Spin-orbit Partners Research Articles

Effects of Residual Tensor and Pairing Forces on the Gamow–Teller states in Magic Nuclei, 48Ca, 90Zr, 132Sn, and 208Pb

Abstract We investigate the effects of residual tensor force (TF) and pairing force on the Gamow–Teller (GT) transitions in four magic nuclei, 48Ca, 90Zr, 132Sn and 208Pb. The TF is taken into account by using the Brückner G-matrix theory with the charge-dependent (CD) Bonn potential as the residual interaction of charge-exchange quasiparticle random phase approximation (QRPA). We found that particle–particle (p–p) tensor interaction does not affect the GT transitions because of the closed shell nature in the nuclei, but repulsive particle–hole (p–h) residual interaction for the p–h configuration of spin-orbit partners dominates the high-lying giant GT states for all of the nuclei. It is also shown that appreciable GT strengths are shifted to a lower energy region by the attractive p–h TF for the same jπ = jν configuration, and produce the low-lying GT peak about 2.5 MeV in 48Ca. Simultaneously, in 90Zr and 132Sn, the low-energy GT strength appears as a lower energy shoulder near the main GT peak. On the other hand, the shift of the low-lying GT state is not seen clearly for 208Pb because of the strong spin-orbit splitting of high j orbits, which dominates the GT strength.

Correlations between nuclear Schiff moment and electromagnetic measurements

We study the nuclear Schiff moments of 129Xe and 199Hg induced by the nucleon electric dipole moment using large-scale shell model calculations. For 129Xe, we find a linear relation between the leading-order contribution and magnetic moment, which would be useful in reducing the theoretical uncertainty. The conventional model space does not contain the 0g9/2 and 0h9/2 orbitals, which are connected to the spin-orbit partners by large matrix elements. Thus, to evaluate the influence of the relevant single-particle orbitals outside the conventional model space, we apply the quasiparticle vacua shell model method. Moreover, the next-to-leading-order contribution arises from parity and time-reversal violation in the nucleus. We demonstrate that these secondary effects do not induce any significant disturbance to the correlation. Additionally, we report the shell model results for the nuclear Schiff moment coefficients of 199Hg. Compared to previous studies, the results obtained in this study are rather large, indicating a higher sensitivity to the neutron electric dipole moment.

Charge Radii of ^{55,56}Ni Reveal a Surprisingly Similar Behavior at N=28 in Ca and Ni Isotopes.

Nuclear charge radii of ^{55,56}Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus ^{56}Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the ^{56}Ni core is supposed to be much softer than the ^{48}Ca core. The very low magnetic moment μ(^{55}Ni)=-1.108(20) μ_{N} indicates the impact of M1 excitations between spin-orbit partners across the N,Z=28 shell gaps. Our charge-radii results are compared to abinitio and nuclear density functional theory calculations, showing good agreement within theoretical uncertainties.

Calculated Event Rates for Axion Detection via Atomic and Nuclear Processes

The possibility of detection of 5.5 MeV and 14.4 keV solar axions by observing axion-induced nuclear and atomic transitions is investigated. The presence of nuclear transitions between spin orbit partners can be manifested by the subsequent deexcitation via gamma ray emissions. The transition rates can also be studied in the context of radiative axion absorption by a nucleus. The elementary interaction is obtained in the context of the axion-quark couplings predicted by existing axion models. Then, these couplings will be transformed to the nucleon level utilizing reasonable existing models, which lead to effective transition operators. Using these operators, we calculate the needed nuclear matrix elements employing wave functions obtained in the context of the nuclear shell model. With these ingredients, we discuss possibilities of experimental observation of the axion-induced nuclear gamma rays. In the second part, we will examine the axion-induced production of X-rays (axion-photon conversion) or ionization from deeply bound electron orbits. In this case, the axion electron coupling is predicted by existing axion models; no renormalization is needed. The experimental signal is the observation of directly produced electrons and/or the emission of hard X-rays and Auger electrons, following the deexcitation of the final atom. Critical discussion is made on the experimental feasibility of detecting the solar axions by using multiton scale NaI detectors.

