Valence Neutrons Research Articles

Enhanced capability of model fitting to nuclear level density and heat capacity: testing on 93−98Mo nuclei

We propose an improved fitting approach that improves reliability in studying the nuclear level density (NLD) and thermodynamic quantities. The proposed method, which relies on the fact that experimental fluctuations or outliers, if they exist, should not be involved in the fitting process, is validated with a set of data artificially generated with anomalous data points being intentionally inserted. In order to showcase the advantages of the proposed technique, we have applied it to re-investigate the back-shifted Fermi gas (BSFG) level density parameters and thermodynamic quantities, particularly the heat capacities, of 93−98Mo isotopes. We have found that the range of values for the level density parameter of 93Mo (approximately from 8.5 to 9.0 MeV−1) is notably smaller than that obtained for the other isotopes of Mo (approximately from 10.5 to 11.5 MeV−1). This observation is different from previous predictions, in which the values of level density parameter of all Mo isotopes are in the same range. This is because among the Mo isotopes under examination, 93Mo (N = 51 neutrons) has the smallest number of valence neutrons, namely only a single neutron away from the closed N = 50 shell. In addition, thanks to the proposed method, we have discussed the effects of data fluctuations on the BSFG NLDs and thermodynamic quantities of 93−98Mo isotopes, from which our recommendation for future works is announced. On top of that, we should notice that the proposed approach can be further applied to any work involving the fitting of a phenomenological model to empirical data.

Lambda motion and cluster states of [formula omitted] predicted via neural networks guided microscopic calculation

We investigate the Λ particle motion and cluster states of BeΛ9−11 using a novel multiple cooling approach guided by the Control Neural Networks method (Ctrl.NN). The numerical results are well reproduced, and the Ctrl.NN method shows rapid convergence concerning the set of the basis states in comparison to traditional generator coordinate method (GCM) calculations. Taking advantage of this merit, we calculate ground state energies and rotational bands of BeΛ9−11 which agree well with experimental observations. By analyzing the density distributions of the main basis, a slight short-range repulsive correlation between Λ particle and α clusters in directions perpendicular to the axis of the Be8 core is revealed. The Λ particle presents a significant broad distribution as a consequence of this correlation, which we call an “analog π-orbit” structure. Furthermore, we prove that this correlation originates from the competition between kinetic energy and Λ-N interaction, as indicated by the energy curves for different configurations of BeΛ9. In the ground states of BeΛ10 and BeΛ11, the Λ particle is confined in a cage-like structure of core nuclei formed by two α clusters and valence neutrons. These structures lead to the development of more compact Λ particle configurations, and the shrinkage of α-α relative distance is also well reproduced.

Search of effective interaction in dipole bands of an odd–odd trans-lead Nucleus: the case of 204At

Role of effective interaction potential in shears band structure in [Formula: see text]At has been investigated in more detail than in previous studies. A semi-classical geometric model is used to obtain the interaction strengths between valence protons and neutron holes constituting the shears blades. The value produces overall good agreement with this region’s nuclei. Band crossing is observed in the spin-parity range [Formula: see text] – [Formula: see text]. Configurations of the Magnetic Rotational (MR) band are assigned in the light of the Shears mechanism with the Principal Axis Cranking (SPAC) model. Experimental rotational frequencies and the deduced ratio of [Formula: see text] are well reproduced by SPAC calculations, suggesting the dipole band in [Formula: see text]At can undoubtedly be interpreted as the MR band resulting from the effective interaction of repulsive potential.

Kink of the nuclear charge radius isotope shift and overlaps of the neutron and proton orbitals in lead

Within the relativistic mean field approximation, we analyse the kink effect (KE) in the evolution of the charge radius isotope shift of lead isotopes as a function of the neutron number N. We show that if the interactions between neutron and proton states responsible for the KE are assumed to be proportional either to the overlaps of their corresponding wave functions or to those of their corresponding probability density distributions, it is not possible, by themselves, to explain the KE. However, we find that the small component of the single-particle Dirac spinors plays a relevant role in the kink formation. By considering the contribution of the N−126 valence neutrons to the proton central potential, we can explain the generation of the KE and why neutrons in the 1i11/2 orbital are more kinky than when they are in the 2g9/2 orbital.

