P-shell Nuclei Research Articles

Bloch–Horowitz schemes

I review the different methods used in calculating the effective interaction given by the energy-dependent Bloch–Horowitz (BH) equation. These methods are grouped into non-perturbative schemes, such as the Lanczos-based calculations and Faddeev-like calculations, and perturbative schemes. I show leading order BH calculations for p-shell nuclei and address convergence issues of this formalism. I comment on the need for some form of confining mean-field interaction within the BH formalism.

Direct evidence of core excitation in the giant resonance through the(e,e'n)reaction

Angular correlations and cross sections for the $^{40}\mathrm{Ca}(e,{e}^{'}n)^{39}\mathrm{Ca}$ reaction have been measured in the continuum above the giant resonance. A comparison of the missing energy spectra between the peak and the tail regions of the giant resonance indicates that neutron emission in the peak region leads to populating the ground and first excited states, whereas emission in the tail region leads to populating excited states at an energy about 4.5 MeV higher. The latter seems to be because of the $2{s}_{1/2}$ and $1{d}_{5/2}$ hole excitation, that is core excitation. The same tendency was observed in the $^{28}\mathrm{Si}(e,{e}^{'}n)^{27}\mathrm{Si}$ reaction of the sd shell nuclei but it did not appear as clearly in the $^{12}\mathrm{C}(e,{e}^{'}n)^{11}\mathrm{C}$ reaction of the 1p shell nuclei.

Self-consistent nuclear shell-model calculation starting from a realistic NN potential

First self-consistent realistic shell-model calculation for the light p-shell nuclei is performed, starting from the high-precision nucleon–nucleon (NN) CD-Bonn potential. This realistic potential is renormalized deriving a low-momentum NN potential Vlow-k that preserves exactly the two-nucleon low-energy physics. This Vlow-k is suitable to derive a self-consistent Hartree–Fock basis that is employed to derive both effective single-particle energies and residual two-body matrix elements for the shell-model Hamiltonian. Results obtained show the reliability of such a fundamental microscopic approach.

THE CONTINUUM SHELL MODEL WITH FULL CORRECTION FOR TARGET RECOIL

A brief history of the continuum shell model with full correction for target recoil is provided. Past applications to nucleon induced reactions, nucleon capture, knockout reactions by pions and electrons, and strangeness exchange reactions are provided. Recent progress of the model is reviewed. Examples of continuum states for p-shell nuclei, derived from both two and three-body interactions, are given. Finally, the general model is presented in which any core states and any states of the composite system may be incorporated in a calculation.

High resolution hypernuclear spectroscopy

Hypernuclear spectroscopy provides fundamental information for understanding the effective Λ-Nucleon interaction. Jefferson Laboratory experiment E94-107 was designed to perform high resolution hypernuclear spectroscopy by electroproduction of strangeness in four 1p-shell nuclei: 12C, 9Be, 16O, and 7Li. The first part of the experiment on 12C and 9Be has been performed in January and April-May 2004 in Hall A at Jefferson Lab. Significant modifications were made to the standard Hall A apparatus for this challenging experiment: two septum magnets and a RICH detector have been added to get reasonable counting rates and excellent particle identification, as required for the experiment. A description of the apparatus and the preliminary analysis results are presented here. PACS: 21.80.+a – 25.30.Rw

AB INITIO NUCLEAR STRUCTURE AND NUCLEAR REACTIONS IN LIGHT NUCLEI

There has been significant progress in the ab initio approaches to the structure of light nuclei. One such method is the ab initio no-core shell model (NCSM). Starting from the realistic two- and three-nucleon interactions, this method can predict the low-lying levels in p-shell nuclei. It is a challenging task to extend the ab initio methods to describe nuclear reactions. In this contribution, we present a brief overview of the NCSM with examples of recent applications as well as the first steps taken toward nuclear reaction applications.

SU(3) model description of Be isotopes

Experimental data on light nuclei close to dripline suggests that as the nucleon number asymmetry increases, the shell structure from stability line is not preserved. In contrast with spherical shell model, Elliott's SU(3) model, uses a deformed multi-nucleon basis to describe nuclear states. The SU(3) symmetry is a strong feature of 1p shell nuclei, where symmetry breaking spin-orbit force is rather weak. We have calculated the binding energies and low-lying energy spectra of Be isotopes (A=6 to A=14), within the framework of Elliott's SU(3) model, with special emphasis on effects due to the presence of intruder orbit 1S1/2 in the region. The model space includes SU(3) basis states that maximize the quadrupole-quadrupole interaction (-chiQ.Q). An extended model space includes, in addition, a set of 2p-2h excitations, with excited nucleons occupying lowest energy SU(3) states in harmonic oscillator shell N=2. Group theoretical methods have been used to classify the states and calculate the nuclear interaction matrix elements. Good angular momentum states are projected out from intrinsic deformed SU(3) states by using standard angular momentum projection techniques. The interaction used contains the monopole-monopole, quadrupole-quadrupole and isospin dependent terms. Interaction parameters are fixed so as to reproduce the binding of 4 nucleons in N=1 orbit for the N=Z isotope-8Be in ground state and first excited 2+ state, along with the known systematics of single neutron separation energies for Be isotopes. The calculated energy espectra are compared with available experimental data. The calculated excitation energies of intruder states in 8Be and 10Be, are discussed in the light of available experimental evidence and theoretical results from shell model as well as deformed oscillator model calculations of Fayache et al..

