Collective gyromagnetic ratio and moment of inertia from density-dependent Hartree-Fock calculations

The collective gyromagnetic ratio and moment of inertia of deformed even-even axially symmetric nuclei are calculated in the cranking approximation using wave functions obtained with the Skyrme force S-III. Good agreement is found for g_R, while the moment of inertia is about 20 % too small. The cranking formula leads to better agreement than the projection method.     

Elastic scattering of protons and neutrons on 40Ca by the density-dependent Hartree-Fock field

We use the self-consistent density-dependent Hartree-Fock field as the real part of the optical model potential. Introducing a phenomenological imaginary potential, we describe elastic scattering of protons and neutrons on ⁴⁰Ca at several incident energies. Results show that the density-dependent Hartree-Fock field, including the rearrangement potential, well reproduces differential cross sections and polarizations simultaneously. This calculation explicitly shows a unified way to understand the ground-state properties and the scattering problem. Detailed study is given the properties of the non-local Hartree-Fock field, via the WKB equivalent local potential.     

Pion-nucleus interaction and the range of πN forces

We examine several definitions for the ranges r_πN of the pion-nucleon (πN) forces and conclude that 0.25 ≦ r_πN ≦ 0.5 fm. We investigate two consequences of the finite range of the p-wave πN interaction: the additional spatial extension of the p-wave π-nucleus optical potential and the quenching of the Lorentz-Lorenz effect. For 0.25 ≦ r_πN ≦ 0.5 fm (i) the additional extension of the p-wave optical potential gives negligible contributions to shifts and widths in π-mesic atoms and (ii) the Lorentz-Lorenz effect is largely quenched making nuclear correlations hard to detect by mesic atoms measurements.     

Nuclear field theory

By using path integral techniques nuclear field theory (NFT) is developed for Fermi systems interacting via a general two-body force. The NFT Lagrangian is strictly derived. As a by-product, the corresponding graphical rules are obtained. The relation between the NFT and the conventional Feynman diagrammatic many-body perturbation theory is established for processes connecting initial and final states, too.     

Nuclear reactions between oxygen isotopes

Elastic and inelastic cross sections have been measured for the system ¹⁶O + ¹⁷O at c.m. energies from 12.5 to 15.5 MeV, and for ¹⁶O + ¹⁸O at c.m. energies from 12 to 20 MeV, at angles between 60° and 125°. Position-sensitive detectors were employed, using the kinematic coincidence technique. The data have been analyzed with particular attention to the contributions of multiple-exchange processes.     

Nuclear levels in 238Np

Low and high energy spectra from thermal neutron capture in ²³⁷Np have been studied over the energy ranges 25 to 650 keV and 2600 to 5500 keV. Primary transitions from neutron capture in four resonances have been observed between about 4800 and 5400 keV. Using 12 MeV deuterons, (d, p) spectra at three angles have been observed with a magnetic spectrograph. A nuclear level scheme for ²³⁸Np has been constructed by combining the results of the above measurements with previous data from a study of the ^242mAm α-decay. The Nilsson model has been used to interpret the level structure. Including results from the previous α-decay study, nine rotational bands can be assigned. The Nilsson configurations (K^π [Nn₃ΛΣ]) and band-head energies are: 2⁺π[642↑]?ν[631↓], 0.0 keV; 3⁺π[642↑]+ν[631↓], 86.6 keV; 3^?π[523↓]+ν[631↓], 136.0 keV; 2^?π[523↓]?ν[631↓], 182.8 keV; 5⁺π[642↑]+ν[622↑], 278.1 keV; 0⁺π[642↑]?ν[622↑], 332.5 keV; 5^?π[523↓]+ν[622↑], 342.6 keV; 0^?π[523↓]?ν[622↑], 286.0 keV; 6^?π[642↑]+ν[743↑], 301 keV. The measured (d, p) reaction cross sections are compared with theoretical calculations based on these assignments. The Gallagher-Moszkowski rule is found to be valid in the four cases where we have observed both parallel and antiparallel coupled bands with $\text{K}{}^{\mathrm{+}}\text{= Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{+Ω}{}_{\mathrm{<mtext>n</mtext>}}$ and $\text{K}{}^{\mathrm{?}}\text{= |Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{?Ω}{}_{\mathrm{<mtext>p</mtext>}}\text{|}$. The lowest levels of the two K = 0 bands have spin I = 1; Newby odd-even shifts can be determined in both cases.     

