Neutron-rich Ca Isotopes Research Articles

Spectroscopy of deeply bound orbitals in neutron-rich Ca isotopes

The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in 53Ca and 55Ca, populated from 54,56Ca(p,pn) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum l assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)keV in 53Ca and 6000(250)keV in 55Ca indicate a significant l =3 component, providing the first experimental evidence for the ν0f7/2 single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the ν0f7/2 orbital in 55Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and ab initio calculations and diverge markedly from the experimental distributions in the nickel isotones at Z=28.

Shell evolution and emerging paradigm changes

The shell structure conceived by Mayer and Jensen in 1949 has been shown to be quite appropriate for stable and near-stable nuclei, but substantial deviations from it have also been observed more recently for exotic nuclei with notable neutron excess. Such changes of the basic picture of the nuclear shell structure, called the shell evolution, seem to be the subject studied most extensively and most elaborately by RI beam experiments worldwide. An overview of the shell evolution is presented in this talk, from both theoretical and experimental perspectives. The shell structure is shown to be varied, for instance, from the one presented by Mayer and Jensen, by particular types of the monopole components of the effective nucleon-nucleon interaction in nuclei. Among various contributions, the importance of the tensor force is illuminated here, with an outstanding example: the emergence of new neutron magic number 34 in neutron-rich Ca isotopes. The mechanism of the shell evolution produces significant impacts also on the nuclear shapes. Type II shell evolution shifts the excitation energies of intruder deformed bands, for instance, in some Ni isotopes. In other more general cases, the monopole interaction is shown to produce unexpected crucial effects on the patters of rotational bands of heavy deformed nuclei. In fact, the shape of the ellipsoidal deformation is investigated by large-scale shell model calculations, which is nothing but the Monte Carlo Shell Model. The unique role of the monopole component of the tensor force is clarified: the interplay between this monopole interaction and the quadrupole interaction provides us with various patterns of triaxial shapes for many nuclei, such as 166Er, one of the traditional prolate deformed heavy nuclei. Thus, the prolate preponderance hypothesis by Aage Bohr is investigated for its microscopic validity. Some of the nuclear paradigms are changing now in this way, due to emerging aspects of nuclear-force effects.

Continuum Skyrme Hartree–Fock–Bogoliubov theory with Green’s function method for neutron-rich Ca, Ni, Zr, and Sn isotopes

Continuum Skyrme Hartree–Fock–Bogoliubov theory with Green’s function method for neutron-rich Ca, Ni, Zr, and Sn isotopes

Extended p_{3/2} Neutron Orbital and the N=32 Shell Closure in ^{52}Ca.

The one-neutron knockout from ^{52}Ca in inverse kinematics onto a proton target was performed at ∼230 MeV/nucleon combined with prompt γ spectroscopy. Exclusive quasifree scattering cross sections to bound states in ^{51}Ca and the momentum distributions corresponding to the removal of 1f_{7/2} and 2p_{3/2} neutrons were measured. The cross sections, interpreted within the distorted-wave impulse approximation reaction framework, are consistent with a shell closure at the neutron number N=32, found as strong as at N=28 and N=34 in Ca isotopes from the same observables. The analysis of the momentum distributions leads to a difference of the root-mean-square radii of the neutron 1f_{7/2} and 2p_{3/2} orbitals of 0.61(23)fm, in agreement with the modified-shell-model prediction of 0.7fm suggesting that the large root-mean-square radius of the 2p_{3/2} orbital in neutron-rich Ca isotopes is responsible for the unexpected linear increase of the charge radius with the neutron number.

Shell evolution in neutron-rich nuclei: the single particle perspective * *Supported by the National Natural Science Foundation of China (12075121, 11605089), and the Natural Science Foundation of Jiangsu Province (BK20190067, BK20150762)

The isospin dependence of spin-orbit (SO) splitting becomes increasingly important as N/Z increases in neutron-rich nuclei. Following the initial independent-particle strategy toward explaining the occurrence of magic numbers, we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term. It is found that new magic numbers N = 14 and N =16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling, whereas the traditional magic number, N = 20, may disappear. The magic number N = 28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting, corresponding to the strength of the SO coupling term. Meanwhile, the N = 50 and 82 shells may persist within the single particle scheme, although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei. Besides, an appreciable energy gap appears at N = 32 and 34 in neutron-rich Ca isotopes. All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model. The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrè chart.

