Valence Neutrons Research Articles

Dynamic chirality in the interacting boson model

The chiral interpretation of twin bands in odd-odd nuclei is investigated in the Interacting Boson Model framework. The analysis of the wave functions shows that the possibility for angular momenta of the valence proton, neutron and core to find themselves in the favorable, almost orthogonal geometry is present, but not dominant. Such behavior is found to be similar in nuclei where both the level energies and the electromagnetic decay properties display the chiral pattern, as well as in those where only the level energies of the corresponding levels in the twin bands are close together. The difference in the structure of the two types of chiral candidates nuclei can be attributed to different β and γ fluctuations, induced by the exchange boson-fermion interaction, i.e. by the antisymmetrization of odd fermions with the fermion structure of the bosons. In both cases the chirality is weak and dynamic. Among the nuclei that are candidates for chiral behavior, the best candidate is probably the odd-even 135Nd, where the β and γ fluctuations are strongly reduced and chirality, although dynamic in origin, is rather close to the static limit.

New aspects of chiral symmetry breaking in atomic nucleus

The significant progresses of the chirality in atomic nuclei are briefly reviewed for both experimental and theoretical sides. A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core and applied to investigating the chirality in odd-A nucleus 135Nd. Static chirality has been shown to be a transient phenomenon surrounding by chiral vibrations. It is found that the B(M1) staggering is associated strongly with the characters of nuclear chirality, i.e., the staggering is weak in chiral vibration region while strong in the static chirality region.

Halo Structure of the Island of Inversion NucleusNe31

The cross sections for single-neutron removal from the very neutron-rich nucleus 31Ne on Pb and C targets have been measured at 230 MeV/nucleon using the RIBF facility at RIKEN. The deduced large Coulomb breakup cross section of 540(70) mb is indicative of a soft E1 excitation. Comparison with direct-breakup model calculations suggests that the valence neutron of 31Ne occupies a low-l orbital (most probably 2p(3/2)) with a small separation energy (S(n) approximately < 0.8 MeV), instead of being predominantly in the 1f(7/2) orbital as expected from the conventional shell ordering. These findings suggest that 31Ne is the heaviest halo system known.

Linear-chain structure of three α-clusters in 16C and 20C

Using a Skyrme mean-field model, we investigate the linear-chain configurations of three α-clusters with four or eight additional valence neutrons in 16C and 20C and discuss the relation between the stability of such states and the neutron number. The Hartree–Fock solution is sought from an initial configuration with three α-clusters and the additional neutrons are prepared in wave functions of various symmetries. We find at least five different chain configurations in 16C and one “closed shell” configuration in 20C that appear as highly converged states in the Hartree–Fock iterations. We investigate their stability with respect to quadrupole and octupole distortions and find that they appear unstable with respect to bending deformations, but show lifetimes that may lead to observable resonances.

DI-NEUTRON CORRELATION IN LIGHT NEUTRON-RICH NUCLEI

Using a three-body model with density-dependent contact interaction, we discuss the root mean square distance between the two valence neutrons in 11 Li nuclues as a function of the center of mass of the neutrons relative to the core nucleus 9 Li . We show that the mean distance takes a pronounced minimum around the surface of the nucleus, indicating a strong surface di-neutron correlation. We demonstrate that the pairing correlation plays an essential role in this behavior. We also discuss the di-neutron structure in the 8 He nucleus.

Two-particle correlations in continuum dipole transitions in Borromean nuclei

We study the energy and angular distributions of two emitted neutrons from the dipole excitation of two typical, weakly bound Borromean nuclei, $^{11}\mathrm{Li}$ and $^{6}\mathrm{He}$, by using a three-body model. Our calculation indicates that those distributions are considerably different between the two nuclei, even though both the nuclei exhibit similar strong dineutron correlations in the ground state to each other. We point out that this different behavior primarily reflects the interaction between the neutron and the core nucleus, especially the $s$-wave virtual state in $^{10}\mathrm{Li}$, rather than the interaction between the valence neutrons.

Effective operators from exact many-body renormalization

We construct effective two-body Hamiltonians and E2 operators for the p shell by performing 16h Q ab initio no-core shell model (NCSM) calculations for A = 5 and A = 6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the 0hΩ space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.

