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Nuclear ground-state observables from relativistic mean-field
models: masses, densities, radii, single-particle levels
T. J. Buervenich* and D. G. Madland*
* T-Division, Los Alamos National Laboratory, NM87545
Abstract. We report on the current status of relativistic mean-field models for the calculation and prediction of nuclear
ground-state observables. These models are quite powerful and can be applied to light (A > 16), medium, and heavy nuclei
(spherical and deformed) and allow realistic extrapolations to the drip lines and to superheavy nuclei. From a single calculation
one obtains a plethora of microscopic information about the chosen nucleus. We discuss several of the corresponding
observables that are then simultaneously calculated as well as the accuracy with which they can be determined within the
current models. Finally, we discuss recent model enhancements, connections to more fundamental physics, and future work.
As of today, we are facing a plethora of nuclear data in-
cluding many data on nuclear ground-states. These in-
clude masses, form factors, life times, etc. Additional
information can be deduced from these quantities, such
as separation energies, shell gaps, and radii. With new
RIA facilities ramping up in the near future, even more
data, especially of exotic nuclei, will become available.
Nuclear ground-state properties still constitute a great
challenge to our theoretical understanding of the nuclear
many-body system. Our understanding of its structure
progresses with our possibility to describe all ground-
state observables simultaneously in one approach. Self-
consistent mean-field models constitute such an attempt.
The calculation of single-particle wave-functions allows,
in principle, the calculation of all ground-state observ-
Relativistic mean-field (RMF) models [1, 2] have
reached a high degree of accuracy in the description of
nuclear ground-state observables. Such models, which
typically have 6-9 parameters (plus two more for the
proton and neutron pairing strengths), deliver all the
single-particle wave-functions for protons and neutrons
self-consistently. All ground-state observables can, in
principle, be obtained from them. The various terms in
the RMF model Lagrangian are motivated by experi-
ence and phenomenology. Most predominantly, strong
scalar and vector fields are needed, delivering both the
relativistic saturation mechanism of nuclear matter as
well as the strong spin-orbit force in nuclei with correct
magnitude and sign. Relativistic effects in nuclei reveal
themselves not through their kinetic motion (roughly
1/3 of the speed of light), but rather through the strong
spin-orbit force. This force is generated in relativistic
mean-field models through the large scalar and vector
fields of the order of 300 MeV, which add with the same
sign for the spin-orbit force, but almost cancel for the
binding energy, producing the -16 MeV binding energy
in symmetric nuclear matter. Nonlinear isoscalar-scalar
terms need to be introduced for a quantitative description
of nuclei and nuclear matter. Each term introduces a
coupling constant which needs to be adjusted to nuclear
ground-state observables. The adjustment process is
not unique, and the choices of observables and their
chosen uncertainties in the x2 adjustment determine
the predictive power of the model for the various kinds
of observables. Recently we found that modern RMF
models show a trade-off between the binding energy and
form-factor-related observables .
RMF models can be formulated using 'mesons' ,
i.e., boson fields with certain quantum numbers that only
have a very loose correspondence with the physical me-
son spectrum occuring in nature, or by emplying contact
interactions (point couplings) between the nucleons and
gradient terms . Both ways lead to a covariant frame-
work. The Lagrangian of our most successful model so
far is displayed in Eq. (1). The corresponding force, PC-
F1 , has 9 parameters adjusted simultanesously to nu-
clear ground-state observables.
Since the ansatz of these models is a covariant La-
grangian from which everything else follows, no assump-
tions on the nuclear shape or potential have to be made.
The actual deformation and density distribution of the
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Chen, Bin; Lin, Jung-Fu; Chen, Jiuhua; Zhang, Hengzhong & Zeng, Qiaoshi. Synchrotron-based high-pressure research in materials science, article, June 1, 2016; (digital.library.unt.edu/ark:/67531/metadc935468/m1/2/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.