Neutron Pairing Energy Research Articles

Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory

This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.

Isobaric-multiplet mass equation in a macroscopic-microscopic approach

We study the a, b and c coefficients of the isobaric-multiplet mass equation using a macroscopic-microscopic approach developed by P. Moeller and his collaborators in ADNDT 59, 185 (1995) and ADNDT 109-110, 1 (2016). We show that already the macroscopic part of the finite-range liquid-drop model (FRLDM) describes the general trend of the a and b coefficients relatively well, while the staggering behavior of b coefficients for doublets and quartets can be understood in terms of the difference of average proton and neutron pairing energies. The sets of isobaric masses, predicted by the full macroscopic-microscopic approaches, are used to explore the general trends of IMME coefficients up to A=100. We conclude that while the agreement for a coefficients is quite satisfactory, the global approaches have less sensitivity to predict the staggering pattern observed for b coefficients of doublets and quartets. The best set of theoretical b coefficients for multiplets up to about A=100 is used to predict masses of proton-rich nuclei based on the known experimental masses of neutron-rich mirror partners, and subsequently to investigate their one- and two-proton separation energies. The estimated position of the proton-drip line is in fair agreement with known experimental data. These masses are important for simulations of the astrophysical rp-process.

Shell evolution in neutron-rich Ge, Se, Kr and Sr nuclei within RHB approach

The exotic even–even isotopic chains from [Formula: see text] to [Formula: see text] are investigated by means of the relativistic Hartree–Bogoliubov (RHB) approach with the explicit Density Dependent Meson-Exchange (DD-ME2) and Density-Dependent Point-Coupling (DD-PC1) models. The classic magic number [Formula: see text] is reproduced and the new number [Formula: see text] is predicted to be a robust shell closure by analysing several calculated quantities such as: two-neutron separation energies, two-neutron shell gap, neutron pairing energy, potential energy surface and neutron single particle energies. The obtained results are compared with the predictions of finite range droplet model (FRDM) and with the available experimental data. A reasonable and satisfactory agreement between the theoretical models and experiment is established.

Microscopic description of structural, surface, and decay properties of Z=124, 126 superheavy nuclei

A systematic investigation has been carried out for even-even isotopic series of two superheavy nuclei with Z=124 and Z=126 in the region 160≤N≤220, and 162≤N≤218, respectively, within the framework of covariant density functional theory (CDFT). Based on the potential energy curves calculated using the explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models, many sensitive observables have been analyzed to understand the structural evolution, shape coexistence, and to predict the possible candidates for neutron shell-closure within the isotopic series of Z=124 and Z=126. The shell correction energy and nuclear symmetry energy have been evaluated within the Strutinsky shell correction approach and the Coherent Density Fluctuation Model (CDFM), respectively. All the sensitive observables i.e. two-neutron separation energy, its differential, neutron-pairing energy, single-particle energy levels, and total shell-correction energy reproduce known spherical neutron magic numbers, and present evidence on new deformed neutron magic numbers at N=168, 174 and 178. The symmetry energy shows a direct correlation with the shape of the system. The α-decay chain of four isotopes 124298,302 and 126300,304 have been studied within three different semi-empirical approaches named UNIV2, SemFIS2 and ImSahu, and compared with the available experimental data, FRDM2012 and the WS4 mass model. All the models, DD-ME2, DD-PC1, FRDM2012, and WS4 have predicted around 8α to 10α decay before spontaneous fission (SF) can start.

A search for neutron magicity in the isotopic series of Z = 122, 128 superheavy nuclei

The superheavy nuclei have been examined systematically in the region 158 ⩽ N ⩽ 218, 162 ⩽ N ⩽ 212 for Z = 122 and 128, respectively. The explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models within the framework of covariant density functional theory (CDFT) have been used to study the structural and decay properties of the isotopic series which includes the separable form of a finite range of pairing interaction. From the potential energy curves, the ground state properties of nuclei are predicted. Due to the importance of the shell effect in the superheavy region, the Strutinsky shell correction method has been employed for a better understanding of the extra stability of nuclei. The results from neutron pairing energy, two-neutron separation energy (S 2n ), single-particle energy levels, and total shell-correction energy strongly support N = 168, 174, and 178 as deformed neutron-magic numbers from both the force parameter, in both the isotopic series. N = 172 and 184 are predicted as spherical magic with DD-ME2 interaction in the Z = 122 isotopic series. Using three different semi-empirical approaches named UNIV2, SemFIS2, and ImSahu, the α-decay properties are studied and compared with available experimental data, FRDM2012 and the WS4 mass model. The stability of synthesized superheavy nuclei can be determined by comparing spontaneous fission half-lives with α-decay half-lives.