Effects of pairing correlation on the quasiparticle resonance in neutron-rich Ca isotopes

We investigated the effects of the pairing correlation on the quasiparticle resonant energy and width in the neutron-rich Ca isotopes by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method. The resonant energy and width can be read from three kinds of quasiparticle spectra, including the quasiparticle-state probability density, the occupation probability density, and the pair probability density. The results read from different quasiparticle spectra calculated with the same potential are exactly the same for the narrow resonances, while for the broad resonances, the difference among the results are relatively larger. From the comparison between the quasiparticle-state probability density calculated with and without the pairing field, we could separate the effect only from the pairing correlation on the quasiparticle resonances. We found that the pairing correlation can increase the resonant energy and width for both the hole-like and particle-like quasiparticle resonances. And this increase is larger when the state is closer to the Fermi energy, especially for the particle-like quasiparticle resonance originated from the unbound single-particle states with smaller angular momentum $l$ in weakly bound nucleus.

Core swelling in spherical nuclei: An indication of the saturation of nuclear density

Background: Nuclear radius is one of the most important and basic properties of atomic nuclei and its evolution is closely related to the saturation of the nuclear density in the internal region but the systematics of the nuclear radii for the neutron-rich unstable nuclei is not well known. Purpose: Motivated by the recent interaction cross section measurement which indicates the 48Ca core swelling in the neutron-rich Ca isotopes, we explore the mechanism of the enhancement of the neutron and proton radii for spherical nuclei. Methods: Microscopic Hartree-Fock calculations with three sets of Skyrme-type effective interactions are performed for the neutron-rich Ca, Ni and Sn isotopes. The total reaction cross sections for the Ca isotopes are evaluated with the Glauber model to compare them with the recent cross section data. Results: We obtain good agreement with the measured cross sections and charge radii. The neutron and proton radii of the various "core" configurations are extracted from the full Hartree-Fock calculation and discuss the core swelling mechanism. Conclusions: The core swelling phenomena occur depending on the properties of the occupying valence single-neutron states to minimize the energy loss that comes from the saturation of the densities in the internal region, which appears to be prominent in light nuclei such as Ca isotopes.

Tensor force effect on the exotic structure of neutron-rich Ca isotopes * * Supported by the National Natural Science Foundation of China (U1832120, 11675265), the State Scholarship Fund of China Scholarship Council (201708130035) and the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China (A2018210146)

The structure of neutron-rich Ca isotopes is studied in the spherical Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach with SLy5, SLy5+T, and 36 sets of TIJ parametrizations. The calculated results are compared with the available experimental data for the average binding energies, two-neutron separation energies and charge radii. It is found that the SLy5+T, T31, and T32 parametrizations reproduce best the experimental properties, especially the neutron shell effects at N = 20, 28 and 32, and the recently measured two-neutron separation energy of 56Ca. The calculations with the SLy5+T and T31 parametrizations are extended to isotopes near the neutron drip line. The neutron giant halo structure in the very neutron-rich Ca isotopes is not seen with these two interactions. However, depleted neutron central densities are found in these nuclei. By analyzing the neutron mean-potential, the reason for the bubble-like structure formation is given.

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.

Impact parameter dependence of the yield ratios of light particles as a probe of neutron skin

