Central depression of the nuclear charge distribution

doi:10.1016/0375-9474(86)90053-9

Nuclear Physics A

Volume 459, Issue 1, 27 October 1986, Pages 10-34

https://doi.org/10.1016/0375-9474(86)90053-9 Get rights and content

Abstract

As a systematic feature of all measured charge distributions we find a shift in the form-factor zeroes as compared to a simple folding model. To first order, this shift can be interpreted as resulting from the central depression w, caused by the Coulomb repulsion. Accounting for it leads to an increase in the surface width of nuclear charge distributions by 0.105 fm. This interpretation of the experimental findings is compared with the droplet model, which relates w with the compression modulus K and the asymmetry energy J. Accounting for w leads to an increase in the extrapolated nuclear matter density by 7.5%. However, this macroscopic model is not able to describe the experimental results in detail since w is also influenced by shell effects. HF + BCS calculations with effective Skyrme-type interactions reproduce part of the data, revealing the influence of shells on w. Here, too, there remain discrepancies in details. A level of accuracy is reached at which most probably also the skewness of the charge distribution must be taken into account.

References (31)

J. Friedrich et al.
Nucl. Phys.
(1982)
B. Dreher et al.
Nucl. Phys.
(1974)
H. Euteneuer et al.
Nucl. Phys.
(1978)
H. Euteneuer
thesis
(1976)
J.P. Blaizot et al.
Nucl. Phys.
(1976)
J. Friedrich et al.
Phys. Rev. Lett.
(1981)
W.D. Myers
Droplet model of atomic nuclei
(1977)
J. Friedrich et al.
Phys. Rev.
(1986)
W. Myers, private...
J. Heisenberg et al.
Phys. Rev. Lett.
(1969)
J.L. Friar et al.

H.-J. Krappe, private...

G. Lahm

dissertation

(1982)

G. Lahm and R. Neuhausen, to be...

H. Rothhaas, private...

H. Miessen

dissertation

(1983)

Cited by (31)

Prospects for electron scattering on unstable, exotic nuclei
2017, Progress in Particle and Nuclear Physics
Electron scattering off radioactive ions becomes feasible for the first time due to advances in storage ring and trapping techniques in conjunction with intense secondary beams from novel beam facilities. Using a point-like purely leptonic probe enables the investigation of charge distributions and electromagnetic excitations in $β$ -unstable exotic nuclei with an enhanced overshoot in proton and neutron numbers and the use of QED, one of the most precisely studied theories, for describing the scattering process.
The electronion scattering experiment ELISe at the International Facility for Antiproton and Ion Research (FAIR) - A conceptual design study
2011, Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
The electron–ion scattering experiment ELISe is part of the installations envisaged at the new experimental storage ring at the International Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany. It offers an unique opportunity to use electrons as probe in investigations of the structure of exotic nuclei. The conceptual design and the scientific challenges of ELISe are presented.
Pairing interaction and self-consistent densities in neutron-rich nuclei
2001, Nuclear Physics A
Particle and pairing densities in spherical even–even neutron-rich nuclei are studied within the Skyrme–Hartree–Fock–Bogoliubov approach with the density-dependent pairing interaction. The influence of the density dependence of the pairing interaction on asymptotic properties of nucleonic distributions are analyzed. It is demonstrated that the size of the neutron halo dramatically depends on the behavior of the pairing interaction at low density.
A generalized Helm model for nuclear charge densities
1992, Nuclear Physics, Section A
A generalized Helm model for the nuclear charge density is introduced, which is capable of providing a “model-independent” fit to elastic-electron-scattering data. The model, which is related to the leptodermous picture of the nucleus, is illustrated by fitting the form factors of representative nuclei ⁴⁰Ca, ⁵⁸Ni, ¹²⁴Sn and ²⁰⁸Pb as deduced from previous analyses. The proton number density for the above nuclei is also obtained from their charge densities and its dependence on the size of the proton inside the nuclear medium is considered.
Experimental study of shell-model occupancies employing a new sum rule
1992, Progress in Particle and Nuclear Physics
Despite of the obvious success of the nuclear shell model the occupation numbers of nucleons in the shell model orbitals could not be determined precisely. The interpretation of one-nucleon transfer and quasi-free knock-out experiments, the classical tools for nuclear structure studies, did not yield reliable absolute spectroscopic factors mainly because of the uncertain distortions. In contrast, relative spectroscopic factors can be extracted with high precision because many sources of systematic experimental errors vanish and the uncertain DWBA or DWIA predictions enter as corrections only. On the other hand, elastic electron scattering represents a high precision tool to study nuclear charge density distributions which, however, offers no direct model-independent access to occupation numbers. To exploit the advantages of the different probes a Combined Evaluation of Relative spectroscopic factors and Electron Scattering, the CERES approach, has been developed to study the occupation numbers of the $3s_{12}$ proton orbital in ²⁰⁶Pb. New precise relative experiments on ²⁰⁴Hg,²⁰⁵Tl and ^205,206Pb provide the necessary input data for the CERES sum rule. The occupation number n_3s(208) for the $3s_{12}$ proton orbital in ²⁰⁶Pb is found as n_3s(208) = 2.46(16)★z, where z represents the absolute $3s_{12}$ contribution to the charge density difference of ²⁰⁶Pb-²⁰⁵Tl. Based on the most recent interpretation of z = 0.64(6) we obtain n_3s(208) = 1.57(10)[17]. The resulting depletion of ≈ 20% agrees well with other recent experimental findings and constrains the mean-field predictions.
Center-of-mass projection of skyrme-hartree-fock densities
1991, Nuclear Physics, Section A
We investigate the effects of center-of-mass projection on the nuclear charge density resulting from self-consistent calculations using the effective Skyrme interaction. We compare the full projection with the widely used standard recipe which corrects for the spurious center-of-mass motion by unfolding a harmonic oscillation. We find that full projection is necessary for a quantitative description in light nuclei at least up to the Ca isotopes. The variations of the effect with varying Skyrme forces are studies. A microscopic derivation of the standard recipe, the oscillator correction is given.

View all citing articles on Scopus

View full text

Central depression of the nuclear charge distribution

Abstract

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

thesis

Nucl. Phys.

Phys. Rev. Lett.

Phys. Rev.

Phys. Rev. Lett.

dissertation

dissertation