Valence Neutrons Research Articles

Single-particle motion of excess neutrons around parity-asymmetric clusters

To investigate structure of 21Ne, where the core has a parity asymmetric property, we superpose thousands of Slater determinants. Applying the method we can see importance of α-correlation for several low-lying states and also property of a valence neutron. The 13C nucleus is studied as parity asymmetric core with 3α. We confirm the change of spin quantization.

Proton-neutron coupling in the Gamow shell model: The lithium chain

The shell model in the complex k-plane (the so-called Gamow Shell Model) has recently been formulated and applied to structure of weakly bound, neutron-rich nuclei. The completeness relations of Newton and Berggren, which apply to the neutron case, are strictly valid for finite-range potentials. However, for long-range potentials, such as the Coulomb potential for protons, for which the arguments based on the Mittag-Leffler theory do not hold, the completeness still needs to be demonstrated. This has been done in this paper, both analytically and numerically. The generalized Berggren relations are then used in the first Gamow Shell Model study of nuclei having both valence neutrons and protons, namely the lithium chain. The single-particle basis used is that of the Hartree-Fock-inspired potential generated by a finite-range residual interaction. The effect of isospin mixing in excited unbound states is discussed.

Neutron removal reactions of 17C

Measurement of one-, two- and three-neutron removal cross sections of 17C at 79 A MeV on a 12C target has been carried out using the fragment separator RIPS of RIKEN. The one-neutron removal cross sections were compared with the few-body Glauber calculations coupled with the spectroscopic factors from the shell model. A fair agreement between the calculation and the experimental data was found. The prediction of the relation between the reaction cross sections and one-neutron removal cross section can be well satisfied, which means that 17C could be described by a core plus valence neutron system. The two- and three-neutron removal cross sections of 17C are reported for the first time.

High-spin isomers and three-neutron valence configurations in 211Pb

Deep-inelastic reactions between a beam of 1360 MeV 208Pb ions and a thick 238U target have been used to populate the neutron-rich nucleus 211Pb. The observation of its γ decay has allowed identification of excited states up to the highest spin which can be formed from the three valence neutrons, including identification of three high-spin isomers. Level energies and transition strengths are compared to shell-model calculations with empirical interactions and predictions are made for the expected behaviour of more neutron-rich lead isotopes. The evidence for a possible increase in the neutron effective charge moving away from the N=126 shell gap is evaluated.

Extended sudden approximation modeling of high-energy nucleon-removal reactions

Calculations based on the sudden approximation have been performed to describe high-energy single-nucleon removal reactions. Within this approach, which takes as its starting point the formalism developed to describe the breakup of well-developed single-neutron halo systems, the nucleon-removal cross section and the full three-dimensional momentum distributions of the core fragments, including absorption, diffraction, Coulomb, and nuclear-Coulomb interference amplitudes, have been computed. The Coulomb, breakup has been treated to all orders for the dipole interaction. The results are compared here to experimental data for a range of light, neutron-rich $psd$-shell nuclei taken at beam energies of $43--68\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\text{nucleon}$. Good agreement is found for the inclusive cross sections and both the longitudinal and transverse momentum distributions. In the case of $^{17}\mathrm{C}$, comparison is also made with the results of calculations using the transfer-to-the-continuum model. The three-dimensional momentum distributions computed within the sudden approximation model exhibit longitudinal and transverse momentum components that are strongly coupled by the reaction for $s$-wave states, while no such effect is apparent for $d$ waves. Incomplete detection of transverse momenta arising from limited experimental acceptances thus leads to a narrowing of the longitudinal distributions for nuclei with significant $s$-wave valence neutron configurations, as confirmed by the data. Asymmetries in the longitudinal momentum distributions attributed to diffractive dissociation are also explored.

Observation of bound excited states in 15B

The structure of the A/Z = 3 nucleus 15B has been investigated using the in-beam $\gamma$ -spectroscopy technique with a fragmentation reaction of a 36S beam on a 9Be target at 77.5 ${\rm MeV}\cdot A$ . The fragments were identified and selected by their energy loss and time of flight using the SPEG spectrograph. $\gamma$ -ray energies and intensities have been measured in coincidence with the projectile-like fragments. From this information as well as from the $\gamma\gamma$ -coincidence relationships a level scheme is proposed for 15B up to the neutron separation energy. The experimental results have been interpreted using shell model calculations in the psd valence space. Effects of the weakly bound nature of the valence neutrons have been observed.