The yield ratios of neutron/proton (R(n/p)) and $${^3}\hbox {H}/{^3}{\text{He}}$$ ( $$R(t/{^3}{\mathrm{He}})$$ ) with reduced rapidity from 0 to 0.5 are investigated for 50 MeV/u $${^{42,44,46,48,50,52,54,56}}{\text{Ca}} + {^{40}}{\text{Ca}}$$ . This was conducted at whole reduced impact parameters using the isospin-dependent quantum-molecular-dynamics model in which the initial neutron and proton densities are sampled within the Skyrme–Hartree–Fock model, using which the neutron skin thickness ( $$\Delta {R_{\rm{np}}}$$ ) is determined for different neutron-rich Ca isotopes. The results show that both R(n/p) and $$R(t/{^3}{\mathrm{He}})$$ have strong linear correlations with $$\Delta {R_{\rm{np}}}$$ of different Ca isotopic projectiles from five different centralities. It is suggested that R(n/p) and $$R(t/{^3}{\mathrm{He}})$$ , from the same centrality, could be treated as possible experimental observables to extract the neutron skin or halo thickness for neutron-rich isotopic nuclei, including the nuclei near the neutron drip line.

β -decay properties of neutron-rich Ca, Ti, and Cr isotopes

Beta-decay properties of neutron-rich Ca, Ti, and Cr isotopes are studied within a deformed proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual spin-isospin interactions in the particle-hole and particle-particle channels are also included in the formalism. The energy distributions of the Gamow-Teller strength, the beta-decay feedings, the beta-decay half-lives, and the beta-delayed neutron emission probabilities are discussed and compared with other theoretical results, as well as with the available experimental information. The evolution of these nuclear beta-decay properties is investigated in isotopic chains in a search for structural changes. A reliable estimate of the beta-decay properties in this mass region is a valuable information for evaluating decay rates in astrophysical scenarios.

Microscopic description of the pygmy dipole resonance in neutron-rich Ca isotopes

We study the effects of the phonon-phonon coupling on the low-energy electric dipole response within a microscopic model based on an effective Skyrme interaction. The finite rank separable approach for the quasiparticle random phase approximation is used. Choosing as an example the isotopic chain of Calcium, we show the ability of the method to describe the low-energy E1 strength distribution. With one and the same set of parameters we describe available experimental data for 48Ca and predict the electric dipole strength function for 50Ca.

Spectroscopy of Ti54 and the systematic behavior of low-energy octupole states in Ca and Ti isotopes

Excited states of the $N=32$ nucleus $^{54}$Ti have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from $^{55}$Ti by a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array. Inelastic proton-scattering cross sections and deformation lengths have been determined. A low-lying octupole state has been tentatively identified in $^{54}$Ti for the first time. A comparison of $(p,p')$ results on low-energy octupole states in the neutron-rich Ca and Ti isotopes with the results of Random Phase Approximation calculations demonstrates that the observed systematic behavior of these states is unexpected.

Charge-exchange dipole excitations in neutron-rich nuclei: −1ℏω0 , anti-analog pygmy and anti-analog giant resonances

The occurrence of the low-lying charge-exchange non spin-flip dipole modes below the giant resonance in neutron-rich nuclei is predicted on the basis of nuclear density functional theory. The ground and excited states are described in the framework of the self-consistent Hartree-Fock-Bogoliubov and the proton-neutron quasiparticle-random-phase approximation employing a Skyrme-type energy density functional. The model calculations are performed for the spherical neutron-rich Ca, Ni, and Sn isotopes. It is found that the low-lying states appear sensitively to the shell structure associated with the $-1 \hbar \omega_0$ excitation below the Gamow-Teller states. Furthermore, the pygmy resonance emerges below the giant resonance when the neutrons occupy the low-$\ell (\ell \leq 2 -3)$ orbitals analogous to the pygmy resonance seen in the electric dipole response.

Low-lying electric-dipole strengths of Ca, Ni, and Sn isotopes imprinted on total reaction cross sections

