We use properties of doubly-magic nuclei, ab-initio calculations of low-density neutron matter, and of neutron stars to constrain the parameters of the Skyrme energy-density functional. We find all of these properties can be reproduced within a constrained family of Skyrme parameters. The maximum mass of a neutron star is found to be sensitive to the neutron effective mass. A value of [$ m^{*}_{\rm n}/m](ρ_0) = 0.60-0.65 $ is required to obtain a maximum neutron star mass of 2.1 solar masses. Using the constrained Skyrme functional with the aforementioned effective mass, the predicted radius for a neutron star of 1.4 solar masses is 12.4(1) km and $Λ$ = 423(40).
I use properties of doubly-magic nuclei to constrain nuclear matter and neutron matter equations of state. I conclude that the data determined the value of the neutron equation of state and the symmetry energy near a density of $ρ_{on}$ = 0.10 nucleons/fm$^{3}$. The slope at that point is constrained by the value of the neutron skin.
We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutron skins for $^{208}$Pb and $^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Ot…
We calculate the single particle spectrum of the double magic nucleus $^{78}$Ni in a Hartree-Fock approach using the Skyrme density-dependent effective interaction containing central, spin-orbit and tensor parts. We show that the tensor part has an important effect on the spin-orbit splitting of the proton $1f$ orbit which may explain the survival of magicity so far from the stability valley. We confirm the inversion of the $1f5/2$ and $2p3/2$ levels at the neutron number 48 in the Ni isotopic chain expected from previous Monte Carlo shell model calculations and supported by experimental obser…
We study systematically the impact of the time-even tensor terms of the Skyrme energy density functional, i.e. terms bilinear in the spin-current tensor density, on deformation properties of closed shell nuclei corresponding to 20, 28, 40, 50, 82, and 126 neutron or proton shell closures. We compare results obtained with three different families of Skyrme parameterizations whose tensor terms have been adjusted on properties of spherical nuclei: (i) TIJ interactions proposed in the first paper of this series [T. Lesinski et al., Phys. Rev. C 76, 014312 (2007)] which were constructed through a c…
Melting of N=20 shell and development of N = 16 and N = 34 shells for neutron-rich nuclei have been studied extensively through inclusion of tensor interaction in Skyrme Hartree Fock theory optimized to reproduce the splitting neutron 1f states of 40, 48Ca and 56Ni nuclei. Evolution of gap generated by the energy difference of single particle levels neutron 2s1/2 and neutron 1d3/2 state has been found to be responsible for the development of a shell closure at N = 16. The splitting pattern of spin-orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates formation of a ne…
The role of the tensor part of the nuclear interaction is actively investigated in recent years due to experimental advancement yielding new data in nuclei far from the $β$-stability line. In this article we study the effect of this part of the nuclear interaction on deformed neutron magic numbers in the rare-earth region within the Skyrme energy-density functional for various TIJ \cite{lesinski:2007} parametrizations. Two quantities signaling magic numbers are considered: two-neutron separation energies and single-particle energies. They are calculated in isotopic series involving well-deform…
We study the effects of correlations beyond the independent particle model in the evaluation of neutron skins of various neutron-rich doubly magic nuclei. We consider short- and long-range correlations to take into account the presence of the strongly repulsive core of the bare nucleon-nucleon interaction and collective nuclear phenomena, respectively. Despite the strong sensitivity on the structure of the nucleus considered, our results indicate that, in general, correlations increase the values of the neutron skins.
We present recent developments obtained in the so-called N2LO extension of the usual Skyrme pseudo-potential. In particular, we discuss the isovector splitting mass in infinite nuclear matter and the pairing gaps of selected semi-magic even-even nuclei.
Using HF+BCS method with Skyrme forces we analyze the neutron drip line. It is shown that around magic and new magic numbers the drip line may form stability peninsulas. It is shown the location of these peninsulas does not depend on the choice of Skyrme forces. It is found that the size of the peninsulas is sensitive to the choice of Skyrme forces and the most extended peninsulas appear with the SkI2 set.
