Isospin Effects Research Articles

Nuclear charge radius predictions based on eXtreme Gradient Boosting

Nuclear charge radii with 8 ≤ Z ≤ 100 are studied based on the eXtreme Gradient Boosting (XGBoost) method. Besides the proton, neutron, and mass numbers, the physical quantities related to the isospin, shell, and pairing effects are important to improve the performance of the XGBoost method by including them as the input variables. The XGBoost method describes the nuclear charge radii better than the Skyrme-Hartree–Fock-Bogoliubov (HFB)-21 model, especially for odd-Z nuclei. The root-mean-square deviation with respect to the experimental data is reduced from 0.025 fm of the HFB-21 model to 0.012 fm of the XGBoost method in the learning set. It is found that the XGBoost method has reliable extrapolation ability at least for the nuclei not far from the learning region, which is verified by comparison with the data in the newly measured experimental data. When extrapolated to the unknown region, the XGBoost predictions of charge radii are close to the HFB-21 results, and the deviations between them are generally less than 0.1 fm even within about 20 steps from the known region.

Isospin influence on nuclear dynamics in the reactions 78,86Kr+40,48Ca at 10 AMeV

An investigation of the influence of the isospin (N/Z ratio) on the thermometric characteristics, in the reactions 78Kr+40Ca and 86Kr+48Ca at 10 AMeV is presented. The experiment was performed at the INFN Laboratori Nazionali del Sud in Catania by using the beams delivered by the Superconductive Cyclotron and the 4π multidetector CHIMERA. The isospin effects on the decay modes of the two produced composite systems and on the competition between statistical and dynamical break-up of the projectile have been studied. The thermal evaporation from both compound nucleus (CN) and Quasi-Projectile Like Fragment (PLF) has been investigated by extracting the temperature with two different thermometric methods, namely the slope thermometer, with the alpha particles as probe, and the double isotope yields ratio thermometer. The results of the analysis suggest the influence of the N/Z ratio on the system (CN or PLF) temperature, regardless of the nature of the method used for its determination.

Influence of Fragment Size on Isospin Effects in Transverse and Elliptic Flows and Nuclear Stopping in Intermediate Energy Heavy-Ion Collision

Influence of Fragment Size on Isospin Effects in Transverse and Elliptic Flows and Nuclear Stopping in Intermediate Energy Heavy-Ion Collision

The description of dynamical fission process using improved quantum molecular dynamics model incorporated with microscopic potential energy surface

A new method, namely the improved quantum molecular dynamics model incorporated with the microscopic potential energy surface, is proposed to simulate the dynamical evolution from saddle to scission point and to calculate the isotope yields of fission fragments in thermal neutron-induced fission of actinide nuclei near 236U. With this approach, the shell and pairing effects are introduced by the microscopic potential energy, while the isospin effect, the dynamical effects of fluctuations and correlations in fission process are automatically included in the improved quantum molecular dynamics model. These two aspects eventually influence the productions of fission fragments. The calculated both charge and mass distributions of fission fragments for a series of actinide nuclei are in overall agreement with the evaluated data from JEFF-3.3 and ENDF/B-VIII.0. The isotope distributions of fission fragments in the fission of 236U reproduce the data reasonable well, from which we extract the relationship between peak mass number of the isotope distributions and the charge number of fission fragments. We find that this relationship deviates linear relation slightly at certain cases, which indicates the isospin nonequilibrium effect. By tracking back to the fission process on the two dimension plane of elongation and mass asymmetry of prefragments, we find that the necked-in shape and the separation of two parts happen much faster for the 132Sn than 128,136Sn in the time evolution of the distance R between the centers of two parts of the fissioning system. The events producing 128,132,136Sn and 136,140,144Xe present two kinds of average fission paths with bypassing and going through the minimum-energy valley of the microscopic potential energy surface, respectively.

