Odd-even effect
chemical potential
J. Phys. G 39 093101 (2012)
Pairing energy
N-odd
B(N +1, Z ) + B(N −1, Z )
Δn =
− B(N, Z )
2
B(N, Z +1) + B(N, Z −1)
Δp =
− B(N, Z )
2
Z-odd
A common phenomenon in
mesoscopic systems!
Example: Cooper electron pairs
in superconductors…
Find the relation between the neutron pairing gap
and one-neutron separation energies. Using
http://www.nndc.bnl.gov/chart/
plot neutron pairing gaps for Er (Z=68) isotopes
as a function of N.
Pairing and binding
I. Tanihata et al., PRL 55 (1985) 2676
For super
achievers:
Halos
Neutron Drip line nuclei
HUGE!
Dif
f use
d!
PA IR ED!
4He! 5He! 6He! 7He! 8He! 9He! 10
He!
The Grand Nuclear Landscape
(finite nuclei + extended nucleonic matter)
Z=118, A=294
superheavy!
nuclei!
known up to Z=91
protons
82!
126!
known nuclei
terra incognita
50!
82!
28!
20!
50!
8!
2!
20!
2! 8!
28!
stable nuclei
probably known only up to oxygen
neutrons
neutron stars
The limits: Skyrme-DFT Benchmark 2012
ine
stable nuclei
l
288
rip
d
known nuclei ~3,000
ton
o
r
drip line
-p
o
tw
S2n = 2 MeV Z=82
SV-min
80
line
p
i
dr
N=258
n
o
r
t
u
e
-n
two
Asymptotic freedom ?
N=184
110
Z=50
40
N=126
Z=28
N=82
Z=20
0
N=28
N=20
0
N=50
40
proton number
proton number
120
100
90 230
Nuclear Landscape 2012
80
120
160
244
232
200
240
248
neutron number
240
from
B. Sherrill
neutron
number
How many protons and neutrons can be bound in a nucleus?
Erler et al. Nature 486, 509 (2012) Literature: 5,000-12,000
Skyrme-­‐DFT: 6,900±500syst 256
280
Neutron star, a bold explanation
A lone neutron
star, as seen by
NASA's Hubble
Space Telescope
B = avol A − asurf A
2/ 3
(N − Z) 2
Z2
3 G
2
− asym
− aC 1/ 3 − δ(A) +
M
A
A
5 r0 A1/ 3
Let us consider a giant neutron-rich nucleus. We neglect Coulomb, surface, and
pairing energies. Can such an object exist?
B = avol A − asym A +
3 G
2
1/ 3 (m n A) = 0
5 r0 A
limiting condition
3 G 2 2/3
mn A = 7.5MeV ⇒ A ≅ 5×10 55, R ≅ 4.3 km, M ≅ 0.045M
⊙
5 r0
More precise calculations give M(min) of about 0.1 solar mass (M⊙). Must neutron
stars have
R ≅ 10 km, M ≅ 1.4 M
⊙
Nuclear isomers
The most stable nuclear isomer occurring in
nature is 180mTa. Its half-life is at least 1015
years, markedly longer than the age of the
universe. This remarkable persistence results
from the fact that the excitation energy of the
isomeric state is low, and both gamma deexcitation to the 180Ta ground state (which
itself is radioactive by beta decay, with a halflife of only 8 hours), and direct beta decay to
hafnium or tungsten are all suppressed, owing
to spin mismatches. The origin of this isomer
is mysterious, though it is believed to have
been formed in supernovae (as are most other
heavy elements). When it relaxes to its ground
state, it releases a photon with an energy of
75 keV.
Discovery of a Nuclear Isomer in 65Fe with Penning Trap Mass Spectrometry
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.132501