Octupole vibrations are studied in some doubly magic nuclei using the time-dependent Hartree-Fock (TDHF) theory with a Skyrme energy density functional. Through the use of the linear response theory, the energies and transition amplitudes of the low-lying vibrational modes for each of the nuclei were determined. Energies were found to be close to experimental results. However, transition amplitudes, quantified by the deformation parameter $β_3$, are underestimated by TDHF. A comparison with single-particle excitations on the Hartree-Fock ground-state shows that the collective octupole vibratio…
Relativistic mean field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus $^{132}$Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in $^{132}$Sn as well as the Nilsson spin-orbit parameter $C$ and orbit-orbit parameter $D$ thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin…
We use the nuclear density functional theory to determine nuclear electric quadrupole and magnetic dipole moments in all one-particle and one-hole neighbours of eight doubly magic nuclei. We align angular momenta along the intrinsic axial-symmetry axis with broken time-reversal symmetry, which allows us to explore fully the self-consistent charge, spin, and current polarisation. Spectroscopic moments are determined for symmetry-restored wave functions and compared with available experimental data. We find that the obtained polarisations do not call for using quadrupole- or dipole-moment operat…
Nuclear $β$-decay in magic nuclei is investigated, taking into account the coupling between particle and collective vibrations,on top of self-consistent random phase approximation calculations based on Skyrme density functionals. The low-lying Gamow-Teller strength is shifted downwards and at times becomes fragmented; as a consequence, the $β$-decay half-lives are reduced due to the increase of the phase space available for the decay. In some cases, this leads to a very good agreement between theoretical and experimental lifetimes: this happens, in particular, in the case of the Skyrme force S…
Alpha-decay half-lives for 104,105,106Te and 108,109,110Xe close above the doubly-magic 100Sn are calculated from systematic double-folding potentials. The derived alpha preformation factors are compared to results for 212,213,214Po and 216,217,218Rn above the doubly-magic 208Pb. Alpha-decay energies of Q_alpha = 5.42 \pm 0.07 MeV and 4.65 \pm 0.15 MeV are predicted for 104Te and 108Xe; the corresponding half-lives are T_{1/2} approx 5 ns for 104Te and of the order of 60 μs for 108Xe. Additionally, the properties of rotational bands in 104Te are analyzed, and the first excited 2+ state in 104T…
The properties of the low-energy dipole response are investigated for the proton-rich doubly magic nucleus $^{48}$Ni, in a comparative study of two microscopic models: fully self-consistent Relativistic Random-Phase Approximation(RRPA) based on the novel density-dependent meson-exchange interactions, and Continuum Random-Phase Approximation(CRPA) using Skyrme-type interactions with the continuum properly included. Both models predict the existence of the low-energy soft mode, i.e. the proton pygmy dipole resonance (PDR), for which the transition densities and RPA amplitudes indicate the dynami…
We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as th…
Large scale shell model calculations have been performed to study the excitation spectra of 132Sn and its nearest neighbours with a new cross-shell interaction constructed from two widely used interactions, sn100pn and CWG, of this mass region. A few of the two-body matrix elements have been tuned to reproduce the low-lying multiplet states of 132Sn. This is the first full scale shell model study of 132Sn energy spectra as well as transition probabilities. The excitation spectra for other nearest neighbours are reproduced reasonably well. The most important observable calculated are the E1 tra…
