Neutron Drip Research Articles

β-decay and isospin symmetry breaking

<p indent=0mm>The elegant concept of isospin symmetry is of fundamental importance in nuclear and elementary particle physics. As a β-decay process changes an up quark to a down quark or <italic>vice versa</italic>, studies of nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, can be a powerful means to probe isospin symmetry breaking. A series of β-decay experiments of sd-shell nuclei near the proton drip line produced by projectile fragmentation were performed at the Radioactive Ion Beam Line of the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1) using a silicon array with a high detection efficiency and a low detection threshold. The secondary ions were identified by the combination of Δ<italic>E</italic>-TOF and magnetic rigidity (<italic>Bρ</italic>) in which the time of flight (TOF) was measured by two plastic scintillators at the second and fourth focal planes of the RIBLL1 and the energy loss (Δ<italic>E</italic>) was measured by two silicon detectors in the front of the silicon array. Double-sided silicon strip detectors (DSSDs) in the center of the array served to measure the residual energies of secondary ions on an event-by-event basis and study their decay properties with an implantation-decay correlation. Several quadrant silicon detectors (QSDs) placed behind DSSDs were used for anticoincidences of the penetrating fragments and light particles coming along with the beam, and measurements of β particles and high-energy protons. The β-delayed proton peaks with known energies and their corresponding absolute intensities were used for the energy and detection efficiency calibrations of the DSSDs. The system allows us to measure protons with energies down to about <sc>200 keV</sc> without obvious β background in the proton spectrum and was successful to measure the energies, time, and positions of implanted ions and decay protons efficiently, supporting researchers to study the decay properties of nuclei towards the proton drip line. The β-decay data, together with the large-scale shell-model calculations, allows detailed investigations on the mirror-nuclei systems resulting in the systematic study of isospin symmetry breaking in the sd-shell nuclear region. It was found that the mirror asymmetry parameters become larger due to the smaller separation energies while approaching the proton drip line for the extremely proton-rich sulfur nuclei ^27,28,29S and the Coulomb forces and other isospin-symmetry nonconserving forces acting between protons would lead to extended proton wave functions and cause mirror asymmetries. The properties of ²²Si β-decay for the transitions to the low-lying states of ²²Al were measured, and the reduced transition probabilities were determined. Comparing with the data on the β-decay of the mirror nucleus ²²O, we found a mirror asymmetry of <italic>δ</italic>=209(96)% in the transition to the first 1⁺ excited state of the respective daughters. This is by far the largest value of <italic>δ</italic> observed in the low-lying states. Shell-model calculations with isospin-nonconserving forces, including the <italic>T</italic>=1,<italic> J</italic>=2, 3 interactions related to the s_1/2 orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s_1/2 orbit, can reproduce the observed data well and demonstrate that this dramatically large mirror asymmetry is attributed to the significant proton occupation and loosely bound nature of the wave functions of the s_1/2 orbit, which suggests that ²²Al is a proton-halo nucleus.

Temperature dependence of nuclear properties: A systematic study along the isotopic and isotonic chains of nuclei

In this work, we study the changes in the nuclear properties by performing systematic calculations on the selected isotopic and isotonic chains of nuclei with increasing temperature. The finite temperature Hartree–Fock–Bogoliubov (FT-HFB) calculations are performed using the Skyrme-type SkM* functional and mixed-type pairing interaction. The changes in the pairing properties, internal excitation energies, entropy, two-neutron separation energies, and neutron skin thickness of nuclei are systematically studied. It is shown that both the internal excitation energy and entropy are sensitive to the changes in the pairing properties of nuclei below the critical temperatures. At high temperatures and after T≥1 MeV, both of them increase rapidly. The nuclei near the neutron drip lines are affected more by the temperature effects since the continuum effects start to become dominant around these regions. On the other hand, the internal energy and entropy are not sensitive to the increase in the proton number, and the changes remain almost stable along an isotonic chain with increasing temperature. We also found that some nuclei near the neutron drip lines become bound at finite temperatures, whereas they are unstable against the two-neutron emission (S2n≤0 MeV). Investigation of the neutron skin thickness of nuclei shows that the temperature has a big impact on nuclei close to the neutron drip lines, and it considerably increases the neutron skin thickness of these nuclei at high temperatures.

