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Register a new userInfrared extrapolations of quadrupole moments and transitions
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We study the convergence of bound-state quadrupole moments in finite harmonic oscillator spaces. We derive an expression for the infrared extrapolation for the quadrupole moment of a nucleus and benchmark our results using different model interactions for the deuteron. We find good agreement between the analytically derived and numerically obtained convergence behavior. We also derive an extrapolation formula for electric quadrupole transitions and find good agreement with the numerical calculation of a simple system.
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The static quadrupole moments (SQMs) of nuclear chiral doublet bands are investigated for the first time taking the particle-hole configuration $pi(1h_{11/2}) otimes u(1h_{11/2})^{-1}$ with triaxial deformation parameters in the range $260^circ leq gamma leq 270^circ$ as examples. The behavior of the SQM as a function of spin $I$ is illustrated by analyzing the components of the total angular momentum. It is found that in the region of chiral vibrations the SQMs of doublet bands are strongly varying with $I$, whereas in the region of static chirality the SQMs of doublet bands are almost constant. Hence, the measurement of SQMs provides a new criterion for distinguishing the modes of nuclear chirality. Moreover, in the high-spin region the SQMs can be approximated by an analytic formula with a proportionality to $cosgamma$ for both doublet bands. This provides a way to extract experimentally the triaxial deformation parameter $gamma$ for chiral bands from the measured SQMs.
Electric quadrupole (E2) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many p-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio calculations for quadrupole moments are particularly challenging, due to sensitivity to long-range behavior of the wave functions. We therefore study more robustly-converged ratios of quadrupole moments: across mirror nuclides, or of proton and neutron quadrupole moments within the same nuclide. In calculations for mirror pairs in the p-shell, we explore how well the predictions for mirror quadrupole moments agree with experiment and how well isospin (mirror) symmetry holds for quadrupole moments across a mirror pair.
The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and angular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.
A method of calculating static moments of excited states and transitions between excited states is formulated for non-magic nuclei within the Green function formalism. For these characteristics, it leads to a noticeable difference from the standard QRPA approach. Quadrupole moments of the first 2+ states in Sn and Pb isotopes are calculated using the self-consistent TFFS based on the Energy Density Functional by Fayans et al. with the set of parameters DF3-a fixed previously. A reasonable agreement with available experimental data is obtained.
The electric-quadrupole coupling constant of the ground states of the proton drip line nucleus $^{20}$Na($I^{pi}$ = 2$^{+}$, $T_{1/2}$ = 447.9 ms) and the neutron-deficient nucleus $^{21}$Na($I^{pi}$ = 3/2$^{+}$, $T_{1/2}$ = 22.49 s) in a hexagonal ZnO single crystal were precisely measured to be $|eqQ/h| = 690 pm 12$ kHz and 939 $pm$ 14 kHz, respectively, using the multi-frequency $beta$-ray detecting nuclear magnetic resonance technique under presence of an electric-quadrupole interaction. A electric-quadrupole coupling constant of $^{27}$Na in the ZnO crystal was also measured to be $|eqQ/h| = 48.4 pm 3.8$ kHz. The electric-quadrupole moments were extracted as $|Q(^{20}$Na)$|$ = 10.3 $pm$ 0.8 $e$ fm$^2$ and $|Q(^{21}$Na)$|$ = 14.0 $pm$ 1.1 $e$ fm$^2$, using the electric-coupling constant of $^{27}$Na and the known quadrupole moment of this nucleus as references. The present results are well explained by shell-model calculations in the full $sd$-shell model space.
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