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.     

On the origin of the Wigner energy

Surfaces of experimental masses of even-even and odd-odd nuclei exhibit a sharp slope discontinuity at N = Z. This cusp (Wigner energy), reflecting an additional binding in nuclei with neutrons and protons occupying the same shell model orbitals, is usually attributed to neutron-proton pairing correlations. A method is developed to extract the Wigner term from experimental data. Both empirical arguments and shell-model calculations suggest that the Wigner term can be traced back to the isospin T = 0 part of nuclear interaction. The structure of the Wigner energy is analyzed in terms of neutron-proton pairs of a given angular momentum and isospin. In particular, we find that the Wigner term cannot be solely explained in terms of correlations between the neutron-proton J = 1, T = 0 (deuteron-like) pairs.     

The effect of neutron-proton pairing correlations on the transfer of a neutron-proton pair

A theory of neutron-proton pairing interaction is developed considering bothJ=0T=1 andJ≠0T=0 correlations. The model of a singlej-shell is investigated explicitly forN=Z nuclei. Instead of solving the full HFB (Hartree Fock Bogoliubov) problem a variational method is used for determining the ground state energy and wavefunction. Our model shows that the best solutions contain either onlyT=0 or onlyT=1 correlations. A solution mixingT=0 andT=1 is energetically worse. It is estimated in PWBA (Plane Wave Born Approximation) that for ground state transitions at light nuclei in the transfer of a neutron-proton pair the cross section is enhanced up to a factor 3 by pairing correlations compared with shell model calculations.     

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.     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.     

Investigation on phase and shape transitions in the hot rotating nucleus <Superscript>154</Superscript>Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus ¹⁵⁴Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.     

Atomic masses above146Gd derived from a shell model analysis of high spin states

From a shell model analysis of high-spin states in neutron deficient nuclei above¹⁴⁶Gd we have derived the ground state masses of theN=82 and 83 isotones of Eu, Tb, Dy, Ho, and Er. The results can be used to calculate the energies of aligned multiparticle yrast configurations. They also link ten α-decay chains to the nuclei with known masses, providing many new absolute mass values which are compared with predictions. An examination of the two-proton separation energies atN=82 shows an 0.5 MeV break in the nuclear mass surface atZ=64.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.     

The role of isospin on the N=Z line

The role played by isospin in nuclear structure phenomena encountered on the N=Z line is discussed. New results on Coulomb energy differences (CED) at high spin for odd-A nuclei in the f _7/2 shell are presented and interpreted in the framework of a simple Cranked Shell Model treatment involving an exact numerical diagonalisation. Results for the CED between the A=46 even-even mirror pairs are also discussed. The CED between the T=1 states in N=Z odd-odd nuclei and their isobaric analogues are suggested as a possible probe of np pairing on the N=Z line. First results from a numerical diagonalization of IBM-4 are cited.     

The skyrme-plus-pairing effective interaction and the global neutron-excess dependence of the pairing gap

The neutron and proton pairing gaps were recently found to have a global dependence on neutron excess. We investigate whether the couplings necessary to obtain this behaviour can be provided by a mean field associated with a Skyrme-type plus usual pairing effective interaction. The parameters of this effective interaction are constrained by nuclear-matter properties, such as binding energy, saturation density, effective mass and values of the second derivatives of the energy with respect to the four densities (neutron and proton with spin-up and spin-down), together with the surface energy. The pairing gaps are then calculated as a function of neutron excess for various parameter sets for very large systems and for finite nuclei in the local-density approximation. We find that the empirical results cannot be reproduced by this procedure. We put forward therefore the hypothesis that, to account for this failure, the usual phenomenology of effective interactions in nuclei ought to be modified; we propose a simple residual neutron-proton interaction that can do that, yet maintains all the previous successes.     