Probing the single-particle behavior above Sn132 via electromagnetic moments of Sb133,134 and N=82 isotones

Magnetic and quadrupole moments of the $7/{2}^{+}$ ground state in $^{133}\mathrm{Sb}$ and the $({7}^{\ensuremath{-}})$ isomer in $^{134}\mathrm{Sb}$ have been measured by collinear laser spectroscopy to investigate the single-particle behavior above the doubly magic nucleus $^{132}\mathrm{Sn}$. The comparison of experimental data of the $7/{2}^{+}$ states in $^{133}\mathrm{Sb}$ and neighboring $N=82$ isotones to shell-model calculations reveals the sensitivity of magnetic moments to the splitting of the spin-orbit partners $\ensuremath{\pi}0{g}_{9/2}$ and $\ensuremath{\pi}0{g}_{7/2}$ across the proton shell closure at $Z=50$. In contrast, quadrupole moments of the $N=82$ isotones are insensitive to cross-shell excitations, but require the full proton model space from $Z=50\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}82$ for their accurate description. In fact, the linear trend of the quadrupole moment follows approximately the expectation of the seniority scheme when filling the $\ensuremath{\pi}0{g}_{7/2}$ orbital. As far as the isomer in $^{134}\mathrm{Sb}$ is concerned, its electromagnetic moments can be perfectly described by the additivity rule employing the moments of $^{133}\mathrm{Sb}$ and $^{133}\mathrm{Sn}$, respectively. These findings agree with shell-model calculations and thus confirm the weak coupling between the valence proton and neutron in $^{134}\mathrm{Sb}$.

New α-Emitting Isotope ^{214}U and Abnormal Enhancement of α-Particle Clustering in Lightest Uranium Isotopes.

A new α-emitting isotope ^{214}U, produced by the fusion-evaporation reaction ^{182}W(^{36}Ar,4n)^{214}U, was identified by employing the gas-filled recoil separator SHANS and the recoil-α correlation technique. More precise α-decay properties of even-even nuclei ^{216,218}U were also measured in the reactions of ^{40}Ar, ^{40}Ca beams with ^{180,182,184}W targets. By combining the experimental data, improved α-decay reduced widths δ^{2} for the even-even Po-Pu nuclei in the vicinity of the magic neutron number N=126 are deduced. Their systematic trends are discussed in terms of the N_{p}N_{n} scheme in order to study the influence of proton-neutron interaction on α decay in this region of nuclei. It is strikingly found that the reduced widths of ^{214,216}U are significantly enhanced by a factor of two as compared with the N_{p}N_{n} systematics for the 84≤Z≤90 and N<126 even-even nuclei. The abnormal enhancement is interpreted by the strong monopole interaction between the valence protons and neutrons occupying the π1f_{7/2} and ν1f_{5/2} spin-orbit partner orbits, which is supported by the large-scale shell model calculation.

Magnetic dipole excitations based on the relativistic nuclear energy density functional

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.

Study of light tellurium isotopes along the yrast line

The projected shell model is employed to study the light tellurium isotopes along the yrast line. The results are obtained for yrast bands, moment of inertia and B(E2) transition probabilities. Besides this, the systematics of E21+,E41+/E21+ and B(E2;21+⟶01+) and BCS subshell occupation numbers are investigated in light 106−112Te isotopes. The results on moment of inertia predict the occurrence of phenomenon of backbending around the band crosssing region due to the alignment of a pair of neutrons in the neutron 1h11/2 subshell. The maximum collectivity is observed at N = 60 due to the large neutron-proton (n-p) interaction between spin-orbit partner (SOP) [(g9/2)π, (g7/2)ν] orbits and occupation of down slopping components of νh11/2 subshell.

Gamow–Teller transitions and neutron–proton-pair transfer reactions

We propose a schematic model of nucleons moving in spin–orbit partner levels, j=l±12, to explain Gamow–Teller and two-nucleon transfer data in N=Z nuclei above 40Ca. Use of the LS coupling scheme provides a more transparent approach to interpret the structure and reaction data. We apply the model to the analysis of charge-exchange, 42Ca(3He,t)42Sc, and np-transfer, 40Ca(3He,p)42Sc, reactions data to define the elementary modes of excitation in terms of both isovector and isoscalar pairs, whose properties can be determined by adjusting the parameters of the model (spin–orbit splitting, isovector pairing strength and quadrupole matrix element) to the available data. The overall agreement with experiment suggests that the approach captures the main physics ingredients and provides the basis for a boson approximation that can be extended to heavier nuclei. Our analysis also reveals that the SU(4)-symmetry limit is not realized in 42Sc.