The structure of the collective low-energy $J^π=0^{-}$ (T=0 and T=1) modes is studied for a doubly magic nucleus in a schematic analytic model of RPA. The $0^{-}$ phonon states ($T= 0,1$) lie at energies $E_{T=0}(0^{-}) \alt ω$ and $E_{T=1}(0^{-}) > ω$, where $ω$ is the oscillator frequency. The matrix elements of P-odd and P- and T-odd weak one-body potentials connecting the ground state to these $0^{-}$-states, $W_{coll}$, are enhanced by the factor $\sim 2 (\fracω{E})^{1/2}A^{1/3} \sim 10$ as compared to the single-particle value $w_{sp}$ what can result in values $|W_{coll}| \sim 20-30 eV$…
Effects of the relativistic correction of the Coulomb interaction on doubly-magic nuclei are discussed with Skyrme Hartree--Fock calculations. The relativistic correction is treated by using the local density approximation. It is found that the correction to the total energy is about $ 2.4 \, \mathrm{MeV} $ for $ {}^{208} \mathrm{Pb} $, while proton and neutron radii do not change significantly. This difference is larger than the difference of the Coulomb exchange (Fock) energy calculated with the local density (Hartree--Fock--Slater) approximation and that with the exact treatment and the neu…
In this work, we identify a unique and novel feature of central density depletion in both proton and neutron named as doubly bubble nuclei in 50$\leq$Z(N)$\leq$82 region. The major role of 2d-3s single-particle (s.p.) states in the existence of halo and bubble nuclei is probed. The occupancy in s.p. state 3s$_{1/2}$ leads to the extended neutron density distribution or halo while the unoccupancy results in the central density depletion. By employing the Relativistic Mean-Field (RMF) approach along with NL3* parameter, the separation energies, single-particle energies, pairing energies, proton,…
The scope of the paper is to apply a state-of-the-art beyond mean-field model to the description of the Gamow-Teller response in atomic nuclei. This topic recently attracted considerable renewed interest, due, in particular, to the possibility of performing experiments in unstable nuclei. We study the cases of $^{48}$Ca, $^{78}$Ni, $^{132}$Sn and $^{208}$Pb. Our model is based on a fully self-consistent Skyrme Hartree-Fock plus random phase approximation. The same Skyrme interaction is used to calculate the coupling between particles and vibrations, which leads to the mixing of the Gamow-Telle…
Quartet Structure Above \(^{100}\)Sn and \(^{132}\)Sn Doubly Magic Isotopes
Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering（霍里亚·胡卢贝伊核物理与核工程研发国家研究所）；University of Bucharest（布加勒斯特大学）；Academy of Romanian Scientists（罗马尼亚科学家学院）
We present a microscopic calculation of $α$-cluster formation in heavy nuclei $^{104}$Te ($α$+$^{100}$Sn), $^{212}$Po ($α$+$^{208}$Pb) and their neighbors $^{102}$Sn, $^{102}$Te, $^{210}$Pb and $^{210}$Po by using the quartetting wave function approach. Improving the local density approximation, the shell structure of the core nucleus is considered, and the center-of-mass (c.o.m.) effective potential for the quartet is obtained self-consistently from the shell model wavefunctions. The $α$-cluster formation and decay probabilities are obtained by solving the bound-state of the c.o.m. motion of …
An effective $α$ particle equation is derived for cases where an $α$ particle is formed on top of a doubly magic nucleus. As an example, we consider $^{212}$Po with the $α$ on top of the $^{208}$ Pb core. We will consider the core nucleus infinitely heavy, so that the $α$ particle moves with respect to a fixed center, i.e., recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function concept that has been successfully applied to light nuclei. Shell model calculations are improved by incl…
Recent results of the Fayans energy density functional (EDF) for spherical nuclei are reviewed. A comparison is made with predictions of several Skyrme EDFs. The charge radii and characteristics of the first 2^+ excitations in semi-magic nuclei are briefly discussed. The single-particle spectra of doubly magic nuclei are considered in more detail. The phonon-particle coupling effects are analyzed including the so-called tadpole term.
