Valence Nucleons Research Articles

Magnetic properties of K = 1/2 states in deformed odd-mass nuclei

A method for calculation of the ground-state magnetic moment, effective spin gyromagnetic factors and rotational decoupling parameter of the K=1/2 states in deformed odd-mass nuclei has been described by using the concept of the Quasiparticle Phonon Nuclear Model (QPNM). The model includes a Woods-Saxon potential as a mean field with pairing correlations and the residual separable spin-spin force in both isovector and isoscalar channels. The method has been employed to investigate K=1/2 ground-state magnetic properties of 169Er, 167,169Tm, and 171Yb nuclei, as an example. It has been shown that two different quenched spin gyromagnetic factors, i.e., gsz(eff.) and gs+(eff.) have a significant effect on the magnetic properties of K=1/2 states in odd-mass nuclei. Whereas the first one is occurred due to the interaction between the valence nucleon and IπK=1+0 excitations of the core, second one is associated with the coupling of the valence nucleon to IπK=1+1 excitations of the core. The observed magnetic moments and the phenomenological value of gsz(eff.) for considered odd-mass nuclei have been reproduced very well by the calculations. The role of the isoscalar and isovector interactions on the magnetic properties of K=1/2 states in these nuclei has been also discussed.

Ground-state shape evolution in Er and Yb isotopes

The ground-state shape (phase) evolution in Er and Yb isotopes is manifested in the axially deformed Nilsson mean-field plus extended pairing model. The energy ratio R02+/21+, the odd-even mass differences, the ground-state occupation probabilities of valence nucleon pairs with different angular momenta and the information entropy are calculated. It is shown from these quantities as functions of the quadrupole deformation parameter and the overall pairing interaction strength that the ground-state shape (phase) evolution is mainly driven by the pairing interaction and less affected by the quadrupole deformation, which thus provides a possible origin of the ground-state shape (phase) evolution of these isotopes.

α clustering from the quartet model

$\ensuremath{\alpha}$ clustering in nuclei is considered with the quartet model (QM) where four valence nucleons (the quartet) move on the top of the core (daughter) nucleus. In the QM approach, it is assumed that the intrinsic wave function of the quartet is changed from the pure cluster configuration to the shell-model configuration when it crosses some critical radius and enters into the core nucleus. The QM approach could give not only the level scheme, the electromagnetic transition, and the nuclear radius but also the $\ensuremath{\alpha}$-cluster formation probability. Numerical results are calculated for $^{20}\mathrm{Ne}$, $^{44}\mathrm{Ti}$, and $^{212}\mathrm{Po}$, where a quartet moves on top of a double magic nucleus. Good agreement with experimental data and previous theoretical studies is obtained. The QM approach is a useful complement to the present phenomenological and microscopic models and could help deepen our understanding of $\ensuremath{\alpha}$ clustering across the nuclide chart.

Systematic studies of the influence of single-particle resonances on neutron halo and skin in the relativistic-mean-field and complex-momentum-representation methods

The newly developed relativistic-mean-field and complex-momentum-representation (RMF-CMR) method is used to explore the exotic structure for the neutron-rich Ca, Ni, Sn, and Pb isotopes. The results are compared with the relativistic Hartree-Bogoliubov (RHB) calculations as well as the available data. The calculated root mean square (rms) radius of the neutron and proton suggests a halo or giant halo structure in the Ca isotopes with neutron number more than $N=40$, and a thick neutron skin in the extremely neutron-rich Ni, Sn, and Pb isotopes. The extracted two-neutron separation energies agree the experimental data as well as the RHB calculations. The conclusions are supported by the available single particle levels, the valence nucleon occupations, the contributions of resonant and weakly bound levels to the neutron rms radius, the density distributions of the occupation levels, and the total neutron, proton, and matter densities. Especially, it is found that the unusually increasing radius comes mainly from the contributions of the weakly bound levels with lower orbital angular momentum, and the diffuse density distributions, like the halo, originate mostly from the resonant levels with lower orbital angular momentum in the vicinity of the continuum threshold. The predication on the structure of halo and skin in the neutron-rich Ca, Ni, Sn, and Pb isotopes are of referential value for experiment.

