A new simple formula for fusion cross-sections of light nuclei

Abstract

The recent ENDF/B VII.0 data are compared with the fitting formula (NRL handbook—Plasma Formulary). The differences between experimental data and the fitting formula for three major fusion cross-sections reveal the need for a replacement to the old 5-parameter fitting formula. The new formula in this paper has only 3 parameters, but its fit with the experimental data is greatly improved because the energy dependence of the incident-channel (deuteron) width is taken explicitly into account through a penetrability function of the Mott form.

Resonant tunneling of deuteron-triton fusion in strong high-frequency electromagnetic fields

“…3, respectively. In the absence of field, our calculations are consistent with the experimental data [29]. Comparing with that of field-free case, the total fusion cross sections are enhanced in low-energy region while descrease in high-energy region.…”

“…Due to the lack of a full understanding of nuclear potential during fusion, the phenomenological complex potentials, also known as the "optical model" [27], are exploited to readily calculate fusion cross section within the framework of quantum scattering theory. A simple complex spherical square-well optical potential is widely applied to describe the nuclear potentials of light nuclear fusion [28][29][30][31] where an imaginary part of potential implies the decay of compound nucleus. This model only contains three parameters and can overcome the insufficiencies of Gamow tunneling formula: it shows that the tunneling and decay of compound nucleus are no longer independent in light nuclear fusion process and need to be combined as a selective resonant tunneling [30].…”

A Review of Fusion and Tokamak Research Towards Steady-State Operation: A JAEA Contribution

“…The wave front should be perpendicular to the classical hyperbolic orbit and the incident wave is modified as exp[ik{z + b 0 lnk(r − z)}], where b 0 = e i e j /(4 0 m r u 2 ) = 7.2 × 10 −10 Z i Z j /E r (eV), where (m) is the Landau parameter. In fact, as seen in Figure 2, the measured fusion cross-section is fitted well by the truncated summation of equation (1) as A recent paper [58] revisited this fusion reaction questioning the discussion above and gave a simpler three-parameter fitting based on the approximate analytical collision cross section using the optical potential (= U r + iU i ) for D + T reaction. This simpler formula gives better agreement with the fusion cross-section data at low energy.…”

Neutron emission from KSTAR Ohmically heated plasmas

“…Unfortunately, no spectra were taken in 2010 with a maximum energy calibration near 10 MeV. The spectra show photons above the threshold of 2.2 MeV for photo-nuclear dissociation of the deuteron [5]. Linear extrapolations of each spectrum taken at 2.5 s and later indicate that photons above 9 MeV would be expected.…”