Nuclear charge radii in Bayesian neural networks revisited

In this work, a refined Bayesian neural network (BNN) based approach with six inputs including the proton number, mass number, and engineered features associated with the pairing effect, shell effect, isospin effect, and “abnormal” shape staggering effect of 181,183,185Hg, is proposed to accurately describe nuclear charge radii. The new approach is able to well describe the charge radii of atomic nuclei with A≥40 and Z≥20. The standard root-mean-square deviation is 0.014 fm for both the training and validation data. In particular, the predicted charge radii of proton-rich and neutron-rich calcium isotopes are found in good agreement with data. We further demonstrate the reliability of the BNN approach by investigating the variations of the root-mean-square deviations with extrapolation distances, mass numbers, and isospin asymmetries.

Systematic analysis of the decay of Fl*287,288,290,292 formed in the complete fusion reactions Pu239,240,242,244+Ca48 including Skyrme forces

The fusion evaporation residue cross sections for the decay of the compound nuclear system $^{287,288,290,292}\mathrm{Fl}^{*}$ via $2n$- to $5n$-decay channels, synthesized in $^{239,240,242,244}\mathrm{Pu}+^{48}\mathrm{Ca}$, are studied using the dynamical cluster-decay model (DCM), including quadrupole deformations ${\ensuremath{\beta}}_{2i}$ for compact hot orientations ${\ensuremath{\theta}}_{i}$ at various excitation energies ${E}^{*}=32.5$ to 52.6 MeV. For the nucleus-nucleus interaction potentials, we have employed the Skyrme energy density functional based on the semiclassical extended Thomas-Fermi approach under frozen density approximation. Here, within the DCM, the Skyrme forces used are SLy4, ${\mathrm{SkM}}^{*}$, and, KDE0(v1). The DCM makes use of a single parameter, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ that takes different values for different processes at a given temperature and provides an excellent fit to the measured data, independently of the choice of Skyrme force used. We make predictions of probable fusion-fission and quasifission mass regions of fragments and then calculate the evaporation residue cross sections ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for experimentally unobserved neutron channels. Further, the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$ of compound nucleus (CN) fusion probability ${P}_{\mathrm{CN}}$ and survival probability ${P}_{\mathrm{surv}}$ is calculated to determine the reduced evaporation residue cross section ${\ensuremath{\sigma}}_{\mathrm{ER}}/{\ensuremath{\sigma}}_{\mathrm{fusion}}$, denoted as ${\ensuremath{\sigma}}_{\mathrm{ER}}^{\mathrm{reduced}}$, and we have seen that ${P}_{\mathrm{surv}}$ is the main dominant factor in the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$. To this end, we have analyzed the effects of mass asymmetry and isospin effect of target nucleus on the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ and have found that the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for the production of superheavy element ${\mathrm{Fl}}^{*}$ increases slowly with increasing neutron number of the target nucleus. We have also searched for all possible target-projectile combinations forming the hot compound nucleus ${\mathrm{Fl}}^{*}$ at the excitation energy ${E}^{*}$ for compact-hot configurations and have also calculated the fusion evaporation residue cross sections for the proposed new reactions synthesizing Fl.

Influence of entrance channel on production cross sections of exotic actinides in multinucleon transfer reactions

Within the framework of the dinuclear system model, the influence of mass asymmetry and the isospin effect on the production of exotic actinides have been investigated systematically. The isotopic yields populate in multinucleon transfer reactions of Ca(48), Kr(86), Xe(136), and U(238) bombarding on Cm(248) are analyzed and compared to the available experimental data. Systematics on the production of unknown actinides from Ac to Lr via the available stable elements on the earth (from Ar to U) as projectiles-induced reactions with $^{232}$Th, $^{238}$U and $^{248}$Cm are investigated thoroughly. Potential energy surface and total kinetic energy distribution for the reaction system are calculated and can be used to predict the production cross-section trends. It is found that the heavier projectile leads to the wider isotopic chain distribution for the same target. The heavier target-based reactions prefer to produce plenty of exotic actinides through both mechanisms of deep-inelastic and quasi-fission reactions. Isospin relaxation plays a crucial role in the colliding process, resulting in actinide isotopic distribution tends to shift to the drip lines. Massive new actinides have been predicted at the level of nanobarn to millibarn. The optimal projectile-target combinations and beam energies were proposed for the forthcoming experiments.