Electric dipole transitions in neutron-rich nuclei

The structure of neutron-rich nuclei in several isotopes is investigated by shell model calculations. We study the electric dipole (E1) transitions in C isotopes focusing on the interplay between the low-energy Pigmy strength and the giant dipole resonance (GDR). Reasonable agreement is obtained with available experimental data for the photoreaction cross sections in 12C, 13C, and 14C with the inclusion of the quenching effects. A low-energy peak in the dipole strength in 15C is associated with a single-particle motion of the 1s1/2 valence neutron relative to the 14C core. The calculated transition strength below the GDR in C isotopes heavier than 15C is found to exhaust about 50–80% of the cluster sum rule value and 12–16% of the classical Thomas-Reiche-Kuhn sum rule value. Next, we point out that the quadrupole and magnetic moments in the odd C isotopes strongly depend on configuration, which will be useful to determine the spin parities and the deformations of the ground states of these nuclei. The electric quadrupole (E2) transitions in even C isotopes are also studied. The isotopic dependence of the E2 transition strength is found to be reasonably well explained, although the calculated strength largely overestimates the unexpectedly small strength observed in 16C. The E1 strength in 18N and 19N as well as in Ne isotopes is also investigated.

Di-neutron elastic transfer in the 4He(6He, 6He)4He reaction

Elastic 6He+4He data measured at Ec.m.=11.6, 15.9, and 60.3 MeV have been analyzed within the coupled reaction channels (CRC) formalism, with the elastic-scattering and two-neutron (2n) transfer amplitudes coherently included. Contributions from the direct (one-step) and sequential (two-step) 2n-transfers were treated explicitly based on a realistic assumption for the 2n-transfer form factor. The oscillatory pattern observed in 4He(6He,6He)4He angular distribution at low energies was found to be due to an interference between the elastic scattering and 2n-transfer amplitudes. Our CRC analysis shows consistently that the direct 2n-transfer strongly dominates over the sequential transfer and thus confirms the dominance of 2n–4He configuration over the n–5He one in the 6He wave function. This result suggests a strong clusterization of the two valence neutrons and allows, therefore, a reliable estimate for the di-neutron spectroscopic amplitude.

Extended optical model analyses of elastic scattering and fusion cross sections for heavy-ion collisions with loosely bound projectiles at near-Coulomb-barrier energies

Within the framework of an extended optical model, simultaneous ${\ensuremath{\chi}}^{2}$ analyses are performed for elastic scattering and fusion cross-section data for $^{9}\mathrm{Be}+^{209}\mathrm{Bi}$ and $^{6}\mathrm{Li}+^{208}\mathrm{Pb}$ systems, both involving loosely bound projectiles, at near-Coulomb-barrier energies to determine the polarization potential as decomposed into direct reaction $(\text{DR})$ and fusion parts. We show that both $\text{DR}$ and fusion potentials extracted from ${\ensuremath{\chi}}^{2}$ analyses separately satisfy the dispersion relation, and that the expected threshold anomaly appears in the fusion part. The $\text{DR}$ potential turns out to be a rather smooth function of the incident energy, and has a magnitude at the strong absorption radius much larger than the fusion potential, explaining why a threshold anomaly has not been seen in optical potentials deduced from fits to the elastic-scattering data without such a decomposition. Using the extracted $\text{DR}$ potential, we examine the effects of projectile breakup on fusion cross sections ${\ensuremath{\sigma}}_{F}$. The observed suppression of ${\ensuremath{\sigma}}_{F}$ in the above-barrier region can be explained in terms of the flux loss due to breakup. However, the observed enhancement of ${\ensuremath{\sigma}}_{F}$ in the subbarrier region cannot be understood in terms of the breakup effect. Rather, the enhancement can be related to the $Q$ value of the neutron transfer within the systems, supporting the ideas of Stelson et al. [Phys. Lett. B 205, 190 (1988); Stelson et al.Phys. Rev. C 41, 1584 (1990)] that subbarrier fusion starts to occur when the colliding ions are at a distance where the barrier against the flow of the valence neutrons disappears and thus neutron exchange can take place freely.