Generalized molecule-like structure in atomic nuclei

Starting from a |ϕ|4 field theory with universal pn interacting angular and distance coordinates (θ,r) to depict nuclear long-range correlations, we have derived a cubic Schrödinger equation for NpNnpn interacting virtual bosons, which are believed to dominate the generic evolution of nuclear structure from spherical multi-nucleon shell-model states to deformed collective rotational states. It is shown that two-soliton solution in θ space manifests two opposite pn-type Ising-like chains existing in ground states and their gradual alignment responsible for nuclear rotational excitations. Of particular prominence is two-soliton solution with respect to r: the mutual relative motion of valence protons and neutrons around valence-nucleon mass centers considered as the dynamic equilibrium positions of a non-linear Schrödinger breather. And the resulting non-vanishing root mean square 〈r2〉 divides half the valence nucleons belonging to a chain into four local mass centers and proposes two chain-corresponding molecule-like tetrads outside inert cores pairwise hidden in ground states. Such solitons turn out to be an analogue of opposite axion fluids around a local mass center in the galactic dark-matter halo outside the soliton core (Garnier et al. (2021) [67]) and the present study facilitates making the latter more clear. The generalized molecule-like structure arouses a requisite to the addition of cluster-interior and cluster-to-core electric dipole moments in particular to pear-shaped nuclei, whose variants Schiff moments play an important role in measuring diamagnetic atomic electric dipole moments and therefore understanding CP-violating new physics beyond the standard model. We put additional parts in evidence by befitting the NpNn scheme verified already by electric quadrupole moments in same nuclei.

Relativistic effects on the kink of nuclear charge radii in lead

The kink in the nuclear charge radii of lead isotopes is studied in the relativistic mean field approximation framework, using the parameter set NL3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}. Within this approach, it is shown that the small component of the single-particle Dirac spinors plays an essential role in the kink formation through its effects on the single-particle central potential. This is because the structure of this potential in terms of the σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-scalar and ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}-vector fields and the contributions of the small component to the scalar and nucleon densities have opposite signs. The impact of the spin-orbit interaction of the valence neutrons on the kink, through its effects on their wave functions, is very small for 1i states but significant for 2g states. Due to relativistic contributions, the effects on the kink of neutrons in the valence levels of a spin-orbit doublet with j=l+1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l+1/2$$\\end{document} and j=l-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l-1/2$$\\end{document} are rather different from each other, even in the limit case of neglecting their spin-orbit interaction.

Neutron rearrangement of the magic number 90Zr-core determined by the matter density difference between 90Zr and 92Zr

Matter density distributions and root-mean-square matter radii for 90Zr and 92Zr were determined through fitting the small-angle differential cross sections of proton elastic scattering at 0.8 GeV with the Glauber model. With the obtained neutron densities, a neutron rearrangement beyond the expectation for the magic number 90Zr-core was found from 90Zr to 92Zr by adding two valence neutrons. By considering the surface-peaked term, the rearrangement was reproduced by the shell model calculations with the realistic Woods-Saxon potentials. It indicates that the surface-peaked term related to surface nucleon interactions plays an important role in describing the nucleon rearrangement, since the surface-peaked term would improve the description of the radial wave functions.

Shell Evolution and Structure of Two-Neutron Halo in Exotic Nuclei

Shell evolution in neutron-rich carbon isotopes is studied with repulsive contributions from three-nucleon forces among valence neutrons. Three-nucleon forces are shown to determine the dripline and improve the energy levels of the isotopes. A three-body model with low-energy neutron-neutron interaction is used to study structure of two-neutron halos of exotic nuclei. Observed halo radii in 22C and 29F are found to be well explained by the three-body model. A possible existence of an excited 2+ state in the halo of 29F and its consequences are discussed. The halo in 17B is found to be d-wave dominant, while the halo in 19B has s-wave component with about 40% probability.

