Ca Nuclei Research Articles

Medium-Mass Nuclei from Chiral Nucleon-Nucleon Interactions

We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ a bare chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the coupled-cluster singles-doubles approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.

PROTON-NUCLEUS ELASTIC SCATTERING AT ~1 GeV AND THE NN AMPLITUDE

Working within the framework of Coulomb modified correlation expansion of the Glauber amplitude, we analyse the elastic scattering of ~1 GeV protons on 4 He , 12 C , 16 O and 40 Ca nuclei. Emphasis has been put on the use of different parametrizations of the basic (input) NN amplitude, which provide equivalently good accounts of the elastic NN scattering observables up to the available momentum transfer region. Using realistic form factors for target nuclei, it is found that the proton-nucleus collisions could provide a test to know which is the better choice of the NN amplitude. The analysis also considers the possibility of extracting some additional information about the matter density distributions.

In-Medium Properties of Nucleon Resonances

Recent experimental results for the in-medium properties of nucleon resonances are discussed. The experiments were done with the TAPS detector at the tagged photon beam of the MAMI accelerator in Mainz. Measured was the photoproduction of mesons (final states π 0 X, η X, 2π 0 X and π 0 π± X) from the nuclei 12C, 40Ca, 93Nb and 208Pb up to the second resonance region. The results were analyzed in view of the in-medium properties of the P33(1232), the D13)(1520), and the S11(1535) resonances.

Stochastic mean-field dynamics for fermions in the weak-coupling limit

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond mean-field is first presented. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states $D=| \Phi_a > < \Phi_b |/< \Phi_b . |\Phi_a >$ where $| \Phi_a >$ and $| \Phi_b >$ are antisymmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical $^{40}$Ca nucleus under the influence of a statistical ensemble of two-body contact interaction. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. Restricting to two particles-two holes residual interaction, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as $D = | \Phi >< \Phi |$ where $| \Phi >$ is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave-functions is given.

Neutron drip line in odd and even mass calcium and nickel nuclei

Neutron-rich Ca and Ni nuclei have been studied in a spherical relativistic mean-field formalism in coordinate space. A \ensuremath{\delta} interaction has been adopted to treat the pairing correlations for the neutrons. Odd nuclei have been treated in the blocking approximation. The effect of the positive-energy continuum and the role of pairing in the stability of nuclei have been investigated by use of the resonant-BCS approach. In Ca isotopes, $N=50$ is no longer a magic number, whereas in Ni nuclei, a new magic number emerges at $N=70$. There is a remarkable difference in the relative positions of the drip lines for odd and even isotopes. In Ca isotopes, the last bound even and odd nuclei are found to be $^{72}\mathrm{Ca}$ and $^{59}\mathrm{Ca}$, respectively. In Ni isotopes, the corresponding nuclei are $^{98}\mathrm{Ni}$ and $^{97}\mathrm{Ni}$, respectively. The origin of this difference in relative positions of the drip line in even and odd isotopes in the two chains is traced to the difference in the single-particle level structures and consequent modification in the magic numbers in the two elements. Pairing interaction is seen to play a major role. The effect of the width of the resonance states on pairing has also been investigated.

1H, 13C and 15N Resonance Assignments of URNdesign, a Computationally Redesigned RRM Protein

Protein design represents one of the great challenges of computational structural biology. The ability to successfully design new proteins would allow us to generate new reagents and enzymes, while at the same time providing us with an understanding of the principles of protein stability. Here we report 1H, 15N and 13C resonance assignments of a redesigned U1A protein, URNdesign. U1A has been studied extensively by our group and hence was chosen as a design target. For the assignments we sued 2D and 3D heteronuclearNMR experiments with uniformly 13C, 15N-labeled URNdesign. The assignments for the backbone NH, CO,Ca and Cb nuclei are 94%complete. Sidechain 1Hand13C, aromatic andQ/NNH2 resonances are essentially complete with guanidinium and K NH3 residues unassigned. BMRB deposit with accession number 6493

Shape Coexistence and Band Termination in DoublyMagic Nucleus 40Ca

Shape coexistence and band structure near yrast line of the Z = N doublymagic nucleus 40Ca have been investigated by theconfiguration-dependent cranked Nilsson–Strutinsky approach. The observednormal deformed and superdeformed bands are explained and the terminatingstates are confirmed by the calculations. The transition quadrupole momentQt of the calculated superdeformed band is in good agreement withthe observed one at high spin. There is shape coexistence within the sameconfiguration. Possible normal deformed and superdeformed bands withrotation around the intermediate axis in several interesting configurationsof 40Ca are discussed. Possible favored superdeformed band terminationsin 38Ca and 38Ar are predicted. The experimental results in38Ar are discussed simply.

