The breaking of intrinsic reflection symmetry in nuclear ground states

Negative-parity excited states of doubly even nuclei have earlier been attributed to vibrational excitations. This paper shows that an interpretation starting from a reflection asymmetric intrinsic state is more appropriate for certain nuclei in the radium region. Theoretical evidence for stable octupole deformation comes from a deformed shell-model calculation in which we use a single-particle potential with a realistic radial shape and a finite-range interaction for the surface energy. The octupole effect systematically improves the agreement between theoretical and experimental masses. The low-lying O⁺ excitations observed in experiment are compatible with the calculated collective octupole potentials. The possibility of obtaining further evidence from the spectroscopy of odd-mass nuclei is considered in an exactly solvable model, which shows that the smaller energy splitting observed in odd-A parity doublets mainly reflects single-particle fragmentation of the collective mode. The systematics of theoretical shell structure and experimental spectroscopy suggests the presence of other regions of octupole collectivity near the limits of stability.     

Effects of nuclear structure in double charge exchange reactions on 16O and 40Ca

The energy dependence of forward double charge exchange (DCX) reaction is studied for the doubly closed shell nuclei ¹⁶O and ⁴⁰Ca. A common characteristic of the two DCX reactions is a resonance-like peak around 50 MeV pion lab energy. While some authors have interpreted this peak as the evidence of a dibaryon resonance state, we show that it arises naturally in a two-step process in the conventional pion—nucleon system with proper handling of nuclear structure. The effects of nuclear structure are demonstrated through a comparison among different nuclear structure models: the symmetry model SU(4) ? SU(3), the single particle shell model and the «realistic” shell model.     

The reactions 6, 7Li, 9Be, 10B(e,e′p) at 700 MeV and DWIA analysis

The proton spectral functions of ⁶Li, ⁷Li, ⁹Be and ¹⁰B obtained from the (e, e′p) reactions at 700 MeV are presented. The results were analyzed in the distorted-wave impulse approximation, using the shell-model single-particle wave functions consistent with the elastic electron scattering results. The observed Ip proton momentum distributions for the nuclei ⁶Li, ⁷Li and ⁹Be show significant disagreement with the shell-model momentum distributions. The occupation probabilities of the proton single-particle states are around 0.7, with a few exceptions.     

Rotational bands from shell-model Hamiltonians

Shell-model Hamiltonians with eigenstates forming rotational bands are considered. Such states have eigenvalues proportional to J(J+ 1) and can be projected from a Slater determinant of deformed orbitals. The latter are linear combinations of single-nucleon wave functions of j-orbits in a major shell. Conditions on matrix elements and single-nucleon energies are obtained in terms of the deformation parameters. An actual effective interaction is constructed yielding exact ground-state rotational bands for ²⁰Ne and ²⁴Mg which gives reasonable agreement with energies of other sd shell nuclei. Unlike the case of SU(3) symmetry, spin-orbit interaction and different single-nucleon energies can be accommodated and the procedure is not confined to oscillator major shells. Other welcome departures of our effective interaction from the SU(3) picture are the absence of rotational spectra in oxygen isotopes and that the ²⁴Mg ground-state band is projected from a Nilsson-type deformed state with axial symmetry.     

Studies of the electric dipole transition of deformed rare-earth nuclei

Spectrum and electric dipole transition rates and relative intensities in ^152–154Sm, ^156–160Gd, ^160–162Dy are studied in the framework of the interacting boson model with s,p,d,f, bosons. It is found that E1 transition data among the low-lying levels are in good agreement with the SU(3) dynamical symmetry of the spdf interacting boson model proposed by Engel and Iachello to describe collective rotation with octupole vibration. These results show that these nuclei have SU(3) dynamic symmetry to a good approximation. Also in this work many algebraic expressions for electric dipole transitions in the SU(3) limit of the spdf-IBM have been obtained. These formulae together with the formulae given previously exhaust nearly all the E1 transitions for low-lying negative parity states. They are useful in analyzing experimental data.     