Special features of nuclear structure of [formula omitted]Xe

The special spectral features of valence neutron hole deficient (N=74, 76, 78) 128-132Xe isotopes are studied, with respect to the shape phase changes with N. Besides the study of the excited 02+, 03+ states, vis-a-vis the critical point symmetry E(5), the study of the ground band and K=π2+γ-vibrational band provides a wholesome view of the nuclear structure of these isotopes. An in-depth analysis of the spectral features is presented. Comparison is made with the Interacting boson model-1 predictions.

Excited states of zero seniority based on a pair condensate

We study the excited states of zero seniority for various like-particle systems interacting by pairing forces and by general two-body interactions. We consider two types of excitations, generated from a ground state described by a pair condensate. One type is obtained by breaking a pair from the ground state condensate and replacing it by "excited" collective pairs built on time-reversed single-particle orbits. The second type of zero seniority excited states is described by a condensate of identical excited pairs. The structure of these excited states is analysed for the picked fence model and for the valence neutrons of $^{108}$Sn. For a state-depending pairing interaction, the first type of excited states agree well with the J=0 states which are known in $^{108}$Sn. At the same time, these states can be also associated unambiguously with those exact states which are the closest in energy to the experimental levels. The states corresponding to the excited pair condensate appear at low energies, around the energy of the second excited state of the first type, and they do not have a simple correspondence with exact eigenstates. However, at a much higher excitation energy there is an exact state which is similar in structure to an EPC state. It is shown that this EPC state has the features of a giant pairing vibration.

Searching for universality of dineutron correlation at the surface of Borromean nuclei

The dineutron correlation is systematically studied in three different Borromean nuclei near the neutron dripline, 11Li, 14Be and 17B, via the (p,pn) knockout reaction measured at the RIBF facility in RIKEN. For the three nuclei, the correlation angle between the valence neutrons is found to be largest in the same range of intrinsic momenta, which can be associated to the nuclear surface. This result reinforces the prediction that the formation of the dineutron is universal in environments with low neutron density, such as the surface of neutron-rich Borromean nuclei.

Structure of low-lying states of 9Ве nucleus

Glauber's theory of multiple scattering is applied to the calculation of differential cross sections and polarization characteristics of particle scattering on light nuclei. All calculations were carried out within the framework of a reliable spectroscopic approach to nuclear reactions. Its essence consists in the use of nuclear models that reproduce practically all the spectroscopic characteristics of the nuclei under consideration. These include three-particle models of 6Li and 9Be nuclei, a many-particle shell model for nuclei with А = 6–14, and a particle-hole model of shells for nuclei with А = 15; three-body models for the 8Li and 9Li nuclei and a two-particle αt-model for the 7Li nucleus. As our experience shows, when implementing the spectroscopic approach, when the dominant mechanism of the process is also established, one can not only obtain a description of the main characteristics of the process, but also rely on the predictive nature of the theory. In the present work, the results obtained are supplemented by calculations of the structure of the low-lying 5/2+ and 5/2– levels. This allows us to draw a general conclusion: the negative parity levels in 9Be, in which the valence neutron is in the p state, do not have a halo structure; at the same time, low-lying levels of positive parity, in which the valence neutron passes into the next (2s-1d) shell, have such. A special place is occupied by our recent direct evidence of the halo structure of low-lying excited states of the 9Be nucleus with quantum numbers 1/2+ and 3/2+. Within the framework of the ααn model of the 9-Be nucleus, it was shown that a valence neutron with a high probability is located at 11 fm from the center of gravity of two α-particles, while in the 3/2- ground state this distance is several times smaller. The conclusions about the structure of low-lying levels of 9Be, obtained on the basis of the ααn model, are supported by calculations of p9Be scattering: only taking into account the halo structure makes it possible to reproduce the experimental data on inelastic scattering to positive parity levels.

