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Register a new userConstraining level densities using spectral data
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Several models of level densities exist and they often make simplified assumptions regarding the overall behavior of the total level densities (LD) and the intrinsic spin and parity distributions of the excited states. Normally, such LD models are constrained only by the measured $D_0$, i.e. the density of levels at the neutron separation energy of the compound nucleus (target plus neutron), and the sometimes subjective extrapolation of discrete levels. In this work we use microscopic Hartree-Fock-Bogoliubov (HFB) level densities, which intrinsically provide more realistic spin and parity distributions, and associate variations predicted by the HFB model with the observed double-differential cross sections at low outgoing neutron energy, region that is dominated by the LD input. With this approach we are able to perform fits of the LD based on actual experimental data, constraining the model and ensuring its consistency. This approach can be particularly useful in extrapolating the LD to nuclei for which high-excited discrete levels and/or values of $D_0$ are unknown. It also predicts inelastic gamma (n,n$^{prime}gamma$) cross sections that in some cases can differ significantly from more standard LD models such as Gilbert-Cameron.
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The adopted level densities (LD) for the nuclei produced through different reaction mechanisms significantly impact the calculation of cross sections for the many reaction channels. Common LD models make simplified assumptions regarding the overall behavior of the total LD and the intrinsic spin and parity distributions of the excited states. However, very few experimental constraints are taken into account: LD at neutron separation energy coming from average resonance spacings, whenever they have been previously measured, and the sometimes subjective extrapolation of discrete levels. These, however, constrain the LD only for very specific spins, parities and excitation energies. This work aims to establish additional experimental constraints on LD through quantitative correlations between cross sections and LD. This allows for the fitting and determination of detailed structures in LD. For this we use the microscopic Hartree-Fock-Bogoliubov (HFB) LD to associate variations predicted by the model with the structure observed in double-differential spectra at low outgoing neutron energy, which is dominated by the LD input. We also use uc{56}{Fe} ($n,p$) as an example cross sections are extremely sensitive to LD. For comparison purposes we also perform calculations with the GC model. With this approach we are able to perform fits of the LD based on actual experimental data, constraining the model and ensuring its consistency. This approach can be particularly useful in extrapolating the LD to nuclei for which high-excited discrete levels and/or resonance spacings are unknown. It also predicts inelastic gamma cross sections that can significantly differ from more standard phenomenological LD.
Photon strength, $f(E_{gamma})$, measured in photonuclear reactions, is the product of the average level density per MeV, $rho(E_x)$, and the average reduced level width, $Gamma_{gamma}/E_{gamma}^3$ for levels populated primarily by E1 transitions at an excitation energy $E_x=E_{gamma}$. It can be calculated with the Brink-Axel (BA) formulation modified to include contributions from the Giant Dipole Resonance (GDR) and higher lying resonances. Level densities and reduced widths have been calculated for 17 nuclei with atomic numbers between Z=14-92. Level densities below the GDR energy were calculated with the CT-JPI model and combined with the BA photon strength to determine the associated reduced widths. The reduced widths varied exponentially with level energy and could be extrapolated up to higher energies. The extrapolated widths were then combined with the BA photon strength to determine the level densities at higher energies. The level densities are found to increase exponentially at low energies, peak near the GDR energy due to the appearance of new states at the $2hbaromega$ shell closure, and continue to increase less rapidly up to at least 30 MeV. The average level densities have been compared with the Fermi Gas Level Density (FGLD), Back-Shifted Fermi Gas (BSFG), and Hartree-Fock-Bogoliubov (HFB) models. Good agreement is found with the nearly identical FGLD and BDFG models, while the HFB models gives substantially lower level densities. A universal set of FGLD model parameters were determined as a function of mass and temperature that are applicable to all nuclei.
The main formalisms of partial level densities (PLD) used in preequilibrium nuclear reaction models, based on the equidistant spacing model (ESM), are considered. A collection of FORTRAN77 functions for PLD calculation by using 14 formalisms for the related partial-state densities is provided and 28 sample cases (
Pairing correlations have a strong influence on nuclear level densities. Empirical descriptions and theoretical models have been developed to take these effects into account. The present article discusses cases, where descriptions of nuclear level densities are inconsistent or in conflict with the present understanding of nuclear properties. Phenomenological approaches consider a back-shift parameter. However, the absolute magnitude of the back-shift, which actually corresponds to the pairing condensation energy, is generally not compatible with the observation that stable pairing correlations are present in essentially all nuclei. It is also shown that in the BCS model pairing condensation energies and critical pairing energies are inconsistent for light nuclei. A modification to the composite Gilbert-Cameron level-density description is proposed, and the use of more realistic pairing theories is suggested.
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 measuring 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.
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