Neutron-rich Cr Research Articles

Merging of the island of inversion at N = 40 and N = 50

We performed a quantitative study of the nuclei with proton numbers from Z=20 (Ca) to Z=28 (Ni) and neutron numbers ranging from N=38 to 52 using the realistic shell model, which merged the descriptions of nuclei around N=40 and N=50 within an extended model space. The 21+ excitation energy (E(21+)) is calculated for neutron-rich Cr, Fe, and Ni isotopes. The results suggest that the islands of inversion at N=40 and N=50 merge around the Cr chain, and the N=50island of inversion is located below 78Ni. To demonstrate the prediction of the N=50island of inversion, we calculated and compared the E(21+), B(E2;01+→21+), effective single-particle energies (ESPEs), the probability of particle-hole excitation, and the average occupations in the N=40 and N=50 isotones. Similar parabolic trends of E(21+) and B(E2;01+→21+) in the N=40 and 50 isotones are obtained. The calculated ESPEs give that the N=40 and N=50 shell gaps both increase with the variation of proton number from Z=20 (Ca) to Z=28 (Ni). However, our calculations indicate that different particle-hole excitations dominate in the ground states of the N=40 and N=50islands of inversion, with 2p2h and 4p4h configurations being prominent in N=40 isotones, whereas 2p2h excitations are most important in the N=50 isotones. Furthermore, large occupations of the intruder quadrupole partner orbitals are also obtained in N=40 and N=50 isotones in our realistic shell model calculations.

In-beam γ -ray spectroscopy of Cr62,64

The region of neutron-rich Cr isotopes has garnered much attention in recent years due to a rapid onset of collectivity near neutron number $N=40$. We report here on the first $\ensuremath{\gamma}$-ray spectroscopy beyond the $({4}_{1}^{+})$ state in $^{62,64}\mathrm{Cr}$, using nucleon removal reactions from several projectiles within a rare-isotope beam cocktail. A candidate for the ${6}^{+}$ state in $^{64}\mathrm{Cr}$ is presented as well as one for, possibly, the second excited ${0}^{+}$ state in $^{62}\mathrm{Cr}$. The results are discussed in comparison to the LNPS shell-model predictions that allow for neutron excitations across the $N=40$ harmonic oscillator gap into the ${g}_{9/2}$ and ${d}_{5/2}$ orbitals. The calculated level schemes for $^{62,64}\mathrm{Cr}$ reveal intriguing collective structures. From the predicted neutron particle-hole character of the low-lying states in these Cr isotopes, $^{62}\mathrm{Cr}$ emerges as a transitional system on the path to the center of the $N=40$ island of inversion.

Collectivity of neutron-rich Cr and Fe toward N=50

Within the SEASTAR project at RIKEN-RIBF, 66 Cr and 70,72 Fe have been produced via protonknockout reactions, and their first excited 2+ and 4+ states have been discovered. The combination of the liquid-hydrogen target and TPC system MINOS has been used in combination with the DALI2 detector array for the first time. A 345 MeV/u 238 U beam with a mean intensity of about 12 pnA impinged on a Be target. Fission fragments were separated and identified using the BigRIPS spectrograph, and reaction products were analyzed using the ZeroDegree spectrograph. A plateau of excitation energies, with a small change in the systematic trends past N = 44, reveals an extension of the N = 40 region of collectivity toward N = 50. Hence, the isotopes of interest are located within the N = 40 island of inversion. An interpretation of the observed trends is offered through large scale shell model calculations.

Reduced transition strengths of low-lying yrast states in chromium isotopes in the vicinity ofN=40

