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

Radiocarbon Dating

http://www.answersingenesis.org/assets/images/articles/nab/1-carbon.gif

•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