Fermi-gas Level-density Parameter Research Articles

Spallation of 56Fe by 1.0 GeV Protons

Mass, charge and isotopic distributions observed in spallation reactions of 56Fe with 1 GeV protons are analysed in the framework of the intranuclear cascade code ISABEL coupled with the sequential binary decay code MECO. The code MECO provides a description of the equilibrated nuclear decay by the emission of gamma-rays, light-mass particles and clusters as well as intermediate mass fragments emitted in their ground, excited bound and excited unbound states (continuum) according to a generalized Weisskopf formalism. A good overall description of the experimental data is obtained with a global Fermi gas level density parameter and inverse cross sections based on the Christensen and Winther nuclear potential. Multifragmentation decay events are simulated with the code SMM and their influence on the above observables is discussed.

Level densities ofSc44andTi47from different experimental techniques

The level densities of $^{44}\mathrm{Sc}$ and $^{47}\mathrm{Ti}$ have been determined from measurements of particle evaporation spectra from the compound nuclear reaction $^{3}\mathrm{He}+^{45}\mathrm{Sc}$ with an 11 MeV $^{3}\mathrm{He}$ beam. The level density of $^{44}\mathrm{Sc}$ has been compared to the level density obtained from an independent experimental method based on an analysis of $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidences from the transfer reaction $^{45}\mathrm{Sc}$($^{3}\mathrm{He}$,$\ensuremath{\alpha}\ensuremath{\gamma}$)$^{44}\mathrm{Sc}$. The good agreement between the two experiments indicates the reliability of the level density obtained. Some level density systematics have been tested against the experimental data. New Fermi-gas level density parameters have been derived.

Thermal properties and dynamics of hot nuclei

The heat capacities and the dynamics of hot medium mass nuclei have been explored by studies of light particle emission. The variation in heat capacity with temperature, expressed in terms of an effective Fermi gas level density parameter appropriate to the statistical description of nuclear de-excitation, corresponds to a decrease in a from A/8 to A/13 as the excitation energy increases from 1 to 2 MeV/nucleon. This result is compared to recent theoretical predictions. An apparent sudden change in the heat capacity observed at slightly higher excitation energies per nucleon is also discussed. Prescission and post-scission particle multiplicities and temperatures in coincidence with evaporation residues and fission fragments provide further information on the decay dynamics of hot nuclei. Possible means of isolating presaddle emission and of determining the temperature dependence of the fission barrier are discussed.

Energy equilibration in composite nuclei at high energy and spin: Correlations between evaporativeH1,He4, and fission

Correlations have been studied between evaporative H/He emission and fissionlike products for the reactions 333 MeV $^{40}\mathrm{Ar}$ + $^{116}\mathrm{Sn}$, $^{154}\mathrm{Sm}$, and $^{197}\mathrm{Au}$. Fission products were detected at 60\ifmmode^\circ\else\textdegree\fi{} and 320\ifmmode^\circ\else\textdegree\fi{} in coincidence with H and He at 120\ifmmode^\circ\else\textdegree\fi{} in plane and 27\ifmmode^\circ\else\textdegree\fi{} and 60\ifmmode^\circ\else\textdegree\fi{} out of plane. The coincidence energy spectra of H and He are not consistent with evaporation from the moving fragments. An analysis has been made with the assumption of complete energy equilibration in the particle emission (i.e., evaporation) prior to scission. The rather large data set is essentially consistent with this assumption. From the spectral shapes one can deduce level density parameters and barriers to evaporation. Values inferred for the Fermi gas level density parameters are similar to those inferred from experiments at much lower energies. Values deduced for the emission barriers are much smaller than those from systematics of fusion barriers. The observed cross sections for fission and $^{1}\mathrm{H}$ and $^{4}\mathrm{He}$ evaporation are not easily reconciled with statistical model calculations. In particular, the proton evaporation seems to compete more favorably with fission and $^{4}\mathrm{He}$ evaporation than implied by phase space considerations alone.NUCLEAR REACTIONS $^{116}\mathrm{Sn}$, $^{154}\mathrm{Sm}$, $^{197}\mathrm{Au}$($^{40}\mathrm{Ar}$; H/He, fission), $E=333$ MeV, measured energy and angular correlations of evaporative H/He in coincidence with fission. Values deduced for emission barriers, temperatures and ${J}_{\mathrm{rms}}$ for the emitter. Comparisons made to evaporation calculations.

Analysis of evaporation spectra from the reactions 64, 66, 68Zn(p, α) induced by 15 MeV protons

The spectra of emitted α-particles resulting from the reactions 64, 66, 68Zn(p, α) 61, 63, 65Cu at 15 MeV bombarding energy were measured at angles between 30° and 150°. The results are analyzed in the frame of the equilibrium and preequilibrium compound nucleus models. Back-shifted Fermi gas level density parameters for the relevant residual nuclei are deduced.