Isospin effect on first-chance fission probability

A delayed fission due to nuclear dissipation results in a drop of first-chance fission probability (${P}_{f0}$) with respect to predictions by standard statistical models. Using the stochastic Langevin model, we calculate ${P}_{f0}$ as a function of presaddle dissipation strength ($\ensuremath{\beta}$) for fissioning nuclei $^{220}\mathrm{U}$, $^{230}\mathrm{U}$, $^{240}\mathrm{U}$, and $^{240}\mathrm{Cm}$. We find that with decreasing the isospin of the U nucleus, the sensitivity of ${P}_{f0}$ to $\ensuremath{\beta}$ is substantially enhanced, and that low-isospin $^{240}\mathrm{Cm}$ exhibits a significantly larger dependence on $\ensuremath{\beta}$ than high-isospin $^{240}\mathrm{U}$. Furthermore, it is shown that ${P}_{f0}$ becomes more sensitive to $\ensuremath{\beta}$ at low energy. These findings suggest that to accurately probe presaddle dissipation properties with first-chance fission probability, on the experimental side, it is best to produce those heavy fissioning systems with small isospin and low excitation energy.

Isospin effects on $$\alpha $$ decay and cluster radioactivity

Isospin effects on $$\alpha $$ decay and cluster radioactivity

An improved Gamow-like formula for α-decay half-lives

An improved Gamow-like (IMGL) formula for α-decay half-lives is proposed by introducing an accurate charge radius formula, an analytic expression of assault frequency, the angular momentum taken by α-particle and the isospin effect. The parameters of the IMGL formula are obtained by fitting the experimental α-emitter data with Zp=52–118 (515 α emitters. Zp is the charge number of a parent nucleus) and those with Zp=92–118 (178 α emitters). Correspondingly, the IMGL formula with the parameters fitted the experimental data with Zp=52–118 is named as the IMGL1 formula and the other one is called as the IMGL2 formula. By using the two formulas, a large number of α-decay half-lives are calculated. It is shown that the accuracy of the IMGL1 and IMGL2 formulas is improved significantly compared to their predecessors. Moreover, the accuracy of the IMGL1 and IMGL2 formulas is higher than that of other types of empirical formulas, including the Royer formula, modified Royer (MR) formula, Viola-Seaborg-Sobiczewski (VSS) formula, modified Viola-Seaborg-Sobiczewski (MVSS) formula, formula proposed by Y. Qian and Z. Ren (YQZR) and modified YQZR (MYQZR) formula. In addition, the experimental α-decay half-lives of the synthesized newly neutron-deficient Actinide nuclei and the superheavy nuclei are reproduced well by the two formulas. Then, the α-decay half-lives of the neutron-deficient nuclei with Zp=94-119 are predicted within the IMGL2 formula because its accuracy is higher slightly than that of the IMGL1 formula. Finally, the competition between α-decay and spontaneous fission (SF) with Zp=120 α-decay chains is investigated in detail within the IMGL2 formula and the modified Swiatecki's formula. The predictions of the neutron-deficient nuclei with Zp=94-119 and the superheavy nuclei with Zp=120 are useful for identifying the new nuclides in future experiments.

Influence of Spontaneous Fission Rates on the r-process Nucleosynthesis

The effects of spontaneous fission on r-process nucleosynthesis are investigated in the hot wind r-process scenario. We perform network calculations using three sets of spontaneous fission rates to study how the abundance pattern is shaped when different sets of fissioning nuclei are encountered by the r-process nuclear flow. The relative contributions from spontaneous fission, neutron-induced fission, and β-delayed fission to the nucleosynthesis process are studied by calculating the corresponding fission flow. We show that the relative contributions of various fission channels in r-process nucleosynthesis depend on the astrophysical conditions and fission models used. By using the spontaneous fission rates from a modified Swiatecki’s formula with isospin and blocking effects, the spontaneous fission and neutron-induced fission play an equally important role in r-process nucleosynthesis under an extreme neutron-rich astrophysical scenario with Y e = 0.1. The fissioning nuclei are located in different regions of the nuclear chart when different spontaneous fission models are used. The fission fragment distributions of fissioning nuclei in different regions have apparent diversity, which affects the mass regions where fission products are deposited, leading to the difference of the final abundance around the second r-process peak and rare-earth subpeak.