Shell model calculations on natural parity states in 10≦ A≦14 nuclei

Shell model calculations of natural parity states in the 10≦A≦14 mass region have been performed by assuming an inert⁴He core with the residual interaction in the 1p shell only. The modified surface delta interaction (MSDI) has been used as an effective two-body interaction. The MSDI parameters as well as the single-particle binding energies have been deduced from a least-squares fit to experimentally known levels in, firstly, the seperate¹⁰B,¹¹B-C,¹²C,¹³C-N and¹⁴N nuclei, and secondly, the whole mass region 10≦A≦14. Multipole moments for ground states and M1 and E2 radiative widths for excited states have been calculated with the resultant wave functions.     

Shape variables and the shell model

The irreducible representation labelsλ andμ of the SU(3) shell model are related to the shape variablesβ andγ of the collective model by invoking a linear mapping between eigenvalues of invariant operators of the two theories. All but one parameter of the theory is fixed if the shell-model result is required to reproduce the collective-model geometry. And for one special value of the remaining free parameter there is a simple linear relationship between the eigenvalues, λ_α, of the quadrupole matrix of the collective model and the SU(3) representation labels: $$\lambda _1 = ( - \lambda + \mu )/3, \lambda _2 = ( - \lambda + 2\mu + 3)/3, \lambda _3 = (2\lambda + \mu + 3)/3.$$ The correspondence between hamiltonians that describe rotations in each theory is also given. Results are shown for two cases,²⁴Mg and¹⁶⁸Er, to demonstrate that the simplest mapping yields excellent results for both energies and transition rates. For λ and/or μ large, the (β, γ)?(λ,μ) correspondence introduced here reduces to the symplectic shell-model result.     

Calculated isospin-mixing corrections to Fermi β-decays in 1s0d-shell nuclei with emphasis on A = 34

Corrections to the Fermi matrix element due to analogue symmetry breaking are evaluated for the superallowed β-decays of ²²Mg, ³⁴Cl, and ³⁴Ar by considering the effects of Coulomb and other isospin-nonconserving potentials. Analogue symmetry breaking is calculated within the shell-model formalism by considering: (i) the deviations from unity of the radial overlap between the proton and neutron single-particle wave functions, and (ii) isospin mixing between states within the 0d$\text{5}\text{2}$0d$\text{3}\text{2}$0d$\text{1}\text{2}$ shell. The radial-overlap corrections for several cases of interest in the sd shell are evaluated with single-particle wave functions obtained from a self-consistent Hartree-Fock calculation. The sd-shell isospin-mixing corrections are calculated with an isospin-non-conserving potential which reproduces the experimental isobaric mass shifts. Comparisons with previous calculations are made. The Fermi matrix elements for the isospin-forbidden (β-decays of ³⁴Cl and ³⁴Ar to excited 0⁺ states are also calculated.     

A comparative study of double beta decay by shell model and quasiparticle RPA

Nuclear matrix elements of the two-neutrino and neutrinolessββ decays of⁴⁸Ca(0 _g.s. ⁺ )→⁴⁸Ti(0 _g.s. ⁺ ) are calculated by shell model and QRPA. The two-neutrino matrix elementM _GT ^2v is rather reliably evaluated in the QRPA approach by a careful fit of the particle-particle interaction strength in the 1⁺ channel, which governs the spinisospin ground-state correlations. The shell-model value ofM _GT ^2v depends not only on the 1⁺ interaction but largely on the pairing and quadrupole interactions. Concerning the neutrinoless-mode nuclear matrix elements, the shell model gives generally smaller values than the QRPA. A detailed analysis indicates that the discrepancies originate mainly from the truncation of shell-model configurations (fp-space). The QRPA calculation in a larger model space well takes into account transitions from/to single-particle orbits far from the Fermi surface, and those transitions give rise to sizable contributions because of large momentum transfers due to the exchange of a virtual neutrino.     