Investigation of some nuclear structure properties of213Bi,201Tl,188Re,186Re,133Xe,131I,125I,123I,111In,94Tc,90Y,67Ga,67Cu,62Cu,61Cu,55Co, and48Vnuclei used in SPECT in axial deformation

The present work mainly purposed to investigate significant nuclear structure properties nuclei used in single photon emission computed tomography (SPECT), in addition to ground state nuclear properties such as the binding energy per particle, the root mean square (rms) charge, and proton and neutron radii. Besides, we calculated the neutron skin thicknesses (NST), the proton, neutron quadrupole moments ($Q_{P}, Q_{N})$, quadrupole deformation parameter ($\beta_{2})$, and the proton and neutron pairing energies ($P_{P}, P_{N})$ to determine shapes and deformations of SPECT nuclei including odd-odd or odd-even/even-odd nuclei in axial symmetry for Skyrme and Gogny interactions. To analyze the accuracy of the calculated results, the calculated results were compared with available experimental and the theoretical finite-range liquid-drop model (FRDM), and discussed for 12 different force interactions. Notably, the results provide thorough nuclear data to the literature for deformed nuclei of SPECT.

Neutron Pairing Energy of Finite Nuclei

Neutron pairing energies of some of the finite nuclei have been calculated to understand how the neutron pairing changes as the neutron and proton numbers change from odd to even values in isotopes. How its value changes for even (N) - even (Z), even (N) - odd (Z), odd (N) - even (Z) and odd (N) - odd (Z) nuclei has been brought out. The values of pairing energies have been calculated for light nuclei (20 ≤ A ≤ 55), medium nuclei (100 ≤ A ≤ 140) and heavy nuclei (190 ≤ A ≤ 238) and found to lie between: -16 ≤ Pn ≤ 14 MeV, -6 ≤ Pn ≤ 6 MeV and -5 ≤ Pn ≤ 5 MeV respectively. Positive pairing energies only occurred in odd (N) - even (Z) nuclei and this indicated the most stable isotopic nuclei.

Precision Mass Measurements on Neutron-Rich Rare-Earth Isotopes at JYFLTRAP: Reduced Neutron Pairing and Implications for r-Process Calculations.

The rare-earth peak in the r-process abundance pattern depends sensitively on both the astrophysical conditions and subtle changes in nuclear structure in the region. This work takes an important step towards elucidating the nuclear structure and reducing the uncertainties in r-process calculations via precise atomic mass measurements at the JYFLTRAP double Penning trap. ^{158}Nd, ^{160}Pm, ^{162}Sm, and ^{164-166}Gd have been measured for the first time, and the precisions for ^{156}Nd, ^{158}Pm, ^{162,163}Eu, ^{163}Gd, and ^{164}Tb have been improved considerably. Nuclear structure has been probed via two-neutron separation energies S_{2n} and neutron pairing energy metrics D_{n}. The data do not support the existence of a subshell closure at N=100. Neutron pairing has been found to be weaker than predicted by theoretical mass models. The impact on the calculated r-process abundances has been studied. Substantial changes resulting in a smoother abundance distribution and a better agreement with the solar r-process abundances are observed.

Going Beyond the Neutron Drip-Line with MoNA

Understanding the structure of very neutron-rich nuclei is critical to developing reliable and robust models of the nucleus. For nuclei near the neutron drip-line, where the neutron removal energy approaches zero, several features of nuclear structure are much more important than they are in stable nuclei. The neutron pairing energy becomes comparable to the neutron removal energy and nuclei with odd neutron numbers tend to be unbound while their even neighbors remain bound. Additionally, shell effects can be greatly altered by the absence of protons in the same valence orbitals occupied by the neutrons. The lack of the stabilizing influence of protons in similar orbits allows for the tensor interaction between these weakly bound neutrons and the core nucleons to alter the energies of single particle levels. These changes lead to the disappearance of well-known magic numbers and the appearance of new sub-shell closures that have the requisite properties of a magic number: enhanced stability, a large excitation energy for the first excited state, and spherical shape.

