Continuum Quasiparticle Random Phase Approximation Research Articles

Global Calculations of Beta-Decay Properties Based on the Fayans Functional

An effective approximation to a fully self-consistent global description of beta-decay properties of nuclei within the theory of finite Fermi systems is presented. It is based on describing the ground state properties within the energy density functional proposed by Fayans and coauthors (DF3) and on the continuum quasiparticle random-phase approximation (CQRPA). The accuracy of global DF3 $$+$$ CQRPA calculations is analyzed. For more than 200 (quasi)spherical nuclei with $$Z=18$$ to 51 having half-lives in the range of $$T_{1/2}<5$$ s, the experimental half-lives and delayed neutrons emission probabilities are described within a factor of two and three, respectively. A comparison is performed with the results of similar calculations based on state-of-the-art self-consistent models : the relativistic spherical RHB $$+$$ RQRPA approach and deformed finite-amplitude method (FAM) and HFB $$+$$ QRPA approaches, as well as the interacting shell model. A detailed analysis of beta-decay properties in the nickel isotopic chain that were obtained in various calculations allows us for determining basic mechanisms responsible for the sudden shortening of the half-lives that was found experimentally at RIKEN for isotopes heavier than the doubly magic $${}^{78}$$ Ni nucleus. These are the contributions of first-forbidden (FF) transitions and multiphonon configurations and spin inversion of the respective ground states. The acceleration effect in question is highly sensitive to the balance of the contributions of Gamow–Teller (GT) and FF transitions to the total beta-decay rate. It is shown that, in nickel isotopes, the ratio of these contributions takes different values before and after the neutron-shell crossing at $$N=50$$ .

Fayans Functional: Self-Consistent Description of Isospin Excitations

The energy density functional proposed earlier by Fayans and his coauthors is modified in such a way as to apply it in fully self-consistent calculations of isobaric analog resonances (IAR) in nuclei featuring pairing. The continuum quasiparticle random-phase approximation is used. Limits on the parameters of screening of exchange Coulomb interaction are deduced from a systematic analysis of binding energies of isobaric doublets and transition energies for isobaric triplets in mirror nuclei. A comparison with experimental data shows that the IAR energies for neutron-rich tin and lead isotopes involving fully developed pairing are described better on the basis of the new functional DF3-f than on the basis of self-consistent calculations performed with the DC3$$\ast$$ relativistic functional or with the SAMi Skyrme functional. The DF3-f functional is applied to calculating the properties of IARs in ruthenium, palladium, and cadmium isotopes featuring pairing in both neutron and proton subsystems, as well as to calculating similar properties in the chain of $$N=82$$ isotones.

Self-Consistent Description of Isobaric Analog Resonances in Neutron-Rich Nuclei with Pairing

A self-consistent approach to describing isobaric analog resonances (IAR) in neutron-rich nuclei that involve pairing is developed. The continuum quasiparticle random-phase approximation based on a new modification of the energy density functional proposed by Fayans and his coauthors is used for this purpose. The properties of IAR in heavy calcium, tin, and lead isotopes, including those that are close to doubly magic ones and those that involve developed neutron pairing, are calculated. The results are compared with their counterparts calculated on the basis self-consistent models implemented by employing various relativistic functionals and Skyrme functionals.

Delayed Multineutron Emission in the Region of Heavy Calcium Isotopes

A brief survey of self-consistent models used to perform global calculations of β-decay properties of neutron-rich nuclei is given. These models include the continuum quasiparticle randomphase approximation (CQRPA) based on the energy density functional (DF) proposed by Fayans and his colleagues (DF + CQRPA), relativistic quasiparticle random-phase approximation (RQRPA), and the finite-amplitude method (FAM). These models take into account allowed Gamow–Teller transitions and first-forbidden transitions. Models that allow for complex configurations beyond the QRPA framework are also analyzed. The β-decay properties of heavy calcium, potassium, and scandium isotopes in the vicinity of the N = 32 and 34 neutron subshells, which are new magic subshells for neutrons, are calculated on the basis of the self-consistent DF + CQRPA approach. The predicted high probability for two-neutron emission is found to be correlated with the anomalous nuclear radii measured for potassium and calcium isotopes in the region around N = 32. The results ofDF3 + CQRPA calculations are compared with their counterparts obtained within the self-consistent models implemented with the SkO’ Skyrme functional and the D3C* relativistic functional.

Collective Excitations in the $^{14}$C Nucleus Populated by the $^{12}$C($^{18}$O,$^{16}$O) Reaction at 84 MeV

The 12C(18O,16O)14C reaction at 84 MeV incident energy has been explored up to high excitation energy of the residual nucleus thanks to the use of the MAGNEX spectrometer to detect the ejectiles. In the region above the two-neutron separation energy, a resonance at 16.9 MeV has been observed. Continuum quasi-particle random phase approximation calculations of the response function, corresponding to the transfer of a neutron pair to the 12C nucleus, have been performed to investigate the possible presence of the Giant Pairing Vibration in that energy region.

