P. Olbratowski

Critical frequency in nuclear chiral rotation

Self-consistent solutions for the so-called planar and chiral rotational bands in 132La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as Plancks omega(crit) approximately 0.5-0.6 MeV. However, the exact values of Plancks omega(crit) may vary, to an extent, depending on the microscopic model used, in particular, through the pairing correlations and/or calculated equilibrium deformations. The existence of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) hfodd (v2.40h): A new version of the program ✩

We describe the new version (v2.38j) of the code hfodd which solves the nuclear SkyrmeHartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for statedependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D T transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected two insignificant errors.

Search for the Skyrme-Hartree-Fock Solutions for Chiral Rotation in N=75 Isotones

A search for self-consistent solutions for the chiral rotational bands in the N=75 isotones {sup 130}Cs, {sup 132}La, {sup 134}Pr, and {sup 136}Pm is performed within the Skyrme-Hartree-Fock cranking approach using SKM* and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the four isotones considered, self-consistent chiral solutions are obtained only in {sup 132}La. The microscopic calculations are compared with the {sup 132}La experimental data and with results of a classical model that contains all the mechanisms underlying the chirality of the collective rotational motion. Strong similarities between the Hartree-Fock and classical model results are found. The suggestion formulated earlier by the authors that the chiral rotation cannot exist below a certain critical frequency is further illustrated and discussed, together with the microscopic origin of a transition from planar to chiral rotation in nuclei. We also formulate the separability rule by which the tilted-axis-cranking solutions can be inferred from three independent principal-axis-cranking solutions corresponding to three different axes of rotation.

Time-reversal violating Schiff moment of 225Ra

Experiments with K and B mesons indicate that timereversal invariance ~T! is violated through phases in the Cabibbo-Kobayashi-Maskawa matrix that affect weak interactions @1#. The suspicion that extra-standard-model physics, e.g., supersymmetry, also violates T has motivated a different kind of experiment: measuring the electric dipole moments ~EDMs! of the neutron and atoms. Because any such dipole moment must be proportional to the expectation value of the T-odd spin operator, it can only exist when T ~and parity, P) is violated @2,3#. So far the experiments have measured no dipole moments, but they continue to improve and even null results are useful, since they seriously constrain new physics. Whatever the experimental situation in the future, therefore, it is important to determine theoretically what the presence or absence of EDMs at a given level implies about T-violating interactions at elementary-particle scales. Our focus here is on atoms, which for some sources of T violation currently provide limits as good or better than the neutron @4#. One way an atom can develop an EDM is through T and P violation in its nucleus. Let us assume that given a fundamental source of the broken symmetry, one can use effectivefield theory and QCD to calculate the strength of the resulting T-violating nucleon-pion interaction. One then needs to connect the strength of that interaction to the resulting nuclear ‘‘Schiff moment,’’ which, because the nuclear EDM is screened @5#, is the quantity responsible for inducing an EDM in electrons orbiting the nucleus. The Schiff moment is defined classically as a kind of radially weighted dipole moment: S5 1

