Residual Neutron-proton Interaction Research Articles

Octupole deformation and Ra puzzle with covariant density functional theory in three-dimensional lattice space

The anomaly of the residual proton–neutron interaction [Formula: see text] for Ra isotopes around [Formula: see text] deviating from the general trend, the so-called Ra puzzle, is investigated within the framework of covariant density functional theory in three-dimensional lattice space. The potential energy surfaces in [Formula: see text] plane for Ra isotopes are given by the constrained calculations. The average values of proton–neutron interaction [Formula: see text] extracted from the binding energies of Ra and Rn isotopes with axial, triaxial and reflection asymmetric calculations are compared with the data from AME2020 atomic mass evaluation. It is found that the octupole deformation provides a reasonable interpretation of the Ra puzzle.

Mass Measurement of Upper fp-Shell N=Z-2 and N=Z-1 Nuclei and the Importance of Three-Nucleon Force along the N=Z Line.

Using a novel method of isochronous mass spectrometry, the masses of ^{62}Ge, ^{64}As, ^{66}Se, and ^{70}Kr are measured for the first time, and the masses of ^{58}Zn, ^{61}Ga, ^{63}Ge, ^{65}As, ^{67}Se, ^{71}Kr, and ^{75}Sr are redetermined with improved accuracy. The new masses allow us to derive residual proton-neutron interactions (δV_{pn}) in the N=Z nuclei, which are found to decrease (increase) with increasing mass A for even-even (odd-odd) nuclei beyond Z=28. This bifurcation of δV_{pn} cannot be reproduced by the available mass models, nor is it consistent with expectations of a pseudo-SU(4) symmetry restoration in the fp shell. We performed abinitio calculations with a chiral three-nucleon force (3NF) included, which indicate the enhancement of the T=1 pn pairing over the T=0 pn pairing in this mass region, leading to the opposite evolving trends of δV_{pn} in even-even and odd-odd nuclei.

Brho -defined isochronous mass spectrometry and mass measurements of ^{58}Ni fragments

A novel isochronous mass spectrometry, termed as Brho -defined IMS, has been established at the experimental cooler-storage ring CSRe in Lanzhou. Its potential has been studied through high precision mass measurements of ^{58}Ni projectile fragments. Two time-of-flight detectors were installed in one of the straight sections of CSRe, thus enabling simultaneous measurements of the velocity and the revolution time of each stored short-lived ion. This allows for calculating the magnetic rigidity Brho and the orbit length C of each ion. The accurate Brho (C) function has been constructed, which is a universal calibration curve used to deduce the masses of the stored nuclides. The sensitivity to single stored ions, fast measurement time, and background-free characteristics of the method are ideally suited to address nuclides with very short lifetimes and smallest production yields. In the limiting case of just a single particle, the achieved mass resolving power allows one to determine its mass-over-charge ratio m/q with a remarkable precision of merely sim 5 keV. Masses of T_z=-3/2fp-shell nuclides are re-determined with high accuracy, and the validity of the isospin multiplet mass equation is tested up to the heaviest isospin quartet with A=55. The new masses are also used to investigate the mirror symmetry of empirical residual proton-neutron interactions.

Neutron Matter and Interactions for Ni nuclei in a Supernova 1987A

Structure of neutron matter and neutron-interactions in a Supernova (SN) are investigated by the theoretical model approach. For that purpose, we calculate the neutron skin thicknesses, neutron-proton interactions, density distributions, central depletions in nuclei using Skyrme Hartree-Fock (SHF) model. The neutron skin thickness (NST) properties are obtained by bulk and surface contributions, based on two-parameter Fermi (2pF) distributions, as a function of the relative neutron excess I = (N− Z)/A. For the central depletion in the nucleus, the depletion fraction (DF) of nuclei is calculated by bubble parameters b and b′. To demonstrate the accuracy of the mass model in the theoretical model, calculated binding energies are compared with the theoretical and experimental data in the literature, namely the relativistic mean-field theory (RMFT), atomic mass evaluation (AME), and finite-range droplet model (FRDM). The fluctuations in the mass model are shown for average neutron-proton interactions δ,V1n−1p and the residual neutron-proton interaction δnp for both odd-A and even-A nuclei. Additionally, the single-particle energy levels and charge form factors for some nuclei are presented for the contribution experimental processes. The based on the theoretical and experimental data, the importance and relevance of results of the calculated results are discussed.