Study of the Static and Dynamic Nuclear Properties and Form Factors for Some Magnesium Isotopes 29-34 Mg

Nuclear structure of 29-34Mg isotopes toward neutron dripline have been investigated using shell model with Skyrme-Hartree–Fock calculations. In particular nuclear densities for proton, neutron, mass and charge densities with their corresponding rms radii, neutron skin thicknesses and inelastic electron scattering form factors are calculated for positive low-lying states. The deduced results are discussed for the transverse form factor and compared with the available experimental data. It has been confirmed that the combining shell model with Hartree-Fock mean field method with Skyrme interaction can accommodate very well the nuclear excitation properties and can reach a highly descriptive and predictive power when investigating different nuclear configurations of stable and unstable nuclei.

Exploring the halo phenomena of medium-mass nuclei having approximately Z= 40 with point-coupled parameters in complex momentum representations * *Supported by the National Natural Science Foundation of China (11875070) and the Natural Science Foundation of Anhui Province (1908085MA16)

To explore the properties of neutron-rich nuclei with approximately 40 protons, the density-dependent point coupling (DD-PC1) effective interaction parameter is adopted in the relativistic mean-field theory with the complex momentum representation (RMF-CMR). The calculated two-neutron separation energy (S 2n ) and root-mean-square (rms) radii support the halo structure that appear in Mo and Ru isotopic chains. Besides, the neutron skin structures appear in Kr and Sr isotopes. The conclusions drawn are also supported by the single-particle energy levels and their occupancy probability and density distribution. Particularly, the energy levels, which reduce to bound states or are approximately 0 MeV with a small orbital angular momentum, are suggested to provide the primary contribution to increasing the neutron radius. Moreover, the single-particle energy levels significantly reflect the shell structure. In addition, the neutron drip line nuclei for Kr, Sr, Mo, and Ru elements are proposed via the changes in S 2n .

Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton (2p) radioactivity, the 2p decay energies (Q 2p ) are extracted by the Weizsäcker–Skyrme-4 (WS4) model, the finite-range droplet model (FRDM), the Koura–Tachibana–Uno–Yamada (KTUY) model and the Hartree–Fock–Bogoliubov mean-field model with the BSk29 Skyrme interaction (HFB29). Then, the 2p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q 2p values. By the energy and half-life constraints, it is found that the probable 2p decay candidates are the nuclei beyond the proton-drip line in the region of Z ≤ 50 based on the WS4 and KTUY mass models. For the FRDM mass model, the probable 2p decay candidates are found in the region of Z ≤ 44. However, the 2p-decaying candidates are predicted in the region of Z ≤ 58 by the HFB29 mass model. It means that the probable 2p decay candidates of Z > 50 are only predicted by the HFB29 mass model. Finally, the competition between the true 2p radioactivity and α-decay for the nuclei above the N = Z = 50 shell closures is discussed. It is shown that 101Te, 111Ba and 114Ce prefer to 2p radioactivity and the dominant decay mode of 107Xe and 116Ce is α-decay.

Experimental study of the F17+C12 fusion reaction and its implications for fusion of proton-halo systems

The halo nature of the low-lying $1/2$+ first excited state of the exotic weakly-bound proton drip-line nucleus $^{17}$F has long been hypothesized. The structure of such a halo nucleus would imply special nuclear properties including, possibly, an enhancement in its fusion cross section above the barrier. The total fusion cross section of $^{17}$F + $^{12}$C near the Coulomb barrier was studied using the newly developed "Encore" active-target detector at Florida State University. Total fusion cross sections for the stable counterpart systems $^{16}$O + $^{12}$C and $^{19}$F + $^{12}$C were also measured to enable a systematic comparison. No influence of the halo nature of the $^{17}$F $1/2$+ first excited state on its fusion excitation function was observed when compared with the stable counterpart systems.

Compression Modulus and Symmetry Energy of Nuclear Matter with KIDS Density Functional

Equation of state of dense nuclear matter is explored in the KIDS density functional theory. Parameters of the equation of state which are coefficients of the energy density expanded in powers of $(\rho - \rho_0)/3\rho_0$ where $\rho$ is the nuclear matter density and $\rho_0$ is its density at saturation are constrained by using both nuclear data and the mass-radius relation of the neutron star determined from the modern astronomy. We find that the combination of both data can reduce the uncertainty in the equation of state parameters significantly. We confirm that the newly constrained parameters reproduce the basic properties of spherical magic nuclei with high accuracy. Neutron drip lines, on the other hand, show non-negligible dependence on the uncertainty of the nuclear symmetry energy.

