arXiv subjects
Publications and source records attributed to K. Hagino.
We investigate the applicability of finite temperature random phase approximation (RPA) using a solvable Lipkin model. We show that the finite temperature RPA reproduces reasonably well the temperature dependence of total strength, both for the positive energy (i.e., the excitation) and the negative energy (i.e., the de-excitation) parts. This is the case even at very low temperatures, which may be relevant to astrophysical purposes.
Quantum fluctuations concerning the shape of nuclei are treated within the framework of covariant density functional theory. Long range correlations beyond mean field are taken into account by configuration mixing of wave functions with triaxial shapes and the restoration of spontaneously broken rotational symmetries through three-dimensional angular momentum projection. The "controversial" nucleus 16C is treated as an example and it is found that its ground state has a triaxial shape but with large shape fluctuations. They are of crucial importance for a proper description of the spectroscopic properties of such nuclei.
Fission-related phenomena of heavy $Λ$ hypernuclei are discussed with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method, in which a similar Skyrme-type interaction is employed also for the interaction between a $Λ$ particle and a nucleon. Assuming that the $Λ$ particle adiabatically follows the fission motion, we discuss the fission barrier height of $^{239}_Λ$U. We find that the fission barrier height increases slightly when the $Λ$ particle occupies the lowest level. In this case, the $Λ$ particle is always attached to the heavier fission fragment. This indicates that one may produce heavy neutron-rich $Λ$ hypernuclei through fission, whose weak decay is helpful for the nuclear transmutation of long-lived fission products. We also discuss cases where the $Λ$ particle occupies a higher single-particle level.
We discuss the energy and angular distributions of two emitted neutrons from the dipole excitation of typical weakly-bound Borromean nuclei, $^{11}$Li and $^6$He. To this end, we use a three-body model with a density dependent contact interaction between the valence neutrons. Our calculation indicates that the energy distributions for the valence neutrons are considerably different between the two nuclei, although they show similar strong dineutron correlations in the ground state to each other. This different behaviour of the energy distribution primarily reflects the interaction between the neutron and the core nucleus, rather than the interaction between the valence neutrons. That is, the difference can be attributed to the presence of s-wave virtual state in the neutron-core system in $^{11}$Li, which is absent in $^6$He. It is pointed out that the angular distribution for $^{11}$Li in the low energy region shows a clear manifestation of the strong dineutron correlation, whereas the angular distribution for $^{6}$He exhibits a strong anticorrelation effect.
We use the self-consistent mean-field theory to discuss the ground state and decay properties of $Λ$ hypernuclei. We first discuss the deformation of $Λ$ hypernuclei using the relativistic mean-field (RMF) approach. We show that, although most of hypernuclei have a similar deformation parameter to the core nucleus, the shape of $^{28}$Si is drastically altered, from oblately deformed to spherical, if a $Λ$ particle is added to this nucleus. We then discuss the pionic weak decay of neutron-rich $Λ$ hypernuclei using the Skyrme Hartree-Fock + BCS method. We show that, for a given isotope chain, the decay rate increases as a function of mass number, due to the strong neutron-proton interaction.
Using a three-body model with density-dependent contact interaction, we discuss the root mean square distance between the two valence neutrons in $^{11}$Li nuclues as a function of the center of mass of the neutrons relative to the core nucleus $^9$Li. We show that the mean distance takes a pronounced minimum around the surface of the nucleus, indicating a strong surface di-neutron correlation. We demonstrate that the pairing correlation plays an essential role in this behavior. We also discuss the di-neutron structure in the $^8$He nucleus.
For a single potential barrier, the barrier penetrability can be inverted based on the WKB approximation to yield the barrier thickness. We apply this method to heavy-ion fusion reactions at energies well below the Coulomb barrier and directly determine the inter-nucleus potential between the colliding nuclei. To this end, we assume that fusion cross sections at deep subbarrier energies are governed by the lowest barrier in the barrier distribution. The inverted inter-nucleus potentials for the $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions show that they are much thicker than phenomenological potentials. We discuss a consequence of such thick potential by fitting the inverted potentials with the Bass function.