Prediction of halo structure in nuclei heavier than Mg37 with the complex momentum representation method

The discovery of the halo phenomenon has changed the traditional understanding of nuclear structure and opened up a new frontier in nuclear physics. The resonant states are thought to play a critical role at the formation of a halo. In this paper, we adopt the complex momentum representation method to explore the single-particle resonances for several slightly heavier nuclei than those halo nuclei found in experiment. The single particle bound and resonant levels and their evolution with the quadruple deformation ${\ensuremath{\beta}}_{2}$ are obtained and accompanied by a clear shell structure. The configuration occupations and density distributions of valence nucleon support the existence of halo structure. Namely, an $s$-wave halo may be formed in the range of $\ensuremath{-}0.06\ensuremath{\le}{\ensuremath{\beta}}_{2}\ensuremath{\le}0.13$ ($\ensuremath{-}0.12\ensuremath{\le}{\ensuremath{\beta}}_{2}\ensuremath{\le}0.12$) in $^{77}\mathrm{Fe}$ ($^{75}\mathrm{Cr}$), and a $p$-wave halo may be formed in the range of $0.09\ensuremath{\le}{\ensuremath{\beta}}_{2}\ensuremath{\le}0.13$ in $^{53}\mathrm{Ar}$. This prediction is of referential value for the exploration of heavier halo nuclei in experiment.

Isovector and isoscalar proton-neutron pairing in N>Z nuclei

We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-revered orbits. It is proven that the ground state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away of N=Z line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.

Study of Grodzins relation of B(E2) with E(21+) in A = 130, 100 and 80 regions

The nuclei in the [Formula: see text] [Formula: see text] and [Formula: see text] regions, lying on both sides of the [Formula: see text]-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. [Formula: see text], for the ground bands of even-[Formula: see text] even-[Formula: see text] nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of [Formula: see text] to [Formula: see text], is illustrated for the [Formula: see text] Zn to [Formula: see text] Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of [Formula: see text], and 28 rather than [Formula: see text], for Mo to Cd isotopes for a microscopic calculation.

Octupole phonon model based on the shell model for octupole vibrational states

A model is proposed for a description of the octupole vibrational states based on the nuclear shell model. In this model, a one-octupole-phonon representing the collective octupole vibration across the magic core is introduced onto the shell-model states that are microscopically calculated within the valence nucleon space. With this model, a unified description is now possible for the pure shell-model states made by valence nucleons, and the octupole-phonon states excited on the shell-model states. The model is applied to various nuclei around the $^{208}\mathrm{Pb}$ nucleus. Energy levels and electric octupole transition probabilities are well reproduced for both the pure shell-model states and the octupole vibrational states.

Realistic shell-model calculations for p -shell nuclei including contributions of a chiral three-body force

In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced - turned on by the two-body potential - and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. In order to establish the reliability of our approximations, we focus attention on nuclei belonging to the p shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell-model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.

Symmetrical level schemes of the even–even Sm[formula omitted] and Yb[formula omitted] nuclei up to 10+ in the yrast bands

For the first time, we show here that three isotopes of the Sm isotopic chain almost overlay with three isotopes of the Yb isotopic chain in terms of experimental observables within the NπNν scheme. A recent systematic work by Sayğı on reduced transitional probabilities in pseudo-mirror nuclei revealed that nuclei having particle–hole symmetry tend to manifest alike experimental structures. The NπNν quantity is an indicator of the symmetry and depends on valence nucleon (or holes) number from the nearest closed shell by considering the subshell closures, which simplifies the systematics of excitation energies and related B(E2; L+→(L−2)+) values of excited states in nuclei placed in the different mass regions of nuclear chart. In the light of available data, the experimental observables in the group of 136Sm–160Yb, 134Sm–162Yb and 132Sm–164Yb nuclei have been analyzed in a vertical and horizontal perspectives and the ratio of reduced transition probabilities of the first excited states compared with existing theoretical predictions. The data brought to light that the structure of each group reflects identical yrast bands up to 10+.

