Comparison of neutron resonance spacings with microscopic theory for spherical nuclei

The nuclear level spacings determined from neutron resonance experiments for nuclei with 20 ≦ A ≦ 148 and 181 ≦ A ≦ 209 are compared with spacings calculated for spherical nuclei with a microscopic theory which includes the nuclear pairing interaction. Single particle levels of Seeger et al. and Nilsson et al. are used in the calculations. The gross features of the experimental data due to nuclear shells are reproduced with the microscopic theory. In addition, the absolute agreement between experiment and theory is reasonable (67 % of the 151 cases examined agree to within a factor of 2) in view of uncertainties in the experimental data, the theoretical single particle levels and the pairing strength. Values of the spin cutoff parameter σ²(E), calculated with a microscopic theory, are included also for several doubly even nuclei and discussed in terms of nuclear shells.     

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.     

Second Coulomb energy differences of isospin triplets in the 2s-1d shell

Second Coulomb energy differences, which in the present case are proportional to the tensor Coulomb energy, are calculated for 0⁺, T = 1 ground states in the region 18 ≦ A ≦ 42 using a shell model that includes a pairing interaction. The calculation is done with a mathematical formalism that includes p-n pairs as well as p-p and n-n pairs. Besides an enhancement of proton-pair Coulomb energies, the pairing interaction is responsible for lowering the Coulomb energy of N = Z members of isospin triplets and also gives rise to an important term in the second energy difference. Using pairing strengths derived from fitting energy levels for mass-18 and mass-42 nuclei, results of the calculation reproduce experimental second energy differences extremely well.     

Quasiparticle spectra near the yrast line

The yrast spectra of the nuclides 68 ≦ Z ≦ 70, 89 ≦ N ≦ 99 are analysed in terms of quasiparticle configurations in a deformed field rotating with the frequency ω. The excitation energy, e', in the rotating frame (Routhian) and the aligned angular momentum, i, relative to the ground state band as functions of ω are extracted from the experimental rotational bands which are classified with respect to their signature, α, and parity, π. These experimental quantities are compared with the ones calculated from the quasiparticle level diagrams. Phenomena like backbending and the occurrence of aligned bands in both even-even and odd-mass nuclei and their mutual relationship are interpreted in terms of quasiparticle configurations that may cross each other with increasing frequency.     

Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of ^296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.     

Investigations with two-neutron transfer reactions on the even isotopes of samarium

The (p, t) reaction on the even isotopes of samarium has been investigated at a proton energy of 25.5 MeV. Angular distributions were obtained in the range 18° ≦ θ ≦ 148° with angular steps between 2° and 5°. The experimental energy resolution varied between 35 keV and 50 keV FWHM. Spin and parity assignments are performed by comparing the measured angular distributions to zero-range DWBA calculations. Some difficulties of DWBA calculations for (p, t) reactions are pointed out. The relative cross sections for transitions to different levels of the final nuclei are compared with other (p, t) and (t, p) measurements in the same region of the rare earth isotopes. The dependence of the (p, t) cross sections for different transitions on the neutron number of the final nuclei is discussed. Some 2⁺ states observed in (p, t) and (t, p) reactions are described in the quadrupole pairing vibrational picture.     

Alpha clusters in nuclei with 41 ≦ A ≦ 45

The effect of pairing and surface α-clustering structure was studied by means of a Hamiltonian with pairing and four-body interaction terms in a simple two-level model in odd nuclei with 41 ≦ A ≦ 45. It was shown that the dynamical α-structures can be induced by the pairing correlation alone, but with an unusually large value of the strength G of the pairing interaction. The addition of a small four-body interaction term allowed us to diminish the G-value to a physically reasonable one and, at the same time, to get meaningful α-clustering. The four-body term added to the Hamiltonian is a simplified way to improve, in this respect, the two-body pairing interaction (itself a simplified model interaction). For example, in the ground state of ⁴⁵Ti the “α-clusters” appeared with larger probability than that for separate nucleons, while in ⁴⁵Ca both probabilities are approximately equal. The calculated binding energy was also applied to reproduce the experimental difference of the masses of neighbouring nuclei. With the eigenstates of the Hamiltonian, schematic spectroscopic factors for two-nucleon transfer, α-transfer, and elastic scattering of α-particles were also calculated. Spectroscopic factors for the transitions from ground state to ground state and from ground state to excited state were then used to distinguish between superfluid or normal behaviour of these nuclei. In addition to the superfluidity induced by pairing forces, a superfluidity due to four-body correlations was also predicted.     

