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

I. Tanihata et al., PRL 55 (1985) 2676 Halos

For super achievers:

HUGED i f f u s e d

PA IR ED4He 6He 8He

Neutron Drip line nuclei

5He 7He 9He 10He

Pairing and binding

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.