Simple parametrization of an α-decay spectroscopic factor in the 150 ⩽ A ⩽ 200 region

Half-life values for α-decay in the mass region A = 150–200 have been calculated in the microscopic super asymmetric fission model. The interaction between the α-particle and the daughter nucleus has been obtained in the double folding model with the microscopic interaction DDM3Y1. Theoretical densities for the nuclei involved have been calculated in the relativistic mean-field approach with the Lagrangian density FSU Gold. Spectroscopic factors for α-decay, calculated as the ratios of the theoretically calculated and experimentally measured half-life values, show a simple dependence on the mass number and the product of the number of valence protons and neutrons. The implications of the parametrization have been discussed. Finally, based on this simple relation, α-decay half-life values in a number of nuclei have been predicted.

ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

One-neutron removal strength ofHe7intoHe6using the complex scaling method

We study the one-neutron removal strength of the $^{7}\mathrm{He}$ ground state, which provides us with the $^{6}\mathrm{He}\text{\ensuremath{-}}n$ component in $^{7}\mathrm{He}$. The He isotopes are described on the basis of the $^{4}\mathrm{He}+\mathit{Xn}$ cluster model ($X=1,2,3$). The complex scaling method is applied to describe not only the Gamow resonances but also the nonresonant continuum states of valence neutrons, with the correct boundary condition of particle decays. The one-neutron removal strength of $^{7}\mathrm{He}$ into the unbound states of $^{6}\mathrm{He}$ is calculated using the complex-scaled Green's function, in which a complex-scaled complete set of $^{4}\mathrm{He}+n+n$ states is adopted. Using this framework, we investigate resonant and nonresonant contributions of the strength, which individually produce specific structures in the distributions. In addition, we propose a method to obtain the real-value strength using the complex values of spectroscopic factors of Gamow states. As a result, the $^{6}\mathrm{He}$(${2}^{+}$) resonance is found to give the largest contribution.

Resonant and nonresonant breakup ofBe11on a proton target

Full Faddeev-type calculations are performed for the breakup of $^{11}\mathrm{Be}$ on a proton target at 63.7 MeV/nucleon incident energy. A simplified two-body model for $^{11}\mathrm{Be}$ involves an inert $^{10}\mathrm{Be}({0}^{+})$ core and a valence neutron. Inclusive cross sections as a function of the proton angle are calculated around the well known resonance at ${E}_{r}=1.275$ MeV including both resonant and nonresonant contributions. A reasonable agreement between the calculated angular distributions and the data is obtained but a large discrepancy relative to similar CDCC calculations is found at small proton angles.

Low-lying states of heavy nuclei within the nucleon pair approximation

In this article we perform systematic calculations on low-lying states of 33 nuclei with A=202-212, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one J=4 valence neutron pair, and one J=4,6,8 valence proton pair, in addition to the usual S and D pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and E2 transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.

Chirality in odd-A nucleus 135Nd in particle rotor model

A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core. It is applied to investigating the chirality in odd-A nucleus 135Nd with πh11/22⊗νh11/2−1 configuration for the first time in a fully quantal approach. For the two chiral sister bands, the observed energies and the B(M1) and B(E2) values for the in-band as well as interband transitions are reproduced excellently. Root mean square values of the angular momentum components and their probability distributions are used for discussing in detail the chiral geometry of the aplanar rotation and its evolution with angular momentum. Chirality is found to change from a soft chiral vibration to nearly static chirality at spin I=39/2 and back to another type of chiral vibration at higher spin.

Neutrinoless double-βdecay in the microscopic interacting boson model

We present a formalism for calculating nuclear matrix elements of double-$\ensuremath{\beta}$ decay within the framework of the microscopic interacting boson model. We calculate Fermi, Gamow-Teller, and tensor matrix elements in the decay of Ge-Se-Mo-Te-Xe-Nd-Sm and compare our results with those of the shell-model (SM) and of the quasiparticle random-phase approximation (QRPA). Our results are in agreement with QRPA. We discuss simple features of the matrix elements and give a formula that allows one to estimate matrix elements in terms of the number of valence proton and neutron pairs.

Schottky Mass Measurement of theHg208Isotope: Implication for the Proton-Neutron Interaction Strength around Doubly MagicPb208

Time-resolved Schottky mass spectrometry has been applied to uranium projectile fragments which yielded the mass value for the 208Hg (Z=80, N=128) isotope. The mass excess value of ME=-13 265(31) keV has been obtained, which has been used to determine the proton-neutron interaction strength in 210Pb, as a double difference of atomic masses. The results show a dramatic variation of the strength for lead isotopes when crossing the N=126 neutron shell closure, thus confirming the empirical predictions that this interaction strength is sensitive to the overlap of the wave functions of the last valence neutrons and protons.