Boson representation of the antisymmetrizer and many-body forces in the microscopic IBM

In this paper, an exact boson representation for the anti-symmetrizer has been derived. With its aid, the Schrödinger equation for a fermion system can be written down in the boson representation. The effect of the antisymmetrization is expressed by different kinds of many-body forces among the bosons. The relative importance of these forces has been estimated.     

Nuclear level densities with collective rotations included

The level density is calculated from the single particle energies in a Woods-Saxon potential with pairing included in the BCS approximation. The collective rotations are included by addition of a rotational band on top of each of the intrinsic levels. The nuclei investigated have mass numbers in the region 100 ≦ A ≦ 253. At the ground state deformation and at the neutron separation energy for the nucleus in question we compare calculated and observed level densities. The dependence on the parameters in the model are investigated. Considering the uncertainties in these parameters the calculated results are believed accurate to within a factor of 3. The rotations contribute typically a factor of 40. They must be included for deformed and not for spherical nuclei. We underestimate systematically the level density by a factor of 4 with fluctuations around the average value by a factor of 3. The nuclei lighter than ¹³⁸Ba are an exception. We obtain around a factor 100 too few levels in the calculation.     

Nuclear and Coulomb deformation parameters of 142Nd

Nuclear and Coulomb deformation parameters have been deduced from DWBA analyses of angular distributions of 67.5 MeV ¹³C ions inelastically scattered from ¹⁴²Nd. Optical model parameters from fits of measured elastic scattering data were used with previously measured B(EL) values to determine initial deformation parameters. Comparison With the experimental data indicates that DWBA calculations can be used to understand the inelastic scattering from the nearly spherical nucleus ¹⁴²Nd.     

Nuclear polarization and signs of quadrupole moments of high-spin Gd isomers

Time-differential perturbed-angular-distribution (TDPAD) experiments have been performed on polarized intermediate- and high-spin isomers ${}^{144}\text{Gd}\text{(10}{}^{\mathrm{+}}\text{)}\text{and}{}^{147}\text{Gd}\text{(}\text{13}\text{2}{}^{\mathrm{+}}\text{,}\text{27}\text{2}{}^{\mathrm{?}}\text{,}\text{49}\text{2}{}^{\mathrm{+}}\text{)}$. Excited Gd nuclei populated by $\text{(}{}^{28}\text{Si}\text{, x}\text{n}\text{)}$ reactions were polarized by the tilted-multifoil technique and implanted in a Gd single-crystal host. Observation of the subsequent electric quadrupole interaction with the known electric field gradient yielded negative values of the sign of the deformation for all isomers studied. The magnitude of the induced nuclear polarization P_I was also determined from the TDPAD data and compared to model calculations in order to deduce the average atomic angular momentum and polarization of Gd ions at v/c ～ 0.018.     

Nuclear structure effects in sub-barrier fusion cross sections

The total fusion cross sections around and down to ≈ 12 MeV below the Coulomb barrier in the c.m. system have been measured with the Munich heavy-ion recoil spectrometer for 30 projectile-target combinations: ^{32, 36}S + ^{92, 94, 96, 98, 100}Mo, ^{100, 101, 102, 104}Ru, ¹⁰³Rh, ^{104, 105, 106, 108, 110}Pd, The excitation functions can be reproduced with a one-dimensional barrier penetration model by increasing the nuclear radii by $\text{ΔR ? 0.255 ± 0.035}\text{fm}$ and introducing a gaussian distribution of the nuclear radius R with a standard deviation σ_fit(R). The σ_fit(R) can be explained as being due to quadrupole vibrational fluctuations of the surface-to-surface distance at the barrier and to two-neutron-transfer reactions with positive Q-values.     

