Effect of Nucleon Pairing in the Spectra of <Emphasis Type="Italic">N</Emphasis> = 50 Isotones

The emergence of the pairing effect of identical nucleons in the j = 9/2 state in low-lying excited states of nuclei near ⁹⁰Zr (N = 50, Z = 40) is discussed. Multiplets of states with seniority s ≥ 2, the splitting of which is determined by the proton pairing energy, are clearly visible in the nuclear spectra for a chain of N = 50 isotones. A comparison of the spectra of ground state multiplets, calculated in the δ-interaction approximation, with experimental data and results from other theoretical calculations shows this approach can be used to describe the structure of spectra and level positions with high J values.     

Level-density parameters in the back-shifted Fermi gas model

The parameters a and δ_eff appearing in the back-shifted Fermi gas model are determined for about 3000 nuclei on the basis of modern estimated experimental data and the proposed systematics. For 272 of these nuclei, the parameters are deduced from experimental data on the cumulative numbers of low-lying levels and on mean spacings between S-wave neutron resonances at the neutron binding energy in the nuclei. For 952 nuclei, the parameter δ_eff is calculated by using the cumulative numbers of low-lying levels and values of the parameter a that were obtained via an interpolation from the points corresponding to the aforementioned 272 nuclei. For the remaining nuclei, the parameters a and δ_eff are obtained on the basis of the proposed systematics. An expression is constructed for taking into account the damping of shell effects with increasing excitation energy of nuclei. The results are compared with those from other studies.     

Neutron transition densities for the 2<Superscript> + </Superscript>-8<Superscript> + </Superscript> multiplet of states in <Superscript>90</Superscript>Zr

Neutron transition densities for the 2 ⁺ -8 ⁺ levels in ⁹⁰Zr were extracted in the process of analyzing scattering at 400 MeV. They were compared with the calculated neutron transition densities and with the experimental proton transition densities. Radial distributions of the experimental neutron and proton transition densities for each state were found to be different.Received: 9 January 2004, Revised: 4 April 2004, Published online: 14 September 2004PACS: 25.40.Ep Inelastic proton scattering - 21.10.-k Properties of nuclei; nuclear energy levels     

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.     

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.     

Precise model approximation of JINR (Dubna) data on nuclear level densities in the region 40 ≤ <Emphasis Type="Italic">A</Emphasis> ≤ 200 below <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The experimental nuclear level density below the neutron binding energy B _n in the mass region 40 ≤ A ≤ 200 is approximated to a high precision on the basis of the Strutinsky model combined with the assumption that the coefficient of collective enhancement of the level density for a given number of excited quasiparticles decreases exponentially with increasing excitation energy. This combination of model concepts makes it possible to reproduce faithfully not only the general trend revealed by the method developed at the Joint Institute for Nuclear Research (JINR, Dubna) in the change in the level density with increasing excitation energy in any nuclei but also the fine structure of this level density. Realistic experimental information about the change in the relationship between the densities of quasiparticle- and vibrational-type states was obtained for the first time for any nuclei virtually up to the neutron binding energy B _n .     

Search for solar axions emitted in an <Emphasis Type="Italic">M</Emphasis>1 transition in <Superscript>7</Superscript>Li* nuclei

The resonance absorption of solar axions by ⁷Li nuclei, which is accompanied by the excitation of the first nuclear level of lithium a + ⁷Li → ⁷Li* → ⁷Li + γ, is sought. To this end, the energy spectrum has been measured by an HPGe detector that is surrounded by a LiOH layer. A new upper limit m_a ≤ 16 keV (at 90% C.L.) has been determined for the mass of the hadron axion.     