Average g-factors for high-spin states in 78Kr

Inverse reactions of ^{63, 65}Cu beams on ^{18, 16}O targets have been used to populate states of ⁷⁸Kr by fusion-evaporation reactions. The excited nuclei recoiled at high velocity v/c ≈ 7 % through a polarized iron (⁵⁴Fe) layer and were stopped in a copper layer. During the period in iron, 0.05–0.65 ps, the nuclei were subjected to the intense transient magnetic field (initially ～ 3500 T). The resulting precession of the high-spin nuclear states populated during this time was determined by measuring the time integral rotation angle of the discrete γ-ray transitions at low spin.The average g-factor at low spin 2 ≦ J ≦ 8 compared to that at higher spin 8 ≦ J ≦ 12 in ⁷⁸Kr was found to be identical within the experimental uncertainties of ～ 15 %. This result implies that either there are no rotational alignment effects at the backbend in ⁷⁸Kr or more plausibly, proton (g ≈ 1) and neutron (g ≈ 0) aligned bands are equally competitive and both populated in the reaction. It is then likely that the resulting g-factor represents an average over many populated proton and neutron aligned bands.     

An analysis of pion-nucleus scattering lengths within an α-cluster model

Pion-nucleus s-wave scattering lengths are calculated from a multiple scattering series in terms of the π-α scattering length. Agreement on the level of 10–20% with the values obtained from mesic-atom data is achieved for all nuclei with A ≦ 20. This lends weight to the speculation that pion absorption on light nuclei takes place primarily on α-particle substructures.     

Level density and radiative strength functions from (n th,2γ) reactions and basic properties of the 96Mo nucleus

Published data on the intensities of two-step cascades to 12 final-state levels of the ⁹⁶Mo nucleus are approximated by using a set of possible random dependences of the level density and radiative strength functions for primary E1 and M1 transitions. The average values of these parameters of gamma decay for any excitation energies and for gamma transitions agree well with basic dependences revealed to date from similar experiments for 42 nuclei in the mass-number range 40 ≤ A ≤ 200, but they are inconsistent with the generally accepted ideas of the parameters of the cascade gamma decay of compound states of nuclei having high level densities.     

Levels and transitions in 131Xe studied by the decay of oriented 131I

Sources of ¹³¹I were prepared by implantation in iron foils. Nuclear orientation of these sources was obtained by cooling them to temperatures of 30 to 50 mK using a dilution refrigerator and saturating the iron by an external magnetic field. Anisotropies of angular distributions of eleven γ-transitions in ¹³¹Xe have been measured, yielding the following results: the levels at 405 and 637 keV are $\text{3}\text{2}$⁽⁺⁾ and $\text{7}\text{2}$⁽⁺⁾ states and the assignment $\text{5}\text{2}$⁽⁺⁾ for the level a keV is confirmed. Deduced values of E2/M1 multipole mixing ratios are (energies in keV): ?0.5 ≦ δ(318) ≦ + 0.2; δ(364) = ?4.53±0.12; + 0.2 ≦ δ(405) ≦ +2.0; δ(723) = +0.207 ± 0.005. The allowed β-decay branch to the level at 637 keV is for at least 90% of the Gamow- Teller type.     

Systematics of nuclear level density parameters of nuclei deficient in one neutron

Photoneutron mean energies of 38 elements were measured as a function of peak bremsstrahlung energy for elements with 23 ≦ Z ≦ 83. Results are compared with neutron mean energies calculated from statistical theory, using for nuclear level densities modified Fermi gas formulae with and without pairing corrections and a constant temperature formula. Except near closed shells the Fermi gas formula with pairing corrections gives reasonable to good correlation between experimental and theoretical data. Derived values of the nuclear level density parameter a-except near Z = 82-are in quantitative agreement with those from recent neutron resonance data.     

Weak bands in the far-infrared spectrum of HCNO

Several weak transitions in the far-infrared spectrum of H¹²C¹⁴N¹⁶O between the (0000_v) levels with v = 2, 3, and 4 have been analyzed. Vibrational levels of improved accuracy have been calculated for both the (0000_v) series (v ≦ 5) and the (0001_v) series (v ≦ 3). For the latter, some inconsistencies in previous assignments have been removed. Two transitions from the (00020)² level have been assigned tentatively. The two lowest bands of the (0000_v) series of H¹³C¹⁴N¹⁶O have been found. Two new types of graphical plots have been used in the assignment.     