Observation of the Exotic Isotope ^{13}F Located Four Neutrons beyond the Proton Drip Line.

A ^{13}F resonance was observed following a charge-exchange reaction between a fast ^{13}O beam and a ^{9}Be target. The resonance was found in the invariant-mass distribution of 3p+^{10}C events and probably corresponds to a 5/2^{+} excited state. The ground state was also expected to be populated, but was not resolved from the background. The observed level decays via initial proton emissions to both the ground and first 2^{+} state of ^{12}O, which subsequently undergo 2p decay. In addition, there may also be a significant proton decay branch to the second 2^{+} level in ^{12}O. The wave function associated with the observed level may be collectivized due to coupling to the continuum as is it located just above the threshold for proton decay to the 2_{2}^{+} state of ^{12}O.

Constraining the density dependence of the symmetry energy with nuclear data and astronomical observations in the Korea-IBS-Daegu-SKKU framework

The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore symmetry-energy (SE) parameters such as J (value at saturation density), L (slope), Ksym (curvature) and so on independently of each other and of assumptions about the effective mass. Here we examine the performance of EoSs with different SE parameters in reproducing nuclear properties and astronomical observations in an effort to constrain especially L and Ksym or the droplet-model counterpart Ktau. Assuming a standard EoS for symmetric matter, we explore several points on the hyperplane of (J,L,Ksym or Ktau) values. For each point, the corresponding EDF parameters and a pairing parameter are obtained for applications in spherical even-even nuclei. This is the first application of KIDS EDFs with pairing correlations. The EoSs are tested successively on properties of closed-shell nuclei, along the Sn isotopic chain, and on astronomical observations, in a step-by-step process of elimination and correction. A small regime of best-performing parameters is determined. The results strongly suggest that Ksym is negative and no lower than -200MeV, that Ktau lies between roughly -400 and -300MeV and that L lies between 40 and 65MeV with L<55MeV more likely. Correlations between symmetry-energy parameters are critically discussed. Predictions for the position of the neutron drip line and the neutron skin thickness of selected nuclei are reported. They are only weakly affected by the choice of effective mass values. Parts of the drip line can be sensitive to the SE parameters. The results underscore the role of Ktau and of precise astronomical input. Better constraints are possible with precise fits to nuclear energies and, in the future, more-precise input from astronomy.

Hyperheavy spherical and toroidal nuclei: The role of shell structure

The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the $Z\approx 130-180$ region of nuclear chart are established for the first time. These nuclei are stable with respect of breathing deformations. The most compact fat toroidal nuclei are located in the $Z\approx 136, N\approx 206$ region of nuclear chart, but thin toroidal nuclei become dominant with increasing proton number and on moving towards proton and neutron drip lines. The role of toroidal shell structure, its regularity, supershell structure, shell gaps as well as the role of different groups of the pairs of the orbitals in its formation are investigated in detail. The lowest in energy solutions at axial symmetry are characterized either by large shell gaps or low density of the single-particle states in the vicinity of the Fermi level in at least one of the subsystems (proton or neutron). Related quantum shell effects are expected to act against the instabilities in breathing and sausage deformations for these subsystems. The investigation with large set of covariant energy density functionals reveals that substantial proton $Z=154$ and 186 and neutron $N=228$, 308 and 406 spherical shell gaps exist in all functionals. The nuclei in the vicinity of the combination of these particle numbers form the islands of stability of spherical hyperheavy nuclei. The study suggests that the $N=210$ toroidal shell gap plays a substantial role in the stabilization of fat toroidal nuclei.