Continuum quasiparticle random-phase approximation for astrophysical direct neutron capture reactions on neutron-rich nuclei

We formulate a many-body theory to calculate the cross section of direct radiative neutron capture reaction by means of the Hartree-Fock-Bogoliubov mean-field model and the continuum quasiparticle random phase approximation (QRPA). A focus is put on very neutron-rich nuclei and low-energy neutron kinetic energy in the range of O(1 keV) - O(1 MeV), relevant for the rapid neutron-capture process of nucleosynthesis. We begin with the photo-absorption cross section and the E1 strength function, then, in order to apply the reciprocity theorem, we decompose the cross section into partial cross sections corresponding to different channels of one- and two-neutron emission decays of photo-excited states. Numerical example is shown for the photo-absorption of $^{142}$Sn and the neutron capture of $^{141}$Sn.

Continuum dipole response near the threshold and the direct neutron capture cross section at astrophysical energies

We apply the continuum quasiparticle random phase approximation to calculate the direct neutron capture cross section relevant to the r-process nucleo-synthesis. The electric dipole strength function in an even-even n-rich nucleus is decomposed with respect to the channels of direct neutron decays. Using the detailed balance relation, the partial dipole strengths are converted to obtain the direct neutron-capture cross sections. Numerical examples are given for 142Sn.

Di-neutron correlation in monopole pair transfer modes near the neutron-separation energy in Sn, Ni, Ca, Zr isotopes

We discuss the monopole pair transfer by means of the Hartree-Fock-Bogoliubov method and the continuum quasiparticle random phase approximation. We investigate the low-lying pair-vibrational state and the pair-rotational ground state having small separation energy in neutron-rich Sn isotopes and Ni, Zr and Ca isotopes. We show that the transfer amplitudes of the 0+ states are characterized by the coherent superposition of two-quasiparticle configurations up to high orbital angular momenta l ∼ 12. It suggests the transfer motion of a di-neutron.

New half-life measurements of the most neutron-rich arsenic and germanium isotopes

The $\ensuremath{\beta}$-decay properties of several neutron-rich germanium and arsenic isotopes were measured at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. The measurements of almost-pure radioactive sources were enabled by the combination of ion-source chemistry and two-stage mass separation. The half-life of ${}^{86}$Ge ($226\ifmmode\pm\else\textpm\fi{}21$ ms) was determined for the first time, while those of ${}^{84,85}$Ge and ${}^{84\ensuremath{-}87}$As were remeasured. The results are compared to theoretical predictions of the gross theory of $\ensuremath{\beta}$ decay, the finite-range droplet model, and the new calculations using the energy density functional DF3a with continuum quasiparticle random-phase approximation (CQRPA). We confirm the robustness and good predictive power of the latter model for nuclei near closed shells. These DF3a+CQRPA calculations were used recently to analyze $r$-process isobaric abundances.

Gamma-ray strength at low energies using relativistic QRPA with exact coupling to the continuum

Continuum-quasiparticle random-phase Approximation (CQRPA) within the relativistic point-coupling model with density-dependent coupling constants is applied to investigate collective excitations in spherical nuclei. In particular we study the impact of the exact continuum on the giant-dipole and pygmy resonance of several Sn isotopes as well as the radiative neutron capture rates of importance for astrophysical calculations.

Anomalous pairing vibration in neutron-rich Sn isotopes beyond theN=82magic number

Two-neutron transfer associated with the pair correlation in superfluid neutron-rich nuclei is studied with focus on low-lying ${0}^{+}$ states in Sn isotopes beyond the $N=82$ magic number. We describe microscopically the two-neutron addition and removal transitions by means of the Skyrme-Hartree-Fock-Bogoliubov mean-field model and the continuum quasiparticle random phase approximation formulated in the coordinate space representation. It is found that the pair transfer strength for the transitions between the ground states becomes significantly large for the isotopes with $A\ensuremath{\geqslant}140$, reflecting very small neutron separation energy and long tails of the weakly bound $3p$ orbits. In ${}^{132--140}$Sn, a peculiar feature of the pair transfer is seen in transitions to low-lying excited ${0}^{+}$ states. They can be regarded as a kind of pair vibrational mode which is characterized by an anomalously long tail of the transition density extending to far outside of the nuclear surface, and a large strength comparable to that of the ground-state transitions. The presence of the weakly bound neutron orbits plays a central role for these anomalous behaviors.

Continuum quasiparticle linear response theory using the Skyrme functional for multipole responses of exotic nuclei

We develop a new formulation of the continuum quasiparticle random phase approximation (QRPA) in which the residual interaction is derived directly from the Skyrme energy functional, keeping all the velocity dependent terms of the Skyrme effective interaction. Numerical analysis using the SkM$^*$ parameter set is performed for the isovector dipole and the isovector/isoscalar quadrupole responses in $^{20}$O and $^{54}$Ca. It is shown that the energy-weighted sum rule including the enhancement factors for the isovector responses is satisfied with good accuracy. We investigate also how the velocity dependent terms influence the strength distribution and the transition densities of the low-lying surface modes and the giant resonances.