High-spin states and signature inversion in odd-odd Lu168

High-spin states of the odd-odd nucleus $^{168}\mathrm{Lu}$ were populated in the $^{123}\mathrm{Sb}(^{48}\mathrm{Ca},3\mathrm{n})^{168}\mathrm{Lu}$ reaction at a beam energy of 203 MeV and decay $\ensuremath{\gamma}$ rays measured using the Gammasphere spectrometer array. The level scheme has been extended from spin 27 to 50 $\ensuremath{\hbar}$, and three new rotational bands have been added. A number of interband linking transitions were revealed, so that all but two bands could be connected with each other. High-spin band crossings, above the first $\ensuremath{\nu}{i}_{13/2}$ alignment, are delineated in most bands. Significant signature inversions are identified for the first time in the bands involving both favored and unfavored signatures of the $\ensuremath{\pi}{h}_{9/2}$ orbital, which are likely caused by a residual proton-neutron interaction. A signature inversion with small amplitude is also observed in the $\ensuremath{\pi}{d}_{5/2}\ensuremath{\bigotimes}\ensuremath{\nu}{i}_{13/2}$ band. Configurations are suggested for all bands based on their experimental properties, with the help of Cranked Shell Model calculations. No evidence is found for triaxial strongly deformed structures that were predicted by the calculations.

Nuclear binding energy predictions based on BP neural network

Nuclear masses are of great importance in nuclear physics and astrophysics. Descriptive experimental data on nuclear masses and the prediction of unknown masses based on residual proton–neutron interactions are a focus in nuclear physics. The accuracy of the residual interaction determines the accuracy of the nuclear mass values, so the study of residual interactions is essential. Before we carry out this study, there are many papers using artificial neural networks in nuclear physics. But no one uses BP neural network to study residual interactions. In this paper, we obtained a description and prediction model for residual interactions based on BP neural network. By combining experimental values with residual interactions model, we successfully calculate the nuclear masses of [Formula: see text]. Results demonstrate that the differences between our calculated values and experimental values (AME2003, AME2012 and AME2016) show that the root-mean-squared deviations (RMSDs) are small (comparing with AME2003, the odd-A nuclei RMSD and the even-A nuclei RMSD are 112 and 128[Formula: see text]keV; comparing with AME2012, the odd-A nuclei RMSD and the even-A nuclei RMSD are 103 and 121[Formula: see text]keV; comparing with AME2016, the RMSD of odd-A nuclei and even-A nuclei are 106 and 122[Formula: see text]keV, respectively). In addition, we obtained some predicted masses based on AME2003 and AME2012, the predicted values have good accuracy and compared well with experimental values (AME2012 and AME2016). The results show that the study of residual interactions using the proposed BP neural network method is feasible and accurate. This method is helpful for analyzing and extracting useful information from a large number of experimental values and then providing a reference for discovering physical laws and support for physical experiments.

β decay of even- A nuclei within the interacting boson model with input based on nuclear density functional theory

We compute the $\beta$-decay $ft$-values within the frameworks of the energy density functional (EDF) and the interacting boson model (IBM). Based on the constrained mean-field calculation with the Gogny-D1M EDF, the IBM Hamiltonian for an even-even nucleus and essential ingredients of the interacting boson-fermion-fermion model (IBFFM) for describing the neighboring odd-odd nucleus are determined in a microscopic way. Only the boson-fermion and residual neutron-proton interaction strengths are determined empirically. The Gamow-Teller (GT) and Fermi (F) transition rates needed to compute the $\beta$-decay $ft$-values are obtained without any additional parameter or quenching of the $g_A$ factor. The observed $\ft$ values for the $\beta^+$ decays of the even-even Ba into odd-odd Cs nuclei, and of the odd-odd Cs to the even-even Xe nuclei, with mass $A\approx 130$ are reasonably well described. The predicted GT and F transition rates represent a sensitive test of the quality of the IBM and IBFFM wave functions.