A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd-even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the correspo…
We perform ab initio self-consistent Green's function calculations of the closed shell nuclei $^{\rm 4}$He, $^{\rm 16}$O and $^{\rm 40}$Ca, based on two-nucleon potentials derived from Lattice QCD simulations, in the flavor SU(3) limit and at the pseudo-scalar meson mass of 469~MeV/c$^{\rm 2}$. The nucleon-nucleon interaction is obtained using the HAL QCD method and its short-distance repulsion is treated by means of ladder resummations outside the model space. Our results show that this approach diagonalises ultraviolet degrees of freedom correctly. Therefore, ground state energies can be obt…
We study the so-called magic mixing angles for doubly heavy baryons. Defining that a magic mixing angle rotates states with definite $^{2S+1}(l_λ)_J$ to make them heavy-quark symmetric states, we derive the magic mixing angle only in the case $L_ρ=0$ between the heavy quark symmetric states with quantum numbers $\left(J, j_\ell\right)$ and the states with $\left(J, s_q+j_ρ\right)=\left(J, \{^4l_λ/^2l_λ\}\right)$ for a doubly heavy baryon in the standard $ρ-λ$ configuration, where $\vec j_\ell=\vec l_λ+\vec s_q$, $\vec s_ρ=\vec s_{Q1}+\vec s_{Q2}$, and $\vec j_ρ=\vec s_ρ+\vec L_ρ$. We discuss h…
We analyze recent data on a long series of high-spin states in $^{208}$Pb with a self-consistent phonon-coupling model for nuclear excitations based on the Skyrme functionals. The model is the renormalized time-blocking approximation (RenTBA) which takes the coherent one-particle-one-hole (1p1h) states of the random-phase approximation (RPA) as starting point and develops from that more complex configurations beyond RPA. To the best of our knowledge, this is the first investigation of high spin states in $^{208}$Pb using self-consistent nuclear models. The interesting point here is that comple…
New experimental data for the $^{38}$Ar($α$,n)$^{41}$Ca and $^{38}$Ar($α$,p)$^{41}$K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly-magic $^{40}$Ca despite of their relatively low level densities. The present study investigates the sensitivities and finds that the $α$-nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of ($α$,n) …
The ground-state energies and radii for $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated with the unitary-model-operator approach (UMOA). In the present study, we employ the similarity renormalization group (SRG) evolved nucleon-nucleon ($NN$) and three-nucleon ($3N$) interactions based on the chiral effective field theory. This is the first UMOA calculation with both $NN$ and $3N$ interactions. The calculated ground-state energies and radii are consistent with the recent {\it ab initio} results with the same interaction. We evaluate the expectation values with two- and three-body SRG evolved …
[Background] Symmetry restoration and configuration mixing in the spirit of the generator coordinate method based on energy density functionals have become widely used techniques in low-energy nuclear structure physics. Recently, it has been pointed out that these techniques are ill-defined for standard Skyrme functionals, and a regularization procedure has been proposed to remove the resulting spuriosities from such calculations. This procedure imposes an integer power of the density for the density dependent terms of the functional. At present, only dated parameterizations of the Skyrme inte…
We systematically study the effect of the J^2 tensor terms in the Skyrme energy functional on properties of spherical nuclei. We build a set of 36 parameterizations covering a wide range of the corresponding parameter space. We analyze the impact of the tensor terms on the evolution of single-particle-level splittings along chains of semi-magic nuclei in spherical calculations. We find that positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of neutron and proton single-particle level splittings in chai…
We investigate the magicity of the isotopes $^{52}$Ca and $^{54}$Ca, that was recently confirmed by two experimental measurements, and relate it to like--particle and neutron--proton tensor effects within a mean--field description. By analyzing Ca isotopes, we show that the like--particle tensor contribution induces shell effects that render these nuclei more magic than they would be predicted by neglecting it. In particular, such induced shell effects are stronger in the nucleus $^{52}$Ca and the single--particle gaps are increased in both isotopes due to the tensor force. By studying $N=32$ …