Di-Neutron Correlation in Soft Octupole Excitations of Neutron-Rich Ni Isotopes beyond N = 50

We investigate low-lying octupole response of neutron-rich Ni isotopes beyond the N=50 shell closure using the Skyrme-Hartree-Fock-Bogoliubov mean-fields and the continuum quasi-particle random phase approximation. Performing detailed numerical analyses employing the Skyrme parameter set SLy4 and a density-dependent delta interaction of the mixed type, we show that a neutron mode emerges above the neutron separation energy as a consequence of the weak binding of neutrons and it exhibits strong influences of the di-neutron correlation.

Description of double β decay within the continuum quasiparticle random-phase approximation

A method to calculate the nuclear double beta decay ($2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) amplitudes within the continuum quasiparticle random phase approximation (cQRPA) is formulated. Calculations of the $\ensuremath{\beta}\ensuremath{\beta}$ transition amplitudes within the cQRPA are performed for $^{76}\mathrm{Ge}$, $^{100}\mathrm{Mo}$, and $^{130}\mathrm{Te}$. A rather simple nuclear Hamiltonian consisting of a phenomenological mean field and a zero-range residual particle-hole and particle-particle interaction is used. The calculated $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ amplitudes are almost unaffected when the single-particle continuum is taken into account, whereas we find a regular suppression of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ amplitudes that can be associated with additional ground-state correlations owing to collective states in the continuum. It is expected that inclusion of nucleon pairing in the single-particle continuum will somewhat compensate this suppression.

Di-neutron correlations in medium-mass neutron-rich nuclei near the dripline

On the basis of the coordinate-space Hartree-Fock-Bogoliubov and the continuum quasiparticle random phase approximation (QRPA) theories, we demonstrate that a di-neutron correlation exists in the ground states of medium-mass neutron-rich nuclei near the dripline, and we suggest that the soft dipole excitation has the character of di-neutron motion against the remaining A - 2 subsystem.

Continuum QRPA response for deformed neutron-rich nuclei

We discuss properties of the quadrupole collective excitation of the deformed neutron-rich nucleus 38 Mg within the framework of quasi-particle random phase approximation (QRPA). We first solve the coupled-channels equations to obtain the single-particle levels, and construct the ground state by treating the pairing correlations in the BCS approximation. We then solve the QRPA equation using the response function formalism, by including the continuum spectra with the ☐ dicscretization method. We show that the collectivity of the gamma vibration (the lowest K π = 2 + mode) is significantly enhanced if protons and neutrons have different deformations. We also discuss an attempt towards full continuum QRPA calculations for deformed nuclei.

Continuum QRPA response for deformed neutron-rich nuclei

We discuss properties of the quadrupole collective excitation of the deformed neutron-rich nucleus38Mg within the framework of quasi-particle random phase approximation (QRPA). We first solve the coupled-channels equations to obtain the single-particle levels, and construct the ground state by treating the pairing correlations in the BCS approximation. We then solve the QRPA equation using the response function formalism, by including the continuum spectra with the ☐ dicscretization method. We show that the collectivity of the gamma vibration (the lowestKπ = 2+ mode) is significantly enhanced if protons and neutrons have different deformations. We also discuss an attempt towards full continuum QRPA calculations for deformed nuclei.

Continuum QRPA response for deformed neutron-rich nuclei

We discuss properties of the quadrupole collective excitation of the deformed neutron-rich nucleus 38Mg within the framework of quasi-particle random phase approximation (QRPA). We first solve the coupled-channels equations to obtain the single-particle levels, and construct the ground state by treating the pairing correlations in the BCS approximation. We then solve the QRPA equation using the response function formalism, by including the continuum spectra with the ☐ dicscretization method. We show that the collectivity of the gamma vibration (the lowest K π = 2 + mode) is significantly enhanced if protons and neutrons have different deformations. We also discuss an attempt towards full continuum QRPA calculations for deformed nuclei.

Two-neutron transfer in nuclei close to the drip line

We investigate the two-neutron transfer modes induced by (t,p) reactions in neutron-rich oxygen isotopes. The nuclear response to the pair transfer is calculated in the framework of continuum-Quasiparticle Random Phase Approximation (cQRPA). The cQRPA allows a consistent determination of the residual interaction and an exact treatment of the continuum coupling. The (t,p) cross sections are calculated within the DWBA approach and the form factors are evaluated by different methods : macroscopically, following the Bayman and Kallio method, and fully microscopically. The largest cross section corresponds to a high-lying collective mode built entirely upon continuum quasiparticle states.

Distribution of the Gamow-Teller strength in90Nband208Bi

The (He-3,t) charge-exchange reaction has been studied at E(He-3)=450 MeV and angles near 0 degrees on targets of Zr-90 and Pb-208. Fragmentation of the Gamow-Teller (GT) strength into separate components of the particle-hole type has been observed. The distribution of the GT strength in Nb-90 and in Bi-208 has been calculated within the continuum quasiparticle random phase approximation and continuum-random-phase approximation approaches, respectively. These components, especially in Pb-208, could be related with the direct, core polarization, and back-spin-flip Gamow-Teller strength.