Nuclear structure studies of high-spin states in 79Rb and 79Kr

Fluorine and carbon induced fusion-evaporation reactions were used to excite high-spin states in ⁷⁹Rb and ⁷⁹Kr. The level scheme of ⁷⁹Rb was established on the basis of neutron multiplicity measurements, γγ coincidence data and excitation functions. From recoil distance and Doppler shift attenuation lifetime measurements, E2 strengths of the positive-parity yrast states in ${}^{79}\text{Kr}\text{(}\text{up to}\text{I}{}^{\mathrm{\pi }}\text{=}\text{21}\text{2}{}^{\mathrm{+}}$) and the favored and unfavored states in ${}^{79}\text{Rb}\text{(}\text{up to}\text{I}{}^{\mathrm{\pi }}\text{=}\text{25}\text{2}{}^{\mathrm{+}}$) were derived. An interpretation of these data in terms of the asymmetric rotor-plus-particle model and the interacting boson fermion model (with or without separate proton and neutron bosons) is proposed. Energies and lifetimes of a second stretched band in ⁷⁹Rb (probably with negative parity) were also measured.     

Nuclear structure of 18F: (IV). Negative-parity states

Studies via the ¹⁶O(³He, pγ)¹⁸F, ¹⁴N(α,γ)¹⁸F and ¹⁷O(p, γ)¹⁸F reactions have resulted in new J^π assignments for 11 states or negative parity: E_x(keV) (J^π) = 3791(3^?), 4226(2^(?)), 4398(4^?), 4860(1^(?)), 5502(3^(?)), 5785(2^?), 6097(4^?), 6108(1^(?), 2^(?), 3^(?)), 6241(3^?, T = 1), 6643(2^?, T = 1) and 6878(3^(t-), 4^?). The 6241 keV state is probably isospin mixed. New information for 5 states of positive parity has also been obtained: E_x(keV) (J^π) = 3838(2⁺), 4115(3⁺), 4652(4⁺, T = 1), 4753((0⁺), T = 1) and 4964(2⁺, T = 1). Mean lives, branching and mixing ratios are reported for all states. The results for the negative-parity states are discussed in the framework of the various models available. The states at E_x = 1080(0^?), 2100(2^?) and 4398(4^?) keV are interpreted as the first three members of a K^π = 0^? rotational band.     

Nucleon-nucleus optical model potential: (1). Nuclear matter approach

We present a new method for the approximate solution of the Bethe-Goldstone equation when it has a singular kernel. The method reduces the integral equation to a set of coupled differential equations which are easily solved. In the special case of binding energy calculations, non-singular kernel, our method is equivalent to the reference spectrum method. A particular advantage is that there is no ambiguity in the treatment of hard-core N-N interactions. We perform calculations both for the Hamada-Johnston and Reid hard-core internucleon potentials and in intermediate states always use self-consistent single-particle energies. We apply the method to calculate in nuclear matter the binding energy/nucleon and the nucleon optical potential. Our results for the binding energy differ by about 2 MeV from those published for similar calculations. The difference is a consequence of our use of self-consistent energies and a greater number of partial waves, L ≦ 4. For the optical potential we obtain a logarithmic variation with incident energy E for E > 100 MeV, in agreement with experimental data. We also obtain better agreement with experiment than other authors for the energy variation in the the range 40 MeV < E < 100 MeV. This improvement is a consequence of our use of a higher number of partial waves.     

Nuclear structure effects in the feeding of yrast states of Gd,Dy and Er nuclei

The population of the yrast and near-yrast levels in Gd, Dy and Er nuclei has been investigated experimentally in (heavy ion, xn) reactions through high-resolution γ-ray intensity measurements. A clear difference between non-rotor (N ? 86) and rotor nuclei (N > 86) is evident from the data. For the non-rotor nuclei we define the spin value I_sat below which the yrast population saturates. One finds that I_sat is independent of the bombarding energy when the latter becomes sufficiently high. We discuss the feeding pattern in relation to the single-particle structure of the yrast and near-yrast levels and in relation to the effect of shape changes, including the possibility of superdeformed shapes at high spin.     