The neutron dripline at Z = 4: the case of $$^{13,15}\hbox {Be}$$

We review an extensive study of the beryllium isotopic chain carried out at RIKEN. In particular, we discuss the results on $$^{13,15}\hbox {Be}$$ , two key isotopes for the understanding of dineutron configurations and decays in $$^{14,16}\hbox {Be}$$ . In the $$^{13}$$ Be case, a detailed analysis of its spectroscopy, including for the first time a well-founded reaction framework and a realistic three-body model of $$^{14}\hbox {Be}$$ that incorporates core excitations, confirms the dominant $$\ell =1$$ content of the low-lying spectrum. In the $$^{15}$$ Be case, the fragmentation of $$^{18}$$ C, a priori free of any selection rules that may have precluded the observation of states in previous experiments, has confirmed the only known state at about 1.8 MeV, assigned according to shell-model calculations to a spin-parity $$5/2^+$$ . Some perspectives of these studies are also given.

Study of the Nuclear Structure of some Neutron Rich Si Isotopes Using Shell Model with Skyrme Interaction

Abstract&#x0D; The nuclear structure of 28-40Si isotopes toward neutron dripline has been investigated in framework of shell model with Skyrme-Hrtree-Fock method using certain Skyrme parameterizations. Moreover, investigations of static properties such as nuclear densities for proton, neutron, mass, and, charge densities with their corresponding rms radii, neutron skin thicknesses, binding energies, separation energies, shell gap, and pairing gap have been performed using the most recent Skyrme parameterization. The calculated results have been compared with available experimental data to identify which of these parameterizations introduced equivalent results with the experimental data. For all dynamic properties, sdpf shell model space has been used to generate one body transition density matrix element with SDPFK two body effective interaction. The calculations also reproduced the low and higher-laying 2+ energy level scheme, and reduced transition probability B(E2) for even Si-isotopes.

Shell-model based study of the direct capture in neutron-rich nuclei

The radiative neutron capture rates for isotopes of astrophysical interest are commonly calculated within the statistical Hauser-Feshbach reaction model. Such an approach, assuming a high level density in the compound system, can be questioned in light and neutron-rich nuclei for which only a few or no resonant states are available. Therefore, in this work we focus on the direct neutron-capture process. We employ a shell-model approach in several model spaces with well-established effective interactions to calculate spectra and spectroscopic factors in a set of 50 neutron-rich target nuclei in different mass regions, including doubly-, semi-magic and deformed ones. Those theoretical energies and spectroscopic factors are used to evaluate direct neutron capture rates and to test global theoretical models using average spectroscopic factors and level densities based on the Hartree-Fock-Bogoliubov plus combinatorial method. The comparison of shell-model and global model results reveals several discrepancies that can be related to problems in level densities. All the results show however that the direct capture is non-negligible with respect to the by-default Hauser-Feshbach predictions and can be even 100 times more important for the most neutron-rich nuclei close to the neutron drip line.

Systematic study of two-proton radioactivity within a Gamow-like model * *Supported in part by the National Natural Science Foundation of China (11205083, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Natural Science Foundation of Hunan Province, China (2018JJ2321), the Innovation Group of Nuclear and Particle

In this study, based on the Gamow-like model, we systematically analyze two-proton ( ) radioactivity half-lives of nuclei near or beyond the proton drip line. It is found that the calculated results can reproduce experimental data well. Furthermore, using this model, we predict the half-lives of possible radioactivity candidates whose radioactivity is energetically allowed or observed but not yet quantified in the latest table of evaluated nuclear properties, i.e., NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Sreeja formula, and Liu formula.

Proton radioactivity of nuclei with atomic numbers Z = 51–91 and mass number 104–211

Proton radioactivity of neutron-deficient nuclei with atomic numbers [Formula: see text]–91 and mass number 104–211 is investigated using the analytical super-asymmetric fission (ASAF) model — a model used to study [Formula: see text]-decay and cluster radioactivity since 1984. The experimental [Formula: see text] values are compared with calculated ones based on WS4 (Y. Z. Wang et al., 2014–2015), and in few cases KTUY05 (H. Koura et al., 2005) mass models. Proton drip-line and neutron drip-line are determined using the WS4 mass model. We compare the calculated results with experimental half-lives, showing good agreement.

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.