On the role of pairing correlations in calculation of β-decay half-lives within QRPA formalism

In this paper we show that the proton-neutron residual interaction can play an important role in the reliability of calculated β-decay half-lives. It may also improve the prediction power of the quasiparticle random phase approximation (QRPA) model. We further demonstrate that a reasonable choice of the particle-particle (attractive) and particle-hole force (repulsive) parameters can result in calculated half-lives in very good comparison with the measured ones. Pairing gaps have affect on calculated half-lives which we explore in this paper. We present our half-lives calculation using the proton-neutron QRPA (pn-QRPA) model possessing a multi-shell single-particle deformed space including a schematic interaction for some medium mass neutron-deficient nuclei undergoing β+/EC decay. Our study shows a better agreement with the available experimental data as compared to former calculations.

Structure of odd-odd Cs isotopes within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional

The spectroscopic properties of the odd-odd isotopes $^{124-132}$Cs have been studied within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional framework. Major ingredients to build the interacting boson-fermion-fermion Hamiltonian, such as the ($\beta,\gamma$)-deformation energy surfaces for the even-even core nuclei $^{124-132}$Xe as well as single-particle energies and occupation probabilities of the odd nucleons, have been computed microscopically with the constrained Hartree-Fock-Bogoliubov method. A few coupling constants of the boson-fermion and residual neutron-proton interactions are fitted to reproduce with a reasonable accuracy the experimental excitation energy of the low-lying levels of the odd-mass and odd-odd nuclei. The method is applied to describe the low-energy low-spin spectra of the odd-odd Cs nuclei and the band structures of higher-spin higher-energy states, mainly based on the $(\nu h_{11/2})^{-1}\otimes\pi h_{11/2}$ configuration. Many of those odd-odd Cs nuclei have been identified as candidates for exhibiting chiral doublet bands.

Global microscopic calculations of odd-odd nuclei

The macroscopic-microscopic finite-range droplet model is combined with a particle-rotor coupling model in order to systematically describe low-energy spectra of odd-odd nuclei. The odd proton and neutron are allowed to interact through effective nuclear forces representing the residual neutron-proton interaction. In particular, ground-state spins and parities are calculated and compared to data, where all 268 axially symmetric nuclei which have reliable spin and parity assignments in the Nubase 2016 database are considered. Using a residual neutron-proton interaction composed of both central and tensor terms the agreement with experimental ground-state spins and parities reaches 41% for spherical nuclei and 31% for deformed nuclei. The model is applied to study possible $\ensuremath{\alpha}$-decay chains in superdeformed odd-odd nuclei, and ${Q}_{\ensuremath{\alpha}}$ values are calculated considering favored decay-paths as compared to ground-state paths.

Spectroscopy of odd-odd nuclei within the interacting boson-fermion-fermion model based on the Gogny energy-density functional

We present a method to calculate spectroscopic properties of odd-odd nuclei within the framework of the Interacting Boson-Fermion-Fermion Model based on the Gogny energy density functional. The $(\beta,\gamma)$-deformation energy surface of the even-even (boson-)core nucleus, spherical single-particle energies and occupation probabilities of the odd neutron and odd proton, are provided by the constrained self-consistent mean-field calculation within the Hartree-Fock-Bogoliubov method with the Gogny-D1M functional. These quantities are used as a microscopic input to fix most of the parameters of the IBFFM Hamiltonian. Only a few coupling constants for the boson-fermion Hamiltonian and the residual neutron-proton interaction are specifically adjusted to reproduce experimental low-energy spectra in odd-mass and odd-odd nuclei, respectively. In this way, the number of free parameters involved in the IBFFM framework is reduced significantly. The method is successfully applied to the description of the low-energy spectra and electromagnetic transition rates in the odd-odd $^{194,196,198}$Au nuclei.