Staggering of the nuclear charge radii in a superfluid model with good particle number.

A simple superfluid model with an effective four body interaction of monopole pairing type is used to explain the staggering of the charge radii in the isotope chains. The contribution of deformation and of the particle number projection are analyzed for the Sn isotopes. Good results are obtained for the staggering parameters and neutron pairing energies.

Cold fragmentation in thermal-neutron-induced fission of 233U and 235U

The mass spectrometer Lohengrin of the Institut Laue-Langevin in Grenoble was used to measure fission-fragment mass yields in the mass range 80 ≤ A ≤ 107 for light-fission-fragment kinetic energies up to about 115 MeV for the reactions 233,235U(n th, f). The kinetic energies corresponding to a common fixed yield level for each isobar reflect the influence of the proton pairing energy, but not of the neutron pairing energy. By using calculated Q-values for the different mass splits, mass distributions at fixed total excitation energy are deduced from the data. At a fixed total excitation energy of about 7 MeV, the yield increases from very asymmetric mass splits ( A L ≈ 80) to more symmetric mass splits ( A L ≈ 105) by more than two orders of magnitude. This strong dependence on the mass split seems to be correlated with the decreasing surface-to-surface distance of the unaccelerated fission fragments in this range of mass splits, as calculated under the assumption that the total Q-value is represented by the mutual Coulomb repulsion of the two fragments. The influence of the fission-fragment ground-state deformations on the yield in cold fragmentation could not be detected unambiguously.

High-spin rotational bands and pairing reduction in 166Hf

Rotational properties of the 166Hf nucleus have been studied by in-beam spectroscopic methods using the 150Sm( 20Ne, 4n) 166Hf reaction. The ground band was observed up to the I π = 18 + level, the s-band from the I π = 12 + up to I π = 22 + level; in addition two side bands were found. The results are interpreted in terms of the pairing-self-consistent Hartree-Fock-Bogolyubov cranking model. Quantitative agreement between theory and experiment is obtained for the crossing of the ground band and s-band. The calculations predict a reduction of about 50 % in the neutron pairing energy gap of yrast states in the crossing region. The kinematical ( I (1)) and dynamical ( I (2)) moments of inertia are analysed.

Direct measurements of the masses of rubidium and cesium isotopes far from stability

The masses of neutron-deficient and neutron-rich isotopes of rubidium ($^{74\ensuremath{-}79}\mathrm{Rb}$, $^{90\ensuremath{-}99}\mathrm{Rb}$) and of cesium ($^{117\ensuremath{-}124,126}\mathrm{Cs}$, $^{138,140\ensuremath{-}147}\mathrm{Cs}$) have been determined by direct on-line mass spectrometry. The measured masses are compared to current mass predictions. From the trend of neutron separation energies, experimental neutron pairing energies are deduced and evidence is found for the onset of a deformation at $N=60$ in the neutronrich rubidium isotopes.NUCLEAR STRUCTURE $^{74\ensuremath{-}79}\mathrm{Rb}$, $^{90\ensuremath{-}99}\mathrm{Rb}$, $^{117\ensuremath{-}124,126}\mathrm{Cs}$, $^{138,140\ensuremath{-}147}\mathrm{Cs}$; measured masses, on-line mass spectrometry. ${S}_{2n}$ deduced; evidence for deformation at $N=60$. Comparison with mass predictions.

Nucleon separation and pairing energies, decay energies, and atomic masses for 68 ≤ Z ≤ 72

A set of 24 precise determinations of mass spectroscopic doublet spacings, including a new determination of the 176Hf35Cl – 174Hf37Cl mass difference, has been combined with nuclear reaction and decay Q values in a least squares adjustment of the atomic mass differences in the region 68 ≤ Z ≤ 72. The following quantities have been calculated for each nuclide: separation energies for the last neutron and last pair of neutrons (Sn, S2n), the neutron pairing energy (Pn), separation energies for the last proton and last pair of protons (Sp, S2p), the proton pairing energy (Pp), Q values for α and β− decays, and the mass defect. The systematic variations of these quantities with N and Z are discussed.

