Cosmogenic Isotopes:Production Rates

Matt BaillieHWR 696T

2/26/04

The Olden Days

• Elsaesser et al. (1956)– As a first order estimation, the global nuclear

disintegration rate can be described by:

– Where:• Q = global nuclear disintegration rate at field strength M

• M0 is the reference strength (strength of the present field)

• QM0 is the nuclear disintegration rate at the present

field strength

5.0

0*constant

0

MM

QQ

M

M

The Olden Days• Lal (1967)

– Described an equation for production rate:

– Where:• Cj(x,λ) is the production rate in atoms per gram of air of a

nuclide j at an altitude which has an atmospheric pressure of x gm/cm2 at geomagnetic latitude λ

• Ji is the differential energy spectrum of component I• N is Avagadro’s number• A is the atomic weight of the target• KT is the fractional abundance by weight of a particular target

nuclide T in the atmosphere• σi,j,T(E) is the cross section for the production of nuclide j in the

collision of a particle of component i and energy E with a target nuclide T

• θ and φ are the angles of incidence

E

iTjii

T

Tj dEddEExJ

A

NKxC

cos)(),,,,(),( ,,

The Olden Days

• Lal (1967)– However,

• The individual cross-sections as a function of energy are poorly known, so we cannot easily mathematically describe the production rate of a nuclide. It becomes necessary to rely on empirical methods to describe production rates of atmospherically-produced nuclides.

The Olden Days

• Lal (1967)– Begin with:

• Determine the altitudinal and latitudinal reliance of total nuclear disintegrations (Q) on slow neutron flux

• Measure absolute disintegrations in N, O, and Ar produced by cosmic rays using N- and Ar-filled cloud chambers at many different localities

– normalize measurements with 7Be produced in O: O has a known cross section, and the excitation function of 7Be in O is known

The Olden Days

• Lal (1967)– Production mostly achieved through spallation,

except for 14C and 81Kr, which are produced through thermal neutron capture

– At high pressures (>200 g/cm3), altitudinal and latitudinal effects are not important to the production rate directly, so production rate is porportional to the nuclear disintegration rate

• This proportionality does not hold for 3H and 3He, which are produced by secondary reactions within the nucleonic cascade

The Olden Days

• Lal (1967)– It is a fairly simple matter to derive current

production rates, by taking field measurements of the production of nuclides in the atmosphere

– If one can assume that current production rates can be extrapolated into the geologic past, then the direct measurement of production rate can be applied directly to old deposits of nuclides

– However, this is not generally the case. 14C ages, for example, were later shown to be off by well over 10% due to the differences in production rate over time

The Olden Days

• Lal (1967)– 14C can be calibrated using information from

meteorites (which presumably have not been shielded by magnetic fields or affected by altitude or latitude), although they get burned up partially in the atmosphere

– Can also use sediments containing atmospheric and oceanic 14C for the past 10,000 years, assuming that the systems are well-mixed

The Olden Days

• Lal (1967)– In addition to 14C, 26Al and 10Be production in the

atmosphere can be calibrated using slowly accumulating sediments, giving a much longer record

• Indicates that atmospheric production of 26Al and 10Be has been approximately constant for the last 80,000 years

The Olden Days

• Lal (1967)– Determined that 3H production is approximately

inversely proportional to solar activity– In times of greater solar activity, production rates are

decreased• At solar activity maximum in 1958, production was

decreased as much as 22% as compared with 1948-1949

The Olden Days

• Lal (1967)– Uncertainties involved: other sources of isotopes

• Solar neutrons• Solar tritium• Galactic influx of isotopes

The Olden Days

• Lal (1967)– In addition to atmospheric production, terrestrial

production (in-situ) must be considered• Production by natural radioactivity causes increased

production rates when in the presence of a radioactive source which releases neutrons

• Natural secondary cosmic ray interactions cause different depth dependence of production rates depending on the particle type

• Extraterrestrial influx of nuclides such as 53Mn and 59Ni, which are not produced on earth

– Finally, geospheric circulation can complicate production by enriching and depleting areas of nuclides

The New School

• Lal (1988)– The production rate of a nuclide depends directly on

the nuclear disintegration rate multiplied by the average yield of a nuclide

– Solar activity is inversely proportional to cosmic ray flux (sunspot minima are reflected in the 14C records

– Low magnetic field intensity leads to a greater effect by solar modulation on production rates of nuclides

The New School

• Lal (1990)– “Absolute nuclide production rates cannot generally

be predicted with any accuracy because of lack of data on excitation functions of nuclides unless some normalization is possible, as was done in the case of several cosmic ray produced isotopes in the atmosphere.”

– Studied 10Be and 26Al in “zero” erosion quartz• Production rate is based on latitudinal/altitudinal in-situ

production in glacially exposed quartz• Uncertainties include age of exposure, and secular

variations in magnetic field intensity

The New School

• Lal (1990)– 14C directly measured in quartz (produced by

spallation of Si and O) and extrapolated based on altitude and latitude

– Noble gases estimated based on poorly-constrained proton excitation functions (and therefore tentative)

The New School

• Bard (1990)– Calibrated 14C dating based on U-Th ages

• Large error in 14C ages with samples beyond 20,000 years before present

• U-Th ages accurate to within 100 years between 6 and 20ky BP

• U-Th ages match dendrochronological ages