We study the deformation property of $Λ$ hypernuclei using the relativistic mean field (RMF) method. We find that $^{29}_Λ$Si and $^{13}_Λ$C hypernuclei have spherical shape as a consequence of the additional $Λ$ particle, whereas the corresponding core nuclei, $^{28}$Si and $^{12}$C, are oblately deformed. Most of other hypernuclei have a similar deformation parameter to the core nucleus, in accordance with the previous study with the non-relativistic Skyrme-Hartree-Fock method. We discuss the sensitivity of our results to the choice of pairing interaction and to the parameter set of the RMF Lagrangian.
We perform Hartree-Fock-Bogoliubov (HFB) calculations for semi-magic Calcium, Nickel, Tin and Lead isotopes and $N$=20, 28, 50 and 82 isotones using density-dependent pairing interactions recently derived from a microscopic nucleon-nucleon interaction. These interactions have an isovector component so that the pairing gaps in symmetric and neutron matter are reproduced. Our calculations well account for the experimental data for the neutron number dependence of binding energy, two neutrons separation energy, and odd-even mass staggering of these isotopes. This result suggests that by introducing the isovector term in the pairing interaction, one can construct a global effective pairing interaction which is applicable to nuclei in a wide range of the nuclear chart. It is also shown with the local density approximation (LDA) that the pairing field deduced from the pairing gaps in infinite matter reproduces qualitatively well the pairing field for finite nuclei obtained with the HFB method.
We study the spatial structure of four valence neutrons in the ground state of $^8$He and $^{18}$C nuclei using a core+4$n$ model. For this purpose, we employ a density-dependent contact interaction among the valence neutrons, and solve the five-body Hamiltonian in the Hartree-Fock-Bogoliubov (HFB) approximation. We show that two neutrons with the coupled spin of $S$=0 exhibit a strong dineutron correlation around the surface of these nuclei, whereas the correlation between the two dineutrons is much weaker. Our calculation indicates that the probability of the (1p$_{3/2})^4$ and [(1p$_{3/2})^2$ (p$_{1/2})^2$] configurations in the ground state wave function of $^8$He nucleus is 34.9% and 23.7%, respectively. This is consistent with the recent experimental finding with the $^8$He($p,t)^6$He reaction, that is, the ground state wave function of $^8$He deviates significantly from the pure (1p$_{3/2})^4$ structure.
We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium isotopes, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three constraining operators even for neutron-rich nuclei, indicating that the usual way to calculate fission barriers with the mass quadrupole operator is well justified. We also discuss the difference between proton and neutron deformation parameters along the fission paths.
We discuss in detail the coupled-channels approach for the large-angle quasi-elastic scattering in massive systems, where many degrees of freedom may be involved in the reaction. We especially investigate the effects of single, double and triple phonon excitations on the quasi-elastic scattering for $^{48}$Ti,$^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems, for which the experimental cross sections have been measured recently. We show that the present coupled-channels calculations well account for the overall width of the experimental barrier distribution for these systems. In particular, it is shown that the calculations taking into account single quadrupole phonon excitations in $^{48}$Ti and triple octupole phonon excitations in $^{208}$Pb reasonably well reproduce the experimental quasi-elastic cross section and barrier distribution for the $^{48}$Ti$+^{208}$Pb reaction. On the other hand, $^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems seem to require the double quadrupole phonon excitations in the projectiles in order to reproduce the experimental data.
