Structure and Evolution of Single Stars: An Introduction by James MacDonald

Author:James MacDonald
Language: eng
Format: epub
ISBN: 9781681741055
Publisher: IOP Publishing
Published: 2015-11-21T00:00:00+00:00

Here

(11.19)

Since S(E) is a slowly varying function of E, we see that the energies which give the dominant contribution to the integral are those near where the argument of the exponential is stationary. This occurs at energy

(11.20)

where T6 is the temperature in units of 106 K.

For fusion of hydrogen at the solar center, E0 = 6 keV. This is higher than the typical particle energy of 1 keV but much less than the energy needed for fusion in the absence of quantum tunneling, which is of order 1 MeV.

The integral in equation (11.17) is usually performed by some variation of the method of steepest descent. The argument of the exponential term is first expanded in a Taylor series about its stationary point,

(11.21)

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