Neutron-proton Interaction Research Articles

Nuclear matrix elements for0νββdecays with light or heavy Majorana-neutrino exchange

We compute the nuclear matrix elements (NMEs) corresponding to the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of nuclei which attract current experimental interest. We concentrate on ground-state-to-ground-state decay transitions mediated by light (l-NMEs) or heavy (h-NMEs) Majorana neutrinos. The computations are done in realistic single-particle model spaces using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the l-NMEs and the h-NMEs include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak currents. In addition, both types of NMEs are corrected for the isospin symmetry by the recently proposed method in which the particle-particle proton-neutron interaction parameter (${g}_{\mathrm{pp}}$) is decomposed into isoscalar (${g}_{\mathrm{pp}}^{T=0}$) and isovector (${g}_{\mathrm{pp}}^{T=1}$) parts. A detailed analysis of the l-NMEs and the h-NMEs is performed to benchmark our computer code and to compare with other recent calculations which produce h-NMEs that are in tension with each other.

Odd-even staggering in the neutron-proton interaction and nuclear mass models

In this paper we study odd-even staggering of the empirical neutron-proton interaction between the last neutron and the last proton, denoted as $\ensuremath{\delta}{V}_{1n\ensuremath{-}1p}$, and its consequence in the Garvey-Kelson mass relations (GKs) and nuclear mass models. The root-mean-squared deviations of predicted masses respectively for even-$A$ and odd-$A$ nuclei by using two combinatorial GKs suggest a large odd-even staggering of $\ensuremath{\delta}{V}_{1n\ensuremath{-}1p}$ between even-odd and odd-even nuclei, while the odd-even difference of $\ensuremath{\delta}{V}_{1n\ensuremath{-}1p}$ between even-even and odd-odd nuclei is much smaller. The contribution of the odd-even staggering of $\ensuremath{\delta}{V}_{1n\ensuremath{-}1p}$ between even-$A$ and odd-$A$ nuclei in deviations of theoretical $\ensuremath{\delta}{V}_{1n\ensuremath{-}1p}$ values of the Duflo-Zuker model and the improved $\mathrm{Weizs}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{a}}\mathrm{cker}\text{\ensuremath{-}}\mathrm{Skyrme}$ model are well represented by an isospin-dependent term. The consideration of this odd-even staggering improves our description of binding energies and one-neutron separation energies in both the Duflo-Zuker model and the improved $\mathrm{Weizs}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{a}}\mathrm{cker}\text{\ensuremath{-}}\mathrm{Skyrme}$ model.

Probing nuclear forces beyond the drip-line using the mirror nuclei N16 and F16

Radioactive beams of $^{14}$O and $^{15}$O were used to populate the resonant states 1/2$^+$, 5/2$^+$ and $0^-,1^-,2^-$ in the unbound $^{15}$F and $^{16}$F nuclei respectively by means of proton elastic scattering reactions in inverse kinematics. Based on their large proton spectroscopic factor values, the resonant states in $^{16}$F can be viewed as a core of $^{14}$O plus a proton in the 2s$_{1/2}$ or 1d$_{5/2}$ shell and a neutron in 1p$_{1/2}$. Experimental energies were used to derive the strength of the 2s$_{1/2}$-1p$_{1/2}$ and 1d$_{5/2}$-1p$_{1/2}$ proton-neutron interactions. It is found that the former changes by 40% compared with the mirror nucleus $^{16}$N, and the second by 10%. This apparent symmetry breaking of the nuclear force between mirror nuclei finds explanation in the role of the large coupling to the continuum for the states built on an $\ell=0$ proton configuration.

Shell structure, emerging collectivity, and valence p-n interactions

The structure of atomic nuclei depends on the interactions of its constituents, protons and neutrons. These interactions play a key role in the development of configuration mixing and in the onset of collectivity and deformation, in changes to the single particle energies and magic numbers, and in the microscopic origins of phase transitional behavior. Particularly important are the valence proton-neutron interactions which can be studied experimentally using double differences of binding energies extracted from high-precision mass measurements. The resulting quantities, called δV pn , are average interaction strengths between the last two protons and the last two neutrons. Focusing on the Z=50-82, N=82-126 shells, we have considered a number of aspects of these interactions, ranging from their relation to the underlying orbits, their behaviour near close shells and throughout major shells, their relation to the onset of collectivity and deformation, and the appearance of unexpected spikes in δV pn values for a special set of heavy nuclei with nearly equal numbers of valence protons and neutrons. We have calculated spatial overlaps between proton and neutron Nilsson orbits and compared these with the experimental results. Finally we also address the relation between masses (separation energies), changes in structure and valence nucleon number.