Background: In neutron-rich nuclei around $N=40$ rapid changes in nuclear structure can be observed. While $^{68}\mathrm{Ni}$ exhibits signatures of a doubly magic nucleus, experimental data along the isotopic chains in even more exotic Fe and Cr isotopes---such as excitation energies and transition strengths---suggest a sudden rise in collectivity toward $N=40$.Purpose: Reduced quadrupole transition strengths for low-lying transitions in neutron-rich $^{58,60,62}\mathrm{Cr}$ are investigated. This gives quantitative new insights into the evolution of quadrupole collectivity in the neutron-rich region close to $N=40$.Method: The recoil distance Doppler-shift (RDDS) technique was applied to measure lifetimes of low-lying states in $^{58,60,62}\mathrm{Cr}$. The experiment was carried out at the National Superconducting Cyclotron Laboratory (NSCL) with the SeGA array in a plunger configuration coupled to the S800 magnetic spectrograph. The states of interest were populated by means of one-proton knockout reactions.Results: Data reveal a rapid increase in quadrupole collectivity for $^{58,60,62}\mathrm{Cr}$ toward $N=40$ and point to stronger quadrupole deformations compared to neighboring Fe isotopes. The experimental $B(E2$) values are reproduced well with state-of-the-art shell-model calculations using the LNPS effective interaction. A consideration of intrinsic quadrupole moments and ${\mathrm{B}}_{42}$ ratios suggest an evolution toward a rotational nature of the collective structures in $^{60,62}\mathrm{Cr}$. Compared to $^{58}\mathrm{Cr}$, experimental ${\mathrm{B}}_{42}$ and ${\mathrm{B}}_{62}$ values for $^{60}\mathrm{Cr}$ are in better agreement with the $E(5)$ limit.Conclusion: Our results indicate that collective excitations in neutron-rich Cr isotopes saturate at $N=38$, which is in agreement with theoretical predictions. More detailed experimental data of excited structures and interband transitions are needed for a comprehensive understanding of quadrupole collectivity close to $N=40$. This calls for additional measurements in neutron-rich Cr and neighboring Ti and Fe nuclei.

Large-scale shell-model calculations for unnatural-parity high-spin states in neutron-rich Cr and Fe isotopes

We investigate unnatural-parity high-spin states in neutron-rich Cr and Fe isotopes using large-scale shell-model calculations. These shell-model calculations are carried out within the model space of $fp$-shell + $0g_{9/2}$ + $1d_{5/2}$ orbits with the truncation allowing $1\hbar\omega$ excitation of a neutron. The effective Hamiltonian consists of GXPF1Br for $fp$-shell orbits and $V_{\rm MU}$ with a modification for the other parts. The present shell-model calculations can describe and predict the energy levels of both natural- and unnatural-parity states up to the high-spin states in Cr and Fe isotopes with $N\le35$. The total energy surfaces present the prolate deformations on the whole and indicate that the excitation of one neutron into the $0g_{9/2}$ orbit plays the role of enhancing the prolate deformation. For the positive(unnatural)-parity states in odd-mass Cr and Fe isotopes, their energy levels and prolate deformations indicate the decoupling limit of the particle-plus-rotor model. The sharp drop of the $9/2_{1}^{+}$ levels in going from $N=29$ to $N=35$ in odd-mass Cr and Fe isotopes is explained by the Fermi surface approaching the $\nu 0g_{9/2}$ orbit.

βdecay ofV61,63and low-energy level schemes ofCr61,63

Background: Near N = 40, rapid development of collectivity has been inferred based on the low-energy level schemes of the even-even Fe and Cr isotopes and attributed to deformation arising primarily from the influence of the $\ensuremath{\nu}{g}_{9/2}$ intruder orbital. The level schemes of the odd-A Co and Fe isotopes, as well as the odd-odd Co and Mn isotopes, are also influenced by the ${g}_{9/2}$ orbital and suggest prolate deformation. However, scarce information is available regarding the neutron-rich odd-A Cr isotopes.Purpose: Determine low-energy level schemes of the neutron-rich Cr isotopes approaching N = 40 and investigate the influence of the $\ensuremath{\nu}{g}_{9/2}$ orbital.Method: Neutron-rich V isotopes were produced at the NSCL through projectile fragmentation. The $\ensuremath{\beta}$ decay of the V isotopes into Cr isotopes was studied, and the observed $\ensuremath{\beta}$-delayed $\ensuremath{\gamma}$ rays were used to determine the low-energy level schemes of the neutron-rich Cr isotopes.Results: A greatly expanded level scheme is constructed for $^{61}\mathrm{Cr}$, which has an increased low-energy level density relative to isotopic ${}^{55,57,59}$Cr. Excited states are discovered in $^{63}\mathrm{Cr}$ for the first time.Conclusion: The distinct difference between the low-energy level scheme of $^{61}\mathrm{Cr}$ and the lighter neutron-rich odd-A Cr isotopes is inferred to be due to the influence of the $\ensuremath{\nu}{g}_{9/2}$ intruder orbital and suggests the possibility of low-energy positive-parity states in $^{61}\mathrm{Cr}$, leading to the conclusion that a significant change in deformation and orbital occupancies has taken place when $N$ exceeds 36.

Shape coexistence in neutron-rich nuclei nearN=40

Recent data show that both the 2${}^{+}$ and 4${}^{+}$ levels in the even neutron-rich Cr and Fe isotopes decrease in excitation energy toward $N=40$. This observation, along with Coulomb excitation and lifetime data, strongly indicates an increase in collectivity near $N=40$ in contradiction with expectations based on first principles. A straightforward two-band mixing model is used to investigate the structure of these neutron-rich Cr and Fe nuclei. The approach takes advantage of the extensive data available for ${}^{60}$Fe to provide the parameter values with which to reproduce the experimental observations in the ${}^{58\ensuremath{-}64}$Cr and ${}^{60\ensuremath{-}68}$Fe isotopic chains. Comparisons between the model and the data suggest marked structural differences for the ground-state configurations of $N=40$ Cr and Fe.