Matter distribution and spin-orbit force in spherical nuclei

We investigate the possibility that some nuclei show density distributions with a depletion in the center, a semibubble structure, by using a Hartree-Fock plus Bardeen-Cooper-Schrieffer approach. We separately study the proton, neutron, and matter distributions in 37 spherical nuclei mainly in the $s\text{\ensuremath{-}}d$ shell region. We found a relation between the semibubble structure and the energy splitting of spin-orbit partner single particle levels. The presence of semibubble structure reduces this splitting, and we study its consequences on the excitation spectrum of the nuclei under investigation by using a quasiparticle random-phase-approximation approach. The excitation energies of the low-lying ${4}^{+}$ states can be related to the presence of semibubble structure in nuclei.

Effect of Weak Binding on the Apparent Spin-Orbit Splitting in Nuclei.

The apparent splitting between orbitals that are spin-orbit partners can be substantially influenced by the effects of weak binding. In particular, such effects can account for the observed decrease in separation of the neutron 1p_{3/2} and 1p_{1/2} orbitals between the ^{41}Ca and ^{35}Si isotopes. This behavior has been the subject of recent experimental and theoretical works and cited as evidence for a proton "bubble" in ^{34}Si causing an explicit weakening of the spin-orbit interaction. The results reported here suggest that the change in the separation between the 1p_{3/2} and 1p_{1/2} partners occurs dominantly because of the behavior of the energies of these 1p neutron states near zero binding.

Roles of NN-interaction components in shell-structure evolution

Since the importance of the monopole interaction was first emphasized in 1960s, roles of monopole strengths of two-body nucleon–nucleon interaction in shell structure have been discussed. Through the monopole strengths, we study the roles in shell-structure evolution, starting from explicit forms of the interaction. For the tensor component of the interaction, we show the derivation of the relation, (2j>+1)Vjj>+(2j<+1)Vjj<=0, with a detailed manipulation. We show that one-body spin–orbit term appears in the multipole expansion of two-body spin–orbit interaction. Only the spin–orbit components can affect the spin–orbit energy splitting between spin–orbit partners, when the spin–orbit partner orbits are fully occupied.

Testing the importance of collective correlations in neutrinolessββdecay

We investigate the extent to which theories of collective motion can capture the physics that determines the nuclear matrix elements governing neutrinoless double-beta decay. To that end we calculate the matrix elements for a series of isotopes in the full $pf$ shell, omitting no spin-orbit partners. With the inclusion of isoscalar pairing, a separable collective Hamiltonian that is derived from the shell model effective interaction reproduces the full shell-model matrix elements with good accuracy. A version of the generator coordinate method that includes the isoscalar pairing amplitude as a coordinate also reproduces the shell model results well, an encouraging result for theories of collective motion, which can include more single-particle orbitals than the shell model. We briefly examine heavier nuclei relevant for experimental double-beta decay searches, in which shell-model calculations with all spin-orbit partners are not feasible; our estimates suggest that isoscalar pairing also plays a significant role in these nuclei, though one we are less able to quantify precisely.

Electromagnetic properties of neutron-rich nuclei adjacent to the Z = 50 shell closure

Low-lying high-spin yrast states in the exotic odd–odd isotopes 124–128Sb (Z=51) and 118–128In (Z=49), studied for the first time, show a striking difference in their observed γ-ray decay. With a single valence proton particle/hole occupying the g7/2/g9/2 spin-orbit partners, dominant electric quadrupole transitions occur in Sb as opposed to magnetic dipole transitions in In. The observed properties are explained on the basis of general principles of symmetry and with large-scale shell-model calculations, and reveal novel aspects of the competition between the neutron–proton interaction and the like-nucleon pairing interaction.