Microscopic study of the deformed neutron halo of Ne31

The properties of the deformed halo of 31Ne were discussed using the antisymmetrized molecular dynamics plus resonating group method (AMD+RGM). The AMD+RGM calculations describe a large neutron radius for the ground state and reveal that the ground state is dominated by core-excited components. The resonant states were also investigated by applying the analytical continuation of the coupling constant. It was found that the first excited state (the 5/2- state) is also dominated by core-excited components and has a small decay width, whereas the second excited state (the 7/2- state) is dominated by the valence neutron in the $f$-wave coupled to the ground state of 30Ne.

Study of the N=32 and N=34 Shell Gap for Ti and V by the First High-Precision Multireflection Time-of-Flight Mass Measurements at BigRIPS-SLOWRI.

The atomic masses of ^{55}Sc, ^{56,58}Ti, and ^{56-59}V have been determined using the high-precision multireflection time-of-flight technique. The radioisotopes have been produced at RIKEN's Radioactive Isotope Beam Factory (RIBF) and delivered to the novel designed gas cell and multireflection system, which has been recently commissioned downstream of the ZeroDegree spectrometer following the BigRIPS separator. For ^{56,58}Ti and ^{56-59}V, the mass uncertainties have been reduced down to the order of 10keV, shedding new light on the N=34 shell effect in Ti and V isotopes by the first high-precision mass measurements of the critical species ^{58}Ti and ^{59}V. With the new precision achieved, we reveal the nonexistence of the N=34 empirical two-neutron shell gaps for Ti and V, and the enhanced energy gap above the occupied νp_{3/2} orbit is identified as a feature unique to Ca. We perform new MonteCarlo shell model calculations including the νd_{5/2} and νg_{9/2} orbits and compare the results with conventional shell model calculations, which exclude the νg_{9/2} and the νd_{5/2} orbits. The comparison indicates that the shell gap reduction in Ti is related to a partial occupation of the higher orbitals for the outer two valence neutrons at N=34.

Halo EFT for 31Ne in a spherical formalism

We calculate the electromagnetic properties of the deformed one-neutron halo candidate 31Ne using Halo effective field theory (Halo EFT). In this framework, 31Ne is bound via a resonant P-wave interaction between the 30Ne core and the valence neutron. We set up a spherical formalism for 31Ne in order to calculate the electromagnetic form factors and the E1-breakup strength distribution into the 30Ne-neutron continuum at leading order in Halo EFT. The associated uncertainties are estimated according to our power counting. In particular, we assume that the deformation of the 30Ne core enters at next-to-leading order. It can be accounted for by including the J P = 2+ excited state of 30Ne as an explicit field in the effective Lagrangian.

Probing the quadrupole transition strength of C15 via deuteron inelastic scattering

Deuteron elastic scattering from $^{15}\mathrm{C}$ and inelastic scattering reactions to the first excited state of $^{15}\mathrm{C}$ were studied using a radioactive beam of $^{15}\mathrm{C}$ in inverse kinematics. The scattered deuterons were measured using HELIOS. The elastic scattering differential cross sections were analyzed using the optical model. A matter deformation length ${\ensuremath{\delta}}_{d}=1.04(11)\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ has been extracted from the differential cross sections of inelastic scattering to the first excited state. The ratio of neutron and proton matrix elements ${M}_{n}/{M}_{p}=3.6(4)$ has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of $^{15}\mathrm{C}$ were determined and discussed. Results from ab initio no-core configuration interaction calculations were also compared with the experimental observations. This result supports a moderate core decoupling effect of the valence neutron in $^{15}\mathrm{C}$ similarly to its isotone $^{17}\mathrm{O}$, in line with the interpretation of other neutron-rich carbon isotopes.

