $^{171}$Yb and $^{170}$Yb nuclei have been measured using the $^{171}$Yb($^3$He,$^3$He$^\primeγ$)$^{171}$Yb and $^{171}$Yb($^3$He,$αγ$)$^{170}$Yb reactions. New data on $^{171}$Yb are compared to a previous measurement for $^{171}$Yb from the $^{172}$Yb($^3$He,$αγ$)$^{171}$Yb reaction. Systematics of level densities and radiative strength functions in $^{170,171,172}$Yb are established. The entropy excess in $^{171}$Yb relative to the even-even nuclei $^{170,172}$Yb due to the unpaired neutron quasiparticle is found to be approximately 2$k_B$. Results for the radiative strength function from the two reactions lead to consistent parameters characterizing the ``pygmy'' resonances. Pygmy resonances in the $^{170,172}$Yb populated by the ($^3$He,$α$) reaction appear to be split into two components for both of which a complete set of resonance parameters are obtained.
Radiative strength functions (RSFs) in 93-98Mo have been extracted using the (3He,alpha gamma) and (3He,3He' gamma) reactions. The RSFs are U-shaped as function of gamma energy with a minimum at around E_gamma=3 MeV. The minimum values increase with neutron number due to the increase in the low-energy tail of the giant electric dipole resonance with nuclear deformation. The unexpected strong increase in strength below E_gamma=3 MeV, here called soft pole, is established for all 93-98Mo isotopes. The soft pole is present at all initial excitation energies in the 5-8 MeV region.
Radiative strength functions (RSFs) for the 56,57-Fe nuclei below the separation energy are obtained from the 57-Fe(3-He,alpha gamma)56-Fe and 57-Fe(3-He,3-He' gamma)57-Fe reactions, respectively. An enhancement of more than a factor of ten over common theoretical models of the soft (E_gamma ~< 2 MeV) RSF for transitions in the quasicontinuum (several MeV above the yrast line) is observed. Two-step cascade intensities with soft primary transitions from the 56-Fe(n,2gamma)57-Fe reaction confirm the enhancement.
Two-step-cascade spectra in 172-Yb have been measured after thermal neutron capture. They are compared to calculations based on experimental values of the level density and radiative strength function (RSF) obtained from the 173-Yb(3-He,alpha gamma)172-Yb reaction. The multipolarity of a 6.5(15) mu_N^2 resonance at E_gamma=3.3(1) MeV in the RSF is determined to be M1 by this comparison.
Experimental level densities for 171,172Yb, 166,167Er, 161,162Dy, and 148,149Sm are analyzed within the microcanonical ensemble. In the even isotopes at excitation energies E < 2 MeV, the Helmholtz free energy F signals the transition from zero to two quasiparticles. For E > 2 MeV, the odd and even isotopes reveal a surprisingly constant F at a critical temperature Tc of appr. 0.5 MeV, indicating the continuous melting of nucleon Cooper pairs as function of excitation energy.
The level densities and radiative strength functions (RSFs) in 160,161Dy have been extracted using the (3He,alpha gamma) and (3He,3He' gamma) reactions, respectively. The data are compared to previous measurements on 161,162Dy. The energy distribution in the canonical ensemble is discussed with respect to the nucleon Cooper pair breaking process. The gross properties of the RSF are described by the giant electric dipole resonance. The RSF at low gamma-ray energies is discussed with respect to temperature dependency. Resonance parameters of a soft dipole resonance at Egamma = 3 MeV are deduced.
Caloric curves have traditionally been derived within the microcanonical ensemble via dS/dE=1/T or within the canonical ensemble via E=T^2*d(ln Z)/dT. In the thermodynamical limit, i.e., for large systems, both caloric curves give the same result. For small systems like nuclei, the two caloric curves are in general different from each other and neither one is reasonable. Using dS/dE=1/T, spurious structures like negative temperatures and negative heat capacities can occur and have indeed been discussed in the literature. Using E=T^2*d(ln Z)/dT a very featureless caloric curve is obtained which generally smoothes too much over structural changes in the system. A new approach for caloric curves based on the two-dimensional probability distribution P(E,T) will be discussed.
Level densities have been extracted from primary gamma spectra for 56,57-Fe and 96,97-Mo nuclei using (3-He,alpha gamma) and (3-He,3-He') reactions on 57-Fe and 97-Mo targets. The level density curves reveal step structures above the pairing gap due to the breaking of nucleon Cooper pairs. The location of the step structures in energy and their shapes arise from the interplay between single-particle energies and seniority-conserving and seniority-non-conserving interactions.