Final-state interaction and recoil polarization in [formula omitted] reactions: comparison with the polarized target case

A study of the total cross section for polarized proton knockout in ( e , e ′ p → ) reactions is carried out for the closed-shell nucleus 40Ca. The dependence of FSI effects on polarization observables viewed as functions of the nucleon polarization angles is analyzed and interpreted within the basis of a semi-classical model for the orbit of the struck nucleon and trajectory of the ejected nucleon. A comparison with the case of a 39K polarized target and unpolarized protons is performed.

Investigation of the neutron shell structure of the even-even isotopes 40–56Ca within the dispersive optical model

Within the method of matching experimental data obtained in the neutron-stripping and neutron-pickup reactions on 40,42,44,46,48Ca isotopes, the single-particle energies and probabilities that neutron states are filled are obtained for the even-even calcium isotopes. These data are analyzed within the dispersive optical model, and good agreement between the calculated and experimental values of the energies of states is obtained. The dispersive optical potential is extrapolated to the region of the unstable 50,52,54,56Ca nuclei. The calculated single-particle energies of bound states in these isotopes are compared with the results of the calculations within the multiparticle shell model, the latter predicting a new magic number N = 34 for Z = 20 nuclei.

Nonrelativistic description of nucleon-nucleus scattering

Within the three-dimensional semiclassical approximation, an analytic expression is obtained for the amplitude of proton-nucleus scattering at intermediate energies of incident protons. The method for deriving this amplitude is based on the use of the high-energy approximation with distorted waves. In view of the short-range character of proton-nucleon interaction, the process of proton-nucleus scattering is represented as a series of single scattering events occurring on each individual nucleon. With the aid of the proposed mathematical formalism, a recursion relation is derived that makes it possible to express the nuclear form factor obtained within the distorted-wave method in terms of the sum of an infinite Born series. Parameters that characterize the distributions of protons and neutrons in the spherical nuclei 40Ca, 48Ca, 90Zr, and 208Pb and which include the width of the surface layer of nucleons and the root-meansquare radii of the proton-, neutron-, and nucleon-density distributions are determined from an analysis of the measured cross sections for the elastic scattering of 1-GeV protons, a modified Fermi function being employed for the nucleon-density distribution.

Structure of the isovector dipole resonance in neutron-rich 60 Ca nuclei and direct decay from pygmy resonance

The structure of the isovector dipole resonance in neutron-rich calcium isotope, 60Ca, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation (RPA). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy-dipole resonance (PDR) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant-dipole resonance (GDR) was evaluated, bringing on a detailed discussion about its microscopic structure.

Single-particle levels and spin-orbit splitting in the vicinity of the doubly magic nucleus 48Ca

On the basis of a detailed analysis of available experimental data, the spectrum of single-particle states and the isotopic dependence of spin-orbit splitting are determined for nuclei in the vicinity of the doubly magic nuclide 48Ca. The spectrum of excited states of the isobaric nucleus 48Sc is calculated.

Spherical Hartree-Fock calculations with linear-momentum projection before the variation

The hole spectral functions and from these the spectroscopic factors have been calculated in a Galilei-invariant way for the ground-state wave functions resulting from spherical Hartree-Fock calculations with projection onto zero total linear momentum before the variation for the nuclei 4He, 12C, 16O, 28Si, 32S and 40Ca. The results are compared to those of the conventional approach which uses the ground states resulting from usual spherical Hartree-Fock calculations subtracting the kinetic energy of the center-of-mass motion before the variation and to the results obtained analytically with oscillator occupations.

Spherical Hartree-Fock calculations with linear-momentum projection before the variation

Spherical Hartree--Fock calculations with projection onto zero total linear momentum before the variation are performed for the nuclei 4He, 12C, 16O, 28Si, 32S and 40Ca using a density--independent effective nucleon--nucleon interaction. The results are compared to those of usual spherical Hartree--Fock calculations subtracting the kinetic energy of the center of mass motion either before or after the variation and to the results obtained analytically with oscillator occupations. Total energies, hole--energies, elastic charge form factors and charge densities and the mathematical Coulomb sum rules are discussed.

Search for Cluster Emission and Extremely Deformed Shapes Using Charged-Particle Spectroscopy

The possible occurrence of highly deformed configurations is investigated in the N=Z nuclei 40Ca, 44Ti, and 56Ni as formed in the 28Si+12C, 16O+28Si, and 28Si+28Si reactions by using the properties of the emitted light charged particles (LCP). The energy spectra, in-plane and out-of-plane angular correlations of LCP’s are analysed for each of the 3 studied reactions within the framework of the statistical model. Strong deformation effects are deduced from Hauser-Feshbach calculations performed with the Monte Carlo code CACARIZO by using a consistent set of parameters with spin-dependent level densities. The analysis of α particles in coincidence with 32S fragments emitted in 28Si+12C shows a strong contribution from a 8Be cluster emission. The binary nature of this cluster emission has been verified in three other reactions involving a 12C target: 27A1+12C, 31P+12C, and 32S+12C.