Exotic cluster structure in light neutron-rich nuclei

The cluster structure of C isotopes is investigated using a microscopic α+α+α+n+n… model based on the molecular orbit (MO) model. The stability of the linear chain of 3α with respect to the breathing mode and the bending mode for various neutron configurations is investigated. The combination of the valence neutrons in the π- and σ-orbits is promising to stabilize for these modes, and the excited states of 16C with the (3/2π-)2(1/2σ-)2 configuration for the four valence neutrons are one of the most promising candidates for such structure. Furthermore, the equilateral-triangular shape of 3α surrounded by valence neutrons is suggested for 14C. The 3-, 4-, and 5- members of this rotational band appear around the 10Be+α threshold, and these calculated states correspond to the experimentally observed 3- state (9.80 MeV) and 4- state (11.67 MeV). A positive-parity rotational band (0+, 2+, 4+) also arises around this threshold energy, and these results suggest that the picture of inversion doublet structure works also in neutron-rich nuclei.

Resonance structure of 9Be and 10Be in a microscopic cluster model

Structure of the excited states in 9Be and 10Be have been theoretically explored by means of the α+α+n and α+α+n+n microscopic cluster model respectively. Resonance excited states in 9Be and 10Be are localized by solving the two‐body scattering problems of {8Be(0+, 2+, 4+)+n, 5He(3/2−, 1/2−)+α} and {9Be(3/2−, 1/2+, 5/2−)+n, 6He(0+, 2+)+α} respectively. Our models have reproduced satisfactorily the experimental low‐energy spectrum in 9Be and given various resonance excited states in 10Be. Our model shows that the two and three competing configurations are quite essential to reproduce the anomalous 1/2+ state in 9Be and the second 0+ state in 10Be respectively. One of these configurations has a strong core(8Be) distortion which is induced by the valence neutron and is responsible for lowering the s1/2 orbit in these states. Another configuration produces a spatially extended neutron distribution outside the core like the neutron halo.

Parity inversion and breakdown of shell closure in Be isotopes

The coupling of single-particle motion and of vibrations in $_{4}^{11}\mathrm{Be}$ produces dressed neutrons which spend only a fraction of the time in pure single-particle states, and which weighing differently from the bare neutrons lead to parity inversion. The interaction of the two least bound neutrons in the ground state of $_{4}^{12}\mathrm{Be}$ mediated by the ${v}_{14}$ Argonne nucleon-nucleon potential and by the exchange of surface vibrations of the core $^{10}\mathrm{Be}$ gives rise to a strongly correlated state, where the two valence neutrons are distributed over ${s}^{2},{p}^{2}$, and ${d}^{2}$ configurations, resulting in the breaking of the $N=8$ shell closure.

Study of the density distribution of 17C from reaction cross section measurement

The reaction cross section of 17C on a carbon target at 79 A MeV has been measured by the transmission method. The density distribution of 17C was deduced using the finite-range Glauber model (FRGM) combined with the interaction cross section of 17C at high energy. The existence of a tail in the density distribution of 17C is suggested to get a better understanding of both the low energy and high energy data. Under a core plus single-particle assumption, analysis shows a dominant d-wave of the valence neutron in 17C.

Nuclear structure with clusters and covalent valence neutrons

Nuclear structure with clusters and covalent valence neutrons

Nuclear structure with clusters and covalent valence neutrons

Recent studies of excited states in light nuclei with neutron excess showing extreme deformations like super- or hyper-deformation are discussed. The structure of these states is related to nuclear clustering, to combinations of clusters of different size with valence neutrons in covalent binding orbits, which stabilise the unstable cluster states. Octupole deformations related to instrinsically asymmetric cluster configurations appear, these give rise to rotational bands as parity (inversion) doublets. Data with the observation of inversion doublets and of molecular structure in isotopes of Be, C and Ne are shown.

Symmetry Properties of Radioactive N = Z Nuclei

Recent mass measurements of proton-rich nuclei close to the N=Z line were used for the calculation of the interaction strength δVpn between valence protons and neutrons. When compared with δVpn values calculated from mass values of the AME’95 mass tables, the breaking down of the SU(4) symmetry is verified at Z=32,33,34.

Decoupling of valence neutrons from the core in 16C

The neutron and proton excitations in 16C nucleus have been investigated by use of the Coulomb-nuclear interference method applied to the 208Pb+16C inelastic scattering. Angular distribution of the 16C nuclei in the inelastic channel populating the first 2+ state has been measured. The neutron and proton transition matrix elements, Mn and Mp, have been determined from the “Coulomb” and “matter” deformation-length parameters obtained by distorted wave calculations. The Mp or its corresponding B(E2;2+1→0+) value was found to be extremely small: 0.28±0.06 Weisskopf units consistent with a recent lifetime measurement. Furthermore, the extracted Mn/Mp ratio has an unexpectedly large value of 7.6±1.7. These results suggest that the 2+1 state in 16C is a nearly pure valence neutron excitation.

