Ground States Of Even-even Nuclei Research Articles

Confirmation of Giant Pairing Vibration evidence in $$^{\mathrm {12,13}}$$C($$^{\mathrm {18}}$$O,$$^{\mathrm {16}}$$O)$$^{\mathrm {14,15}}$$C reactions at 275 MeV

The Giant Pairing Vibration (GPV) is a correlated two-nucleon excitation mode in atomic nuclei predicted long time ago. It is expected to be excited in two-nucleon transfer reactions, similarly to the pairing vibrations feeding the ground states of even-even nuclei near shell-closure. Recent experiments have provided evidence for this mode in $$^{\mathrm {14}}$$ C and $$^{\mathrm {15}}$$ C nuclei populated via $$^{\mathrm {12}}$$ C, $$^{\mathrm {13}}$$ C( $$^{\mathrm {18}}$$ O, $$^{\mathrm {16}}$$ O) $$^{\mathrm {14}}$$ C, $$^{\mathrm {15}}$$ C two-neutron transfer reactions at 84 MeV beam energy. In the present paper, new data show the persistence of the same structures in the energy spectra of $$^{\mathrm {14}}$$ C and $$^{\mathrm {15}}$$ C populated by the same reactions at a higher bombarding energy of 275 MeV. The extracted centroid, width, spin-parity and transition probability fully agree with the previous observation thus giving a robust confirmation that the GPV mode is populated in such transfer reactions.

Parameter-free predictions for the collective deformation variables β and γ within the pseudo-SU(3) scheme

The consequences of the short range nature of the nucleon-nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters beta and gamma in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC irrep), while in the first half of each shell the two choices are identical. The choice of the hw irrep predicts a transition from prolate to oblate shapes just below the upper end of the rare earth region, between the neutron numbers N=114 and 116 in the W, Os, and Pt series of isotopes, in agreement with available experimental information, while the choice of the hC irrep leads to a prolate to oblate transition in the middle of the shell, which is not seen experimentally. The prolate over oblate dominance in the ground states of even-even nuclei is obtained as a by-product.

Isospin mixing and Coulomb mixing in ground states of even-even nuclei

In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small.

Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory.

We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the T=1 pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing-rotational moments of inertia and demonstrate the mixing of the neutron and proton pairing-rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy density functional.

Octupole deformation in the ground states of even-even nuclei: A global analysis within the covariant density functional theory

A systematic investigation of octupole deformed nuclei is presented for even-even systems with $Z\leq 106$ located between the two-proton and two-neutron drip lines. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range. This allows us to assess theoretical uncertainties within the present covariant models for the prediction of physical observables relevant for octupole deformed nuclei. In addition, a detailed comparison with the predictions of non-relativistic models is performed. A new region of octupole deformation, centered around $Z\sim 98, N\sim 196$ is predicted for the first time. In terms of its size in the $(Z,N)$ plane and the impact of octupole deformation on binding energies this region is similar to the best known region of octupole deformed nuclei centered at $Z\sim 90, N\sim 136$. For the later island of octupole deformed nuclei, the calculations suggest substantial increase of its size as compared with available experimental data.

Peninsula of neutron stability of nuclei in the neighborhood of neutron magic number N = 126

The properties of the ground state of even-even nuclei with extreme neutron excess that are remote from the known neutron drip line (NDL) are calculated. The calculations are based on the Hartree-Fock method with Skyrme forces SkM*, SkI2, Sly4, Ska) with allowance for axial deformation and the BCS pairing approximation. It is shown that the isotone chain at the neutron number N = 126 beyond the NDL forms a peninsula of nuclei that are stable with respect to the emission of one neutron (PNS). The neutron and proton density distributions of the PNS nuclei have spherical symmetry. A mechanism for restoring the stability of nuclei beyond the NDL is discussed. The obtained results are compared with those from Hartree-Fock-Bogoliubov calculations for long isotope chains of Zr and Pd up to the NDL.