We study the effects of double octupole and quadrupole phonon excitations in the 144Sm nucleus on quasi-elastic 16O+144Sm scattering at backward angles. To this end, we use the coupled-channels framework, taking into account explicitly the anharmonicities of the vibrations. We use the same coupling scheme as that previously employed to explain the experimental data of sub-barrier fusion cross sections for the same system. We show that the experimental data for the quasi-elastic cross sections are well reproduced in this way, although the quasi-elastic barrier distribution has a distinct high energy peak which is somewhat smeared in the experimental barrier distribution. We also discuss the effects of proton transfer on the quasi-elastic barrier distribution. Our study indicates that the fusion and quasi-elastic barrier distributions for this system cannot be accounted for simultaneously with the standard coupled-channels approach.
Paring correlations in weakly bound halo nuclei $^{6}$He and $^{11}$Li are studied by using a three-body model with a density-dependent contact interaction. We investigate the spatial structure of two-neutron wave function in a Borromean nucleus $^{11}$Li.The behavior of the neutron pair at different densities is simulated by calculating the two-neutron wave function at several distances between the core nucleus $^9$Li and the center of mass of the two neutrons. With this representation, a strong concentration of the neutron pair on the nuclear surface is quantitatively established for neutron-rich nuclei. Dipole excitations in $^{6}$He and $^{11}$Li are also studied within the same three-body model and compared with experimental data. The small open angles between the two neutrons from the core are extracted empirically by the B(E1) sum rule together with the rms mass radii, indicating the strong di-neutron correlation in the halo nuclei.
We analyze the Coulomb breakup cross sections of $^{11}$Li and $^6$He nuclei using a three-body model with a density-dependent contact interaction. We show that the concentration of the B(E1) strength near the threshold can be well reproduced with this model. With the help of the calculated B(E1) value, we extract the root-mean-square (rms) distance between the core nucleus and the center of mass of two valence neutrons without resorting to the sum rule, which may suffer from unphysical Pauli forbidden transitions. Together with the empirical rms distance between the neutrons obtained from the matter radius study and also from the three-body correlation study in the break-up reaction, we convert these rms distances to the mean opening angle between the valence neutrons from the core nucleus. We find that the obtained mean opening angles in $^{11}$Li and $^6$He agree with the three-body model predictions.
We investigate the consistency of the measured charge radius and dipole response of $^{11}$Li within a three-body model. We show how these observables are related to the mean square distance between the $^9$Li core and the center of mass of the two valence neutrons. In this representation we find by considering the effect of smaller corrections that the discrepancy between the results of the two measurements is of the order of 1.5$σ$. We also investigate the sensitivity to the three-body structure of $^{11}$Li and find that the charge radius measurement favors a model with a 50% s-wave component in the ground state of the two-neutron halo, whereas the dipole response is consistent with a smaller s-wave component of about 25% value.
We investigate the spatial structure of the two-neutron wave function in the Borromean nucleus $^{11}$Li, using a three-body model of $^9$Li $+n+n$, which includes many-body correlations stemming from the Pauli principle. The behavior of the neutron pair at different densities is simulated by calculating the two-neutron wave function at several distances between the core nucleus $^9$Li and the center of mass of the two neutrons. With this representation, a strong concentration of the neutron pair on the nuclear surface is for the first time quantitatively established for neutron-rich nuclei. That is, the neutron pair wave function in $^{11}$Li has an oscillatory behavior at normal density, while it becomes a well localized single peak in the dilute density region around the nuclear surface. We point out that these features qualitatively correspond to the BCS and BEC-like structures of the pair wave function found in infinite nuclear matter.
We invert experimental data for heavy-ion fusion reactions at energies well below the Coulomb barrier in order to directly determine the internucleus potential between the colliding nuclei. In contrast to the previous applications of the inversion formula, we explicitly take into account the effect of channel couplings on fusion reactions, by assuming that fusion cross sections at deep subbarrier energies are governed by the lowest barrier in the barrier distribution. We apply this procedure to the $^{16}$O +$^{144}$Sm and $^{16}$O +$^{208}$Pb reactions, and find that the inverted internucleus potential are much thicker than phenomenological potentials. A relation to the steep fall-off phenomenon of fusion cross sections recently found at deep subbarrier energies is also discussed.