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

Abstract We describe the new version (v2.08k) of the code HFODD which solves the nuclear Skyrme–Hartree–Fock or Skyrme–Hartree–Fock–Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. Similarly as in the previous version (v2.08i), all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. In the new version, three minor errors have been corrected. New Version Program Summary Title of program: HFODD; version: 2.08k Catalogue number: ADVA Catalogue number of previous version: ADTO (Comput. Phys. Comm. 158 (2004) 158) Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVA Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Does the new version supersede the previous one: yes Computers on which this or another recent version has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon Operating systems under which the program has been tested: UNIX, LINUX, Windows-2000 Programming language used: Fortran Memory required to execute with typical data: 10M words No. of bits in a word: 64 No. of lines in distributed program, including test data, etc.: 52 631 No. of bytes in distributed program, including test data, etc.: 266 885 Distribution format: tar.gz Nature of physical problem: The nuclear mean-field and an analysis of its symmetries in realistic cases are the main ingredients of a description of nuclear states. Within the Local Density Approximation, or for a zero-range velocity-dependent Skyrme interaction, the nuclear mean-field is local and velocity dependent. The locality allows for an effective and fast solution of the self-consistent Hartree–Fock equations, even for heavy nuclei, and for various nucleonic ( n -particle n -hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle–particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree–Fock–Bogolyubov method. Solution method: The program uses the Cartesian harmonic-oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constrains are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [J. Dobaczewski, J. Dudek, Comput. Phys. Comm. 102 (1997) 166]. Summary of revisions: 1. Incorrect value of the “ t 0 ” force parameter for SLY5 has been corrected. 2. Opening of an empty file “FILREC” for IWRIRE=−1 has been removed. 3. Call to subroutine “OLSTOR” has been moved before that to “SPZERO”. In this way, correct data transferred to “FLISIG”, “FLISIM”, “FLISIQ” or “FLISIZ” allow for a correct determination of the candidate states for diabatic blocking. These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even–even nuclei and conserved simplex symmetry. Unusual features: The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex Hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpevx.f , respectively. The code is written in single-precision for use on a 64-bit processor. The compiler option -r8 or +autodblpad (or equivalent) has to be used to promote all real and complex single-precision floating-point items to double precision when the code is used on a 32-bit machine. Typical running time: One Hartree–Fock iteration for the superdeformed, rotating, parity conserving state of 152 66 Dy 86 takes about six seconds on the AMD-Athlon 1600+ processor. Starting from the Woods–Saxon wave functions, about fifty iterations are required to obtain the energy converged within the precision of about 0.1 keV. In the case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J ( 2 ) can be obtained within forty minutes of CPU on the AMD-Athlon 1600+ processor. This time can be often reduced by a factor of three when a self-consistent solution for a given rotational frequency is used as a starting point for a neighboring rotational frequency. Additional comments: The actual output files obtained during users test runs may differ from those provided in the distribution file. The differences may occur because various compilers may produce different results in the following aspects: (a) The initial Nilsson spectrum (the starting point of each run) is Kramers degenerate, and thus the diagonalization routine may return the degenerate states in arbitrary order and in arbitrary mixture. For an odd number of particles, one of these states becomes occupied, and the other one is left empty. Therefore, starting points of such runs can widely vary from compiler to compiler, and these differences cannot be controlled. (b) For axial shapes, two quadrupole moments (with respect to two different axes) become very small and their values reflect only a numerical noise. However, depending on which of these two moments is smaller, the intrinsic-frame Euler axes will differ, most often by 180 degrees. Hence, signs of some moments and angular momenta may vary from compiler to compiler, and these differences cannot be controlled. These differences are insignificant. The final energies do not depend on them, although the intermediate results can.

Shell structure fingerprints of tensor interaction

We address the consequences of strong tensor terms in the local energy density functional, resulting from fits to the f5/2 -f7/2 splittings in 40Ca , 48Ca , and 56Ni . In this study, we focus on the tensor contribution to the nuclear binding energy. In particular, we show that it exhibits an interesting topological feature closely resembling that of the shell correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to N(Z) = 14 , 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4T, we show that the proton tensorial magic numbers shift with increasing neutron excess to Z = 14 , 28, and 50.

GLOBAL NUCLEAR STRUCTURE ASPECTS OF TENSOR INTERACTION

A direct fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants to the f(5/2) - f(7/2) SO splittings in Ca-40, Ni-56, and Ca-48 requires (i) a significant reduct ...

SKYRME-HARTREE-FOCK AND HARTREE-FOCK-BOGOLYUBOV CALCULATIONS FOR NUCLEI WITH TETRAHEDRAL DEFORMATION

Hartree-Fock-Bogolyubov solutions corresponding to the tetrahedral deformation are found in six tetrahedrally doubly-magic nuclei. Values of the β32 deformation, depths of the tetrahedral minima, and their energies relative to the co-existing quadrupole minima are determined for several versions of the Skyrme force. Reduction of the tetrahedral deformation energies by pairing correlations is quantitatively analysed. In light nuclei, shallow tetrahedral minima are found to be the lowest in energy, while in heavy nuclei, the minima are deeper but appear at a few MeV of excitation.

ROTATION OF TETRAHEDRAL NUCLEI IN THE CRANKING MODEL

The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the rotating hamiltonian. Self-consistent Hartree-Fock-Bogoliubov calculations show that the tetrahedral minimum remains remarkably stable until the first single-particle crossing.

Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra

Calculations for infinite nuclear matter with realistic nucleon-nucleon interactions suggest that the isoscalar effective mass of a nucleon at the saturation density