It is almost 80 years since Hans Bethe described the level density as a non-interacting gas of protons and neutrons. In all these years, experimental data were interpreted within this picture of a fermionic gas. However, the renewed interest of measu
ring level density using various techniques calls for a revision of this description. In particular, the wealth of nuclear level densities measured with the Oslo method favors the constant-temperature level density over the Fermi-gas picture. From the basis of experimental data, we demonstrate that nuclei exhibit a constant-temperature level density behavior for all mass regions and at least up to the neutron threshold.
Particle-$gamma$ coincidences from the $^{89}$Y($p,p gamma$)$^{89}$Y and $^{89}$Y($d,p gamma$)$^{90}$Y reactions were utilized to obtain $gamma$-ray spectra as function of excitation energy. The Oslo method was used to extract the level density from
the particle-$gamma$ coincidence matrices. The impact of the $N=50$ shell closure on the level densities is discussed within the framework of a combinatorial quasi-particle model.
Particle-gamma coincidences have been measured to obtain gamma-ray spectra as a function of excitation energy for 231-233Th and 237-239U. The level densities, which were extracted using the Oslo method, show a constant temperature behavior. The isoto
pes display very similar temperatures in the quasi-continuum, however, the even-odd isotopes reveal a constant entropy increase Delta S compared to their even-even neighbors. The entropy excess depends on available orbitals for the last unpaired valence neutron of the heated nuclear system. Also, experimental microcanonical temperature and heat capacity have been extracted. Several poles in the heat capacity curve support the idea that an almost continuous melting of Cooper pairs is responsible for the constant-temperature behavior.
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.
Particle-gamma coincidences from the 46Ti(p,p gamma)46Ti inelastic scattering reaction with 15-MeV protons are utilized to obtain gamma-ray spectra as a function of excitation energy. The rich data set allows analyzing the coincidence data with vario
us gates on excitation energy. This enables, for many independent data sets, a simultaneous extraction of level density and radiative strength function (RSF). The results are consistent with one common level density. The data seem to exhibit a universal RSF as the deduced RSFs from different excitation energies show only small fluctuations provided that only excitation energies above 3 MeV are taken into account. If transitions to well-separated low-energy levels are included, the deduced RSF may change by a factor of 2-3, which might be expected due to the involved Porter-Thomas fluctuations.
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 consiste
nt 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.
The nuclear level densities of 116,117Sn below the neutron separation energy have been determined experimentally from the (3He,alpha gamma) and (3He,3He gamma) reactions, respectively. The level densities show a characteristic exponential increase an
d a difference in magnitude due to the odd-even effect of the nuclear systems. In addition, the level densities display pronounced step-like structures that are interpreted as signatures of subsequent breaking of nucleon pairs.
Nuclear level densities for $^{56,57}$Fe have been extracted from the primary $gamma$-ray spectra using ($^3$He,$^3$He$^{prime}gamma$) and ($^3$He,$alpha gamma$) 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 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 experi
mental 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.