Generalized Garvey-Kelson mass relations

In this paper we generalize the Garvey-Kelson mass relations and investigate their deviations from experimental data. We observe a few interesting odd-even staggerings exhibited in these mass relations. Such odd-even staggerings reflect subtle features of neutron-proton interactions. Consideration of these staggerings improves the accuracy of mass relations. A Taylor expansion of nuclear masses provides us with a clue to construct new mass relations.

Relativistic complex separable potential of the neutron–proton system

The multirank relativistic complex separable kernels of the neutron–proton interaction for uncoupled D, F partial waves (with the total angular momentum J=2) are proposed. Using the constructed kernels the experimental data for phase shifts and inelasticity in the elastic neutron–proton scattering for the laboratory energy up to 3 GeV and low-energy parameters are described. The comparison of our results with other model calculations is presented.

Emergent collectivity in nuclei and enhanced proton-neutron interactions

Enhanced proton-neutron interactions occur in heavy nuclei along a trajectory of approximately equal numbers of valence protons and neutrons. This is also closely aligned with the trajectory of the saturation of quadrupole deformation. The origin of these enhanced $p$-$n$ interactions is discussed in terms of spatial overlaps of proton and neutron wave functions that are orbit-dependent. It is suggested for the first time that nuclear collectivity is driven by synchronized filling of protons and neutrons with orbitals having parallel spins, identical orbital and total angular momenta projections, belonging to adjacent major shells and differing by one quantum of excitation along the $z$ axis. These results may lead to a new approach to symmetry-based theoretical calculations for heavy nuclei.

Nonadiabatic quasiparticle approach for deformed odd-odd nuclei and the proton emitter130Eu

Proton emission from deformed nuclei near the drip line is regarded as a versatile tool in nuclear structure physics and such a study in odd-odd nuclei provides us with an excellent opportunity to understand several interesting features including the interaction between the valence proton and the valence neutron. We present a detailed formalism for a full microscopic calculation of such proton emitters, where the nuclear structure and decay aspects are taken into account exactly. This formalism is based on the nonadiabatic approach for the two quasiparticle plus rotor model, where the residual neutron-proton interactions are considered in the mean field represented by a deformed Woods-Saxon potential. We demonstrate a systematic way of unambiguously identifying several parameters involved in the calculations with the aid of the experimental data. The quality of results in the case of ${}^{180}$Ta justifies the approach which is further extended to discuss in detail the proton emission from ${}^{130}$Eu. ${I}^{\ensuremath{\pi}}={1}^{+}$ state in ${}^{130}$Eu still remains to be the proton emitting state irrespective of the choice of several parameters. We also note that the decay widths could be quite sensitive to the residual $np$ interaction in case of proton emission from isomeric states.

Investigatingβ-decay properties of spherical nuclei along the possibler-process path

The spherical QRPA method is used for the calculations of the $\beta$-decay properties of the neutron-rich nuclei in the region near the neutron magic numbers N=82 and N=126 which are important for determination of the r-process path. Our calculations differ from previous works by the use of realistic forces for the proton-neutron interaction. Both the allowed and first-forbidden $\beta$-decays are included. Detailed comparisons with the experimental measurements and the previous shell-model calculations are performed. The results for half-lives and beta-delayed neutron emission probabilities will serve as input for the r-process nucleosynthesis simulations.

Two-neutrino double-βdecay Fermi transition and two-nucleon interaction

An exactly solvable model for a description of the two-neutrino double beta decay transition of the Fermi type is considered. By using perturbation theory an explicit dependence of the two-neutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particle-hole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of double beta decay transition through a single state of the intermediate nucleus. Then, an energy weighted sum rule connecting Delta Z=2 nuclei is presented and discussed. It is suggested that this sum rule can be exploited to study the residual interactions of the nuclear Hamiltonian.