Nuclear level widths in 113Sb from particle-X-ray coincidences

The particle-X-ray coincidence method is applied in (p, p₀) and (p, p′) reactions on ¹¹² Sn at 7.138, 10 and 12 MeV proton energy to measure the width of compound nuclear states in ¹¹³Sb. The united-atom K X-ray intensities observed in coincidence with inelastic proton scattering (35⁺⁷⁸_?35, 80 ± 50 and 250 ± 80 counts at the respective energies) yield mean level widths for ¹¹³Sb of ?3.9 eV, 16.6 ± 15.1 eV, and 19.1 ± 11.1 eV at the excitation energies 10.1, 13 and 15 MeV, respectively. From X-ray coincidences with elastic proton scattering, upper limits for the compound elastic component are derived. No united-atom X-rays were detected in short runs at 7 MeV on ⁹²Mo and ¹⁰⁶Cd. A comparison of nuclear state widths from X-ray method, crystal blocking technique and fluctuation averaging is given.     

Elastic scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.     

Nuclear shapes of the transitional nuclei 186, 188, 190, 192Os

Excitation functions at θ_lab = 130° have been measured for inelastic scattering of 13–24 MeV alpha particles from ^{186,188,190,192}Os. Data have been obtained for 0⁺, 2⁺, 4⁺, 2⁺' states in ^186,188,192Os and for 0⁺, 2⁺ states in ¹⁹⁰Os. Charge and mass quadrupole deformations, β₂^c and β₂^N, were deduced from coupled-channels analysis of the 2⁺ data. No simple model could provide good fits to the 4⁺ data over the entire energy range but the very deep interference minima observed establish the charge and mass hexadecapole moments, β₄^c and β₄^N, to be negative. The energies of the interference minima for the 4⁺ states could be reproduced by coupled-channels calculations only if large differences in β₄^c and β₄^N were allowed. Data for the (J, K)^π = (2, 2)⁺ states are inconsistent with an asymmetric rotational model.     

Nuclear reaction cross sections of 16O + 16O obtained by γ-ray detection

The partial production cross sections for reaction residues produced by the fusion of ¹⁶O with ¹⁶O have been measured at E_c.m = 9–30 MeV by detecting the characteristic γ-rays with a Ge(Li) detector. The dominant products are ²⁴Mg and ²⁷A1 corresponding to 2α and αp emission from the compound nucleus, respectively. The total γ-producing cross sections σ_R were also derived by summing the partial cross sections after correction for the observed (average) γ-ray angular distributions. The trend in the total cross sections is very similar to the trends derived from an optical model or a statistical-evaporation model calculation. The partial production cross sections were compared with other experimental results at 11.9 MeV and 30 MeV and with the results of the statistical-model calculation. It is concluded that the treatment of angular momentum in the calculation is inadequate for describing the partial cross sections. Structure in the partial and total cross section excitation functions is observed with minima occurring at E_c.m. = 27, 24, 20, 17.5, and possibly 15 MeV. Some of this structure is well established by the statistical accuracy of the data and most, but perhaps not all of it, is correlated in the various channels. This structure is compared with that observed in another experiment and some of its implications are discussed.     

Nuclear deformations from inelastic α-scattering on rare earth nuclei at energies near the Coulomb barrier

Alpha particles in the energy range of 10–20 MeV and scattered at various angles were used to excite the 0⁺, 2⁺, 4⁺ members in the ground state bands of ¹⁵²Sm, ¹⁵⁴Sm and ¹⁸⁶W. The measured excitation probabilities for bombarding energies below the Coulomb barrier were analyzed in the framework of Coulomb excitation theory. The resulting matrix elements of the E2 and E4 multipole operators were interpreted in terms of charge deformation parameters β^cλ = 2, 4. The cross sections for higher energies were analyzed in terms of the deformed optical potential and resulted in potential deformation parameters β^pλ = 2, 4. The two sets of deformation parameters show the same general trend of variation with target mass number. Still, significant differences are observed in some particular cases.