Neutron Single-particle States Research Articles

Neutron Single-Particle States in 101Sn by Polynomial Fits and Shell Model Calculations for Light Sn Isotopes

Neutron Single-Particle States in 101Sn by Polynomial Fits and Shell Model Calculations for Light Sn Isotopes

Study of static and dynamic properties of even-even 14–24O and 38–54Ca in the frame of Random Phase Approximation (RPA) method with different Skyrme parameterizations

The static and dynamic nuclear properties for neutron rich oxygen and calcium isotopes have been calculated using the framework of the random phase approximation method with different Skyrme parameterizations namely; SyO-, SyO+, BSk17, SLy4, SLy5, and SkX. The nuclear charge radii, the binding energy per nucleon were calculated and compared to the experimental one to choose the best Skyrme interactions used in the calculations of dynamic properties. The two-neutron separation energy for isotopes under study has been calculated and compared to experimental data. Higher modes of the excited states, energy-weighted sum rule, the centroid, constrained, and scaling energies of the resonances have been studied and illustrated together with available experimental data for comparison. For the low-lying excited states, the energy transition densities for J π = 2+ and J π = 3− are reproduced well in 18–24O and 46–54Ca isotopes. The neutron single particle states as a function of neutron number have been also presented. The results show that the random phase approximation calculations with Skyrme-type interactions is a successful method for describing nuclear structure properties of neutron rich nuclei near the drip line.

Effects of ground-state correlations on dipole and quadrupole excitations of 40Ca and 48Ca

The effects of ground-state correlations on the dipole and quadrupole excitations are studied for $^{40}$Ca and $^{48}$Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Large effects of the ground-state correlations are found in the fragmentation of the giant quadrupole resonance in $^{40}$Ca and in the low-lying dipole strength in $^{48}$Ca. It is discussed that the former is due to a mixing of different configurations in the ground state and the latter is from the partial occupation of the neutron single-particle states. The dipole and quadrupole strength distributions below 10 MeV calculated in ERPA are in qualitatively agreement with experiment.

Gamma Decay of Unbound Neutron-Hole States in ^{133}Sn.

Excited states in the nucleus ^{133}Sn, with one neutron outside the double magic ^{132}Sn core, were populated following one-neutron knockout from a ^{134}Sn beam on a carbon target at relativistic energies at the Radioactive Isotope Beam Factory at RIKEN. Besides the γ rays emitted in the decay of the known neutron single-particle states in ^{133}Sn additional γ strength in the energy range 3.5-5.5MeV was observed for the first time. Since the neutron-separation energy of ^{133}Sn is low, S_{n}=2.402(4) MeV, this observation provides direct evidence for the radiative decay of neutron-unbound states in this nucleus. The ability of electromagnetic decay to compete successfully with neutron emission at energies as high as 3MeV above threshold is attributed to a mismatch between the wave functions of the initial and final states in the latter case. These findings suggest that in the region southeast of ^{132}Sn nuclear structure effects may play a significant role in the neutron versus γ competition in the decay of unbound states. As a consequence, the common neglect of such effects in the evaluation of the neutron-emission probabilities in calculations of global β-decay properties for astrophysical simulations may have to be reconsidered.

Interplay between pairing and tensor effects in the N = 82 even–even isotone chain

The combined effects of the pairing and tensor terms of the nuclear interaction are investigated by analyzing the ground state properties of the nuclei belonging to the isotonic chain N=82. The pairing effects have been taken into account by considering both Hartree–Fock–Bogoliubov and Hartree–Fock plus Bardeen–Cooper–Schrieffer approaches using the same finite-range nuclear interaction, specifically a force of Gogny type. Our results reproduce very well the available experimental data of binding energies and charge radii. The study of the particle number fluctuation indicates that the presence of the tensor terms in the interaction reduces the pairing effects and produces new shell closures in some isotopes. The experimental behavior of the energy difference between neutron single particle states up to A=140 is properly described only if the tensor force is considered.

Evolution of Single-Particle Energies for N=9 Nuclei at Large N/Z

We have studied the nucleus 14 B using the 13 B(d,p) 14 B and 15 C(d, 3 He) 14 B reactions. The two reactions provide complementary information about the negative- parity 1s1/2 and 0d5/2 neutron single-particle states in 14 B. The data from the (d,p) reaction give neutron-spectroscopic strengths for these levels, and the (d, 3 He) results confirm the existence of a broad 2 - excited state suggested in the literature. Together these results provide estimates of the sd-shell neutron effective single-particle energies in 14 B.

Neutron Single Particle Structure inSn131and Direct Neutron Capture Cross Sections

Recent calculations suggest that the rate of neutron capture by (130)Sn has a significant impact on late-time nucleosynthesis in the r process. Direct capture into low-lying bound states is expected to be significant in neutron capture near the N=82 closed shell, so r-process reaction rates may be strongly impacted by the properties of neutron single particle states in this region. In order to investigate these properties, the (d,p) reaction has been studied in inverse kinematics using a 630 MeV beam of (130)Sn (4.8 MeV/u) and a (CD(2))(n) target. An array of Si strip detectors, including the Silicon Detector Array and an early implementation of the Oak Ridge Rutgers University Barrel Array, was used to detect reaction products. Results for the (130)Sn(d, p)(131)Sn reaction are found to be very similar to those from the previously reported (132)Sn(d, p)(133)Sn reaction. Direct-semidirect (n,γ) cross section calculations, based for the first time on experimental data, are presented. The uncertainties in these cross sections are thus reduced by orders of magnitude from previous estimates.