Crystal field of Yb<Superscript>3+</Superscript> tetragonal centers in the YbRh<Subscript>2</Subscript>Si<Subscript>2</Subscript> intermetallic compound

The spectra of electron paramagnetic resonance and inelastic neutron scattering in crystals of the heavy-fermion intermetallic compound YbRh₂Si₂ are interpreted. The phenomenological potentials of the crystal electric field of Yb³⁺ tetragonal centers and the parameter of the Hamiltonian for the spin-orbit interaction of electrons are determined from the experimental energy level schemes. A comparison of the results obtained from experimental data on electron paramagnetic resonance, inelastic neutron scattering, and Mössbauer spectroscopy shows that the most probable ground state of Yb³⁺ ions in the YbRh₂Si₂ crystal is the Kramers doublet Γ _t6 ^? .     

Level densities in the Pairing plus Quadrupole model for Erbium isotopes

The level densities, up to about 100 MeV of excitation energy, for even Erbium isotopes are computed using the Pairing plus Quadrupole model, in the framework of the Static Path Approximation (SPA). The resulting level densities are in reasonable agreement with the empiricalA/8 law below 40 MeV of excitation energy. At higher excitation energies (U?60 MeV) the level densities agree with the Fermi gas formula witha?A/10. The inclusion of small amplitude collective motion (RPA-SPA) does not improve the results over the SPA at high excitation energy, and gives small corrections to the ground state energy.     

Space symmetry in light nuclei. I Application to the 2s−1d shell

The Wigner supermultiplet scheme is studied in the 2s?1d shell using the spectral distribution methods of French. Expressions for the average expectation value of H and H² over states belonging to a definite SU(4) symmetry are derived. Numerical results for these averages are given for the 2s?1d shell. These averages are then used to predict ground state energies and low energy spectra for nuclei in this shell, using Ratcliff's procedure; a comparison with shell model and observed spectra is made. Mixing intensities of SU(4) representations near the ground state are also evaluated. These provide us with a measure of symmetry breaking. It appears from our calculations that the symmetry is strongly mixed. Finally a preliminary application to the theory of level densities is made.     

Self-consistent description of <Emphasis Type="Italic">EL</Emphasis> transitions between one-phonon states in magic nuclei

Transition probabilities between low-lying one-phonon states of magic nuclei are for the first time computed self-consistently within an approach to anharmonic effects based on the quantum theory of many-body systems. In the adopted approach, three-quasiparticle correlations in the ground state are taken into account, and the nuclear mean field is interrelated with the effective nucleon–nucleon interaction. These quantities are derived using the energy density functional method with known parameters of the Fayans functional. The E1 and E2 transitions in the ¹³²Sn and ²⁰⁸Pb nuclei are considered as an example, and a reasonably good agreement with the data on these nuclei is reached. Three-quasiparticle correlations in the ground state are shown to make a significant contribution to the probabilities of the discussed transitions.     

Use of (<Superscript>3</Superscript>He, <Emphasis Type="Italic">t</Emphasis>) charge-exchange reactions in determining radii of excited states of nuclei

A method for determining the radii of excited states of nuclei by means of (³He, t) charge-exchange reactions was proposed. Two versions of a comparison of differential cross sections for (³He, t) reactions were considered. The first relies on a comparison with cross sections for inelastic-scattering processes leading to the formation of isobaric analog states, while the second involves (³He, t) reactions leading to the production of the ground state. The two versions in question yield similar results and make it possible to determine the radius of the first excited state of the ¹³N nucleus. This state has the excitation energy of E* = 2.37 MeV, lying above the proton-emission threshold. The resulting radius proved to be enhanced in relation to the ground state and is close to the radius of the 3.09-MeV isobaric analog state of the ¹³С nucleus, which has a neutron halo. This permitted drawing the conclusion that the ¹³N nucleus in the 2.37-MeV state has a proton halo. The possibility of revealing a proton halo in other states of light nuclei is considered.     