Microscopic study of positive-parity yrast bands of 224−234Th isotopes

The positive-parity bands in 224 − 234Th are studied using the projected shell model (PSM) approach. The energy levels, deformation systematics, B(E2) transition probabilities and nuclear g-factors are calculated and compared with the experimental data. The calculation reproduces the observed positive-parity yrast bands and B(E2) transition probabilities. Measurement of B(E2) transition probabilities for higher spins and g-factors would be a stringent test for our predictions. The results of theoretical calculations indicate that the deformation systematics in 224 − 234Th isotopes depend on the occupation of low k components of high j orbits in the valence space and the deformation producing tendency of the neutron–proton interaction operating between spin orbit partner (SOP) orbits, the [(2g9/2) π –(2g7/2) ν ] and [(1i13/2) π –(1i11/2) ν ] SOP orbits in the present context. In addition, the deformation systematics also depend on the polarization of (1h11/2) π orbit. The low-lying states of yrast spectra are found to arise from 0-quasiparticle (qp) intrinsic states whereas the high-spin states turn out to possess composite structure.

Effect of energy level sequences and neutron–proton interaction on α-particle preformation probability

Abstract A realistic density-dependent nucleon–nucleon (NN) interaction with finite-range exchange part which produces the nuclear matter saturation curve and the energy dependence of the nucleon–nucleus optical model potential is used to calculate the preformation probability, S α , of α-decay from different isotones with neutron numbers N = 124 , 126 , 128 , 130 and 132 . We studied the variation of S α with the proton number, Z, for each isotone and found the effect of neutron and proton energy levels of parent nuclei on the behavior of the α-particle preformation probability. We found that S α increases regularly with the proton number when the proton pair in α-particle is emitted from the same level and the neutron level sequence is not changed during the Z-variation. In this case the neutron–proton (n–p) interaction of the two levels, contributing to emission process, is too small. On the contrary, if the proton or neutron level sequence is changed during the emission process, S α behaves irregularly, the irregular behavior increases if both proton and neutron levels are changed. This behavior is accompanied by change or rapid increase in the strength of n–p interaction.

Many-Body Approach to the Alpha-Correlation inside of the Heavy Nuclei

A model of the interior of the heavy nucleus is proposed. Some experiments suggest that the proton pair and the neutron pair are moving in a strongly correlated manner inside of the heavy nucleus (alpha-correlation). To describe this, the proton-neutron interaction is extended from the pairing force to the many-body force. Accordingly, the BCS model must be extended to go beyond the Gorkov decoupling in order to incorporate the many-body force. As a result, comparing the pairing state, a more stable state where both pairing and the alpha correlation are developed is obtained. This model clarifies an interrelation between the paring and the alpha-correlation, because both are derived from a single interaction. The enhancement of the energy gap and the alpha correlation is derived from a common basis.

Nuclear binding and nuclear structure

Binding in atomic nuclei reflects all the nucleonic interactions in the nucleus. These interactions determine the average nuclear potential and the residual interactions that give rise to correlated behavior in nuclei. Therefore the study of nuclear binding energies can shed light on those interactions and on the emergence of coherence and collectivity in nuclei. This will be discussed in the context of two-neutron separation energies and the specific relation of masses to shell and collective structure. Various additive functions of binding energies can be used to isolate specific interactions that play important roles in the evolution of structure. In particular, one of the main drivers of structural evolution is the proton–neutron interaction among the valence nucleons. A specific double difference of binding energies gives empirical measures of this interaction. These data highlight shell structure and the development of collectivity and deformation. In this paper, we will outline some of these ideas and touch on a few recent developments, including new insights into the roles of specific nucleon orbits. The take-away message is the deep link between nuclear structure and binding and the need to take both spectroscopic and binding energy data into account in attempting to understand atomic nuclei.

Regularities of proton-neutron interactions for nuclei in thesdshell

In this paper we study the proton-neutron interaction of nuclei in the $sd$ shell by using the shell model. The isoscalar proton-neutron interactions of the shell model results are found to be consistent with those empirically extracted by the double difference of binding energies. We point out that there exists an additional binding energy for both even-even and odd-odd nuclei, and both these energies lead to the odd-even staggering for $\ensuremath{\delta}{V}_{1\mathrm{p}\ensuremath{-}1\mathrm{n}}$. We also study the possible origin of the anomaly of proton-neutron interactions.