Evaluation of the theoretical nuclear matrix elements forββdecay ofGe76

The nuclear matrix elements for two-neutrino double-$\ensuremath{\beta}$ and zero-neutrino double-$\ensuremath{\beta}$ decay of $^{76}\mathrm{Ge}$ are evaluated in terms of the configuration-interaction (CI), quasiparticle random-phase approximation (QRPA), and interacting boson model methods. We point out deficiencies in all of these models and suggest ways that some of them can be corrected. The final results are obtained from the CI method corrected for configuration admixtures involving orbitals outside of the CI configuration space by using results from QRPA, many-body-perturbation theory, and the connections to related observables. The CI two-neutrino matrix element is reduced due to the inclusion of spin-orbit partners and to many-body correlations connected with Gamow-Teller $\ensuremath{\beta}$ decay. The CI zero-neutrino matrix element for the heavy neutrino is enhanced due to particle-particle correlations that are connected with the odd-even oscillations in the nuclear masses. The CI zero-neutrino matrix element for the light neutrino contains both types of correlations that approximately cancel each other. The uncertainty from short-range correlations is also considered.

Consequences of omitting spin-orbit partner configurations forB(E2)values and quadrupole moments in nuclei

Shell-model calculations of $B(E2)$'s and quadrupole moments in the even-even nuclei in the ${g}_{9/2}$ shell region below $^{100}\mathrm{Sn}$ are hampered by the fact that the inclusion of the ${g}_{7/2}$ configuration will lead to model spaces that are too large to handle. Understanding the impact of specific orbit wave functions in large-scale shell-model (LSSM) calculations helps to shed light on the validity of the results that are obtained. We therefore examine lighter nuclei in the beginning of the $fp$ region where one can normally include all the orbitals, ${f}_{7/2},{p}_{3/2},{p}_{1/2}$, and ${f}_{5/2}$, for both protons and neutrons. We perform such calculations but then take a step back and exclude the ${f}_{5/2}$ orbital. By comparing the results of the two calculations we can hope to get insight into the importance of the missing spin-orbital partner in other regions.

Transverse response of bound single-nucleon Dirac-4 spinors of spin-orbit partners to elastic electron scattering

Transverse responses of the upper components, lower components, and crossed term of the bound single-nucleon Dirac-4 spinors of spin-orbit partners to elastic magnetic electron scattering are investigated. For the nuclear spin-orbit partners with $l\ensuremath{\le}3$ or in the $s$-d $f$shell or lower, results show that in the elastic magnetic electron scattering process the lower component of the $j=(l\ensuremath{-}\frac{1}{2})$ partner may play a relatively more important role than that of the $j=(l+\frac{1}{2})$ partner, while the upper component of the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than that of $j=(l\ensuremath{-}\frac{1}{2})$ partner. The results also show that for the response of the crossed term the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than the $j=(l\ensuremath{-}\frac{1}{2})$ partner. In addition, it is also found that the dominant $M1$ multipole of the magnetic form factors in the small momentum transfer region may mainly originate from the convection current transition density.

Emergence of new magic numbers, N = 16 and 32 by tensor interaction in Skyrme–Hartree–Fock theory

Melting of N = 20 shell and development of N = 16 and 32 shells for neutron-rich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting Δ1f shells of 40,48Ca and 56Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels ν2s 1/2 and ν1d 3/2 has been found to be responsible for shell closure at N = 16. The splitting pattern of spin–orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at N = 32 region.

Uses of tensor-induced spin–orbit splitting to locate spherical doubly-magic SHE

Using optimized iso-scalar and iso-vector tensor coupling constants in Skyrme Hartree–Fock calculation which reproduces the splitting of spin–orbit partners 1f7/2–1f5/2 in 40,48Ca and 56Ni, the evolution of shells in the nuclear chart have been studied through developments in spin–orbit splitting. Signatures for all the magic numbers have been generated without any exception. The procedure when extended to superheavy region indicates the element with Z = 114 and N = 184 to be a doubly-magic spherical nucleus.

Evidence of momentum-dependent hybridization inCe2Co0.8Si3.2

We studied the electronic structure of the Kondo lattice system Ce2Co0.8Si3.2 by angle-resolved photoemission spectroscopy (ARPES). The spectra obtained below the coherence temperature consist of a Kondo resonance, its spin-orbit partner and a number of dispersing bands. The quasiparticle weight related to the Kondo peak depends strongly on Fermi vectors associated with bulk bands. This indicates a highly anisotropic hybridization between conduction band and 4f electrons - V_{cf} in Ce2Co0.8Si3.2.