THE ENERGY DEPENDENCE OF THE D-D REACTION CROSS SECTION AT LOW ENERGIES

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1962

OSTI ID:4728635

Coyne, J J

The energy variation of the cross section for the D--D reaction can be attributed to the influence of the Coulomb and centrifugal barriers on the approach of the two deuterons. The approach cross section as a function of the energy was calcuiated using several differert methods. The simplest method assumed strong absorption inside the nuclear surface and used the WKB approximation. The results fell on a straight line on a Gamow plot, which is a graph of the nntural logarithm of the product of the cross section times the energy as a function of one over the square root of the energy. Thus the slope of the Gamow plot, called the Gamow factor, was a constant. A more accurate strong absorption calculation was performed using exact Coulomb wave functions in place of the WKB approximation. The results gave a negative energy dependent correction to the constant Gamow factor. Strong absorption implies that there is little coherent scattering from inside the nucleus to interfere with the approach of the incidert particle. However, in the D--D reaction, coherent scattering from inside the nucleus is very probable, so a weak absorption model seemed more applicable. Calculations were, therefore, carried out using a model that ignores the effect of absorption in calculating the approach cross section. It was found that both positive and negative corrections to the constant Gamow factor were possible with the weak absorption modei. Finally, since the amount of absorption seemed important, the effects of absorption were studied using the optical model and varying the ratio of the real and imaginary part of the potential. For very small values of the imaginary part of the potential, the optical model results agreed with the weak absorption model as expected. The calculations, considered so far, included only S-waves. While the experimental results are usually given as a straight line on a Gamow plot, comparison of the results in different energy regions seem to indicate a positive correction to the Gamov factor as a function of the energy. If a more accurate energy dependence for the Gamow factor could be determined experimentally, the comparison of the results with the present calculations would give some information about the optical potential, which one deuteron sees when it approaches another deuteron. (P.C.H.)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-17-009297
• OSTI ID: 4728635
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ALPHA DECAY
BARRIERS
DIAGRAMS
ELECTRIC CHARGES
ELECTRIC FIELDS
GAMOW BARRIER
GAMOW FACTOR
NUCLEAR MODELS
OPTICAL MODEL
PHYSICS
PROBABILITY
QUANTUM MECHANICS
S-WAVE
SCATTERING
STATISTICS
WKB APPROXIMATION