Exotic Structure of 17Ne-17N and 23Al-23Ne Mirror Nuclei

In terms of the core nucleus plus valence nucleon, shell-model calculations using two model spaces and interactions, the relationship between a nucleus' proton skin, and the difference in proton radii of mirror pairs of nuclei with the same mass number are investigated. In this work, two pairs of mirror nuclei will be studied: 17Ne-17N and 23Al-23Ne. For 17Ne-17N nuclei, p-shell and mixing of psd orbits are adopted with Cohen-Kurath (ckii) and psdsu3 interactions. While for 23Al-23Ne, the sd-shell and sdpf shell are adopted with the universal shell model (USD) and sdpfwa interactions. Also, the ground state density distributions, elastic form factors, and root mean square radii of these pairs' nuclei are studied and compared with available experimental data. . In general, it was found that the rms radius of the valence proton(s) is larger than that of the valence neutron(s) in its mirror nucleus. The results show that these nuclei have the exotic structure of a halo or skin.

Observation of the proton emitter {}_{,57}^{116}La59

The quantum tunneling and emission of a single constituent nucleon provide a beautifully simple and unique window into the complex properties of atomic nuclei at the extreme edge of nuclear existence. In particular, for odd-odd proton emitting nuclides, the associated decay energy and partial half-life can be used to probe the correlations between the valence neutrons and protons which have been theoretically predicted to favour a new type of nuclear superfluidity, isoscalar neutron-proton pairing, for which the experimental “smoking gun" remains elusive. In the present work, proton emission from the lanthanum isotope {}_{,57}^{116}La59, 23 neutrons away from the only stable isotope {}_{,57}^{139}La82, is reported. 116La nuclei were synthesised in the fusion-evaporation reaction 58Ni(64Zn, p5n)116La and identified via their proton radioactivity using the mass spectrometer MARA (Mass Analysing Recoil Apparatus) and the silicon detectors placed at its focal plane. Comparisons of the measured proton energy (Ep = 718 ± 9 keV) and half-life (T1/2 = 50 ± 22 ms) with values calculated using the Universal Decay Law approach indicate that the proton is emitted with an orbital angular momentum l = 2 and that its emission probability is enhanced relative to its closest, less exotic, odd-even lanthanum isotope ({}_{,57}^{117}La60) while the proton-emission Q-value is lower. We propose this to be a possible signature for the presence of strong neutron-proton pair correlations in this exotic, neutron deficient system. The observations of γ decays from isomeric states in 116La and 117La are also reported.

Momentum-space structure of dineutrons in Borromean nuclei

A comparative study is made of the momentum-space structure of dineutrons in the Borromean nuclei $^{11}\mathrm{Li}$, $^{6}\mathrm{He}$, $^{22}\mathrm{C}$, and $^{19}\mathrm{B}$. The ground-state properties of these nuclei are well described by a three-body model using a newly constructed finite-range $nn$ interaction in momentum space. I clarify how the mean opening angle between momenta of valence neutrons and the opening-angle distribution reflect the two-neutron density of the Borromean nuclei. By indicating the similarities to the distributions for the correlation angle in the knockout-reaction experiments, I show that the angular correlations of halo neutrons can provide rich information for the characteristic structure of dineutrons in the Borromean nuclei.

Binding energies of proton-rich nuclei determined from their mirror pairs* *Supported by the National Natural Science Foundation of China (12075121 and 11605089), and by the Natural Science Foundation of Jiangsu Province (BK20190067 and BK20150762)

In addition to the Coulomb displacement energy, the residual differences between the binding energies of mirror nuclei (a pair of nuclei with the same mass number plus interchanged proton and neutron numbers) contribute to the shell effect via the valence scheme in this study. To this end, one linear combining type of valence nucleon number, namely, , is chosen to tackle this shell correction, in which and are the valence proton and neutron numbers with respect to the nearest shell closure, respectively. The mass differences of mirror nuclei, as the sum of the empirical Coulomb displacement energy and shell effect correction, are then used to obtain the binding energies of proton-rich nuclei through the available data of their mirror partners to explore the proton dripline of the nuclear chart.