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Realistic nuclear interactions and the problem of the radiocarbon
dating beta decay
Jeremy W. Holt*
* Thesis Advisor: Gerry Brown (+ Tom Kuo)
Nuclear Theory Group
The Nuclear Force
• Parameterize with meson exchange
1 fm
1 Ångstrom
1 fm = 110–15 m1 Ångstrom = 110–
10 m
http://content.answers.com/main/content/wp/en/thumb/f/fd/300px-Helium_atom_QM.svg.png
• Two-body interactions alone cannot describe saturation point
Nuclear matter saturation
A and V
A nucleons in a volume V
A/V = n (constant)
http://www.shef.ac.uk/physics/teaching/phy303/np-6.gif
n
Z. Li et al., PRC 74 (2006) 047304
• Hadronic mass generated dynamically
http://zms.desy.de/sites/site_www/content/e409/e4948/e4950/e4963/e4965/hera_proton_ger.jpg
• u and d quark masses: 5 – 10 MeV/c2• p and n masses: 950 MeV/c2
2/ cEm
8.0)( 0 nN
N
A
A
m
m
g
g
m
m
m
m
m
mn
)(
Original Brown-Rho scaling
G. Brown and M. Rho, PRL 66 (1991) 2720
Tensor force
In-medium nuclear force
Problem
11C 11B + e+ + 1.98 MeV 20.4 min
Decay mode Decay energy Half-life
13N 13C + e+ + 2.20 MeV 10.0 min
14O 14N + e+ + 5.14 MeV 1.18 min
15O 15N + e+ + 2.75 MeV 2.04 min
14C 14N + e– + 0.156 MeV 2109 min
e
e
eee
All allowed decays
•Carbon-14 continuously replenished in atmosphere
• Half-life of carbon-14 is 5760 years
• Can date objects up to about 50,000 years old
• Invented in 1949 by Willard Libby at the University of Chicago
• Revolutionized absolute archaeological dating
• Nobel Prize in Chemistry 1960 for invention of radiocarbon dating
8 neutrons6 protons 7 neutrons
7 protons
Carbon-14 Nitrogen-14
Beta-minus Decay
Antineutrino Electron–
http://education.jlab.org/glossary/betadecay.gif
1949: Nuclear physics still in infancy
1950’s: Nuclear shell model developed
Predictions showed that the decay should not be suppressed
How to calculate the lifetime of Carbon-14
2
,
45
73
02/1
)(
2ln2
),(
1
iiffM
e MJOMJcmEZfT
f
14C
14N
(J,T) = (0+,1)
(J,T) = (1+,0)
– 0
30
1 PySxi
13
11
13 DcPbSaf
3/6 ybxaM GT
3102)()(
kifGT kkM
• Gamow-Teller matrix element highly sensitive to nuclear tensor force
Results
• Suppression due largely to decreasing tensor force
Archaeologically long half-life for densities ~ 0.80-0.85 n0
J. W. Holt et al., PRL 100 (2008) 062501
3/6 ybxaM GT
03
01 PySxi
13
11
13 DcPbSaf
“A new calculation explains the mechanism behind carbon dating”
--Physics News Update, Number 854 #1, January 23, 2008 by Phil Schewe
“Solving the carbon-14 mystery”
--ScienceNOW Daily News, January 28, 2008, by Phil Berardelli
“Unravelling carbon’s chemical secrets”
--NatureNews, February 1, 2008, by Rachel Courtland
“Chance structure makes carbon dating possible”
--PhysicsWorld.com, January 31, 2008, by Belle Dumé
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