Description and prediction of even-A nuclear masses based on residual proton–neutron interactions

The odd–even staggering of neighboring nuclear masses is very useful in calculating local mass relations and nucleon-pair correlations. During the past decades, there has been an increasing interest in the odd–even features of the mass relations and related quantities exhibited in masses of neighboring nuclei. In this work, after choosing a nucleus, we made an analysis of its neighboring nuclei on the upper left corner and the lower right corner, respectively. We empirically obtained a new residual interaction formula of even-A (A is the mass number) nuclei, and it is a revision based on the existing empirical local formula of the proton–neutron interactions between the last proton and the last neutron [Formula: see text]. We then calculated the even-A nuclear masses. The differences between our calculated values and the AME2012 database show that the root-mean-squared deviations (RMSD) are small (for even-A nuclei: A[Formula: see text]42, RMSD[Formula: see text]161 keV; A[Formula: see text]100, RMSD[Formula: see text]125 keV), while for heavy nuclei, some of our calculated values can reach an accuracy of a few tens of keV. With our residual interaction formula including one parameter, we have successfully predicted some unknown masses. Some of our predicted values are compared well with the experimental values (AME2016). In addition, the accuracy and simplicity of our predicted masses for medium and heavy nuclei are comparable to those of the AME2012 (AME2016) extrapolations.

Description and prediction of nuclear masses for ${\boldsymbol~A}\geqslant$100 based on residual proton-neutron interactions

The residual proton-neutron interactions between the last proton and the last neutron ($\delta~V_{\rm~1p-1n}$) are very useful in calculating local mass relations and nucleon-pair correlations.In this paper, after choosing a nuclei, we made an analysis of its neighboring nuclei on the upper left corner and the lower right corner respectively.Based on the two residual proton-neutron interactions empirical formulas of even-A (A is the mass number) nuclei and odd-A nuclei, we obtain a new residual proton-neutron interactions empirical formula exhibited in residual proton-neutron interactions of odd-A nuclei and even-A nuclei.We then calculated the nuclear masses for mass number A$\geqslant$100. The differences between our calculated values and databases show that the RMSDs are small (for $A\geqslant$ 100: the root-mean-squared deviation (RMSD) between our calculated values and the AME2012 databases $\approx$138.4 keV; the RMSD between our calculated values and the AME2016 databases $\approx$ 141 keV).With the $\delta~V_{\rm~1p-1n}$ formula and the known masses (AME2012), we have successfully predicted some unknown masses.We note that our predicted masses are close to those values in the AME2012 and AME2016 databases.In addition, some of our predicted values have good accuracy and compared well with experimental values (AME2016).The result demonstrates that the accuracy of our predicted values for medium and heavy nuclei is comparable to those of the AME2012 extrapolations.

In-beam γ -ray spectroscopy studies of medium-spin states in the odd-odd nucleus Re186

Excited states in Re186 with spins up to J=12 were investigated in two separate experiments using W186(d,2n) reactions at beam energies of 12.5 and 14.5 MeV. Two- and threefold γ-ray coincidence data were collected using the CAESAR and CAGRA spectrometers, respectively, each composed of Compton-suppressed high-purity germanium detectors. Analysis of the data revealed rotational bands built on several two-quasiparticle intrinsic states, including a long-lived Kπ=(8+) isomer. Configuration assignments were supported by an analysis of in-band properties, such as gK-gR values. The excitation energies of the observed intrinsic states were compared with results from multi-quasiparticle blocking calculations, based on the Lipkin-Nogami pairing approach, that included contributions from the residual proton-neutron interactions.