Constraining neutrinoless double β decay matrix elements in 130Te

If a reliable measurement of a neutrinoless double beta decay (0v2β) rate is made, the effective neutrino masses can be determined from the nuclear matrix element. Theoretical calculations of nuclear matrix elements, however, show some disagreement. To test the suitability of various theoretical models, they should be benchmarked against experimentally measured nuclear properties, such as the ground-state distribution of nucleons in the parent-daughter nuclei, and how they change as a result of the decay process. Single neutron-adding reactions have been performed on the 0v2β candidate nucleus, 130Te. The Macfarlane-French sum rules have then been used to determine the single-particle vacancies. Some quasi-random phase approximations (QRPA) can greatly simplify theoretical calculations by describing the ground state of even-even nuclei using a BCS wavefunction. This assumption has been tested using two-neutron removal, (p,t) reactions. The BCS wavefunction appeared to be a valid approximation for valence neutrons.

Patterns of the ground states in the presence of random interactions: Nucleon systems

We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular, we calculate probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory frame) quadrupole moments, and discuss $\ensuremath{\alpha}$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei with $A\ensuremath{\geqslant}70$: positive parity is dominant in the ground states of even-even nuclei, while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition, assuming pure random interactions, we find that, for the ground states, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation is observed, and there is no sign of $\ensuremath{\alpha}$-clustering correlation, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a second-order phase transition for the $\ensuremath{\alpha}$-clustering correlation probability.

Trajectories of ground state(p,t)cross sections and the structural classification of nuclei

Cross sections for the $(p,t)$ reaction to ground states of even-even nuclei from Zr to Hg are interpreted in a simple approach. They are shown to be sensitive both to the degree of shell filling (which is related to the number of $L=0$ pairs in the ground state) and to the difference in the number of these pairs between target and final nuclei (that is, to the overlap of the initial and final systems). The cross sections separate according to the two broad classes of nuclei---vibrational and rotational. The analysis is carried out in both a model-independent way and within the framework of the interacting boson approximation.

Extensive Hartree-Fock+BCS calculation with Skyrme SIII force

We have performed deformed Hartree-Fock+BCS calculations with the Skyrme SIII force for the ground states of even-even nuclei with 2 <= Z <= 114 and N ranging from outside the proton drip line to beyond the experimental frontier in the neutron-rich side. We obtained spatially localized solutions for 1029 nuclei, together with the second minima for 758 nuclei. The single-particle wavefunctions are expressed in a three-dimensional Cartesian-mesh representation, which is suitable to describe nucleon skins, halos, and exotic shapes as well as properties of ordinary stable nuclei. After explaining some of the practical procedures of the calculations, we compare the resulting nuclear masses with experimental data and the predictions of other models. We also discuss the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, the halo radii, and the energy difference between the oblate and the prolate solutions. Our results can be obtained via computer network.

Refinement of the gross theory of β-decay for odd-odd nuclei

Abstract The gross theory of nuclear β-decay is refined for decays of odd-odd nuclei. The main refinement is to take into account the selection rule for the transition to the ground state based on a statistical consideration. The effect of the transition to the first excited 2 + state, which has not explicitly been treated in the conventional gross theory, is also included explicitly if that transition is expected to predominate over the transition to the ground state. The refined theory at this stage gives half-lives in better agreement with experiment than those by the conventional gross theory except for the parents with spin-parity 1 − . The calculated half-lives of 1 − nuclei are generally shorter than the experimental data, and it is shown that the cause for this underestimation is hindrance of the transitions between 1 − ground states of odd-odd nuclei and 0 + ground states of even-even nuclei in actual nuclei. Therefore, the theory is further refined for 1 − parents by incorporating this hindrance in a phenomenological way. While this study has improved the gross theory for β-decays of odd-odd nuclei, it has also revealed a problem inherent in the gross theory, which is briefly discussed together with the problem of half-life prediction.

Spin-isospin SU(4) symmetry in sd- and fp-shell nuclei.