First-order Coriolis-coupling for the rotational spectrum of a tetrahedrally deformed core plus one-particle system

The possible existence of shape-coexisting nuclear configurations with tetrahedral symmetry is receiving an increasing attention due to unprecedented nuclear structure properties, in particular in terms of the exotic 4-fold nucleonic level degeneracies and the expected long lifetimes which may become a new decisive argument in the exotic nuclei research programs. The present article addresses the rotational structure properties of the tetrahedrally-symmetric even-even core configurations coupled with a single valence nucleon. We focus on the properties of the associated Coriolis-coupling Hamiltonian proposing the solutions based on the explicit construction of the bases of the irreducible representations of the tetrahedral point-group on the one-hand side and the microscopic angular-momentum and parity projection nuclear mean-field approach on the other. It is shown that for one-particle occupying an orbital belonging to the $E_{1/2}$ or $E_{5/2}$ irreducible representation, the rotational spectrum splits into two sequences, the structures analogous to those of the $K=1/2$ rotational bands in the axially symmetric nuclei. Although the spectrum is generally more complicated for one-particle occupying a 4-fold degenerate orbital belonging to the $G_{3/2}$ representation, an appearance of the correlated double-sequence structures persists. The spectra of the doubly-magic tetrahedral core plus one-particle systems can be well interpreted using the analytical solutions of the first order Coriolis-coupling Hamiltonian. We introduce the notion of the generalized decoupling parameters, which determine the size of the energy-splitting between the double-sequence structures.

7Li and 7Be isotopes in a new cluster model

One of the cluster characteristics found in light nuclei in the vicinity of a nucleus with doubly magic closure is that valence nucleons act like a cluster rotating around a core. In this paper, cluster structures in 7Be and 7Li isotopes are studied, assuming a two-body system. Also, regarding the non-zero spin of the cluster, the effect of spin-orbit coupling on the splitting of states is investigated. Finally, to verify our model, the charge radius and electric quadrupole moment of the studied isotopes are calculated and compared to the experimental results, and show good agreement.

α decay preformation probabilities across the N = 126 shell closure based on the single particle energy spectra

We put forward a concise approach to calculate the α decay preformation probabilities by defining the microscopic valence nucleon and hole numbers based on the single particle energy spectra, which is obtained within the relativistic Hartree–Bogoliubov model. The residual interactions including neutron–neutron, proton–proton pairing and proton–neutron correlations could trigger the collective motions among the valence nucleons and holes, along with the independent particle motions under the mean field assumption. Therefore the more the number of valence nucleons and holes, the stronger the collective motions such as α particle clustering. We assume that the valence orbits locate around the Fermi surface obeying a Fermi–Dirac distribution, i.e. nucleons (holes) occupying the orbits with much lower (higher) energies away from the Fermi surface can not be considered as the valence nucleons (holes). The α decay preformation probabilities Pα are calculated within the Np Nn scheme in terms of the valence proton–neutron interaction. As an example, in the case of even–even polonium, radon, radium and thorium isotopes the extracted α decay preformation probabilities , which are obtained within the generalized liquid drop model, can be well reproduced by employing two different formulas to take into account the shell effect at N = 126 shell closure.

Multiple chiral doublets in four-j shells particle rotor model: Five possible chiral doublets in [formula omitted]Nd76

A particle rotor model, which couples nucleons in four single-j shells to a triaxial rotor core, is developed to investigate the five pairs of nearly degenerate doublet bands recently reported in the even-even nucleus 136Nd. The experimental energy spectra and available B(M1)/B(E2) values are successfully reproduced. The angular momentum geometries of the valence nucleons and the core support the chiral rotation interpretations not only for the previously reported chiral doublet, but also for the other four candidates. Hence, 136Nd is the first even-even candidate nucleus in which the multiple chiral doublets exist. Five pairs of chiral doublet bands in a single nucleus is also a new record in the study of nuclear chirality.

Occurrence of a chiral-like pair band and a six-nucleon noncollective oblate isomer in 120I

We report for the first time two distinctive features in the odd–odd nucleus 120I: a pair of doublet bands and a high-spin isomer built on the πh11/2νh11/2 configuration. For producing the excited states of 120I, a fusion-evaporation reaction 118Sn(6Li, 4n) at E=lab48 MeV was employed. The beam was provided by the 14UD tandem accelerator of the Heavy Ion Accelerator Facility at the Australian National University. The observed doublet structure built on the positive-parity states is the first case and unique in isotopes with Z=53. The emerging properties are indicative of the known chiral characteristics, leading to a doubling of states for the πh11/2νh11/2 configuration. In contrast, the high-spin isomer with a half-life of 49(2) ns at spin-parity Jπ=25+ can be explained in terms of a noncollective oblate structure with the full alignment of six valence nucleons outside the 114Sn core: three protons (g7/2)1(d5/2)1(h11/2)1 and three neutrons (h11/2)3. This is an outstanding case that reveals a pure single-particle structure consisting of equal numbers of valence protons and neutrons outside the semi-double shell closure of 114Sn with Z=50 and N=64.

