Two-proton Separation Energies Research Articles

A study on ground-state energies of nuclei by using neural networks

One of the fundamental ground-state properties of nuclei is binding energy. Artificial neural networks (ANN) have been performed to obtain binding energies of nuclei based on the data calculated from Hartree–Fock–Bogolibov method with two Skyrme forces SLy4 and SKP. ANN has been employed to obtain two-neutron and two-proton separation energies of nuclei. Statistical modeling of ground-state energies using ANN has been seen as to be successful in this study. Particularly, predictive power of ANN has been drawn from estimations for energies of Sr, Xe, Er and Pb isotopic chains which are not seen before by the network. The study shows that such a statistical model can be possible tool for searching in systematic of nuclei beyond existing experimental data.

Mass of11O

A recent parametrization of two-proton separation energies in O and Ne nuclei allows a prediction of the energy of ${}^{11}$O(g.s.): ${S}_{2p}=\ensuremath{-}5.41(11)$ MeV, which is considerably more unbound than another recent estimate.

Variation in Displacement Energies Due to Isospin-Nonconserving Forces

For mirror nuclei with masses A=42-95, the effects of isospin-nonconserving nuclear forces are studied with the nuclear shell model using the Coulomb displacement energy and triplet displacement energy as probes. It is shown that the characteristic behavior of the displacement energies can be well reproduced if the isovector and isotensor nuclear interactions with J=0 and T=1 are introduced into the f(7/2) shell. These forces, with their strengths being found consistent with the nucleon-nucleon scattering data, tend to modify nuclear binding energies near the N=Z line. At present, no evidence is found that these forces are needed for the upper fp shell. Theoretical one- and two-proton separation energies are predicted accordingly, and locations of the proton drip line are thereby suggested.

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).

Properties of deformed even-even nuclei nearZ=20in an improved quark mass density-dependent model

An improved quark mass density-dependent model is applied to study the ground-state properties of axially deformed even-even nuclei using the deformed quark-meson coupling calculation. The present study is mainly focused on the nuclei with the available experimental data ranging from $Z=14$ to $Z=26$. The ground-state binding energies, two-neutron separation energies, two-proton separation energies, quadrupole deformations, and root-mean-square (rms) charge radii are studied. The shell effect of the neutron magic number $N=20$ can be demonstrated by our model. It has been shown that the improved quark mass density-dependent model can give a reasonable description of the axially deformed nuclei.

Improved Kelson-Garvey mass relations for proton-rich nuclei

The improved Kelson-Garvey (ImKG) mass relations are proposed from the mass differences of mirror nuclei. The masses of 31 measured proton-rich nuclei with $7\ensuremath{\le}A\ensuremath{\le}41$ and $\ensuremath{-}5\ensuremath{\le}(N\ensuremath{-}Z)\ensuremath{\le}\ensuremath{-}3$ can be remarkably well reproduced by using the proposed relations, with a root-mean-square deviation of 0.398 MeV, which is much smaller than the results of Kelson-Garvey (0.502 MeV) and isobar-mirror mass relations (0.647 MeV). This is because many more masses of participating nuclei are involved in the ImKG mass relations for predicting the masses of unknown proton-rich nuclei. The masses for 144 unknown proton-rich nuclei with $6\ensuremath{\le}A\ensuremath{\le}74$ are predicted by using the ImKG mass relations. The one- and two-proton separation energies for these proton-rich nuclei and the diproton emission are investigated simultaneously.

NEUTRON–PROTON PAIRING EFFECT ON ONE-PROTON AND TWO-PROTON SEPARATION ENERGIES IN RARE-EARTH PROTON-RICH NUCLEI

The one-proton and two-proton separation energies are studied for "ordinary" and rare-earth proton-rich nuclei by including the isovector neutron–proton (np) pairing correlations using the BCS approximation. Even–even as well as odd nuclei are considered. In the latter case, the wave function is defined using the blocked-level technique. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the np isovector pairing effects on the one-proton and two-proton separation energies are non-negligible. However, the only isovector BCS approximation seems to be inadequate for a good description of these quantities when including the np pairing effects: either a particle-number projection or the inclusion of the isoscalar pairing effect seems to be necessary. Another possible improvement would be a more realistic choice of the pairing strengths.

An investigation of the nuclear properties of 24O, 30Si, 30S, 54Ca, and 96Zr new magic nuclei

In this study, the binding energies per particle, the two-neutron and two-proton separation energies and the average proton-neutron interaction strengths of the new magic 24O, 30Si, 30S, 54Ca, and 96Zr nuclei are investigated by using the Hartree-Fock-Bogoliubov (HFB) method with SKM*, SLy4, SLy5, and SIII Skyrme-like forces. The calculated results are compared with the experimental data and with the results obtained using the relativistic mean field theory (RMFT).