0νββand2νββnuclear matrix elements, quasiparticle random-phase approximation, and isospin symmetry restoration

Within the quasiparticle random-phase approximation (QRPA) we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ Fermi matrix element ${M}_{F}^{2\ensuremath{\nu}}$ vanishes, as it should, unlike in the previous version of the method. This is accomplished by separating the renormalization parameter ${g}_{pp}$ of the particle-particle proton-neutron interaction into isovector and isoscalar parts. The isovector parameter ${g}_{pp}^{T=1}$ needs to be chosen to be essentially equal to the pairing constant ${g}_{\mathrm{pair}}$, so no new parameter is needed. For the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay the Fermi matrix element ${M}_{F}^{0\ensuremath{\nu}}$ is substantially reduced, while the full matrix element ${M}^{0\ensuremath{\nu}}$ is reduced by $\ensuremath{\approx}$10$%$. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.

2νββ decay within a higher pnQRPA approach with the gauge symmetry preserved

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons, a repulsive dipole-dipole proton-neutron interaction in the particle-hole (ph) channel and an attractive dipole-pairing interaction is treated by a gauge restored and fully renormalized proton-neutron quasiparticle random phase approximation formalism. Application to the 2νββ decay rate show a good agreement with the corresponding data. The Ikeda sum rule is obeyed.

AN INVESTIGATION OF THE NUCLEAR STRUCTURES OF EVEN–EVEN NEUTRON-RICH Sr, Zr AND Mo ISOTOPES

Binding energies and their differences are investigated to evaluate the two-neutron separation energies (S2n), the two-proton separation energies (S2p) and the average proton–neutron interaction strengths (δVpn) of neutron-rich Sr , Zr and Mo isotopes in the mass region A = 86–110, including even–even nuclei. Calculations were performed using the Hartree–Fock–Bogoliubov (HFB) method with different Skyrme force parametrizations. The obtained results are discussed and compared with the results of experimental and relativistic mean-field theory (RMFT).

Exotic nuclei and nuclear forces

I overview new aspects of the structure of exotic nuclei as compared to stable nuclei, focusing on several characteristic effects of nuclear forces. The shell structure of nuclei has been proposed by Mayer and Jensen, and has been considered to be kept valid basically for all nuclei, with well-known magic numbers, 2, 8, 20, 28, 50, …. Nuclear forces were shown, very recently, to change this paradigm. It will be presented that the evolution of shell structure occurs in various ways as more neutrons and/or protons are added, and I will present basic points of this shell evolution in terms of the monopole interaction of nuclear forces. I will discuss three types of nuclear forces. The first one is the tensor force. The tensor force is one of the most fundamental nuclear forces, but its first-order effect on the shell structure has been clarified only recently in studies on exotic nuclei. The tensor force can change the spin–orbit splitting depending on the occupation of specific orbits. This results in changes of the shell structure in many nuclei, and consequently some of Mayer–Jensen's magic numbers are lost and new ones emerge, in certain nuclei. This mechanism can be understood in an intuitive way, meaning that the effect is general and robust. The second type of nuclear forces is central force. I will show a general but unknown property of the central force in the shell-model Hamiltonian that can describe nuclear properties in a good agreement with experiment. I will then demonstrate how it can be incorporated into a simple model of the central force, and will discuss how this force works in the shell evolution. Actually, by combining this central force with the tensor force, one can understand and foresee how the same proton–neutron interaction drives the shell evolution, for examples such as Sn/Sb isotopes, N = 20 nuclei and Ni/Cu isotopes. The distribution of single-particle strength is discussed also in comparison to (e,e′p) experiment on 48Ca. The shell evolution affects shapes of nuclei through Jahn–Teller-type mechanism, and a very interesting example with exotic Si isotopes is discussed. The third type of nuclear force is a three-body force, which originates in the Δ particle excitation as proposed by Fujita and Miyazawa many years ago. This force is shown to produce a repulsive interaction between valence neutrons after averaging effects from the third nucleon in the core. The same three-body force is responsible for neutron stars. By including such effects of the three-body force, one can predict the correct drip line of oxygen isotopes, for instance. Thus, the landscape of atomic nuclei varies in going from stable to exotic nuclei due to particular nuclear forces, leading to a paradigm shift. This paper overviews some basic ideas and selected examples.

The empirical p-n interactions and atomic masses

The systematics of the empirical proton-neutron (p-n) interactions are studied for better understanding of atomic masses. The odd-even staggering of the interaction between the last proton and the last neutron is partly explained by the pairing interaction, further studies on this phenomenon are needed. Two sets of simple and accurate mass formulas are suggested by using the systematics of the empirical p-n interactions.