We perform calculations of the variation after parity projection with Skyrme interaction for ground and excited states of even-even Mg isotopes. Using the 3D real-space representation, we can take into account any kind of deformation; e.g., cluster structure, gamma-deformation. We also perform the full 3D angular momentum projection to obtained rotational spectra and B(E2). In 24Mg, the ground K^pi=0+ and several odd-parity bands are calculated. In 30,32,34Mg, our calculation reproduces a breaking of the N=20 magic number, so-called "Island of inversion" phenomena. Properties of both the groun…
Nuclear magic numbers, which emerge from the strong nuclear force based on quantum chromodynamics, correspond to fully occupied energy shells of protons, or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. While the sequence of magic numbers is well established for stable nuclei, evidence reveals modifications for nuclei with a large proton-to-neutron asymmetry. Here, we provide the first spectroscopic study of the doubly magic nucleus $^{78}$Ni, fourteen neutrons beyond the last…
We have employed RMF+BCS (relativistic mean-field plus BCS) approach to study behaviour of pf shell with the help of ground state properties of even-even nuclei. Our present investigations include separation energies , deformations, single particle energies, wavefunction, potential as well etc density distribution. As per recent experiments showing neutron magicity at N = 32 for Ca isotopes, our results with mass dependent pairing indicate a shell closure at N = 32 in Ca isotopes and a more strong shell closure at N = 34 in proton deficient 48Si because of reorganization of neutron pf shell. I…
Effect of the tensor force on $β$?-decay is studied in the framework of the proton-neutron random-phase-approximation (RPA) with the Skyrme force. The investigation is performed for even-even semi-magic and magic nuclei, $^{34}$Si, $^{68}$, $^{78}$Ni and $^{132}$Sn. The tensor correlation induces strong impact on low-lying Gamow-Teller state. In particular, it improves the ?$β$-decay half-lives. $Q$ and $ft$ values are also investigated and compared with experimental data.
Large scale shell model calculations, with dimensions reaching 10**9, are carried out to describe the recently observed deformed (ND) and superdeformed (SD) bands based on the first and second excited 0+ states of 40-Ca at 3.35-MeV and 5.21-MeV respectively. A valence space comprising two major oscillator shells, sd and pf, can accommodate most of the relevant degrees of freedom of this problem. The ND band is dominated by configurations with four particles promoted to the pf-shell (4p-4h in short). The SD band by 8p-8h configurations. The ground state of 40-Ca is strongly correlated, but the …
Despite a great success of the Skyrme mean-field approach in exploration of nuclear dynamics, it seems to fail in description of the spin-flip M1 giant resonance. The results for different Skyrme parameterizations are contradictory and poorly agree with experiment. In particular, there is no parameterization which simultaneously describes the one-peak gross structure of M1 strength in doubly magic nuclei and two-peak structure in heavy deformed nuclei. The reason of this mismatch could lie in an unsatisfactory treatment of spin correlations and spin-orbit interaction. We discuss the present st…
A systematic study of the ground state properties of the entire chains of even even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82 and 126 has been carried out using relativistic mean field (rmf) plus Bardeen Cooper Schrieffer (BCS) approach. Our present investigation includes deformation, binding energy, two proton separation energy, single particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using non relativistic approach (Skyrme Hartree Fock …
The neutron-proton Fermi-energy difference and the correlation to nucleon separation energies for some magic nuclei are investigated with the Skyrme energy density functionals and nuclear masses, with which the nuclear symmetry energy at sub-saturation densities is constrained from 54 Skyrme parameter sets. The extracted nuclear symmetry energy at sub-saturation density of 0.11 fm$^{-3}$ is 26.2 $\pm$ 1.0 MeV with 1.5 $σ$ uncertainty. By further combining the neutron-skin thickness of 208Pb, ten Skyrme forces with slope parameter of 28<L<65 are selected for the description of the symmetry ener…
We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this…