Effective interaction method for hyperspherical harmonics

The effective interaction hyperspherical harmonics (EIHH) method [1] is outlined. Recent extensions of the approach are discussed. Results for binding energies and radii of various p-shell nuclei are shown.

Effective interaction method for hyperspherical harmonics

The effective interaction hyperspherical harmonics (EIHH) method [1] is outlined. Recent extensions of the approach are discussed. Results for binding energies and radii of various p-shell nuclei are shown.

Ab initioshell model with a genuine three-nucleon force for thep-shell nuclei

The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are discussed in detail. We present results of first applications to ${}^{6,7}\mathrm{Li},$ ${}^{6}\mathrm{He},$ ${}^{7,8,10}\mathrm{Be},$ ${}^{10,11,12}\mathrm{B},$ ${}^{12}\mathrm{N},$ and ${}^{10,11,12,13}\mathrm{C}$ using the Argonne ${\mathrm{V}8}^{\ensuremath{'}}$ nucleon-nucleon (NN) potential and the Tucson-Melbourne ${\mathrm{TM}}^{\ensuremath{'}}(99)$ three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence of the realistic three-body force and an overall improvement in level ordering and level spacing in comparison to experiment. The greatest sensitivity occurs for states where the spin-orbit interaction strength is known to play a role. In particular, with the TNI we obtain the correct ground-state spin for ${}^{10,11,12}\mathrm{B}$ and ${}^{12}\mathrm{N},$ contrary to calculations with NN potentials only.

New aspects of spin degrees of freedom in nuclei

New aspects of quenching effects in Gamow-Teller (GT) transitions and magnetic moments are investigated for p-shell nuclei using an improved shell-model Hamiltonian with enhanced spin-flip neutron-proton interaction and modified single-particle energies. Here, the improved shell model Hamiltonian is used in the configuration space up to 2–3 ħw excitations to study spin dependent transitions. Manifestation of less quenching due to a weakening of intermediate coupling nature of the Cohen-Kurath Hamiltonian is shown in GT transitions; 12C → 12N, 11B → 11Be and 9Li → 9Be. Better agreement with experimental values is obtained by using the present Hamiltonian in most of GT transitions and magnetic moments in p-shell nuclei.

Neutrino-12C scattering in the Ab initio shell model with a realistic three-body interaction.

We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 variant Planck's over 2pi Omega we show that realistic nucleon-nucleon interactions, like, e.g., the CD-Bonn, underpredict the experimental cross sections by more than a factor of 2. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time, the TM'(99) interaction improves the calculated level ordering in 12C. The comparison between the CD-Bonn and the three-body calculations provides strong confirmation for the need to include a realistic three-body interaction to account for the spin-orbit strength in p-shell nuclei.

Gamow-Teller transitions and magnetic properties of nuclei and shell evolution

New aspects of quenching of Gamow-Teller (GT) transitions and magnetic moments are investigated for p-shell nuclei using an improved shell-model Hamiltonian with enhanced spin-flip proton-neutron interaction and modified single-particle energies. The present shell-model Hamiltonian thus obtained is used in the configuration space up to (2--3)\ensuremath{\Elzxh}\ensuremath{\omega} excitations, and GT transitions and magnetic moments are calculated with bare g factors and bare axial-vector coupling constant. Manifestation of variable quenching due to changing gap between ${0p}_{3/2}$ and ${0p}_{1/2}$ is presented in GT transitions such as ${}^{12}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{C}}}^{12}\mathrm{N},$ ${}^{11}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}^{11}\mathrm{Be},$ and ${}^{9}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Li}}}^{9}\mathrm{Be}.$ A similar effect is shown for magnetic moments. Better agreement with experimental values is obtained systematically by using the present Hamiltonian for GT transitions and magnetic moments in most of p-shell nuclei, as well as for energy levels. Thus, the shell structure is changing from nucleus to nucleus in an orderly way (i.e., shell evolution), the inclusion of which leads us to an improved description of the GT and magnetic properties. It is stressed that the anomalous shell structure of exotic nuclei and the GT/magnetic properties of stable and exotic nuclei are linked through the same underlying mechanism.