Nuclear level densities and level spacing distributions from 20F to 244Am

The parameters of nuclear level density formulae have been determined from extensive and complete level schemes and neutron resonance densities for 24 nuclei between ²⁰F and ²⁴⁴Am. The constant temperature level-density formula and the Bethe formula are compared with the experimental level densities. Both formulae reproduce experimental densities equally well. The same nuclei have been used to obtain an A-dependent spin cut-off parameter for low-lying levels. The spacing distribution of levels with equal spins and parities at lower excitation energies is found to be much closer to an exponential distribution than to the Wigner distribution especially for even-even nuclei. This is at variance with previous theoretical expectations and interpretations of nuclear data compilations. It gives evidence for a further good quantum number at low excitation energies in addition to spin and parity or for very different structures.     

An investigation of the odd-A rare-earth nuclei using rotational models

Using recently compiled data for band-head energies of 53 odd-A rare-earth nuclei, rotational models for strongly deformed nuclei have been used to determine the variation of deformations, spin-orbit parameter κ and the l² parameter, μ, in these nuclei. The deformation is found to be consistent with experimental deformations within 20 %. The spin-orbit parameter, κ, is found to vary from 0.037 up to 0.070, a 25 % variation from Nilsson's 0.050. The l² parameter μ is found to vary from 0.30 up to 0.71, a 30 % variation from Nilsson's 0.45. The trends observed in the values of spin-orbit strength C indicate a correlation with deformation, δ. Simultaneous shifts of the l² strength D for neutron numbers 95–97 and 101–103 may be interpreted as a sudden shift in the squareness of the potential well possibly caused by shell filling. Inclusion of hexadecapole deformation greatly improves the band-head energies for the mass region 150 ≦ A ≦ 165.     

The systematics of nuclear single-particle states (I). The region 35 ≦ A ≦ 65

The energies of single-particle states in nuclei with 35 ≦ A ≦ 65 are obtained as eigenvalues of a local Saxon-Woods potential with depth depending linearly on A and on the nuclear symmetry parameter.     

NMR and magnetic susceptibility study of rapidly quenched Ni100-XPX metallic glasses

In order to investigate the electronic structure of the rapidly quenched Ni_100-XP_X metallic glass system (18 ≦ x ≦ 22), NMR and magnetic susceptibility measurements have been carried out for temperatures 4.2 °K ≦ T ≦ 295 °K and magnetic fields H ≦ 20 kOe. The ³¹P Knight shift and relaxation rate behavior demonstrate a metalloid concentration dependence which is consistent with earlier work on the ternary NiPdP and NiPtP metallic glass systems. A consideration of the trends in the magnetic susceptibility indicates that, relative to the Fermi energy, the d-states associated with Ni are higher (the number of d-holes are greater) than those for Pd or Pt.     

6Li-α scattering below 3 MeV

Angular distributions for ⁶Li-α scattering at six α-particle energies between 1.39 and 2.98 MeV (lab) along with the excitation functions for two narrow resonances have been measured. A phaseshift analysis of the off-resonance angular distributions was made for l ≦ 3 with the higher phases fixed at values calculated for d-exchange. The l ≦ 3 phase-shifts are compared with those calculated for d-exchange and known wide resonances.     

Simple phenomenological model of neutron-resonance densities in 60<A<250 even-even compound nuclei

A simple relationship between the observed density of s-neutron resonances and the energy of the first 2⁺ excited level of even-even compound nuclei is established. The corresponding phenomenological parameters are determined from an analysis of data on stable initial nuclei and are compared with available experimental data on β-unstable nuclei.     

A study of the 18O(6Li,d)22Ne reaction at 32 MeV

Results from a study of the ¹⁸O(⁶Li, d)²²Ne reaction at a ⁶Li energy of 32 MeV are reported. The L-dependence of the shapes of the measured angular distributions provide a check on recent J^π assignments for some of the high-lying levels in ²²Ne. A finite range distorted wave analysis assuming a direct cluster transfer has been used to extract from the data α-particle spectroscopic strengths for most of the natural parity levels populated below 8 MeV of excitation. These strengths are compared with theoretical predictions for those few states for which a definite correspondence can be made between the calculated and experimental levels of ²²Ne. For transitions to the members of the ground-state band, the observed strengths disagree with the predictions. This disagreement has also been observed in the ¹⁶O(⁶Li, d) reaction and its cause is not understood. It is in marked contrast with the good agreement found for (⁶Li, d) reactions on targets of mass 20 ≦ A ≦ 24.