E2 Effective Charges Research Articles

Shell-model calculation of E2 effective charges: Application to carbon isotopes

A theoretical approach based on the shell model is presented to calculate effective charges of electric quadrupole transitions. The shell-model calculation with single-particle 2 ℏ ω excitations in the first order perturbation qualitatively reproduces existing experimental B ( E 2 ) values for carbon isotopes with neutron number 5 ⩽ N ⩽ 16 and shows a sudden change of the isovector effective charge beyond N = 8 .

Shell model study on E2 effective charges in light neutron-rich nuclei

Theoretical values of quadrupole moments of neutron-rich nuclei are larger than experimental values if we use E2 effective charges of stable nuclei. We consider that the nucleon excitations to outside model space decrease with neutron excess. Using the shell model, we investigate quadrupole moments and effective charges in the light mass region, from stable nuclei to neutron-rich nuclei.

Giant quadrupole resonances and their effects on neutron-rich nuclei

Quadrupole giant resonances (GQR) play a major role in characterizing dynamical properties of both stable and unstable nuclei. In this paper two topics related with GQR are discussed based on recent experimental findings at RIKEN; 1) clear observation of isovector GQR in a heavy ion charge-exchange reaction, ( 13C, 13N) on 60Ni at 100 MeV/nucleon, and 2) E2 effective charges varying with isospin asymmetry as evidenced by the electric quadrupole moments of neutron rich B isotopes.

RIKEN radioactive beam facility and polarized radioactive beams

The radioactive beam facility at RIKEN, presently consisting of K=540 cyclotron and projectile fragment separator RIPS, has been in operation for about a decade, in which a number of experiments with beams of light neutron-rich nuclei have been conducted. Recently, the construction of new accelerators has been initiated to form a new facility upgraded in energy and intensity, called the RI Beam Factory. In this paper we briefly describe the present and future facilities at RIKEN, and then discuss the physics results obtained up to now. In particular, we focus on results obtained with beams of spin-polarized radioactive nuclei. The polarized radioactive beams are produced in the projectile fragmentation reaction induced by intermediate-energy heavy ion beams, and used for the measurement of magnetic dipole and electric quadrupole moments of nuclei in the regions far from stability. Analyses of the observed magnetic moments in terms of shell models show intriguing results which imply that some of the basic nuclear properties, such as the order in energy of the single-particle orbits, the pairing energy between the excess neutrons, the effective g s -factor for a halo nucleon, and the E2 effective charges tend to alter as the degree of neutron excess increases.

Core polarization effects and giant quadropole resonances in the A ≈ 90 region

The existence, in A ≈ 90 nuclei, of large E2 core polarization effects evident from experimental and shell model fits to decay rates is examined in two independent model calculations: a linearized Hartree-Fock calculation studying the nuclear response function and a macroscopic model involving excitations of giant quadrupole resonances. Both investigations confirm the need for large renormalization of proton and neutron E2 effective charges consistent with the recently discovered isoscalar and isovector giant quadrupole resonances.

Taylor expansions in Hartree-Fock and isoscalar nuclear shifts

We consider changes in the bulk properties of a nucleus when a particle is added to an even system. The main thing we show is that one can determine these changes by doing a Hartree-Fock calculation on the even system only. We must, however, also examine what happens away from equilibrium, or at least get derivates at equilibrium, in the even system. We get expressions for E0 isoscalar effective charges which involve, but do not determine, the nuclear compressibility, likewise expressions for E2 effective charges which involve but do not determine the quadrupolarizability. Illustrative examples using simple interactions are presented. E0 effective charge corrections in a major shell are larger by roughly a factor of two in orbits with high radial quantum number and E2 effective charge corrections are near unity. Finally, we consider simultaneous changes in the radial and quadrupole shapes.