Shell model level densities in evaporation calculations

The energy and spin dependence of nuclear level densities are calculated from realistic shell model potentials in the saddle point approximation. Effective Fermi gas level density parameters are extracted and their behaviour as a function of nucleon number, excitation energy and angular momentum is examined. Evaporation residue distributions following heavy ion induced fusion reactions leading to compound nuclei near doubly magic 56Ni are predicted from Hauser-Feshbach theory with the shell model level densities. Good agreement with experimental residue cross sections is obtained, provided nuclear deformation is included.

Inelastic Scattering of 14MeV Neutrons by Heavy Nuclei

Energy spectra of neutrons scattered inelastically from natural samples of Ta, W, Au, Hg, TI, Pb and Bi have been studied at an incident energy of 14MeV, using time-of-flight technique. Angular distributions were also measured for Ta and Bi. The energy spectra from 2MeV to 4MeV were found to be qualitatively consistent with the prediction from statistical theory taking account of effects of nuclear pairing and shell structure. The Fermi gas level density parameter and the nuclear temperature were obtained by considering the contribution of the (n,2n) reaction. The variation of level density parameter plotted against mass number was found to agree with the trend predicted theoretically by Newton. Angular distributions proved to be symmetric about 90° and the spin cut-off parameter was estimated to be about 5.8 for Ta and 4.3 for Bi. Cross sections for the (n,n′2n) and (n,2n) reactions were obtained.

Level densities from spectra of different reactions populating the same nucleus

Level densities of 56Fe, 59Co, 60Mi, 62Ni, 63Cu and 65Cu are determined from analyses of several charged-particle spectra populating the same residual nucleus. Experimental spectra are reported for the following reactions: 56Fe(α, α′) 56Fe, 59Co(p, α) 56Fe, 59Co(p, p′) 59Co, 59Co (α, α′) 59Co, 56Fe(α, p) 59Co, 62Ni(p, α) 59Co, 60Ni(α, α′) 60Ni, 63Cu(p, α) 60Ni, 62Ni(p, p′) 62Ni, 62Ni(α, α′) 62Ni, 59Co(α, p) 62Ni, 65Cu(p, α) 62Ni, 63Cu(p, p′) 63Cu, 63Cu(α, α′) 63Cu, 60Ni(α, p) 63Cu, 65Cu(p, p′) 65Cu, 65Cu(α, α′) 65Cu and 62Ni(α, p) 65Cu. Each of these experimental spectra is analyzed with an exact theory giving the angular and energy-dependent differential cross sections for compound-nucleus reactions including explicitly the angular momentum. From these analyses we have determined the Fermi-gas level density parameters: 56Fe, a = 5.7 MeV −1, Δ = 0.7 MeV; 59 Co, a = 6.2 MeV −1, Δ = − 0.8 MeV; 60 Ni, a = 6.4 MeV −1, Δ = 1.3 MeV; 62 Ni, a = 6.4 MeV −1, Δ = 0.5 MeV; 63 Cu, a = 6.8 MeV −1, Δ = − 0.5 MeV; and 65 Cu, a = 6.6 MeV −1 and Δ = − 0.5 MeV . All of the spectra were also analyzed with the conventional slope technique which utilizes the Weisskopf expression for the differential cross sections. The results from such an analysis depend on the form of the pre-exponential term in the level-density formula and may give sizeable errors in the Fermi-gas level-density parameter a. A number of theoretical spectra are computed with the exact theory which explicitly includes angular momentum and these spectra are analyzed with the conventional methods to illustrate the errors introduced when angular momentum is not treated properly for such reactions. An estimate of precompound proton emission is made for several (p, p') reactions.

Helium-Ion-Induced Fission of Bi, Pb, Tl, and Au

The fission cross sections have been measured with solid-state detectors for helium-ion-induced fission of bismuth, lead-206, thallium, and gold. The measurements were made at several helium-ion projectile energies between 30 and 43 Mev. The fission cross sections of bismuth, lead-206, thallium, and gold with 42.8-Mev helium ions are 7.3, 1.8, 0.65, and 0.28 mb, respectively, and the cross sections decrease rapidly with reduced-energy projectiles. The competition between fission and neutron emission as a function of excitation energy is compared with theoretical predictions of $\frac{{\ensuremath{\Gamma}}_{f}}{{\ensuremath{\Gamma}}_{n}}$ and some comments are made on the effect of nuclear deformation on the Fermi gas level density parameter $a$. Fission thresholds for ${\mathrm{At}}^{213}$, ${\mathrm{Po}}^{210}$, ${\mathrm{Bi}}^{207,209}$, and ${\mathrm{Tl}}^{201}$ of 15.8\ifmmode\pm\else\textpm\fi{}2.0, 18.6\ifmmode\pm\else\textpm\fi{}2.0, 20.6\ifmmode\pm\else\textpm\fi{}2.0, and 19.9\ifmmode\pm\else\textpm\fi{}2.0 Mev are derived. The saddlepoint masses of these nuclei relative to Cameron's reference mass surface lie on a smooth curve with the heavy element data, indicating that the shell structure is completely destroyed during the distortion from equilibrium to saddle-point deformation. An empirical equation for fission thresholds is deduced from the saddle-point mass surface which is thought to be valid for nuclei with $\frac{{Z}^{2}}{A}$ between 32 and 40.