Statistical spectroscopy for nuclei in the fp shell

Nuclei in the fp shell have been studied using the spectral averaging method. This was attempted with a view to provide a rather simple alternative to detailed microscopic calculations. We have considered a decomposition of the overall spectroscopic space (m particles in the fp shell) in terms of a spherical j-orbit, isospin, configuration-isospin and SU(4) isospin subspaces. Centroid energies and widths of these subspaces are evaluated and used to determine binding energies, low-energy spectra and fractional occupancy of j-orbits. We have also examined the extent of Wigner SU(4) symmetry mixing for nuclei in this shell. The ratio of binding energies of isobars suggested by Franzini and Radicati to test the validity of SU(4) symmetry is also evaluated from the calculated binding energies. Comparisons are made with microscopic calculations like the shell model and Hartree-Fock where available. We find that the distribution method is able to determine ground-state energies and spectra of nuclei very well despite the fact that the vector spaces are quite large. The SU(4) symmetry in the ground-state region of these nuclei is strongly mixed largely due to the single particle spin-orbit coupling.     

Evidence for symplectic symmetry in Ab initio no-core shell model results for light nuclei

Clear evidence for symplectic symmetry in low-lying states of 12C and 16O is reported. Eigenstates of 12C and 16O, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A相似文献   

Yrast traps and high-spin states in 210Rn

Yrast and near-yrast states have been investigated in ²¹⁰Rn to high spin (J > 30) and high energy (E_x > 10 MeV). Three different (HI, xn) reactions were used to populate the states of interest and several different γ-ray spectroscopic techniques were utilized. Three high-spin yrast traps were discovered. Two de-excite by strong E3 transitions while the third decays mainly via an extremely inhibited E2 transition. The E3 decays are interpreted as allowed single-particle transitions between proton or neutron states above the ²⁰⁸Pb shell closure while the inhibited E2 transition is interpreted as indicating a substantial change in structure as the decay proceeds down the yrast line. The interpretation has been given in terms of shell-model calculations.     

Angular Momentum Projected Deformed HF Spectra of 46Ti and 48Cr With MSDI

Taking the modified surface delta interaction (MSDI) and using a spherical shell model basis set, we carry out the deformed Hartree-Fock (HF) calculation for the even-even nuclei ⁴⁶Ti and ⁴⁸Cr in the fp shell, and construct the deformed HF intrinsic states which are the Slater determinants from the HF single-particle states.The angular momentum projection program is then carried out and the reasonable results are obtained.     

Partial dynamical symmetry in a fermion system

The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.     

Intermediate-coupling calculation for 10B in a projected Hartree-Fock basis

A shell-model calculation is carried out for ¹⁰B in intermediate coupling. The deformation of the shell-model field is taken into account by using as a basis the functions obtained from a projected Hartree-Fock calculation. The resulting wave functions give an important improvement for the E2 matrix elements with respect to the conventional shell model. Some remaining difficulties are discussed.     

DWIA calculations of proton momentum distributions in 12C and 16O(e,e'p) reactions

The DWIA analysis of the quasi-free (e, e'p) process on ¹²C and ¹⁶O has been performed within the framework of the single-particle shell model. The spherical Hartree-Fock wave functions for the effective Skyrme forces are used in describing the ground-state properties of these nuclei. The competition between the structure effects and the final proton-nucleus interaction in forming the momentum distributions of outgoing protons is studied in a wide range of recoil momenta (up to 3 fm^?1). The distorting optical potential has been calculated on the basis of the Watson multiple scattering theory. The results of the analysis are compared with the new data obtained at Saclay.     

Sp(4, R) symmetry in light nuclei

A classification of nuclear states according to the non-compact Lie algebra Sp(4, R) is investigated. This model strikes a compromise between the Sp(6, R) and Sp(2, R) models and furnishes a practical, yet algebraically simple means for selecting those shell-model core excitations which are needed for the development of quadrupole collectivity in rotational bands of deformed nuclei. Applications to rotational bands in ²⁴Mg and ¹⁶O, including shell-model excitations with excitation energies up to 10?ω, show that the core excitations needed to fit observed E2 rates in these nuclei are too large to be treated by perturbation theory. Despite this, a definite symplectic band structure emerges. The nature of the core excitations is very simple, so that it may be feasible to incorporate such symplectic excitation structures into more detailed shell-model calculations.