Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

New perspectives on the level density of compound resonances

The level density of compound resonances observed at neutron separation energy is subject of closer investigation and interpretation. The structures in the level density parameter as a function of the mass number allow the determination of the hierarchy of the compound states and the definition of a base line which represents the level density parameter of spherical nuclei with no residual interaction and no shell effects. Using the base line a method becomes available enabling the separation of the residual interaction from properties of the average potential defined in the framework of the shell model. The following examples in different mass regions are discussed: the change of the pairing energy due to the blocking effect atA ≈ 70; the breakdown of the pairing correlation atA ≈ 105 is interpreted as neutron-proton interaction; similar effects in the mass region 150<A<170 are discussed with neutron-proton interaction and the backbending phenomen. Finally it will be shown that there is no enhancement of states due to collective properties of nuclei at high excitation energy.     

The beta-decay of95Rb and97Rb

In this paper the spectra ofα particles emitted in (p, α) reactions induced by ～24 MeV protons on adjacent target nuclei, onemagic, with a magic neutron or proton shell and the othernear magic, with one more nucleon outside the shell, are measured and compared. The nuclei investigated are^{90, 91}Zr,¹²²Sn,¹²³Sb,^{142, 143, 144}Nd,²⁰⁸Pb and²⁰⁹Bi. The weak population of low energy levels of the residual nucleus from thenear magic target nucleus and the excitation of homologous states in the residual nuclei from neighbouringmagic andnear magic target nuclei convincingly prove that in most of the cases the unpaired nucleon outside the magic shell acts as a spectator in the process. The implications of these experimental findings are discussed.     

Competition of isoscalar and isovector proton-neutron pairing in nuclei

We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus ⁴⁶V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in ⁴⁶V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

A PSDPF interaction to describe the 1 ?ω intruder states in sd shell nuclei

In the level schemes of sd shell nuclei, there is generally at relatively low excitation energies, coexistence of normal 0 ?ω positive parity states and of intruder 1 ?ω negative parity states. The aim of the present work is to describe these intruder states in the full p-sd-pf model space with a ⁴He core allowing one nucleon jump between the major shells. To construct our PSDPF interaction, we first modified the p-sd and sd-pf cross-monopole terms and then applied a fitting procedure to adjust all PSDPF parameters by comparing an extended set of experimental and calculated excitation energies. Results obtained with the new interaction have been finally compared with experimental data for nuclei throughout the sd shell.     

A shell-model description of 0+ intruder states in even-even nuclei

Starting from the nuclear shell structure in medium-heavy and heavy nuclei, the excitation energy for low-lying 0⁺ intruder states is studied. Taking as a simplified model two particle-two hole (2p-2h) excitations across closed shells, the effects of the pairing and the proton-neutron (monopole and quadrupole component) residual interaction on the unperturbed energies are calculated. Application to major closed-shell (fZ = 50, Z = 82) and to subshell (Z = 40, Z = 64) regions is performed. We especially concentrate on 0⁺ intruder states in the even-even Pb nuclei.     

A study of the influence of shell effects in nuclear level densities on the decay of the compound nucleus58Ni

Mass andZ-distributions of fusion products from the reaction 5.8 MeV/u⁴⁶Ti+¹²C were measured in the angular range betweenθ _lab=1.5° and 8° using a time-of-flightΔE?E telescope. The results are compared with an earlier measurement of the reaction³² S+²⁶Mg, in which the same compound nucleus was produced at higher excitation energy. The residual nuclide distributions are interpreted with the aid of evaporation calculations and the influence of shell effects in the level densities is discussed. The data are consistent with the assumption that the shell effects vanish above 15 to 20 MeV excitation energy, that is, that they are essentially only important for the last evaporation step.     

Monolayer K-films on Ni(100) — II. Electronic excitations

Electronic excitations in a K layer adsorbed on Ni(100) have been observed by means of electron energy loss spectroscopy. The observed excitation energy depends on the density of K atoms in the layer. In the low density range the loss energy decreases from 3.5 to 1.5 eV as the density increases from 6.10¹³ to 3.10¹⁴ K atoms per cm². This loss is interpreted to be due to an excitation from below the Fermi level to the shifted K valence level Increasing the density further from 3.10¹⁴ to 6.10¹⁴ K atoms per cm² yields a loss peak that increases in energy from 1.5 to 2.3 eV. This loss peak merges into the surface-bulk plasmon complex for a thick K film and the energy vs density dependence is compatible with a plasmon excitation in the K layer.     

Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250

The parameters a and Δ for the Fermi gas model with fictive ground state are determined for about 220 nuclei from experimental level densities at low excitation energy and at the neutron binding energy. In. agreement with previous results it is found that for most nuclei the fictive ground state is back-shifted relative to the conventionally shifted ground state as determined by the pairing energy. Shell effects are evident at the mass numbers 90, 140 and 208 for both the level density parameter a and the back-shift. A comparison is given with previous results and different experimental data on level densities.     

Generalization of the Independent Pair Model to degenerate nuclear states

The equations of the Independent Pair Model for finite nuclei are generalized to nuclear states non describable by a single shell model configuration. As an application of these generalized equations to excited states, the energy of the excitedT=0,J ^π=0⁺ -state of⁴He has been calculated by an approximate solution. Using a spin-averaged square well potential with hard core and Serber exchange character, with all parameters beeing determined from two-nucleon data, the calculation yields an excitation energy of 21.58 MeV compared to the experimental value of about 20.1 MeV.     

Virtual excitation of the GDR mode in the subbarrier23Na(p, γ)24Mg reaction

Differential cross sections for nonresonant radiative capture of low energy protons (E _p = 1,348 keV and 1,370 keV) by²³Na nuclei exhibit features pointing to the virtual excitation of the giant dipole resonance (GDR) mode. Theoretical analysis carried out within the framework of the direct — semidirect capture model reveals an enhanced coupling of the GDR with the incident protonf-wave consistent with the microscopic structure of the GDR in thes-d shell nuclei.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

Experimental investigations of the nuclear level density by using heavy ion reactions

The transition of the level density parameter a _off from the low excitation energy value a _off=A/8 MeV⁻¹ to the Fermi gas value a _FG ∼ A/15 MeV⁻¹ was discovered a few years ago studying particle spectra evaporated from hot compound systems of A∼ 160. A number of experiments have been recently performed to confirm the earlier findings and extend the investigation to other mass regions and to higher excitation energies. Furthermore, precision coincidence experiments have been done in the lead region in which evaporation residues are tagged by low energy gammarays. Those experiments open the possibility of a detailed study of the level densities in nuclei where the shell effects are important.     

The structure of27Al

Gamma decay modes and spin assignments of levels in²⁷Al have been investigated by proton-γ-ray angular correlation measurements in the²⁴Mg(α, pγ) reaction at 14.2, 15 and 15.6 MeV bombarding energy and byγ-ray angular distribution measurements on the E_p=1820, 2114, 2293 and 2574 keV resonances of the²⁶Mg(p, γ) reaction. Unique spin assignments were obtained as follows: I=3/2 for the 5827 keV state, I=5/2 for the 6115, 6465, 6765, 7577, 7721, 8097, 8136, 8324 keV states, I=7/2 for the 5433, 6533, 7413, 8037, 8442, 8586 keV states, I=9/2 for the 5418, 6512, 6713, 7997 keV states, I=11/2 for the 5500, 6948, 7400, 8396 keV states. The level scheme and electromagnetic properties of levels are compared with the results of shell model calculations which use the complete configuration space of the 0d_5/2-1s_1/2-0d_3/2 shell and the unifieds-d shell Hamiltonian. The agreement is good to excellent and extends into the region of high level density above 7 MeV excitation energy. The total B(M1↑) below 8.5 MeV excitation energy is evaluated, using published resonance fluorescence and (e, e′) data, and quenching relative to the free-nucleon predictions is reexamined. Evidence in favour of a prolate ground state deformation of²⁷Al and implications of this work for the astrophysically interesting²⁶Al(p, γ) reaction are discussed.     

Lifetime measurements on the compound nucleus 236U by means of the shadow effect

The lifetime of the ²³⁶U nucleus is measured in the range of excitation energies E_x = 6.7–11.5 MeV by a method based on the shadow (blocking) effect. The results obtained, as well as those of an earlier measurement of the lifetime for the ²³⁹U nucleus in the range E_x = 6.4–9.1 MeV, are compared with the results of calculations based on the level density ρ(E_x) in the Fermi-gas model and on the empirical level density ρ(E)_x) calculated as a result of an analysis of(n, γ) and (n, n') cross sections. An increase of excitation energy produces a substantial reduction in the rate of decrease of the lifetime at E_x ? 7.5 MeV for both compound nuclei as compared to the theoretical dependence τ(e_x).