Gamow-Teller matrix elements of T=12 nuclei and the renormalization of the axial-vector coupling constant

The renormalization of the axial-vector coupling constant is determined by four methods over the mass range 7 ≦ A ≦ 41. The unweighted average value of the renormalization ρ, relative to its free space value, is found to be about 85 %. The value of ρ near closed shells appears to be the same suggesting no strong sensitivity to the size of the nucleus. A substantial decrease is found to occur between closed shells.     

RPA calculation of Gamow-Teller and M1 states including Δ-hole excitation

The self-consistent RPA model with Skyrme type interactions is extended to include Δ-hole excitations. Energies and transition strengths of Gamow-Teller and M1 states are studied systematically. We find that combined effects of RPA correlations and Δ-hole excitation decrease the transition strengths by about 35%.     

Suppression of Gamow-Teller and M1 transitions in deformed mirror nuclei 25Mg and 25Al

The mirror nuclei ²⁵Mg and ²⁵Al are expected to have very similar structures. The Gamow-Teller (GT) transitions from the ground state of ²⁵Mg to the excited states in ²⁵Al were studied by high-resolution measurements of the ²⁵Mg( ) charge-exchange reaction at and at 140 MeV/nucleon. Assuming the usual selection rule for the spin-isospin-type GT transitions, the states with , and 7/2 ⁺ should be excited. However, of the more than ten states with these values below 6 MeV excitation energy, only the 5/2 ⁺ ground state and the 7/2 ⁺ , 1.613 MeV state in ²⁵Al were strongly populated, while all other states were strongly suppressed. The analysis of M1 transitions in ²⁵Mg also suggested a very similar feature for the analogous M1 transitions. Both ²⁵Mg and ²⁵Al are known to be largely deformed, and most low-lying states can be interpreted in terms of one-particle quantum numbers in the deformed potential and the associated rotational spectra. The observed suppression can be explained in terms of the K quantum number selection rules that are inherent to axially deformed nuclei.-1Received: 18 July 2003, Published online: 18 December 2003PACS: 21.10.Re Collective levels - 21.60.Ev Collective models - 25.55.Kr Charge-exchange reactions - 27.30. + t H. Fujita: Present address: Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan.J. Kamiya: Present address: Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan.T. Wakasa: Present address: Department of Physics, Kyushu University, Higashi, Fukuoka 812-8581, Japan.     

Realistic one-particle density matrix and single-particle description of nuclei

Starting from the experimental data on elastic electron scattering, realistic one-particle density matrices for ¹⁶O and ⁴⁰Ca are obtained, both with fractional occupation numbers and full occupation of the first A natural orbitals. A phenomenological single-nucleon Hamiltonian is then constructed and diagonalized. The deduced single-particle energies are compared with those obtained in the Hartree-Fock approximation. The consistency of all experimental data concerning the ground state is checked with the aid of a sum rule for the total binding energy involving only the one-particle density matrix and the hole energies.     

Consistent empirical description of magnetic moments and M1 transitions: Quenching of the diagonal and off-diagonal spin matrix elements

The spin and tensor parts of an effective M1 operator for nuclei around ⁹⁰Zr and ²⁰⁸Pb are empirically determined by minimizing simultaneously the deviation of measured magnetic moments and M1 transitions from standard shell model calculations performed within lowest order shell-model spaces. The results are linked to a previous analysis of sd-shell nuclei and show approximately the mass dependence of the combined influence of high-lying many-particle-many-hole excitations admixed via the tensor force and of Δ-h admixtures.     

Collective contributions to E1, ΔK=1 matrix elements in odd-odd deformed nuclei

The half-life of the 184.3 keV state in¹⁶⁵Dy has been remeasured asT _1/2=1.0±0.1 ns in order to deduce a reliable value for the transition matrix element of the depopulatingE l,ΔK=1 transition. Experimental E1,ΔK=1 transition matrix elements in odd-odd deformed nuclei are found to be systematically larger than similar values in adjacent odd-A isotones. This effect is supposed to be associated with higher-order vibrational admixtures coupled via RPC andp— n interaction mixings.     