Single-particle spatial dispersion and clusters in nuclei

The spatial dispersion of the single-nucleon wave functions is analyzed using the self-consistent mean-field framework based on nuclear energy density functionals, and with the harmonic oscillator approximation for the nuclear potential. It is shown that the dispersion depends on the radial quantum number n, but displays only a very weak dependence on the orbital angular momentum. An analytic expression is derived for the localization parameter that explicitly takes into account the radial quantum number of occupied single-nucleon states. The conditions for single-nucleon localization and formation of cluster structures are fulfilled in relatively light nuclei with $A \leq 30$ and $n=1$ states occupied. Heavier nuclei exhibit the quantum liquid phase of nucleonic matter because occupied levels that originate from $n > 1$ spherical states are largely delocalized. Nevertheless, individual $\alpha$-like clusters can be formed from valence nucleons filling single-particle levels originating from $n=1$ spherical mean-field states.

Investigation of the B9 nucleus and its cluster-nucleon correlations

In order to study the correlation between clusters and nucleons in light nuclei, we formulate a new superposed THSR wave function which describes both spatial large spreading and cluster-correlated dynamics of valence nucleons. By using the new THSR wave function, the binding energy of 9B is essentially improved comparing with our previous studies. We calculate the excited states of 9B and obtain the energy spectrum of 9B which is consistent with the experimental results, including prediction of the 1/2+ excited state of 9B which is not fixed yet experimentally. We study the proton dynamics in 9B and find that the cluster-proton correlation plays an essential role for the proton dynamics in the ground state of 9B. Further more, we discuss the density distribution of the valence proton with special attention to its tail structure. Finally, the resonance nature of excited states of 9B is illustrated by comparing root-mean-square radii between the ground and excited states.

Three-nucleon force contribution in the distorted-wave theory of (d,p) reactions

The distorted-wave theory of A ( d , p ) B reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon ( 3 N ) force. The purpose of this paper is to study the contribution of the 3 N force of the simplest possible form to the A ( d , p ) B reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between A and B . The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the 3 N interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact 3 N force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the 3 N contribution is noticeable, especially at high deuteron incident energies. No 3 N effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the 3 N contribution to the ( d , p ) cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model.

Three-level mixing model for nuclear chiral rotation: Role of the planar component

Three- and two-level mixing models are proposed to understand the doubling of states at the same spin and parity in triaxially-deformed atomic nuclei with odd numbers of protons and neutrons. The Particle-Rotor Model for such nuclei is solved using the newly proposed basis which couples angular momenta of two valence nucleons and the rotating triaxial mean-field into left-handed $|\mathcal{L}\rangle$, right-handed $|\mathcal{R}\rangle$, and planar $|\mathcal{P}\rangle$ configurations. The presence and the impact of the planar component is investigated as a function of the total spin for mass A$\approx$130 nuclei with the valence h$_{11/2}$ proton particle, valence h$_{11/2}$ neutron hole and the maximum difference between principle axes allowed by the quadrupole deformation of the mean field. It is concluded that at each spin value the higher-energy member of a doublet of states is built on the anti-symmetric combination of $|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$ and is free of the $|\mathcal{P}\rangle$ component, indicating that it is of pure chiral geometry. For the lower-energy member of the doublet, the contribution of the $|\mathcal{P}\rangle$ component to the eigenfunction first decreases and then increases as a function of the total spin. This trend as well as the energy splitting between the doublet states are both determined by the Hamiltonian matrix elements between the planar ($|\mathcal{P}\rangle$) and non-planar ($|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$) subspaces of the full Hilbert space.

Generic features of the neutron-proton interaction

We show that fully aligned neutron-proton pairs play a crucial role in the low-energy spectroscopy of nuclei. with valence nucleons in a high-j orbital. Their dominance is valid in nuclei with valence neutrons and protons in different high-j orbitals as well as in N = Z nuclei, where all nucleons occupy the same orbital. We demonstrate analytically this generic feature of the neutron-proton interaction for a variety of systems with four valence nucleons interacting through realistic, effective forces. The dominance of fully aligned neutron-proton pairs results from the combined effect of (i) angular momentum coupling and (ii) basic properties of the neutron-proton interaction.