Self-consistent core polarization near 16O

Self-consistent fully-screened core polarization is evaluated by use of the mutually consistent particle-hole, particle-phonon, hole-phonon, and core-to-2 p2 h vertices. The sensitivity of the results to changes in unperturbed single-particle energies and in reaction matrix elements is tested, and it is found that the usual effects of collective enhancements and screening reductions persist. The final results are remarkably stable, even though individual renormalization effects show strong pathologies. It is argued that the RPA is not a good method for treating vibrations of the nuclear core. The self-consistent vertices are applied to calculations of the hole-hole effective interaction, of shell breaking, and of E2 effective charges, and it is shown that all the renormalization effects found in the particle-particle effective interaction show up in these other quantities as well. The conclusion is that self-consistent core polarization is too weak to account for significant renormalizations of effective operators.

“Exact” shell model calculations in A = 17 and A = 18 nuclei and effective operators in the (2s, 1d) shell

A shell model calculation in an enlarged space spanned by two particles in the (2s, 1d) shell and three-particle-one-hole 2 h ̵ ω excitations is performed using the “bare” G-matrix. An effective interaction for the (2s, 1d) shell is generated and its convergence properties are investigated. It is maintained that the series converges reasonably fast in G and that the singleparticle energies used in the calculation are instrumental in this respect. This conclusion is corroborated by the E2 effective charges and B(E2) strengths that we compute for A = 17 and A = 18 nuclei respectively.

Lifetime measurements on E2 isomers in N = 48 nuclei and E2 effective charges of 1g [formula omitted] nucleons

New E2 isomeric 8 + → 6 + transitions have been identified in three N = 48 nuclei, 86Sr, 88Zr and 90Mo. The half-lives have been determined to be 0.46, 1.75 and 1.05 νs, respectively. The comparison of the B( E2, 8 + → 6 +) values in 86Sr and 90Zr indicates that the E2 polarization charge for the neutron is fairly larger than that for the proton.

Effective operators for the nuclear shell model: (III). E2 effective charge with realistic reaction matrices

The structure of effective operators is determined in time-dependent perturbation theory and compared with the approach using Bloch-Horowitz theory discussed in paper I. The E2 effective charges in the spherical shell model arising from the core polarisation in the oxygen and calcium regions are calculated with the G-matrices of Kahana et al.

E2Effective Charges of thef72Proton and Neutron Deduced from the Lifetimes of the6+States inTi50,Fe54, andCa42

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On the [formula omitted] proton configuration in 51211At 126

The nucleus 85 211At 126 has been studied in the 209Bi( α, 2n nγ) reaction and in the EC decay of 211Rn. Eight excited states belonging to the ( h 9 2 ) 3 configuration with spins from 3 2 to 21 2 have been identified. Three E2 effective charges are deduced which show no significant deviation from the corresponding values in 209Bi and 210Po. A high M1 hindrance is observed in three cases as expected within a j n configuration.

Importance of higher order corrections to the effective charge

Rayleigh-Schrödinger perturbation theory through second order is applied to the problem of electromagnetic transitions in closed-shell-plus-one-nucleon nuclei. The concept of effective charge is introduced and its usefulness as a physical parameter is discussed. Effective charges relevant to quadrupole moments and E2 transitions in 17O and 17F are calculated in first and second order. The semi-realistic Kallio-Kolltveit interaction is used to evaluate two-body matrix elements. The Tamm-Dancoff and random phase approximations are also discussed, and results of effective charge calculations made in these approximations are presented. In a set of appendices, explicit formulas for the second-order corrections to the reduced matrix element which describes electromagnetic transitions between single-particle states are given (appendices 1 and 2). Also included in these appendices is a discussion of state dependent separation distances in the Kallio-Kolltveit interaction (appendix 3). In appendix 4, results of effective charge calculations carried out with Kuo-Brown two-body matrix elements are presented. Finally, in appendix 5, E2 effective charges relevant to the closed-shell-minus-one-nucleon nuclei 15O, 15N, 39Ca and 39K are given.

A shell model approach to the calculation of effective charges

A microscopic core-particle coupling model is used to calculate E2 effective charges in mass-15 and mass-17, N = Z ± 1 nuclei. These charge values are compared with the corresponding ones derived from a perturbation theory approach. The close agreement in the effective charges calculated in these two approaches is due to cancellation of effects in the core-particle coupling model which are neglected in perturbation theory.