Characterization of long-lived isomers in the odd-odd heavy actinide Md254

Bandhead energies of all the physically admissible low-lying two-quasiparticle configuration states in the doubly-odd heavy actinide $_{101}^{254}\mathrm{Md}_{153}$ are evaluated using the well-tested two-quasiparticle rotor model with explicit inclusion of the residual proton-neutron interaction. A critical examination of these results, aimed at characterization of the long-lived (${t}_{1/2}=10$ min and 28 min; $%\ensuremath{\varepsilon}\ensuremath{\le}100$) isomer pair, conclusively rules out a high-spin ($J\ensuremath{\ge}5$) assignment for either of the isomers. Our analysis leads to ${J}^{\ensuremath{\pi}}K={1}^{\ensuremath{-}}0{p:1/{2}^{\ensuremath{-}}[521]\ensuremath{\bigotimes}n:1/{2}^{+})[620]}$ and ${3}^{\ensuremath{-}}3{p:7/{2}^{\ensuremath{-}}[514]\ensuremath{\bigotimes}n:1/{2}^{+}[620]}$ assignments, respectively, to these isomers and designates the 10-min isomer as its ground state. Our study reveals a ``landmark'' position for $^{254}\mathrm{Md}$ in the decay path of super heavy elements. The as-yet unobserved electron capture decay branches from each of the two $^{254}\mathrm{Md}$ isomers to $^{254}\mathrm{Fm}$ levels are specified.

Modification of Even-A Nuclear Mass Formula

In this paper we obtain an empirical mass formula of even-A nuclei based on residual proton-neutron interactions. The root-mean-squared deviation (RMSD) from experimental data is at an accuracy of about 150 Kev. While for heavy nuclei, we give another formula that fits the experimental data better (RMSD ≈ 119 Kev). We have successfully described the experimental data of nuclear masses and predicted some unknown masses (like 200Ir not involved in AME2003, the deviation of our predicted masses from the value in AME2012 is only about 82 keV). The predictive power of our formula is more competitive than other mass models.

Empirical residual neutron-proton interaction in odd-odd nuclei

Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-$A$ nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number $A$ and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-$A$ and odd-$A$ nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-$A$ systems. We explore three possible ways to extract this additional interaction from the binding energy difference of neighboring nuclei. The extracted interactions are positive in nearly all cases and show weak dependence on the mass number. The empirical interactions are also compared with theoretical values extracted from recent nuclear mass models where large unexpected fluctuations are seen in certain nuclei. The reproduction of the residual neutron-proton interaction and the correction of those irregular fluctuations can be a good criterion for the refinement of those mass models.

Proton emission from the deformed odd-odd nuclei near drip line

Proton emission from odd-odd nuclei is studied within the two quasiparticle plus rotor model which includes the non-adiabatic effects and the residual interaction between valence proton and neutron. Justification of the formalism is discussed through corroboration of our results with the experimental spectrum of 180Ta. Exact calculations are performed to get the proton emission halflives. Our results for the proton emitter 130Eu leads to the assignment of spin and parity Jπ = 1+ for the ground state. The role of Coriolis and residual neutron-proton interactions on the proton emission halflives and their interplay are also discussed.

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.

Effects of Coriolis and residual neutron–proton interactions in the proton emission from 130Eu

We present for the first time, the non-adiabatic quasiparticle approach to study proton emission from odd–odd deformed nuclei which includes the residual neutron–proton interaction. We perform exact calculations of decay widths for the proton emission from 130Eu where the Coriolis effects are included in both the parent and daughter wavefunctions. Without assuming an exact Nilsson state from where the decay could happen, we could explain the experimentally observed half-life. We discuss the interplay between the Coriolis and the residual np interaction as well. This is significant because whereas most of the studies on odd–odd nuclei concern only the energies, a description of decay can test the details of the wavefunctions which may be strongly influenced by the residual interaction.