Low-lying electric-dipole ($E1$) strength of a neutron-rich nucleus contains information on neutron-skin thickness, deformation, and shell evolution. We discuss the possibility of making use of total reaction cross sections on $^{40}$Ca, $^{120}$Sn, and $^{208}$Pb targets to probe the $E1$ strength of neutron-rich Ca, Ni, and Sn isotopes. They exhibit large enhancement of the $E1$ strength at neutron number $N > 28$, $50$, and $82$, respectively, due to a change of the single-particle orbits near the Fermi surface participating in the transitions. The density distributions and the electric-multipole strength functions of those isotopes are calculated by the Hartree-Fock+BCS and the canonical-basis-time-dependent-Hartree-Fock-Bogoliubov methods, respectively, using three kinds of Skyrme-type effective interaction. The nuclear and Coulomb breakup processes are respectively described with the Glauber model and the equivalent photon method in which the effect of finite-charge distribution is taken into account. The three Skyrme interactions give different results for the total reaction cross sections because of different Coulomb breakup contributions. The contribution of the low-lying $E1$ strength is amplified when the low-incident energy is chosen. With an appropriate choice of the incident energy and target nucleus, the total reaction cross section can be complementary to the Coulomb excitation for analysing the low-lying $E1$ strength of unstable nuclei.

Influence of complex configurations on the properties of the pygmy dipole resonance in neutron-rich Ca isotopes

Starting from the quasiparticle random phase approximation based on the Skyrme interaction SLy5, we study the effects of phonon-phonon coupling~(PPC) on the low-energy electric dipole response in $^{40-58}$Ca. Using the same set of parameters we describe available experimental data for $^{40,44,48}$Ca and give prediction for $^{50-58}$Ca. The inclusion of the PPC results in the formation of low-energy $1^-$ states. There is an impact of the PPC effect on low-energy $E1$~strength of $^{40,44,48}$Ca. The PPC effect on the electric dipole polarizability is discussed. We predict a strong increase of the summed $E1$~strength below 10MeV, with increasing neutron number from $^{48}$Ca till $^{58}$Ca.

Toward neutron-rich nuclei via transfer reactions with stable and radioactive beams

The possibilities of production of yet-undiscovered neutron-rich isotopes of Ca, Gd, Dy, Er, Yb, Hf, W, Os, Hg, Pb, and Th are explored in various multinucleon transfer reactions with stable and radioactive beams. The probable projectile-target combinations and bombarding energies to produce these neutron-rich isotopes are suggested for future experiments.

Production cross section of neutron-rich isotopes with radioactive and stable beams

The production cross section of neutron-rich isotopes of Ca, Zn, Te, Xe, and Pt are predicted in the diffusive multi-nucleon transfer reactions with stable and radioactive beams. With these isotopes one can treat the neutron shell evolution beyond N = 28, 50, 82, and 126. Because of the small cross sections, the production of nuclei near the neutron drip line requires the optimal choice of reaction partners and bombarding energies.

Tensor force effect on proton shell structure in neutron-rich Ca isotopes

In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TIJ parameterizations, the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated. It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter β T associated with the intensity of the tensor force. To understand this phenomenon, we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail. In addition, it is found that some TIJ interactions could cause the 2s1/2-1d3/2 energy level inversion in 48Ca.

Shell closures, loosely bound structures, and halos in exotic nuclei

Inspired by the recent experiments [1, 2] indicating doubly magic nuclei that lie near the drip-line and encouraged by the success of our relativistic mean-field (RMF) plus state-dependent BCS approach to the description of the ground-state properties of drip-line nuclei, we develop this approach further, across the entire periodic table, to explore magic nuclei, loosely bound structures, and halo formation in exotic nuclei. In our RMF+BCS approach, the single-particle continuum corresponding to the RMF is replaced by a set of discrete positive-energy states for the calculations of pairing energy. Detailed analysis of the single-particle spectrum, pairing energies, and densities of the nuclei predict the unusual proton shell closures at proton numbers Z = 6, 14, 16, 34, and unusual neutron shell closures at neutron numbers N = 6, 14, 16, 34, 40, 70, 112. Further, in several nuclei like the neutron-rich isotopes of Ca, Zr, Mo, etc., the gradual filling of lowlying single-particle resonant state together with weakly bound single-particle states lying close to the continuum threshold helps accommodate more neutrons but with an extremely small increase in the binding energy. This gives rise to the occurrence of loosely bound systems of neutron-rich nuclei with a large neutron-to-proton ratio. In general, the halo-like formation, irrespective of the existence of any resonant state, is seen to be due to the large spatial extension of the wave functions for the weakly bound single-particle states with low orbital angular momentum having very small or no centrifugal barriers.