Cold fragmentation in thermal-neutron-induced fission of 233U and 235U

The mass spectrometer Lohengrin of the Institut Laue-Langevin in Grenoble was used to measure fission-fragment mass yields in the mass range 80 ≤ A ≤ 107 for light-fission-fragment kinetic energies up to about 115 MeV for the reactions ^233,235U(n_th, f). The kinetic energies corresponding to a common fixed yield level for each isobar reflect the influence of the proton pairing energy, but not of the neutron pairing energy. By using calculated Q-values for the different mass splits, mass distributions at fixed total excitation energy are deduced from the data. At a fixed total excitation energy of about 7 MeV, the yield increases from very asymmetric mass splits (A_L ≈ 80) to more symmetric mass splits (A_L ≈ 105) by more than two orders of magnitude. This strong dependence on the mass split seems to be correlated with the decreasing surface-to-surface distance of the unaccelerated fission fragments in this range of mass splits, as calculated under the assumption that the total Q-value is represented by the mutual Coulomb repulsion of the two fragments. The influence of the fission-fragment ground-state deformations on the yield in cold fragmentation could not be detected unambiguously.     

Analysis of fissionability data at high excitation energies

A level density formula that takes into account the smoothed volume, surface and curvature dependence of the single particle level density at the Fermi surface using the results of Balian and Bloch, is shown to be compatible with the level spacings found in neutron resonance data if complemented by a simple Ansatz for shell effects (due to Ignatyuk) and pairing effects. The three parameters involved, a scaling parameter, a shell damping energy and a pairing energy shift are compatible, respectively, with known nuclear radii, microscopic level density calculations and odd-even mass fluctuations. At excitation energies on the order of the neutron binding energy no evidence for an absolute level density problem or a different behaviour of level densities (collective contributions) for deformed nuclei as opposed to spherical nuclei is found. The proposed level density formula allows to calculate a priori macroscopic ratios of level densities, e.g. at the groundstate and at the saddle point, removing this important parameter from the analysis of fissionability data. As a first application, the fissionability of a number of actinide nuclei at excitation energies a few MeV above the fission barrier is analysed.     

Experimental study on the 3p size-resonance in thep- wave neutron strength function

Using a silicon filtered fission neutron beam of an energy width of 20 keV around 143 keV we measured the total cross sections for 37 nuclides and elements having mass numbers between 87 and 140 and determined thep-wave strength functions. The 3P-resonance atA=98 shows no splitting into theP _3/2?P _1/2 doublet. The narrow resonance peak and the following broad distribution of thep-strength function (A=103 to 140) can approximately be reproduced by deformed optical model calculations. The spin-orbit term in the optical potential is consistent with the spin orbit force in the shell model. For nuclei around the closed (N=50) neutron shell a shell effect in thep-wave strength function is indicated.     

The systematics of nuclear single-particle states of nuclei with 50 ≦ NZ ≦ 82

The depth of the local Woods-Saxon potential corresponding to the experimental binding energies of the single particle states in gdhs nuclei has been parametrized as a function of the mass number A and the symmetry parameter (N?Z)/A. A typical spread of 200 keV of the calculated values of the potentials from the best fit curve was obtained. The implication of the pairing correlations are discussed.     

Mass-surface predictions near the doubly magic nuclide 78Ni

The mass surface of nuclei close to the doubly magic nuclide ⁷⁸Ni is calculated by two methods. The first relies on the multiparticle shell model based on an effective interaction and a mean nuclear potential. The second employs the concept of so-called “magic crosses” and enables us to determine the masses of odd-odd nuclei close to ⁷⁸Ni by using similarity of the shell structure and neutron-proton interaction in the region of nuclei under consideration and in the region of heavy magic nuclides. The energies of the separation of one and two neutrons from nuclei close to ⁷⁸Ni and the energies of the β decay of these nuclei—recall that these quantities of astrophysical interest—are presented.     

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.     

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.     

Nuclear structure around ~(80)Zr

Recent years have witnessed intense activity concerning the study of nuclei with equal numbers of neutrons and protons (N = Z). Exotic properties have been exhibited in the N = Z nuclei, especially in those with atomic masses around 80. In the present paper, the projected shell model(PSM)together with a relativistic Hartree-Bogoliubov (RHB) theory is used to study the nuclear structure near the N = Z line in the mass A ≈ 80 region. For three Zr isotopes 80,82,84Zr, the projected potential energy surfaces and ground state bands are calculated. It is shown that shape coexistence occurs in all of these nuclei. Moreover, we find that the residual neutron-proton interaction strongly affects the ground state band of 80Zr; however, it slightly modifies those of 82Zr and 84Zr.     

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.