Parameters of the proton shell structure of the 40,42,44,46,48Ca nuclei and their analysis within the dispersive optical model

By matching data on proton-stripping and proton-pickup reactions occurring on the same nuclear species, new experimental results for single-particle energies, occupation numbers, and fragmentation widths of proton states in the vicinity of the Fermi energy are obtained for the even-even isotopes 40,42,44,46,48Ca These results, along with the experimental values determined in the relevant (p, 2p) reaction for the single-particle energies of deep hole states in 40Ca, are analyzed on the basis of the dispersive-optical-model version proposed in the present study. The results of this analysis are compared with the predictions of various nuclear models, including the relativistic mean-field model.

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energies $E_b$ and two neutron separation energies $S_{2n}$ very well. The predicted neutron drip line nuclei are $^{28}$O, $^{72}$Ca, $^{98}$Ni, $^{136}$Zr, $^{176}$Sn, and $^{266}$Pb, respectively. Halo and giant halo properties predicted in Ca isotopes with $A>60$ are investigated in detail from the analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes are studied also. Furthermore, we study the neighboring lighter isotopes in the drip line Ca region and find some possibility of giant halo nuclei in the Ne-Na-Mg drip line nuclei.

Effects of Nuclear Structure in Double Charge Exchange Reactions on 16 O and 40 Ca

The energy dependence of forward double charge exchange (DCX) reaction is studied for the doubly closed shell nuclei 16O and 40Ca. A common characteristic of the two DCX reactions is a resonance-like peak around 50 MeV pion lab energy. While some authors have interpreted this peak as the evidence of a dibaryon resonance state, we show that it arises naturally in a two-step process in the conventional pion—nucleon system with proper handling of nuclear structure. The effects of nuclear structure are demonstrated through a comparison among different nuclear structure models: the symmetry model SU(4) ⊗ SU(3), the single particle shell model and the «realistic” shell model.

Scintillation efficiency of nuclear recoils in a CaF2(Eu) crystal for Dark Matter search

The scintillation efficiency (quenching factor) of fluorine and calcium nuclei recoiling in a CaF2(Eu) crystal was measured in an energy region relevant to Dark Matter searches. The recoiling nuclei were obtained via the 19F(n,n′) and 40Ca(n,n′) reactions, where the neutron beam was provided via the d(d,n)3He reaction. The quenching factor of F and Ca nuclei in the CaF2(Eu) crystal was found to be 11–20%, and 9–23% relative to the electron equivalent energy for 53–192keV and 25–91keV recoil energies, respectively, and the energy dependence was observed. The quenching factor we measured here is a little larger than that of previous studies, which may depend on the Eu doping concentration of the crystal.

Study of nuclear medium effects on polarization in (p, 2p) scattering at 1 GeV

We report on experimental investigation of the (p, 2p) reactions on nuclei 6Li, 7Li, 12C and 40Ca. In this experiment, polarizations of the secondary protons from the (p, 2p) reactions are measured using 1 GeV proton beam of the PNPI synchrocyclotron. Two final protons from the reaction are detected in coincidence by means of a two-arm magnetic spectrometer at non-symmetric scattering angles. The resolution of the spectrometer on separation energy of 4.5 MeV (FWHM) is enough to distinguish reliably the shell structure of the investigated nuclei. In order to measure polarization of the two secondary protons, both spectrometer arms are equipped with multiwire proportional chamber polarimeters. Strong reduction of polarizations (large depolarization factor) relatively to free pp scattering is observed in the experiment. The 6Li, 7Li P-shell data are interpreted in terms of this reduction being combined with classical phenomenon of the effective polarization calculated with the help of DWIA. For the S-shell protons the depolarization factors are apparently seen not being obscured by the spin-orbit coupling. In case of the 7Li S-shell data the depolarization factors calculated by deviation from IA are found to be ΔP/P=0.31±0.07 and 0.39±0.04 for the scattered and recoil proton polarization, respectively. As estimations show, significant and roughly equal polarization reduction of the two secondary protons with essentially different energies (≈-200 and 800 MeV) can hardly be explained by a trivial nuclear distortion effect like depolarization due to rescatterings in nuclear matter. Measurements with heavier nucleus targets (12C, 40Ca) show that magnitude of the depolarization is a decreasing function of the nuclear density in the part of the nucleus volume which effectively contributes to the pp scattering in a nucleus. An explanation of the observed depolarization might be done in terms of modification of the pp-scattering amplitude in the nuclear meidum.