STUDY OF TWO-PROTON RADIOACTIVITY WITHIN THE RELATIVISTIC MEAN-FIELD PLUS BCS APPROACH

Inspired by recent experimental studies of two-proton radioactivity in the light-medium mass region, we have employed relativistic mean-field plus state-dependent BCS approach (RMF+BCS) to study the ground state properties of selected even-Z nuclei in the region 20 ≤ Z ≤ 40. It is found that the effective potential barrier provided by the Coulomb interaction and that due to centrifugal force may cause a long delay in the decay of some of the nuclei even with small negative proton separation energy. This may cause the existence of proton-rich nuclei beyond the proton drip-line. Nuclei 38 Ti , 42 Cr , 45 Fe , 48 Ni , 55 Zn , 60 Ge , 63, 64 Se , 68 Kr , 72 Sr and 76 Zr are found to be the potential candidates for exhibiting two-proton radioactivity in the region 20 ≤ Z ≤ 40. The reliability of these predictions is further strengthened by the agreement of the calculated results for the ground state properties such as binding energy, one- and two-proton separation energy, proton and neutron radii, and deformation with the available experimental data for the entire chain of the isotopes of the nuclei in the region 20 ≤ Z ≤ 40.

Two-Particle Separation Energies in the Superdeformed Well

The location of nuclear closed shells, as evidenced through discontinuities in binding energy and one- and two-particle separation energy systematics, remains one of the simplest tests of global nuclear models. How shell gaps evolve, whether with increasing mass, increasing neutron:proton ratio or increasing deformation, is still uncertain, and it has recently been suggested that one must go beyond a static meanfield picture to include the effects of dynamic fluctuations in the nuclear shape even in the ground state. The identification of key properties which may distinguish between competing approaches is thus vital. Comparison of the binding energies of superdeformed nuclei in the A ≈ 190 region shows that two-proton separation energies are higher in the superdeformed state than in the normal state, despite the probably lower Coulomb barrier and lower total binding energy. Possible reasons for this difference are discussed. This somewhat counterintuitive result provides a critical test for global nuclear models.

Spin-orbit and orbit-orbit strengths for the radioactive neutron-rich doubly magic nucleusSn132in relativistic mean-field theory

Relativistic mean field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus $^{132}$Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in $^{132}$Sn as well as the Nilsson spin-orbit parameter $C$ and orbit-orbit parameter $D$ thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.

Mass prediction of proton-rich nuclides with the Coulomb displacement energies in the relativistic point-coupling model

The masses, one- and two-proton separation energies of proton-rich nuclei with Z = 20–55, are computed using the measured masses of mirror neutron-rich nuclei and the Coulomb displacement energies calculated from the relativistic point-coupling model. The implications for the proton drip lines, candidates for two-proton emitters, as well as the impact on the astrophysical rp-process are discussed.

Two-Particle Separation Energy Trends in the Superdeformed Well

A measurement of the energy and spin of superdeformed states in 190Hg, obtained through the observation of transitions directly linking superdeformed and normal states, expands the number of isotopes in which binding energies at superdeformation are known. Comparison with neighboring nuclei shows that two-proton separation energies are higher in the superdeformed state than in the normal state, despite the lower Coulomb barrier and lower total binding energy. This unexpected result provides a critical test for nuclear models.

Theoretical Study on N = 126 Shell Evolution

The nuclei around magic number N = 126 are investigated in the deformed relativistic mean field (RMF) model with effective interactions TMA. We focus investigations on the N = 126 isotonic chain. The N = 126 shell evolution is studied by analyzing the variations of two-neutron (proton) separation energies, quadruple deformations, single particle levels etc. The good agreement of two-neutron separation energies between experimental data and calculated values is reached. The RMF theory predicts that the sizes of N = 126 shell become smaller and smaller with the increasing of proton number Z. However, the N = 126 shell exists in our calculated region all along. According to the calculated two-proton separation energies, the RMF theory suggests 220Pu is a two-proton drip-line nucleus in the N = 126 isotonic chain.