Tracking changes in shell structure in neutron-rich nuclei as a function of spin

Taking advantage of the resolving power of modern gamma-ray spectrometers in combination with different types of nuclear reactions, it has been possible to investigate to fairly high-spin neutron-rich nuclei in a number of regions of the nuclear chart. The primary motivations for such studies are to characterize changes in shell structure as a function of the neutron-to-proton ratio and to document the impact of a large neutron excess on global properties, such as the nuclear shape. Recent data on nuclei close to the ‘island of inversion’ near 32Mg are discussed first. They highlight challenges in describing the observations with modern effective interactions. Subsequently, the nature of excitations in neutron-rich fpg-shell nuclei between Ca and Ni is reviewed. A neutron sub-shell closure at N = 32 has been attributed to the monopole tensor force. Furthermore, the presence of collective excitations at moderate spin in neutron-rich Cr and Fe isotopes illustrates the role of the g9/2 orbital in driving the nuclear shape. The observations suggest that mixing between ‘deformed’ and ‘shell-model’ states needs to be considered. Finally, recent results in the direct vicinity of 68Ni indicate that the impact of the N = 40 neutron shell closure is rather modest.

Microscopic approach to large-amplitude deformation dynamics with local QRPA inertial masses

We have developed a new method for determining microscopically the five-dimensional quadrupole collective Hamiltonian, on the basis of the adiabatic self-consistent collective coordinate method. This method consists of the constrained Hartree-Fock-Bogoliubov (HFB) equation and the local QRPA (LQRPA) equations, which are an extension of the usual QRPA (quasiparticle random phase approximation) to non-HFB-equilibrium points, on top of the CHFB states. One of the advantages of our method is that the inertial functions calculated with this method contain the contributions of the time-odd components of the mean field, which are ignored in the widely-used cranking formula. We illustrate usefulness of our method by applying to oblate-prolate shape coexistence in 72Kr and shape phase transition in neutron-rich Cr isotopes around N = 40.

Shape transition and fluctuations in neutron-rich Cr isotopes aroundN=40

The spherical-to-prolate shape transition in neutron-rich Cr isotopes from N = 34 to 42 is studied by solving the collective Schr\"odinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating excitation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that Cr isotopes around 64Cr are prolately deformed but still possess transitional character; large-amplitude shape fluctuations dominate in their low-lying states.

Shape transition and fluctuations in neutron-rich Cr isotopes around N = 40

Shape transition and fluctuations in neutron-rich Cr isotopes around N = 40

New-generation Monte Carlo shell model for the K computer era

We present a newly enhanced version of the Monte Carlo Shell Model method by incorporating the conjugate gradient method and energy-variance extrapolation. This new method enables us to perform large-scale shell-model calculations that the direct diagonalization method cannot reach. This new generation framework of the MCSM provides us with a powerful tool to perform most-advanced large-scale shell-model calculations on current massively parallel computers such as the K computer. We discuss the validity of this method in ab initio calculations of light nuclei, and propose a new method to describe the intrinsic wave function in terms of the shell-model picture. We also apply this new MCSM to the study of neutron-rich Cr and Ni isotopes using the conventional shell-model calculations with an inert 40Ca core and discuss how the magicity of N = 28, 40, 50 remains or is broken.

In-beam γ-ray spectroscopy towards the nucleon driplines

The contribution of in-beam γ-ray spectroscopy to nuclear structure research in recent years will be described with the example of the experimental efforts focused on neutron-rich Cr and Fe nuclei around neutron number N = 40. Tremendous progress has been made at facilities around the world with complementary spectroscopic techniques, providing important benchmarks for developing shell-model effective interactions and elucidating the driving forces behind shell evolution in the exotic regime.

Shape changes and large-amplitude collective dynamics in neutron-rich Cr isotopes

Shape-phase transition in neutron-rich Cr isotopes around $N=40$ is investigated by employing the collective Hamiltonian approach. The inertial functions for large-amplitude vibration and rotation are evaluated by the local normal modes along the axial quadrupole collective coordinate using the Skyrme and pairing energy-density functionals. The time-odd components of the mean fields are fully included in the derived masses. The low-lying spectra obtained by requantizing the collective Hamiltonian show an excellent agreement with the recent experimental data. Gradual change from spherical to axially deformed shapes in between $N=34$ and 38 is well described.

