States Of Atomic Nuclei Research Articles

Electric dipole polarizability of low-lying excited states in atomic nuclei

New equations for the electric dipole polarizability α E1 of low-lying excited states in atomic nuclei—and the related (−2) moment of the total photo-absorption cross section, σ −2—are inferred in terms of electric dipole and quadrupole matrix elements. These equations are valid for arbitrary angular momenta of the initial/ground and final/excited states and have been exploited in fully converged 1ℏ ω shell-model (SM) calculations of selected p- and sd-shell nuclei that consider configuration mixing; advancing previous knowledge from 17O to 36Ar, where thousands of electric dipole matrix elements are computed from isovector excitations which include the giant dipole resonance (GDR) region. Our results are in reasonable agreement with previous SM calculations and follow—except for 6,7Li and 17,18O—Migdal’s global trend provided by the combination of the hydrodynamic model and second-order non-degenerate perturbation theory. Discrepancies in 6,7Li and 17O arise as a result of the presence of α-cluster configurations in odd-mass nuclei, whereas the disagreement in 18O comes from the mixing of intruder states, which is lacking in the SM interactions. More advanced ab initio calculations of the dipole polarizability for low-lying excited states covering all the isovector states within the GDR region are missing and could be very valuable to benchmark the results presented here and shed further light on how atomic nuclei polarize away from the ground state

Half-life measurement of the 199-keV isomeric state in Ga76

Background: Isomeric states in atomic nuclei are a sensitive probe of their underlying microscopic structure and can be used to study the evolution of shell structure far from stability. Recent studies have identified and provided detailed spectroscopy of isomers in neutron-rich nuclei with $Z=28\text{\ensuremath{-}}50$. Isomeric states in the odd-odd gallium isotopes have been reported for all gallium isotopes from $A=72$ to $A=80$ with the exception of $^{76}\mathrm{Ga}$.Purpose: The purpose of this experiment was to observe short-lived isomeric states in the vicinity of $^{78}\mathrm{Ni}$.Methods: In-beam fragmentation of a $^{86}\mathrm{Kr}$ primary beam at the National Superconducting Cyclotron Laboratory produced radioactive ions which were delivered to and deposited in a $\mathrm{Ce}{\mathrm{Br}}_{3}$ scintillator coupled to a position-sensitive photomultiplier tube. Beta-delayed $\ensuremath{\gamma}$ rays were measured by ancillary HPGe clover and $\mathrm{La}{\mathrm{Br}}_{3}$ detectors which surrounded the implantation detector.Results: The previously observed ${J}^{\ensuremath{\pi}}={1}^{+}$, 199-keV level in $^{76}\mathrm{Ga}$, populated following the $\ensuremath{\beta}$ decay of $^{76}\mathrm{Zn}$, was identified as isomeric with a half-life of $34{(1)}_{\text{stat.}}{(8)}_{\text{sys.}}\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. Shell-model calculations suggest this state is formed by the coupling of protons in negative-parity configurations to $1/{2}^{\ensuremath{-}}$ neutron configurations. Transition strengths assuming a ground-state spin of $J=2$ and $J=3$ were determined from the experimental data.

Illustrations of loosely bound and resonant states in atomic nuclei

Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix and the transmission coefficient when the well supports an anti-bound state. We calculate the phase shift of the atomic nuclei 5He using the three-dimensional potential well and compare it with the experimental one. The paper gives an introduction to some of the properties found in realistic loosely bound and resonant nuclear systems, using mathematics accessible to undergraduate students.

Variational approach for pair optimization in the nucleon pair approximation

We propose a pair-condensate variational approach (PCV) to determine a set of the most important collective pairs in the description of low-lying states in atomic nuclei. Having available the precise details on these key collective pairs -- their spin, parity, and structure -- can be particularly useful in calculations based on the nucleon-pair approximation (NPA), helping to reduce their uncertainties. In trial calculations for the transitional Ba isotopes, our variational approach describes the evolution of quadrupole-deformation properties similar to Hartree-Fock treatments, while at the same time highlighting the $\gamma$ softness of $^{132}$Ba. Our approach can conclusively determine which collective pairs are critical for obtaining the lowest possible yrast, quasi-beta, quasi-gamma bands, producing both the level structure of these bands and related B(E2) values in reasonable consistency with experiment. These trial calculations suggest that with our PCV approach the NPA can be meaningfully applied to transitional nuclei with a wide spectrum of shapes. We also show that while neutron negative-parity pairs could in principle have an important impact on backbending in $^{132}$Ba, they are not favored for this nucleus.

α clustering and its connection to the E1 response of heavy nuclei

The generation of the collective nuclear E1 response is intimately connected to the breaking of proton-neutron symmetry. In this contribution, we present our recent results on a possible α-cluster dipole mode, which were obtained in the framework of the spdf interacting boson model. These extended studies of the low-lying E1 response support the general occurence of α-cluster dipole states in atomic nuclei.

Investigating shape evolution and the emergence of collectivity through the synergy of Coulomb excitation andβdecay

The synthesis of Coulomb excitation and β decay offers very practical advantages in the study of nuclear shapes and collectivity. For instance, Coulomb excitation is unique in its ability to measure the electric quadrupole moments, i.e., matrix elements, of excited, non-isomeric states in atomic nuclei, providing information on the intrinsic shape. However, the Coulomb excitation analysis and structural interpretation can be strongly dependent upon weak transitions or decay branches, which are often obscured by the Compton background. Transitions of particular interest are those low in energy and weak in intensity due to the E γ 5 attenuation factor. These weak decay branches can often be determined with high precision from β -decay studies. Recently, 106 Mo and 110 Cd were studied by both Coulomb excitation and β decay. Preliminary results of new weak decay branches following β decay of 110 m Ag to 110 Cd are presented; these results will challenge competing interpretations based on vibrations and configuration mixing.