STUDY OF NUCLEAR BOUND STATES USING MEAN-FIELD WOODS–SAXON AND SPIN-ORBIT POTENTIALS

The neutron single-particle bound states as solutions of radial Schrödinger equation for the central Woods–Saxon potential together with spin-orbit interaction and centrifugal terms have been obtained analytically. By introducing new variable and using Taylor expansion, the differential equation has been transformed to solvable hypergeometric type. This differential equation has also been solved using Nikiforov–Uvarov (NU) method. Neutron single-particle states have been derived as self-adjoint form of hypergeometric series. By means of boundary conditions, which implies eigenvalue condition as complicated relation between energy eigenvalues and parameters of nuclear potential, the neutron single-particle energy eigenvalues have been derived using graphical method. To examine method, numerical results in special cases of S states are evaluated. Results obtained using this method are in satisfactory agreements with available numerical solutions.

Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions like the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in $^{40}$Ca, $^{208}$Pb and $^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely $^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double-magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.

Isobaric analog resonances of theN=21nucleus35Si

Neutron single-particle states in the neutron-rich nucleus ${}^{35}$Si, which is located beside the $N=20$ shell breaking nucleus ${}^{32}$Mg, were investigated through their isobaric analog resonances. The excitation function for ${}^{34}$Si$+p$ elastic scattering was measured around ${0}^{\ensuremath{\circ}}$ in the laboratory frame by the thick target inverse kinematics method with a ${}^{34}$Si beam around 5 MeV/nucleon and a thick polyethylene target. Eight resonances were successfully observed. Angular momenta and proton and total widths of the resonances were assigned using $R$-matrix analysis. With the help of information of the $\ensuremath{\beta}$ decay study, six isobaric analog resonances were identified. Spectroscopic factors and spin-parities of the corresponding parent states in ${}^{35}$Si are presented.

Neutron single-particle states above theN=164subshell in98251Cfand96249Cmstudied by neutron transfer reactions

Single-particle state assignments in $^{251}\mathrm{Cf}$ and $^{249}\mathrm{Cm}$ at $~1$ MeV excitation have been deduced from cross sections previously measured for the $^{250}\mathrm{Cf}(d,p)^{251}\mathrm{Cf}$ and $^{248}\mathrm{Cm}(^{4}\mathrm{He},^{3}\mathrm{He})^{249}\mathrm{Cm}$ reactions. The assignments are supported by observed cross-section signatures and intraband level spacings. The observed energies of these single-particle states, after pairing effects are removed, are in good agreement with values calculated using a Woods-Saxon single-particle potential. Neutron level diagrams, showing level spacings as a function of ${\ensuremath{\nu}}_{2},{\ensuremath{\nu}}_{4},$ and ${\ensuremath{\nu}}_{6}$, are extended to include neutron orbitals above $N=164$.

High-Kstructure inFm250and the deformed shell gaps atN=152andZ=100

The structure of high-spin and nonyrast states of the transfermium nucleus $^{250}\mathrm{Fm}$ has been studied in detail. The isomeric nature of a two-quasiparticle excitation has been exploited in order to obtain spectroscopic data of exceptional quality. The data allow the configuration of an isomer first discovered over 30 years ago to be deduced, and provide an unambiguous determination of the location of neutron single-particle states in a very heavy nucleus. A comparison to the known two-quasiparticle structure of $^{254,252}\mathrm{No}$ confirms the existence of the deformed shell gaps at $N=152$ and $Z=100$.

Giant neutron halos in the non-relativistic mean field approach

Giant neutron halos in medium-heavy nuclei are studied in the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions. The appearance of such structures depends sensitively on the effective interaction adopted. This is illustrated by comparing the predictions of SLy4 and SkI4 in the Ca and Zr isotopic chains. The latter force predicts a neutron halo in the Zr chain with $A>122$ due to the weakly bound orbitals $3p1/2$ and $3p3/2$. It is found that the energies of states near the separation threshold depend sensitively on effective mass values. The structure of the halo is analyzed in terms of the occupation probabilities of these orbitals and their partial contributions to the neutron density. The antihalo effect is also discussed in the case of $^{124}\mathrm{Zr}$ by comparing the occupation probabilities and wave functions of the Hartree-Fock neutron single-particle states near the Fermi energy with the corresponding HFB quasiparticle states.