Neutron transition strengths of21+states in the neutron-rich oxygen isotopes determined from inelastic proton scattering

A coupled-channel analysis of the $^{18,20,22}\mathrm{O}(p,{p}^{'})$ data has been performed to determine the neutron transition strengths of the ${2}_{1}^{+}$ states in oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and isospin-dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hartree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar (${\ensuremath{\delta}}_{0}$) and isovector (${\ensuremath{\delta}}_{1}$) deformation lengths of the ${2}_{1}^{+}$ states in $^{18,20,22}\mathrm{O}$ have been extracted from the folding model analysis of the $(p,{p}^{'})$ data. A specific $N$ dependence of ${\ensuremath{\delta}}_{0}$ and ${\ensuremath{\delta}}_{1}$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for the ${2}_{1}^{+}$ state in $^{20}\mathrm{O}$, with ${\ensuremath{\delta}}_{1}$ about 2.5 times larger than ${\ensuremath{\delta}}_{0}$, which indicates a strong core polarization by the valence neutrons in $^{20}\mathrm{O}$. The ratios of the neutron/proton transition matrix elements (${M}_{n}/{M}_{p}$) determined for the ${2}_{1}^{+}$ states in $^{18,20}\mathrm{O}$ have been compared with those deduced from the mirror symmetry, using the measured $B(E2)$ values of the ${2}_{1}^{+}$ states in the proton-rich $^{18}\mathrm{Ne}$ and $^{20}\mathrm{Mg}$ nuclei, to discuss the isospin impurity in the ${2}_{1}^{+}$ excitation of the $A=18$, $T=1$ and $A=20$, $T=2$ isobars.

Study of magnetic-rotation in 82Rb by g-factor measurements

Magnetic rotation in 82Rb has been investigated for the first time by g-factor measurement of intra-band states of the magnetic-rotational band built on the 11- state. The g-factors were measured by a TMF-IMPAD method and calculated by a semi-classical model of independent particle angular momentum coupling assumption. The g-factors and deduced shears angles decrease with the increasing of spin along the band, illustrating a step-by-step alignment of the valence protons and neutrons. The rapid alignment of the valence neutrons leads to a decrease of g-factors. The present results vividly reveal the shears mechanism of magnetic rotation.

Density effect of the neutron halo nucleus induced reactions in intermediate energy heavy ion collisions

Using an isospin-dependent quantum molecular dynamics (IQMD) model, we study the 15C induced reactions from 30–120 MeV/nucleon systematically. Here the valence neutron of 15C is assigned at both 1d5/2 and 2s1/2 states respectively in order to study the density effect of reaction mechanism. It is believed that the existent neutron halo structure at the 2s1/2 state of 15C will affect the light particle emission evidently. In our calculation, the different density distributions of 15C at two states are calculated by relativistic mean field (RMF) model and introduced in the initiation of IQMD model, respectively. It is found that some observables such as emission fragmentation multiplicity, emission neutron/proton ratio and emission neutrons' kinetic energy spectrum are sensitive to the initial density distribution.

Relativistic Mean Field Study on Halo Structures of Mirror Nuclei

Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory. The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus, the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smaller with the increase of the mass number A, and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair of mirror nuclei decrease almost linearly with the increase of the mass number A.

Persistent decoupling of valence neutrons toward the dripline: Study ofC20byγspectroscopy

The very neutron-rich nucleus $^{20}\mathrm{C}$ has been investigated by inelastic scattering on $^{208}\mathrm{Pb}$ and liquid hydrogen targets. Through distorted wave analysis, the reduced electric quadrupole transition probability $B(E2;{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})l18.4$ (stat) ${e}^{2} {\mathrm{fm}}^{4}$ and the neutron transition probability ${M}_{n}^{2}=292\ifmmode\pm\else\textpm\fi{}52$ (stat) ${\mathrm{fm}}^{4}$ have been derived. A simple shell model calculation has shown a need for a factor of about 0.4 decrease of the normal polarization charges to elucidate the results. This is interpreted as a decoupling of the valence neutrons from the nuclear core in carbon isotopes heavier than $^{14}\mathrm{C}$.