Pairing energy - Michigan State University
Transcript of Pairing energy - Michigan State University
Pairing energy
Δn =B(N +1,Z )+B(N −1,Z )
2−B(N,Z )
Δ p =B(N,Z +1)+B(N,Z −1)
2−B(N,Z )
A common phenomenon in mesoscopic systems!
Example: Cooper electron pairs in superconductors…
N-odd
Z-odd
pro
ton
s
neutrons
The Grand Nuclear Landscape (finite nuclei + extended nucleonic matter)
82
50
28
28
50
82
2082
28
20stable nuclei
known nuclei 126
terra incognita
neutron stars
probably known only up to oxygen
known up to Z=91
superheavynucleiZ=118, A=294
Binding Blocks http://www.york.ac.uk/physics/public-and-schools/schools/secondary/binding-blocks/
http://www.york.ac.uk/physics/public-and-schools/schools/secondary/binding-blocks/interactive/ https://arxiv.org/abs/1610.02296
http://www.nishina.riken.jp/enjoy/kakuzu/kakuzu_web.pdf
How many protons and neutrons can be bound in a nucleus?
Skyrme-DFT:6,900±500syst
The limits: Skyrme-DFT Benchmark 2012
0 40 80 120 160 200 240 280
neutron number
0
40
80
120
prot
on n
umbe
r two-proton drip line
two-neutron drip line
232 240 248 256neutron number
prot
on n
umbe
r
90
110
100
Z=50
Z=82
Z=20
N=50
N=82
N=126
N=20
N=184
drip line
SV-min
known nucleistable nuclei
N=28
Z=28
230 244
N=258
Nuclear Landscape 2012
S2n = 2 MeV
Literature: 5,000-12,000
288 ~3,000
Asymptotic freedom ?
from B. Sherrill
Erleretal.Nature486,509(2012)
HW: a) Using http://www.nndc.bnl.gov/chart/ find one- and two-nucleon
separation energies of 5He, 24O, 25O, 26O, 48Ni, 56Ni and 208Pb. Discuss the result.
b) 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 Yb (Z=70) isotopes as a function of N.
Neutron star, a bold explanation
A lone neutron star, as seen by NASA's Hubble Space Telescope
€
B = avolA− asurf A2/ 3 − asym
(N − Z)2
A− aC
Z 2
A1/ 3−δ(A) +
35
Gr0A
1/ 3 M2
Let us consider a giant neutron-rich nucleus. We neglect Coulomb, surface, and pairing energies. Can such an object exist?
€
B = avolA− asym A+35
Gr0A
1/ 3 (mnA)2 = 0 limiting condition
More precise calculations give M(min) of about 0.1 solar mass (M⊙). Must neutron stars have
35Gr0mn2A2/3 = 7.5MeV⇒ A ≅ 5×1055, R ≅ 4.3 km,M ≅ 0.045M
⊙
€
R ≅10 km,M ≅1.4M⊙
Nuclear isomers
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.132501
Discovery of a Nuclear Isomer in 65Fe with Penning Trap Mass Spectrometry
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 de-excitation to the 180Ta ground state (which itself is radioactive by beta decay, with a half-life 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.