Nature of the [formula omitted] band in odd-mass neutron-rich Cr nuclei

Neutron-rich Cr and Fe isotopes with N≈35 are soft near the ground state. The shape of the low-lying 9/2+ state at 0.503 MeV in the odd-mass 59Cr thus becomes a particular issue in understanding the role of the neutron g9/2 intruder orbital in this nucleus, and in this mass region in general. We apply the projected shell model and compare the calculated results between the two assumed basis deformations that are deduced with the spectroscopic quadrupole moment of the 9/2+ state obtained from the spherical shell model calculation. By studying moment of inertia, B(E2), and g factor values, it is concluded that different from its ground state, the 59Cr 9/2+ state has a stable prolate shape, consistent with the isotopes 55,57Cr and the isotone 61Fe.

Rotation alignment in neutron-rich Cr isotopes: A probe of deformed single-particle levels acrossN=40

Recent experiments have reached the neutron-rich Cr isotope with N=40 and confirmed enhanced collectivity near this sub-shell. The current data focus on low-spin spectroscopy only, with little information on the states where high-j particles align their spins with the system rotation. By applying the Projected Shell Model, we show that rotation alignment occurs in neutron-rich even-even Cr nuclei as early as spin 8 and, due to shell filling, the aligning particles differ in different isotopes. It is suggested that observation of irregularities in moments of inertia is a direct probe of the deformed single-particle scheme in this exotic mass region.

Shell model study of single-particle and collective structure in neutron-rich Cr isotopes

The structure of neutron-rich Cr isotopes is systematically investigated by using the spherical shell model. The calculations reproduce well the known energy levels for the even-even $^{52\ensuremath{-}62}\mathrm{Cr}$ and odd-mass $^{53\ensuremath{-}59}\mathrm{Cr}$ nuclei, and predict a lowering of excitation energies around neutron number $N=40$. The calculated $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ systematics shows a pronounced collectivity around $N=40$; a similar characteristic behavior has been suggested for Zn and Ge isotopes. Causes for the sudden drop of the $9/{2}_{1}^{+}$ energy in $^{59}\mathrm{Cr}$ and the appearance of very low ${0}_{2}^{+}$ states around $N=40$ are discussed. We also predict a new band with strong collectivity built on the ${0}_{2}^{+}$ state in the $N=40$ isotope $^{64}\mathrm{Cr}$.

LOW-LYING EXCITATION MODES IN DEFORMED NEUTRON-RICH NUCLEI

Low-frequency modes of excitation in deformed neutron-rich nuclei are studied by the use of the deformed quasiparticle-random-phase approximation (QRPA) based on the coordinate-space Hartree–Fock–Bogoliubov formalism. We investigate the microscopic structure of the low-lying Kπ = 0+ modes in neutron-rich Mg , Cr and Fe isotopes. It is found that the spatially extended structure of neutron quasiparticle wave functions around the Fermi level brings about a striking enhancement of the transition strengths. It is also found that the fluctuation of the pairing field plays an important role in generating coherence among two-quasiparticle excitations of neutron. Recent progress towards the self-consistent deformed QRPA calculation using the Skyrme density functional is also presented.

Deformation around Neutron-Rich Cr Isotopes in Axially Symmetric Skyrme-Hatree-Fock-Bogoliubov Method

We analyse the deformation mechanism in neutron-rich Cr, Fe and Ti isotopes with N = 32–44 using a Skyrme-Hartree-Fock-Bogoliubov mean-field code employing a twodimensional mesh representation in the cylindrical coordinate system. Evaluating the quadrupole deformation energy systematically, we show that the Skyrme parameter set SkM* gives a quadrupole instability around the neutron numbers N ∼ 38–42 in Cr isotopes, where the deformation energy curve suggests a transitional behavior with a shallow minimum extending to a large prolate deformation. The roles of a deformed N = 38 gap and the position of the neutron g 9 orbit are analysed in detail.

Pairing effects for rotational excitations unique to neutron-rich nuclei

We investigate the pairing correlations in neutron-rich Mg and Cr isotopes by paying special attention to the roles of continuum states and neutron skins. By performing the coordinate space Hartree-Fock-Bogoliubov calculation with the density-dependent contact pairing force, we show that the predicted pairing properties strongly depend on not only isoscalar but also isovector density dependence of the pairing force. We propose that the moment of inertia of the low-lying rotational excitations can provide desirable information to construct a reliable pairing density functional for exploring the novelty of the pairing correlations in neutron-rich nuclei close to the drip line.