Effects of rotation on the stability of nuclei under fission and the possibility of fusion in heavy-ion reactions

The two-center shell model for fission is extended to include the effects of nuclear rotation or angular momentum $J$. The principle of minimization of total nuclear energy with respect to a constraint on $J$ leads to an effective potential energy which depends on $J$ as well as moment of inertia. This effective potential energy is minimized with respect to nuclear shape variables, neutron pairing energy gap, and proton pairing energy gap for each $J$ value. The resulting potential minima, fission barriers, and moments of inertia are quite sensitive to $J$. Results are given for $_{82}^{208}\mathrm{Pb}$, $_{94}^{240}\mathrm{Pu}$, and for a super-heavy nucleus $_{114}^{298}X$. Our microscopic calculations of the critical angular momentum (at which the fission barrier vanishes) are compared with the rotating liquid drop calculations of Cohen, Plasil, and Swiatecki. The influence of these results on the possibility of fusion in heavy-ion reactions is discussed.NUCLEAR STRUCTURE: Fission and heavy-ion fusion. The two-center shell model calculation of rotational effects in compound nuclei $_{82}^{208}\mathrm{Pb}$, $_{94}^{240}\mathrm{Pu}$, $_{114}^{298}X$.

Nucleon Separation and Pairing Energies, Decay Energies, and Atomic Masses for

A set of 45 precise determinations of doublet spacings in the mass spectra of rare-earth chlorides has been combined with existing nuclear reaction and decay Q values and atomic mass data in a least-squares adjustment of atomic mass differences. For nuclides in the region [Formula: see text] the following quantities have been calculated: separation energies for the last pair of neutrons and for the last neutron (S2n, Sn), the neutron pairing energy (Pn), separation energies for the last pair of protons and for the last proton (S2p, Sp), the proton pairing energy (Pp), Q values for α and β− decays, and the masses. The systematic variations of these quantities are illustrated and discussed.

New atomic mass differences and mass systematics in the region 100 ≦ N ≦ 126

Values are reported for ten atomic mass differences involving isotopes of W, Re and Os. The new mass differences are combined with existing nuclear reaction and decay data to yield single- and double-neutron separation energies and neutron pairing energies for many nucleides in this mass region. The neutron separation energy systematics defined by the nucleides between Hf and Pb indicate that the transition from permanently deformed nuclei at N ≈ 110 to spherical nuclei at N ≈ 120 is not accompanied by a pronounced mass effect.

Neutron Separation and Pairing Energies in the Region82<~N<~126

Results of a systematic study of atomic-mass differences in the region $82<~N<~126$ are presented as plots of double-neutron separation energy and neutron-pairing energy. These plots provide information concerning the extent of the nuclear deformation which begins in the region of 90 neutrons, its dependence upon $Z$, and its gradual dissappearance in the region $106\ensuremath{\lesssim}N\ensuremath{\lesssim}116$.

Atomic Masses from Gallium to Molybdenum

The 16-in. double-focusing mass spectrometer at the University of Minnesota has been employed to measure the atomic mass of 42 stable isotopes in the region $A=69 \mathrm{to} 100$. The standard error associated with these results is approximately 5 parts in ${10}^{8}$. Improvements in the instrument are described that result in an increase of useful resolution of a factor of 2 to 3. A set of 64 radioactive masses is calculated from the stable mass data together with $\ensuremath{\beta}$-decay energies and nuclear reaction $Q$ values. The resultant table of masses is used to calculate total nuclear binding energies, separation energies and pairing energies for a number of nuclei in the region near $N=50$. The systematics of the separation energies display very smooth characteristics except at the shell closure. Neutron pairing energies show a marked decrease in value following the shell closure.

Neutron Separation Energies and Pairing Energies for Heavy Nuclei

A six-inch double-focusing mass spectrometer has been employed to determine 32 mass differences between neighboring isotopes of even-Z elements in the region Z = 64 to 82. Neutron separation energies and neutron pairing energies are easily calculated from the experimental results. These calculated values are sufficientiy precise to conclude that lack of uniformity in neutron separation energy and pairing energy systematics appears in regions where other nuclear properties exhibit changes in their systematics. Neutron separation energy data have also been employed for the isotopic assignments of several nuclear reactions. (auth)