Characterization of molecular structures in the deformed harmonic oscillator

The molecular orbits of the valence neutrons of a range of deformed α-conjugate nuclei were modelled using linear combinations of single-particle wavefunctions in a harmonic oscillator potential. Molecular structures were found for oblate nuclei from 13C to 25Mg, and prolate chain-state nuclei from 9Be to 25Mg, and for the higher order 2:1 prolate nuclei 21Ne and 33S. These orbitals are shown to be commensurate with the energy level scheme of the deformed harmonic oscillator and the Nilsson model. Tentative links with experimentally observed states are also made.

Studies of multi-nucleon transfer reactions in 90Zr(18O,X) and 90Zr(16O,X)

Multi-nucleon transfer reactions in 18O + 90Zr and 16O + 90Zr have been studied at an incident energy of 90 MeV. The energy spectra and angular distributions are measured. The data have been analyzed to obtain cross-section dependence on the number of nucleons transferred and on the ground-state Q-values. In the 90Zr(18O, X); X = 16O, 17,16,15,14N, 14,13,12C, 12,11,10B, 10,9,7Be and 7,6Li reactions, 2n and 2n-correlated transfer cross-sections are observed to be enhanced as compared to the 16O + 90Zr reaction. A detailed comparison in the multi-particle stripping and elastic-scattering cross-section between these two systems are made in order to investigate the possible influence of the two valence neutrons in 18O nucleus. Diffractional model DWBA calculations, based on the direct surface transfer model, have been performed to understand the reaction mechanism of multi-nucleon transfer to continuum.

Structure of the excited states ofBe10in a microscopic cluster model

The structure of the excited states of $^{10}\mathrm{Be}$ is theoretically explored by means of the microscopic $\ensuremath{\alpha}+\ensuremath{\alpha}+n+n$ four-cluster model. The two-body scattering problem of ${^{9}\mathrm{Be}(3∕{2}^{\ensuremath{-}},1∕{2}^{+},5∕{2}^{\ensuremath{-}})+n}+{^{6}\mathrm{He}({0}^{+},{2}^{+})+\ensuremath{\alpha}}$ is solved by the microscopic $R$-matrix method in order to localize the resonance excited states in $^{10}\mathrm{Be}$. The wave functions of $^{9}\mathrm{Be}$ and $^{6}\mathrm{He}$ are given by the microscopic $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ and $\ensuremath{\alpha}+n+n$ three-cluster models, respectively. Our model can reproduce not only the ground ${0}^{+}$ state but also the second ${0}^{+}$ state simultaneously. The second ${0}^{+}$ state has a highly developed $\ensuremath{\alpha}+\ensuremath{\alpha}\phantom{\rule{0.2em}{0ex}}(^{6}\mathrm{He}+\ensuremath{\alpha})$ clustering and is dominated by the $2\ensuremath{\hbar}\ensuremath{\omega}$ excitation in the shell-model configuration wherein two neutrons occupy the $1{s}_{1∕2}$ orbit. The ground state has a more compact structure due to the large binding energy but some weak $\ensuremath{\alpha}+\ensuremath{\alpha}$ clustering still persists. Our microscopic multicluster model is applied to the resonance excited states lying above the $^{9}\mathrm{Be}+n$ threshold, and the present model gives various resonance excited states. Among these states, the ${0}_{2}^{+}$, ${2}_{4}^{+}$, and ${4}_{2}^{+}$ states could constitute a ${K}^{\ensuremath{\pi}}={0}_{2}^{+}$ rotational band which has a large deformation owing to the $\ensuremath{\alpha}+\ensuremath{\alpha}$ clustering. In the wave function for the second ${0}^{+}$ state in $^{10}\mathrm{Be}$, as well as for the $1∕{2}^{+}$ first excited state of $^{9}\mathrm{Be}$, the motion of the valence neutrons around the two $\ensuremath{\alpha}$ particles appears to be consistent with the $\ensuremath{\sigma}$ orbit in the molecular orbital model. We find that two or three competing configurations are necessary to reproduce these two anomalous states (the $1∕{2}^{+}$ and ${0}_{2}^{+}$ states), where one configuration produces a spatially extended neutron distribution outside the $^{8}\mathrm{Be}$ core and another has a strong core $(\ensuremath{\alpha}+\ensuremath{\alpha})$ distortion induced by the valence neutron, with the latter being responsible for lowering the energies of these two states.