Neutron drip line in the deformed relativistic Hartree–Bogoliubov theory in continuum: Oxygen to Calcium

The location of the neutron drip line, currently known for only the lightest elements, remains a fundamental question in nuclear physics. Its description is a challenge for microscopic nuclear energy density functionals, as it must take into account in a realistic way not only the nuclear potential, but also pairing correlations, deformation effects and coupling to the continuum. The recently developed deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) includes all three aforementioned effects in the description of nuclei throughout the nuclear chart. Here, the DRHBc with the successful density functional PC-PK1 is used to investigate whether and how deformation influences the prediction for the neutron drip-line location for even–even nuclei with [Formula: see text], where many isotopes are predicted deformed. The results are compared with those based on the spherical relativistic continuum Hartree–Bogoliubov (RCHB) theory and discussed in terms of shape evolution and the variational principle. It is found that the Ne and Ar drip-line nuclei are different after the deformation effect is included. The direction of the change is not necessarily towards an extended drip line, but rather depends on the evolution of the degree of deformation towards the drip line. Deformation effects as well as pairing and continuum effects treated in a consistent way can affect critically the theoretical description of the neutron drip-line location.

Deformed halo of [formula omitted]F20

Using a simple model based on the knowledge of spherical and deformed Woods-Saxon potentials, it is shown that the recent observation of halo phenomena in 29F can be interpreted as evidence for the prolate deformation of the ground state of 29F. The prolate deformation is the result of the shell structure, which is unique in one-neutron resonant levels, in particular near degeneracy of the neutron 1f7/2 and 2p3/2 resonant levels, together with the strong preference of prolate shape by the proton number Z=9. On the other hand, in oxygen isotopes spherical shape is so much favored by the proton number Z=8 that the presence of possible neutron shell-structure may not make the system deformed. Thus, the strong preference of particular shape by the proton numbers 8 and 9, respectively, together with a considerable amount of the energy difference between the neutron 1d3/2 and 2s1/2 orbits in oxygen isotopes seems to play an important role in the phenomena of oxygen neutron drip line anomaly, as was suggested by H. Sakurai et al. in 1999.

Origin of the heaviest elements: The rapid neutron-capture process

The production of about half of the heavy elements found in nature is assigned to a specific astrophysical nucleosynthesis process: the rapid neutron capture process (r-process). Although this idea has been postulated more than six decades ago, the full understanding faces two types of uncertainties/open questions: (a) The nucleosynthesis path in the nuclear chart runs close to the neutron-drip line, where presently only limited experimental information is available, and one has to rely strongly on theoretical predictions for nuclear properties. (b) While for many years the occurrence of the r-process has been associated with supernovae, more recent studies have cast substantial doubts on this environment. Alternative scenarios include the mergers of neutron stars, neutron-star black hole mergers, but possibly also rare classes of supernovae as well as hypernovae/collapsars with polar jet ejecta and also accretion disk outflows related to the collapse of fast rotating massive stars with high magnetic fields. Stellar r-process abundance observations, have provided insights into, and constraints on the frequency of and conditions in the responsible stellar production sites. One of them, neutron star mergers, was just identified and related to the Gravitational Wave event GW170817. High resolution observations, increasingly more precise due to improved experimental atomic data, have been particularly important in defining the heavy element abundance patterns of the old halo stars, and thus determining the extent, and nature, of the earliest nucleosynthesis in our Galaxy. Combining new results and important breakthroughs in the related nuclear, atomic and astronomical fields of science, this review attempts to provide an answer to the question "How Were the Elements from Iron to Uranium Made?" (Abridged)

Ground-State Properties of Even–Even Nuclei from He (Z = 2) to Ds (Z = 110) in the Framework of Skyrme–Hartree–Fock–Bogoliubov Theory

The ground-state properties of 2094 even–even nuclei with $$2\le Z\le 110$$ over a wide range of isotopes have been calculated and studied in the framework of the Hartree–Fock–Bogoliubov (HFB) theory with the SKI3 Skyrme type effective nucleon–nucleon interaction. The calculated ground-state values of the binding energy per nucleon (B.E/A), quadrupole deformation parameter (β2), two-neutron separation energy (S2n), charge radii (RC), proton rms radii, neutron rms radii and neutron pairing gap have been compared with the available experimental data of the atomic mass evaluation (AME2016), the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny effective nucleon–nucleon interaction and predictions of some nuclear models such as the finite range droplet model (FRDM2012) and relativistic mean-field model. Based on the HFBTHO results, the parameters of the Skyrme SKI3-HFB method can be successfully used for describing the ground-state properties of the investigated nuclei, in particularly the neutron-rich nuclei and the exotic nuclei near the neutron drip-line.