Effect of Coriolis Interaction on the Decay of Isotones with <Emphasis Type="Italic">N</Emphasis> = 149 and <Emphasis Type="Italic">N</Emphasis> = 153

The quasi-neutron structure of nuclei in two chains of odd isotones with N = 149 and N = 153: ^243,247Pu, ^245,249Cm, ^247,251Cf, ^249,253Fm, ^251,255No, and is considered. Single-particle energy spectra are calculated using the two center shell model (TCSM). Minimizing the potential energy with respect to the collective coordinates gives the ground state of the studied nucleos, which is subsequently used to describe low-lying quasi-neutron states. The K-mixing of the basis TCSM wave functions is considered by including the Coriolis correction in the total Hamiltonian of the system. The effect of level blocking is also considered in the calculations. The probabilities of the E2 transitions to the ground states and the corresponding lifetimes of the quasi-neutron levels are estimated.     

Production of the (<Emphasis Type="Italic">I</Emphasis> = 19/2) high-spin isomer <Superscript>135</Superscript>Cs in photonuclear reactions

The yields of ¹³⁵Cs nuclei in a high-spin (19/2) isomeric state and of nuclei neighboring it were measured for photonuclear reactions of the (γ, f) and (γ, α) types. The experiments in question were performed by using bremsstrahlung from a microtron at the maximum electron energy of 25 MeV. The product nuclei were identified by their half-lives and by the lines of gamma radiation emitted in their decay, and the reaction yields R were determined by the ratios of the intensities of these lines to the bremsstrahlung flux. The cross sections for isomer production were calculated, and the angular momenta of product nuclei immediately before the cascade of gamma transitions populating the ground or an isomeric nuclear state were evaluated on the basis of these results. An enhanced yield of the high-spin isomer of ¹³⁵Cs in the fission reaction in relation to the respective (γ, α) reaction and in relation to the results of the calculations is found.     

Potential energy surfaces for<Emphasis Type="Italic">N</Emphasis> =<Emphasis Type="Italic">Z</Emphasis>,<Superscript>20</Superscript>Ne-<Superscript>112</Superscript>Ba nuclei

We have calculated the potential energy surfaces forN = Z,²⁰Ne-¹¹²Ba nuclei in an axially deformed relativistic mean field approach. A quadratic constraint scheme is applied to determine the complete energy surface for a wide range of the quadrupole deformation. The NL3, NL-RA1 and TM1 parameter sets are used. The phenomenon of (multiple) shape coextistence is studied and the calculated ground and excited state binding energies, quadrupole deformation parameters and root mean square (rms) charge radii are compared with the available experimental data and other theoretical predictions.     

Pairing of Neutrons and Protons in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> Nuclei

Values of neutron–proton pairing based on mass relations are estimated. It is shown that substantially different formulas for calculating the np-pairing energy in self-conjugate nuclei yield similar results. Comparison of the obtained values and the structure of ground state multiplet spectra shows that mass relations can be used to describe the isovector (T = 1) component of np-pairing to sufficient accuracy, but provides little or no information on isoscalar component T = 0.     

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.     

Interaction of intermediate-energy protons with <Superscript>20</Superscript>Ne and <Superscript>24</Superscript>Mg nuclei within the multiple-scattering model

Observables of the elastic and inelastic scattering of 800- and 250-MeV protons on ²⁰Ne and ²⁴Mg nuclei were calculated on the basis of the theory of multiple diffractive scattering and the dispersive α-cluster model. The ²⁰Ne and ²⁴Mg nuclei were assumed to consist of a core (¹⁶O nucleus) and additional alpha-particle clusters, which could be situated with the highest probability both in the vicinity of the center of mass of the core and outside the core. The multiparticle densities of these nuclei and single-particle nucleon-distribution densities as obtained from the dispersive α-cluster model were used in the calculations. The differential cross sections and polarizations for elastic and inelastic p ²⁰Ne and p ²⁴Mg scattering at the energy of 800 MeV are in better agreement with experimental data than the analogous calculations at the energy of 250 MeV. The spin-rotation functions calculated in the singleparticle approximation for elastic p ²⁰Ne and p ²⁴Mg scattering at these two energy values differ qualitatively from their counterparts calculated on the basis of the dispersive α-cluster model.