We study the effect of a $Λ$ hyperon immersed in the doubly magic nuclei, $^{16}$O, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb, as well as the neutron magic nucleus $^{90}$Zr. For a $Λ$ in the $1s$ and $1p$ states in $^{17}_Λ$O, $^{41}_Λ$Ca, $^{49}_Λ$Ca, $^{91}_Λ$Zr, and $^{209}_Λ$Pb, we compare the single-particle energies and density distributions of the core nucleons with those of the nuclei without the $Λ$, as well as the point proton and neutron radii. A remarkable finding is that the bound $Λ$ induces a significant asymmetry in the proton-neutron density distributions in the core nucleus. This…
A density dependent, effective nucleon-nucleon force of the Skyrme type is derived from the quark-meson coupling model -- a self-consistent, relativistic quark level description of nuclear matter. This new formulation requires no assumption that the mean scalar field is small and hence constitutes a significant advance over earlier work. The similarity of the effective interaction to the widely used SkM$^*$ force encourages us to apply it to a wide range of nuclear problems, beginning with the binding energies and charge distributions of doubly magic nuclei. Finding acceptable results in this …
We present the state-of-the art shell model calculations in a large model space (pf for protons, fpgd for neutrons), which allow to study simultaneously excitations across the Z=28 and N=50 shell gaps. We explore the region in the vicinity of 78Ni, being a subject of intense experimental investigations. Our calculations account correctly for the known low lying excited states in this region, including those which may correspond to cross-shell excitations. We observe the minimum of the N=50 mass gap at Z=32 consistent with experimental data and its further increase towards Z=28, indicating a ro…
Quantum stabilization of superheavy elements is quantified in terms of the shell-correction energy. We compute the shell correction using self-consistent nuclear models: the non-relativistic Skyrme-Hartree-Fock approach and the relativistic mean-field model, for a number of parametrizations. All the forces applied predict a broad valley of shell stabilization around Z=120 and N=172-184. We also predict two broad regions of shell stabilization in hyperheavy elements with N approx 258 and N approx 308. Due to the large single-particle level density, shell corrections in the superheavy elements d…
Doubly magic nuclei have a simple structure and are the cornerstones for entire regions of the nuclear chart. Theoretical insights into the supposedly doubly magic $^{78}$Ni and its neighbors are challenging because of the extreme neutron-to-proton ratio and the proximity of the continuum. We predict the $J^π=2_1^+$ state in $^{78}$Ni from a correlation with the $J^π=2_1^+$ state in $^{48}$Ca using chiral nucleon-nucleon and three-nucleon interactions. Our results confirm that $^{78}$Ni is doubly magic, and the predicted low-lying states of $^{79,80}$Ni open the way for shell-model studies of …
The magic nature of the $^{54}$Ca nucleus is investigated in the light of the recent experimental results. We employ both HFB and HF+BCS methods using Skyrme-type SLy5, SLy5+T and T44 interactions. The evolution of the single-particle spectra is studied for the N=34 isotones: $^{60}$Fe, $^{58}$Cr, $^{56}$Ti and $^{54}$Ca. An increase is obtained in the neutron spin-orbit splittings of $p$ and $f$ states due to the effect of the tensor force which also makes $^{54}$Ca a magic nucleus candidate. QRPA calculations on top of HF+BCS are performed to investigate the first $J^π$=$2^{+}$ states of the…
Angle-integrated cross-section measurements of the $^{56}$Ni(d,n) and (d,p) stripping reactions have been performed to determine the single-particle strengths of low-lying excited states in the mirror nuclei pair $^{57}$Cu-$^{57}$Ni situated adjacent to the doubly magic nucleus $^{56}$Ni. The reactions were studied in inverse kinematics utilizing a beam of radioactive $^{56}$Ni ions in conjunction with the GRETINA $γ$-array. Spectroscopic factors are compared with new shell-model calculations using a full $pf$ model space with the GPFX1A Hamiltonian for the isospin-conserving strong interactio…
An ab-initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly-magic and semi-magic nuclei employing state-of-the-art microscopic nuclear interactions and explicitly treating pairing correlations through the breaking of U(1) symmetry associated with particle number conservation. The present paper introduces the formalism, necessary to undertake applications at (self-consistent) second-order using two-nucleon interactions, in a detailed and self-contained fashion. First applications of…