From the classical field with sources to the multipole matrix elements

Starting with the classical interaction of the electromagnetic field with sources and then quantizing, the interaction Hamiltonian is expanded in multipoles. Explicit expressions for the multipole operators are obtained. Transformation properties, under time reversal and Hermitian conjugation, of nuclear states and multipole operators are studied.     

The change of sign of E2 and M1 matrix elements,and of δ-values of166Er at high spins

Calculations of the Dynamic Deformation Model for the E2/M1 mixing ratios for ψ-band to ground-band transitions in¹⁶⁶Er have been extended to higher spins (up to I=20). Previous comparisons with the experimental values and with the IBA-1 predictions, available at present up to spins 8 only, are also included for the sake of completeness. Additional comparison with the Frankfurt Model is also given. While all three models give reasonable magnitudes of the mixing ratios, only the DDM gives the sign changes at the correct spin values. Predictions are presented for additional sign changes of the mixing ratios, as well as those of the E2 and the M1 transition moments.     

Corrections to the effective orbital g-factor of diatomic 1Δ states

Anisotropies in the diamagnetic susceptibilities of coronene, anthracene and chrysene are reported. They have been determined from the quadrupolar magnetic field effect on the ²H N.M.R. spectra of the compounds. Results from this method are compared with those obtained from other techniques and the differences are discussed.     

Krylov-space approach to the equilibrium and nonequilibrium single-particle Green's function

The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to obtain the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane which describes the system's nonperturbative response to a sudden parameter switch in the Hamiltonian. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss its efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.     

Spectroscopy and single-particle structure of the odd- Z heavy elements 255Lr, 251Md and 247Es

The odd-Z isotope ²⁵⁵Lr, its daughter ²⁵¹Md and grand-daughter ²⁴⁷Es were studied in two experiments performed at GANIL and the University of Jyv?skyl?. The ²⁵⁵Lr nuclei were produced using the cold fusion-evaporation reaction ²⁰⁹Bi(⁴⁸Ca, 2n)²⁵⁵Lr at a bombarding energy of 217MeV. The single-particle structure and decay properties were investigated using α, γ and electron spectroscopy. The ground-state spin and parity could be assigned for ²⁵⁵Lr (1/2^-) and ²⁵¹Md (7/2^-). States corresponding to the 7/2⁺[633], 7/2^-[514] and 1/2^-[521] Nilsson orbitals were observed. Results are compared to experimental data obtained in neighbouring isotopes and to Hartree-Fock-Bogoliubov calculations using the Skyrme interaction SLy4 and a density-dependent pairing interaction. The position of the 1/2^-[521] orbital from the spherical 2f _5/2 shell is discussed.     

The dynamic stiffness matrix of two-dimensional elements: application to Kirchhoff's plate continuous elements

This paper describes a procedure for building the dynamic stiffness matrix of two-dimensional elements with free edge boundary conditions. The dynamic stiffness matrix is the basis of the continuous element method. Then, the formulation is used to build a Kirchhoff rectangular plate element. Gorman's method of boundary condition decomposition and Levy's series are used to obtain the strong solution of the elementary problem. A symbolic computation software partially performs the construction of the dynamic stiffness matrix from this solution. The performances of the element are evaluated from comparisons with harmonic responses of plates obtained by the finite element method.     

Dirac-kahler equation and calculation of matrix elements for spin-1/2 particles

An explicit tensor method presented for calculating the matrix elements of the interaction of massive spin-1/2 particles does not involve calculation of traces from the products of Dirac matrices.Belorussian State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 39–42, October, 1994.     

Mean single-particle potentials and single-particle energies in a microscopic model of the nucleus

A method for calculating mean single-particle potentials and the corresponding single-particle energy levels in nuclei is presented. Specific formulas for these quantities are written for Slater determinant wave functions in the case of polarized orbitals and a central exchange nucleon-nucleon potential featuring a Gaussian radial dependence. The resulting theoretical estimates of single-particle properties of the nuclei considered in the present study are in satisfactory agreement with relevant experimental data.     

Spatial decay of the single-particle density matrix in insulators: analytic results in two and three dimensions

Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions (D = 1,2,3) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown to be dependent on the energy parameters of the model. The existence of the power-law prefactor, proportional, variant r(-D/2), is demonstrated.