For all even-A nuclei in the sd shell we evaluate the overlap between several low-lying states, obtained by diagonalizing the realistic Wildenthal interaction, and the eigenstates of the SU(4) Casimir operator. We find that the J=0+ ground states of even-even nuclei near the middle of the shell have rather small overlaps (less than 0.5) with the lowest SU(4) Young tableaux, while the J=0+ and 1+ lowest states of odd-odd nuclei have noticeably larger overlaps (0.6–0.7). We also find that the expansion in the SU(4) Young tableaux converges quite rapidly, and that the two or three lowest tableaux usually account for more than 90% of the nuclear wave function. We then extend the calculation to the fp shell and evaluate the overlaps between the J=0+ ground states obtained by diagonalizing a realistic interaction and the SU(4) eigenstates for even-even nuclei with maximum isospin. For the fp shell the overlaps are even smaller than in the sd shell. Since we observe such sizable SU(4) symmetry breaking effects in the relatively simple sd and pf nuclei, we are rather pessimistic about the prospects of using conclusions based on SU(4) in heavier, more complex nuclei.

On the (3He,n) reaction in theA ? 100 region

The available experimental data on the (3He,n) reaction between the ground states of even-even nuclei and lowest 1/2− levels of odd-A nuclei in theA ≈ 100 region are analyzed in a systematic way by the DWBA. The deduced relative intensities of these two-proton transfers, and their uncertainties, are compared to the predictions of various nuclear models. In particular, the influence of the finite dimension of the configuration space available to the transferred protons, and of the blocking effect of a 2p 1/2− proton, are examined.

The nuclear radius from alpha decay

Nuclear radii for mass numbers between A = 140 and 252 have been computed from 121 alpha decays between ground states of even-even nuclei. We use for that the two-body solution for the square well potential that we gave recently. The computed radii obey the A1/3 law and they are consistent with the precise radii obtained from electron scattering. These two sets of radii show structures which are correlated.

Possible triaxial shape of even-Amercury nuclei and a phase transition between ≤Hg80196andHg80198,200

Evidences for the existence of triaxial shapes in the ground states of even-even nuclei are considered. Most if not all previous reports that support the existence are not definite. The observed decreasing of the energies of the ${2}_{1}^{+}$ and ${4}_{1}^{+}$ states for $^{198,200}\mathrm{Hg}$ compared to the lighter Hg nuclei is opposite to the expected when $N$ increases and deformation decreases. We show that a triaxial model with a phase transition between $N=116 \mathrm{and} 118$ qualitatively can explain the regularities in $B(E2)$ ratios and ${E}_{I}$ for the collective levels with ${I}^{\ensuremath{\pi}}={2}_{1}^{+}, {4}_{1}^{+}, {6}^{+}, \mathrm{and} {2}_{2}^{+}$ in $^{192\ensuremath{-}200}\mathrm{Hg}$.NUCLEAR STRUCTURE Analysis of levels in $^{192\ensuremath{-}200}\mathrm{Hg}$ in triaxial rotor model.

On correlations between reduced partial alpha widths and neutron and radiative widths in neutron resonances

Cases are considered in which there may exist correlations between reduced partial alpha widths Λ αλf o and reduced neutron widths Λ nλ o in neutron resonances. It is shown that there may occur large correlations between Λ nλ o for s-wave neutron capture by an even-even spherical nucleus and the alpha transition to the j π = 1 2 + state. Significant correlations between the alpha and gamma widths may be expected in the cases when alpha and E1 transitions proceed to the ground states of even-even nuclei as well as in the cases when alpha transition goes to the ground state and E1 transitions go to the one-phonon and two-phonon states.

Systematics of some beta-transitions

0+ excited states of even-even nuclei can arise in several ways. In order to throw some light on the mechanism of excitation of these states, the log (ft) values for beta-transitions to the 0+ excited state and the 0+ ground state of even-even nuclei have been compared. In this analysis both allowed and forbidden beta-transitions have been considered. This survey is similar to that of beta-transitions by M. Sakai. Results of the present analysis are presented and compared to that of Sakai.