Superheavy nuclei: relativistic mean field outlook

1
Superheavy nuclei relativistic mean field outlook
Anatoli Afanasjev
University of Notre Dame

• Motivation
• 2. Reliability of RMF parametrizations
• 3. Is that possible to find some common
  ingredient in the predictions
• of magic gaps in superheavy spherical
  nuclei? ? Central depression
• in the density and its impact on shell
  structure.
• 4. Pairing in superheavy nuclei.
• 5. Conclusions

Disclaimer few results with Gogny and Skyrme
forces used in the present
presentation are from J.-F. Berger et, NP A685
(2001) 1c and M. Bender et,
PRC 60 (1999) 034304
In collaboration with Stefan Frauendorf
2
Nucleonic densities
Magic gaps in spherical superheavy
nuclei
Self-consistency
Self-consistent theories give the largest
variations in the predictions of
magic gaps at Z120, 126 and 172, 184
Single- particle spectra
Potentials nucleonic, spin-orbit
1. A pair of the RMF sets which indicate
Z114 and N184 gaps are eliminated as
candidates by performing the analysis of
quasiparticle spectra in deformed nuclei
in actinide region, A.V.Afanasjev et, PRC
67 (2003) 024303
neutrons
protons
Self- consistency
2. Skyrme SkI4 also predicts Z114 (K. Rutz et
al, PRC 56 (1997) 238) but it reproduces
spin-orbit splitting very badly (M. Bender et,
PRC 60 (1999) 034304)
Circles are broken in the macroscopic- microscopic
method which consistently predicts Z114,
N184
3
Reliability of parametrizations
of parametrizations Skyrme gt 80 RMF gt 20
All animals theories, parametrizations are
equal, but some animals theories,
parametrizations are more equal than others
George Orwell,
Animal farm
Goal To find the RMF parametrizations best
suited for the description of superheavy nuclei
Method perform detailed analysis of the
spectroscopic data in the A250 deformed mass
region in the framework of cranked relativistic
Hartree-Bogoliubov (CRHB) theory see
A.V.Afanasjev et al, PRC 67 (2003) 024309 for
results
4
CRHBLN results
sometimes called as 2-nucleon gap
An analysis of experimental data
only in terms of these quantities
can be misleading Example of
NLSH indicates Z100 gap but between wrong s-p
states
5
For each configuration (blocked solution) the
binding energy Ei is calculated fully
self- consistently (including also
time-odd mean fields)
6
RMF analysis of single-particle energies in
spherical Z120, N172 nucleus
corrected by the empirical shifts obtained
in the detailed study of quasiparticle spectra
in odd-mass nuclei of the deformed A250 mass
region (PRC 67 (2003) 024309)
Self-consistent solution
Pseudospin doublets
2g7/2-3d5/2
172
172
1i11/2-2g9/2
1h9/2-2f7/2
7
Accuracy of the description of single-particle
energies Best sets (NL1,NL3,NL-Z2) ---- for most
subshells better than 0.5 MeV for a few subshells
the discrepancies reach 0.7-1 MeV Worst sets
(NLSH, NLRA1) --- much higher errors in the
energies of single-particle states (the only sets
which predict Z114 as shell gap) ? should be
excluded Important no-single particle
information is used in the fit of the RMF forces
Additional constraint by the study
single-particle states in nuclei with N162
and/or Z108
Single-particle states are observed
8
Macroscopic microscopic approach predicts Z114
and N184, but basic assumptions (see below)
are VIOLATED.
pairing
liquid drop
quantum (shell) correction
The radial density dependence used in
liquid drop model
FLAT DENSITY distribution in the central
part of nucleus
Woods-Saxon potential
R0r0A1/3
r01.2 fm
a 0.5 fm
V050 MeV
9
Lesson from quantum mechanics spherical
harmonic oscillator
A
B
A the radial wave function
B effective radial potential, i.e. with the
centrifugal term
added.
10
Densities of superheavy nuclei spherical RMF
calculations with the NL3 force
x
11
The clustering of single-particle states into the
groups of high- and low-j subshells is at the
origin of the central depression in the nuclear
density distribution in spherical superheavy
nuclei.
12
A.V.Afanasjev and S.Frauendorf, PRC 71, 024308
(2005)
g-s ground state configuration
exc-s excited state configuration
Occupied state
Unoccupied state
p
p -
3p1/2
particle-hole excitation leading to flatter
neutron and proton density
distribution
126
3d5/2

Self-consistency effects related to density
redistribution define the shell
structure Z114 shell gap can be
excluded
Spherical RMF calculations with NL3 forces
13
Impact of particle-hole excitations on the
densities and potentials (nucleonic,
spin-orbit)
densities
densities
General conclusion (tested on large of
particle-hole excitations in different nuclei)
potentials

• Large density depression
• in the central part of nucleus
• shell gaps at Z120,
• N172

2. Flat density distribution in the central
part of nucleus Z126 appears,
N184 becomes larger and Z120
(N172) shrink
14
Skyrme SkP m/m1 double shell closure at
Z126, N184 (SkM, ????
Large effective mass m/m0.8-1.0
Skyrme SkI3 m/m0.57 gaps at Z120, N184
no double shell closure, SLy6
Which role effective mass plays???
Gogny D1S Z120, N172(?) Z126, N184
Low effective mass m/m 0.65
RMF double shell closure at
Z120,N172
15

• Why macroscopicmicroscopic
• models are working so well
• in known superheavy nuclei???
• They are deformed
• Deformation leads to more equal
• distribution of the states emerging from
  high- and low-j subshells (and, thus, removes the
  clustering of high-j subshells seen in spherical
  superheavy nuclei).
• This leads to almost flat density distribution in
  the central part of nucleus.
• Single-particle features are fitted
• to experimental data

CRHBLN results
16
The importance of particle number projection
(PNP) in spherical superheavy nuclei
Most of other calculations were performed with
no PNP
Pairing collapse at magic gaps
Approximate PNP by Lipkin-Nogami (LN) no pairing
collapse
Calc. with no PNP overestimate d2p (2-proton
shell gap)
17
Stability against fission
RMF - low barriers, Skyrme HF high barriers
Experiment fission barrier heights in heavy
actinides (A240) RMF somewhat
underestimates Skyrme HF overestimates by few
MeV
From M.Bender et al, PRC (2003)
18
Conclusions

• The central depression in density distribution of
  spherical superheavy
• nuclei plays an important role in the
  definition of their shell structure

• Large density depression
• in the central part of nucleus favors
• shell gaps at Z120, N172

2. Flat density distribution in the central
part of nucleus favors Z126 and N184
Intermediate situations appear dependent on the
quality of force with respect of single-particle
degrees of freedom (position of j-subshells,
spin-orbit splitting, pseudospin splitting)
The check of quality of force with respect of
deformed single-particle states is MUST BE
2.
3. Particle number projection is important for
proper description of pairing properties of
spherical superheavy nuclei and calculation of
indicators of low-level density (d2n
2-nucleon gaps)
19
A.V.Afanasjev et al, PRC 67 (2003) 024309
Discrepancy between theory and experiment
? ? empirical shifts for the positions of
spherical subshells
20
The Sleep of Reason Produces Monsters.
(Caprichos, no. 43, Goya)
21
How magic are magic shell gaps?
Calculated spherical Z120 gap versus
experimental deformed Z100 gap
Similar relation for neutron spherical N172 and
deformed N152 gap
It might be that the effect of spherical shell
gaps in superheavy nuclei is only 30-40 more
pronounced than the effect of deformed gaps in
the A250 region