Antibound states and halo formation in the Gamow shell model

The open quantum system formulation of the nuclear shell model, the so-called Gamow shell model (GSM), is a multiconfigurational SM that employs a single-particle basis given by the Berggren ensemble consisting of Gamow states and the non-resonant continuum of scattering states. The GSM is of particular importance for weakly bound/unbound nuclear states where both many-body correlations and the coupling to decay channels are essential. In this context, we investigate the role of $\ensuremath{\ell}=0$ antibound (virtual) neutron single-particle states in the shell model description of loosely bound wave functions, such as the ground state wave function of a halo nucleus $^{11}\mathrm{Li}$.

Identification of Nilsson states in transcurium nuclei

In recent years, we have studied the structure of transcurium nuclei using the best available actinide sources and state-of-the-art instruments. These include the largest amount of high-purity samples produced in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory and the GAMMASPHERE spectrometer located at Argonne. Proton single-particle states in 249Bk were investigated by measuring the γ-ray spectra of an extremely pure 253Es sample and reactor-produced 249Cm sources. Neutron single-particle states were identified in 251Cf by measuring γ-ray spectra of 255Fm sources and a cyclotron-produced 251Es source. By combining the results of these measurements with the results of one-nucleon transfer reactions, we were able to identify almost all the single-particle states up to 1 MeV excitation in 249Bk and 251Cf. The level energies in these nuclei are in good agreement with energies calculated with a Woods–Saxon potential and pairing interactions.

β-decay studies of neutron-rich nuclei

Recent results of β-decay studies performed along the expected neutron shell closures at N = 20, 28, 50 and 82 are reviewed and discussed in view of the potentially dynamic nature of neutron single-particle states in nuclei having extreme neutron-to-proton ratios.

Neutron Single-Particle States in r-Process Nuclei Near Closed Shells

We have begun a program to measure (d,p) reactions on neutron-rich nuclei, probing the single-particle states near the N = 50 and N = 82 closed shells. We have measured the neutron transfer on two N = 50 isotones, 82 Ge and 84 Se, at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. We have also performed a test measurement of transfer on 124 Sn to develop the techniques to study the 2 H( 130,132 Sn,p) 131,133 Sn reactions. Preliminary results for 85 Se are consistent with 5/2 + ground state and 1/2 + first excited state assignments, and the successful measurement of the 2 H( 124 Sn,p) 125 Sn reaction demonstrates the feasibility to measure the (d,p) reaction with neutron-rich 130,132 Sn beams.

Studies of the neutron single-particle structure of exotic nuclei at the HRIBF

The study of neutron single-particle strengths in neutron-rich nuclei is of interest for nuclear structure and nuclear astrophysics. The distribution of single-particle strengths constrains the effective Hamiltonian and pairing interactions and determines neutron interaction rates that are crucial for understanding the synthesis of heavy nuclei in supernovae via the rapid neutron capture process. Particularly important are the neutron single-particle levels in nuclei near closed neutron shells. Radioactive ion beams from the Holifield Radioactive Ion Beam Facility have been used to study (d,p) reactions in inverse kinematics in order to probe neutron single-particle states in exotic nuclei. The results of a measurement with a 82 Ge beam will be presented.

A dispersive optical model for n + 120Sn from −15 to +80 MeV and properties of neutron single-particle and single-hole states

Data for σ(θ) and Ay(θ) previously obtained at the Triangle Universities Nuclear Laboratory for 120Sn(n, n) are combined with other measurements of σ(θ) and Ay(θ) to create an elastic-scattering database from 9.9 to 24 MeV. In addition, relatively recent high-accuracy measurements of the neutron total cross section σT for Sn from 5 to 80 MeV are combined with earlier σT data to form a detailed σT database from 0.24 to 80 MeV. All of these data are analysed in the framework of a dispersive optical model (DOM). The DOM is extended to negative energies to investigate properties of single-particle and single-hole bound states. The DOM also is used in calculations of compound-nucleus contributions to σ(θ), so that DOM predictions can be compared to σ(θ) measurements. Excellent agreement is obtained for the entire set of scattering data from 0.4 to 24 MeV, and for σT values from 0.05 to 80 MeV. Calculations of bound-state quantities are compared to values derived from experiment for energies down to −15 MeV. Reasonable agreement for the binding energies is achieved, while the predicted spectroscopic factors disagree somewhat with the values found in stripping and pickup experiments. Finally, the DOM is modified to investigate two features (volume absorption that is asymmetric about the Fermi energy and zero absorption in the vicinity of the Fermi energy) that have been ignored in many DOM models. These modifications have little effect on the agreement of the calculations with the scattering data or with the bound-state quantities.

Is the nuclear spin-orbit interaction changing with neutron excess?

The difference in the energies of the lowest states corresponding to the two nodeless single-particle orbitals outside the Z=50 closed proton shell, h(11/2) and g(7/2), increases with neutron excess. We have measured the Sn(alpha,t) reaction for all seven stable even Sn isotopes and found that the spectroscopic factors are constant for these two states, confirming their characterization as single-particle states. The trend in energies is consistent with a decrease in the nuclear spin-orbit interaction. A similar trend, also suggesting a decreasing spin-orbit splitting, is seen in the energies of the neutron single-particle states outside the N=82 core, i(13/2) and h(9/2).