Single-particle quadrupole electromagnetic transitions in p-shell and sd-shell nuclei

Electron scattering Coulomb form factors for the single-particle quadrupole transitions in p-shell and sd-shell nuclei have been studied. Core polarization effects are included through a microscopic theory that includes excitations from the core orbits up to higher orbits with 2ω excitations. The modified surface delta interaction is adopted as a residual interaction. The results are discussed for the ( 1p1/2-1↦1p3/2-1) proton transition in 15N, ( 1d5/2↦2s1/2) neutron transition in 17O and ( 1d3/2-1↦2s1/2-1) proton transition in 39K. The inclusion of core polarization effects modifies the form factors markedly and describes the experimental data very well in both the absolute strength and the momentum transfer dependence.

On the asymmetry of Gamow–Teller β-decay rates in mirror nuclei in relation with second-class currents

The theoretical evaluation of major nuclear structure effects on the asymmetry of allowed Gamow–Teller β-decay rates in light mirror nuclei is presented. The calculations are performed within the shell model, using empirical isospin-nonconserving interaction and realistic Woods–Saxon radial wave functions. The revised treatment of p-shell nuclei is supplemented by systematic calculations for sd-shell nuclei and compared to experimental asymmetries when available. The results are important in connection with the possible existence of second-class currents in the weak interaction.

Margenau–Brink alpha model with central Jastrow and linear state-dependent correlations for p-shell nuclei

Wave functions based on the alpha cluster model of Margenau–Brink without effective interactions have been obtained for p-shell nuclei. In this approach the constituent clusters are located at fixed centers which are taken as variational parameters. The trial wave functions have been built up with correct total angular momentum and include central Jastrow and linear state dependent correlations. The ground state and the 2 + and 4 + excited states of 8Be, 12C, and the ground state of 16O are studied. The role of the different correlation mechanisms incorporated by the trial wave function is analyzed and the results are compared with previous calculations. The energies of the different bound states have been calculated by using the Variational Monte Carlo method.

The p-shell with one particle in the continuum

A continuum shell model is now available for p-shell nuclei with exactly the same important properties as a bound-state p-shell model calculation. This means that one can obtain all solutions that correspond to coupling one nucleon to the possible p-shell states of a bound-state calculation. The resulting coupled-channels solutions are antisymmetric and contain no spurious components. This model can be used to describe a very broad range of nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. Example calculations are shown for the compound systems 7Be and 7Li. Here it is demonstrated that agreement between theoretical and experimentally determined elastic and inelastic cross sections and analyzing power values can be improved by coupling to all open channels.

Study of the Dynamic Properties of Nuclei at Short Nucleon-Nucleon Distances

Results of investigations into the effects of non-nucleonic degrees of freedom and short-range dynamic correlations in nuclei for the reactions of interaction of real photons with light nuclei carried out in the Tomsk synchrotron are reviewed. The measured asymmetry of deuteron photodisintegration upon exposure to linearly polarized photons below the pion production threshold and the measured cross sections of reactions (γ, π+p) and (γ, π–, 0p) on p-shell nuclei are examined for a wide range of kinematic variables.

Quantum Monte Carlo Calculations of Light Nuclei

Accurate quantum Monte Carlo calculations of ground and low-lying excited states of light p-shell nuclei have been made for realistic nuclear forces. These include two-nucleon potentials that reproduce nucleon-nucleon scattering data and meson-exchange three-nucleon potentials constrained to reproduce the binding energies of s-shell nuclei. At present, results for more than 40 different (J ϖ ; T) states in A < 10 nuclei, plus isobaric analogs, have been obtained, with an excellent reproduction of the experimental energy spectrum. These microscopic calculations show that nuclear structure, including both single-particle and clustering aspects, can be explained starting from elementary two- and three-nucleon interactions.

QUANTUM MONTE CARLO CALCULATIONS OF LIGHT NUCLEI

▪ Abstract Accurate quantum Monte Carlo calculations of ground states and low-lying excited states of light p-shell nuclei are now possible for realistic nuclear Hamiltonians that fit nucleon-nucleon scattering data. Results for more than 30 different (Jπ;T) states, plus isobaric analogs, in A ≤ 8 nuclei have been obtained with an excellent reproduction of the experimental energy spectrum. These microscopic calculations show that nuclear structure, including both single-particle and clustering aspects, can be explained starting from elementary two- and three-nucleon interactions. Various density and momentum distributions, electromagnetic form factors, and spectroscopic factors have also been computed, as well as electroweak capture reactions of astrophysical interest.