PARTICLE-NUMBER PROJECTED TWO-PROTON SEPARATION ENERGY OF THE PROTON-RICH EVEN–EVEN RARE-EARTH NUCLEI USING AN ISOVECTOR PAIRING APPROACH

The two-proton separation energy (S2P) has been studied by describing the pairing correlations using four various approaches: in the pairing between like-particles case with (SBCS) and without (BCS) inclusion of the particle-number projection, as well as in the isovector pairing case with (NP-PROJ) and without (NP) inclusion of the particle-number projection. It has been numerically evaluated for the even–even rare-earth proton-rich nuclei such as Δnp ≠ 0. Among the four used methods, NP-PROJ is the one that provides the results that are closest to the experimental data when available. On the other hand, it has been shown that the S2P values deduced from the four approaches join, for almost all the considered elements, for the highest values of (N - Z). The fact that the BCS and NP (respectively, SBCS and NP-PROJ) values join may be explained by the fact that Δnp decreases with increasing values of (N - Z). It has also been shown that the BCS and SBCS (respectively, NP and NP-PROJ) values of S2P are very close because the discrepancy between the projected and unprojected energy values is quasi-constant as a function of the deformation. Finally, the four used methods lead to the same prediction of the two-proton drip-line position except for the Dysprosium and the Tungsten.

Comment on “Pygmy dipole response of proton-rich argon nuclei in random-phase approximation and no-core shell model”

In a recent article by C. Barbieri, E. Caurier, K. Langanke, and G. Mart\'inez-Pinedo~\cite{;Bar.08};, low-energy dipole excitations were studied in proton-rich ${;32, 34}; Ar with random-phase approximation (RPA) and no-core shell model (NCSM) using correlated realistic nucleon-nucleon interactions obtained by the unitary correlation operator method (UCOM)~\cite{;Fel.98};. The main objective of this Comment is to argue that the article~\cite{;Bar.08}; contains an inconsistency with respect to previous study of excitations in the same UCOM-RPA framework using identical correlated Argonne V18 interaction~\cite{;Paa.06};, it does not provide any evidence that the low-lying state declared as pygmy dipole resonance in ${;32}; $Ar indeed has the resonance-like structure, and that prior to studying exotic modes of excitation away from the valley of stability one should ensure that the model provides reliable description of available experimental data on nuclear ground state properties and excitations in nuclei. Although the authors aimed at testing the UCOM based theory at the proton drip line, available experimental data that are used as standard initial tests of theory frameworks at the proton drip line have not been considered in the UCOM case (e.g., binding energies, one-proton separation energies, two-proton separation energies).

Properties of proton-rich nuclei in a three-body model

Using a three-body model and realistic two-body potentials, we investigate the properties of the nuclei 18Ne and 28S near the proton dripline. We figure out the two-proton separation energies, occupation of the valence protons, root-mean-square radii of matter and the valence protons. Besides, the spatial correlation densities are displayed to reflect the correlation between the two valence protons. The first excited 0+ state of 18Ne is most likely to be a halo state according to our calculation. Turning off the Coulomb interactions among the three-body systems, we get the two-neutron separation energies and configuration of the valence neutrons of their corresponding mirror nuclei. The results indicate that the three-body model is proper to describe some proton-rich nuclei and can be used to deduce reliable information.

Two-proton decay energy and width ofMg19(g.s.)

We use a weak-coupling procedure and results of a shell-model calculation to compute the two-proton separation energy of $^{19}\mathrm{Mg}$. Our result is at the upper end of the previous range, but $^{19}\mathrm{Mg}$ is still bound for single proton decay to $^{18}\mathrm{Na}$. We also calculate the $2p$ decay width.

Anomalously Large Deformation in Some Medium and HeavyNuclei**The project supported by National Natural ScienceFoundation of China under Grant No. 10125521, the 973National Major State Basic Research and Development of Chinaunder Grant No. G2000077400, the CAS Knowledge InnovationProject No. KJCX2-SW-N02, and the Research Fund for theDoctoral Program of Higher Education of China under Grant No. 20010284036

We investigate the properties of theCe isotopes with neutron number N = 60–90 and the propertiesof the heavy nuclei near 242Am within the framework of deformedrelativistic mean-field (RMF) theory. A systematic comparison betweentheoretical results and experimental data is made. The calculatedbinding energies, two-neutron separation energies, and two-protonseparation energies are in good agreement with experimental ones.The variation trend of experimental quadrupole deformationparameters on the Ce isotopes can be approximately reproduced bythe RMF model. It is found that there exists an abnormally largedeformation in the ground state of proton-rich Ce isotopes. Thisphenomenon can be the general behavior of proton-rich nuclei on theneighboring isotopic chains such as Nd and Sm isotopes. For theheavy nuclei near 242Am the properties of the ground stateand superdeformed isomeric state can be approximatelyreproduced by the RMF model. The mechanism of the appearance ofanomalously large deformation or superdeformation is analyzed andits influence on nuclear properties is discussed. Furtherexperiments to study the anomalously largedeformation in some proton-rich nuclei are suggested.

Staggering behavior of0+state energies in theSp(4)pairing model

We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron (pn) and like-particle isovector pairing interactions as well as interactions with higher J multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the N=Z region, and the like-particle and pn isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.