Effects of isospin and shell on probing nuclear dissipation with survival probabilities of heavy systems

Using the Langevin model, we calculate the survival probability (Peva) of 228U, 234U and 240U as a function of the presaddle dissipation strength (β). It is shown that Peva displays a greater sensitivity to β with increasing the isospin of the U system and with decreasing excitation energy and angular momentum, and that shell effects can significantly enhance the sensitivity. Furthermore, we compare calculated and measured evaporation residue cross sections of heavy compound nuclei 224Th produced in the 16O + 208Pb reaction and find that the best-fit value of β required to satisfactorily describe the measured data has an apparent drop as shell effects are taken into account in the calculation compared to that neglecting the effects, clearly indicating a strong influence of shell effects on the precise determination of β. These results demonstrate that to more stringently constrain the strength of presaddle dissipation with survival probabilities of heavy nuclei, on the experimental side, it is best to produce high-isospin compound systems with low energy and low spin; theoretically, it is important to account for the shell effects in the calculations.

Predictions for the synthesis of the Z=119 superheavy element

The optimal projectile-target combination and bombarding energy for the production of the new superheavy element (SHE) $Z=119$ are predicted within the framework of a dinuclear system (DNS) model, in which the evaporation residue cross section (ERCS) is the product of capture cross section, fusion probability, and survival probability. To this end, the effects of mass asymmetry and isospin effect of target nucleus on the ERCS are analyzed. It is found that the ERCS for the production of SHE $Z=119$ is relatively large with the $^{45}\mathrm{Sc}$ projectile, while the ERCS in most cases decreases slowly with increasing neutron number of the target nucleus. We hope these predictions will shed new light timely for the recent experiments on the synthesis of the $Z=119$ superheavy element.

Isospin effects on intermediate mass fragments at intermediate energy-heavy ion collisions

Isospin effects on intermediate mass fragments at intermediate energy-heavy ion collisions

Analytic meronic black holes, gravitating solitons, and higher-spins in the EinsteinSU(N)-Yang-Mills theory

We construct meronic black holes and solitons in the Einstein $SU(N)$-Yang-Mills theory in $D=4$ and $D=5$ dimensions. These analytical solutions are found by combining the generalized hedgehog ansatz with the Euler parameterization of the $SU(N)$ group from which the Yang-Mills equations are automatically satisfied for all values of $N$ while the Einstein equations can be solved analytically. We explicitly show the role that the color number $N$ plays in the black hole thermodynamics as well as in the gravitational spin from isospin effect. Two remarkable results of our analysis are that, firstly, meronic black holes can be distinguished by colored black holes by looking at the spin from isospin effect (which is absent in the latter but present in the former). Secondly, using the theory of non-embedded ansatz for $SU(N)$ together with the spin from isospin effect, one can build fields of arbitrary high spin out of scalar fields charged under the gauge group. Hence, one can analyze interacting higher spin fields in asymptotically flat space-times without "introducing by hand" higher spin fields. Our analysis also discloses an interesting difference between the spin from isospin effect in $D=4$ and in $D=5$.