How to Study Efimov States in Exotic Nuclei?

The existence of Efimov states in atomic nuclei has been predicted by several authors considering 3-body systems of the form Core–neutron–neutron. While these states appear elusive and very challenging experimentally, we discuss possible reactions that can be used to produce and study them in exotic (weakly-bound) nuclei. Following simple arguments, we show that cross-sections relative to the ground states should scale with the parameter \({\lambda_0}\), which is the same scale factor for binding energies and radii. We derive back of the envelope estimates for: one- and two-neutron transfer reactions, and inelastic scattering. The (d, p) reaction appears as the most promising approach and we discuss in more detail some experimental considerations using the example of \({^{19}C(d, p)^{20}C}\). These initial estimates could serve as a starting point for more refined and realistic calculations, which will be required for careful experimental planning and further analysis.

Regularities in low-lying states of atomic nuclei with random interactions

In this paper we study low-lying states of atomic nuclei with random interactions, within the framework of the nuclear shell model. The distributions of R-6 versus R-4 (where R-I = E-I1(+) / E-21(+)), empirical proton-neutron interaction, and charge radius are investigated by using a two-body random ensemble. The Mallmann plot exhibits statistical correlations between R-6 and R-4. The proton-neutron interaction between the last proton and the last neutron in even-A nuclei is found to be stronger than that in odd-A nuclei, and that in N = Z nuclei is even stronger. Simple relations of nuclear charge radii for neighboring nuclei are found to survive remarkably for the random ensemble.

Pseudospin Symmetry in Single Particle Resonant States

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of PSS in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of the PSS are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.

Aage Niels Bohr

Aage Niels Bohr

Unified framework for understanding pair transfer between collective states in atomic nuclei

A new interpretation of two-nucleon pair transfer in collective nuclei is presented. It differs from traditional models and unifies, within a consistent framework, the entire range of monopole pair-transfer phenomenology in collective nuclei. This includes the well-known examples of large cross sections to excited ${0}^{+}$ states in phase transitional nuclei, and small ones in many other nuclei, but also predicts large cross sections elsewhere under particular circumstances. These predictions can be tested experimentally.

Cluster states in atomic nuclei and cluster-decay processes

The relationship between decay properties of nuclei (primarily cluster properties) and cluster-decay characteristics is discussed. Both purely microscopic and microscopically substantiated semimicroscopic and semiempirical methods are considered. The current state of the proton-, α-, and cluster-radioactivity theory is presented.

Staggering behavior of0+state energies in theSp(4)pairing model

We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron (pn) and like-particle isovector pairing interactions as well as interactions with higher J multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the N=Z region, and the like-particle and pn isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

Sp(3, R) coadjoint orbit theory

The algebraic mean field method is applied to the symplectic Lie algebra sp(3, R) that describes geometrical collective states in atomic nuclei. The expectations of sp(3, R) generators define a symplectic density matrix. The mean field approximation restricts the densities to a manifold that is a coadjoint orbit of the transformation group Sp(3, R) and a level surface of the symplectic Casimir functions. Compared to representation theory, mean field theory is technically simpler, but yields similar predictions for physical properties of collective states. The critical points of the energy functional on a coadjoint orbit surface define rotational bands. The deformation, kinetic energy and Kelvin circulation of principal axis symplectic rotors are determined as a function of the angular momentum. Illustrative applications of coadjoint orbit theory are reported for the yrast rotational bands of a light 20Ne and a heavy 166Er deformed isotope.

Exotic Isomers in Deformed Atomic Nuclei

Excited states of atomic nuclei can have long half lives, due to the angular-momentum couplings of unpaired nucleons. Such isomeric states provide opportunities for exploring novel nuclear physics, astrophysics and physics at the atomic/nuclear interface. This review focuses on the properties of isomers in deformed nuclei, and emphasises the importance of axial symmetry in preserving the integrity of the K quantum number. A region of neutron-rich nuclei around 188Hf (Z=72, N=116) is predicted to have exceptional isomer properties, and experimental advances are now opening up this region to detailed investigation.

From regular to chaotic states in atomic nuclei

An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order$\to$chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).

A variety of shapes occurring in different states of atomic nuclei

Some of the recent developments in understanding the occurrence of various nuclear deformations are reviewed. In particular, the phenomena connected with the appearance of very large distortions in some nuclear states (the superdeformed shapes) are discussed.

Investigation of high-spin states in atomic nuclei

A short review of the recent investigations of nuclear properties at high angular momentum is given. At the same time, the discussion on the high-spin states and some of the contributions submitted to the Conference high-spin session are summed up.

Model with multipole and spin-multipole forces for studying highly excited states of atomic nuclei

The fundamental equations of the model describing the structure of highly excited states of nuclei are obtained. Interaction between nucleons is represented in the form of an average nuclear field plus interactions leading to the pair correlations of superconducting type and multipole and spin-multipole forces. The interaction of quasiparticles with phonons is taken into account, which gives rise to the complications of the structure of states with the growth of the excitation energy. (auth)

Der Einflu� der Nullpunktschwingungen der Kernoberfl�che auf die Formfaktoren der inelastischen Elektronenstreuung

The transition densities from the ground state to exited states of atomic nuclei are calculated from the drop model, taking the zero-point oscillations of the nuclear surface into account. The calculation yields transition densities smeared out over a distance of 2–3 fm near the nuclear surface. In the case ofn-surfon transitions the radial dependence of these densities is proportional to then-th derivative of the ground-state density.