Exploring isospin effects in nuclear fragmentation at 600 MeV/nucleon

Exploring isospin effects in nuclear fragmentation at 600 MeV/nucleon

A study of alpha-decay using effective liquid drop model

In this paper, we have made an attempt to analyze the alpha-decay half-lives of in the atomic number range [Formula: see text] by considering an effective liquid drop model. The role of pre-formation probability by including iso-spin effect is included during an evaluation of half-lives. We have also compared the studied alpha-decay half-lives with that of semi-empirical formulae such as Viola Seaborg semi-empirical formulae (VSS) [J. Inorg. Nucl. Chem. 28 (1966) 741; Nucl. Phys. A 848 (2010) 279], Royer formulae [J. Phys. G: Nucl. Part. Phys. 26 (2000) 1149; Phys. Rev. C 101 (2020) 034307] and also with that of the available experiments. From this comparison, it can be concluded that the effective liquid drop model produces an alpha-decay half-lives close to the experiments.

Shell evolution in neutron-rich nuclei: the single particle perspective * *Supported by the National Natural Science Foundation of China (12075121, 11605089), and the Natural Science Foundation of Jiangsu Province (BK20190067, BK20150762)

The isospin dependence of spin-orbit (SO) splitting becomes increasingly important as N/Z increases in neutron-rich nuclei. Following the initial independent-particle strategy toward explaining the occurrence of magic numbers, we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term. It is found that new magic numbers N = 14 and N =16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling, whereas the traditional magic number, N = 20, may disappear. The magic number N = 28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting, corresponding to the strength of the SO coupling term. Meanwhile, the N = 50 and 82 shells may persist within the single particle scheme, although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei. Besides, an appreciable energy gap appears at N = 32 and 34 in neutron-rich Ca isotopes. All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model. The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrè chart.

First direct lattice calculation of the chiral perturbation theory low-energy constant ℓ7

We evaluate by means of lattice QCD calculations the low-energy constant ${\ensuremath{\ell}}_{7}$ which parametrizes strong isospin effects at next-to-leading order (NLO) in SU(2) chiral perturbation theory. Among all low-energy constants at NLO, ${\ensuremath{\ell}}_{7}$ is the one known less precisely, and its uncertainty is currently larger than 50%. Our strategy is based on the RM123 approach in which the lattice path-integral is expanded in powers of the isospin breaking parameter $\mathrm{\ensuremath{\Delta}}m=({m}_{d}\ensuremath{-}{m}_{u})/2$. In order to evaluate the relevant lattice correlators we make use of the recently proposed rotated twisted-mass (RTM) scheme. Within the RM123 approach, it is possible to cleanly extract the value of ${\ensuremath{\ell}}_{7}$ from either the pion mass splitting ${M}_{{\ensuremath{\pi}}^{+}}\ensuremath{-}{M}_{{\ensuremath{\pi}}^{0}}$ induced by strong isospin breaking at order $\mathcal{O}((\mathrm{\ensuremath{\Delta}}m{)}^{2})$ (mass method), or from the coupling of the neutral pion ${\ensuremath{\pi}}^{0}$ to the isoscalar operator $(\overline{u}{\ensuremath{\gamma}}_{5}u+\overline{d}{\ensuremath{\gamma}}_{5}d)/\sqrt{2}$ at order $\mathcal{O}(\mathrm{\ensuremath{\Delta}}m)$ (matrix element method). In this pilot study we limit the analysis to a single ensemble generated by the Extended Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quark flavors, which corresponds to a lattice spacing $a\ensuremath{\simeq}0.095\text{ }\text{ }\mathrm{fm}$ and to a pion mass ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}260\text{ }\text{ }\mathrm{MeV}$. We find that the matrix element method outperforms the mass method in terms of resulting statistical accuracy. Our determination, ${\ensuremath{\ell}}_{7}=2.5(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, is in agreement and improves previous calculations.

Isospin effect on quark matter instabilities

We have studied the mechanical and chemical instabilities as well as the liquid-gas-like phase transition in isospin asymmetric quark matter based on the NJL and the pNJL model. Areas of the mechanical instability region and the liquid-gas coexistence region are seen to be enlarged with a larger quark matter symmetry energy or in the presence of strange quarks. Our study shows that the light cluster yield ratio observed in relativistic heavy-ion collisions may not be affected much by the uncertainties of the isospin effect, and favors a smooth hadron-quark phase transition in compact stars as well as their mergers.