Measurements of the D+D Reaction in Ti Metal with Incident Energies between 4.7 and 18 keV

Abstract

The D+D reactions in Ti metal were investigated for the deuteron incident energies between 4.7 and 18 keV. Observed were protons, tritons and 3 He particles emitted in the deuteron bombardment on TiD x . Thick target yields for the D(d, p) T and D(d, n) 3 He reactions were measured at bombarding energies down to 4.7 and 5.4 keV, respectively, for the first time. They were well explained with the reported astrophysical S-factors which were deduced from gas target measurements at E d > 6 keV for the D(d, p)T reaction and E d > 13.3 keV for the D(d, n) 3 He reaction. The cross section ratio σ(d, p)/σ(d, n) was obtained down to 6.4 keV, and was found to be constant at around 1.0 for E d <20 keV. KEYWORDS: D+D reaction in Ti, D(d, p)T and D(d, n)3 He reactions, thick target yields, astrophysical S-factor, cross section ratios §1. Introduction At energies far below the Coulomb barrier, cross sections of nuclear reactions are essentially dominated by the Coulomb penetration factor. An astrophysical S-factor, which contains information on pure nuclear part, is deduced by dividing the reaction cross section by the Coulomb penetration factor of two nuclei. Recently, in several reactions with light nuclei, such as the 3 He + d, 6,7 Li + d and 6,7 Li + p reactions, the deduced astrophysical S-factors for very low energies were found to be larger than those extrapolated from higher energy data.1,2) The deviation seems to occur below the incident energy of about 20 keV for the 3 He + d reaction and about 80 keV for the Li+p,d reactions; corresponding classical closest distances at theses energies are 140 and 70 fm, respectively. Therefore, nuclei which sit each other in the distance farther than about 100 fm might experience a weaker repulsive potential than the Coulomb potential between the two bare nuclei. This behavior is associated with an effect of the screening caused by surrounding electrons, since the target nuclei are in the form of neutral atoms or molecules in the laboratory. However, the observed enhancement of the S-factors is not fully understood as the electron screening effect.3) Thus, measurements of reaction cross sections at very low energies under various circumstances are highly interested.

Strongly Enhanced DD Fusion Reaction in Metals Observed for keV D+Bombardment

“…[10][11][12][13] The screening energy in a solid was first deduced with Ti as the host and with protons detected from the D(d,p)T reaction. 12) The result, U s ¼ 19 AE 12 eV, is almost the same as for the gas target.…”

Theoretical Interpretation of Anomalous Enhancement of Nuclear Reaction Rates Observed at Low Energies with Metal Targets

“…There is an indication of this prediction on c from recent deuteron beam experiments. Kasagi et al 7) find that a PdO target produces a larger enhanced rate for the reaction D(d,p)T compared with Pd target, and Cruz et al 14) find that a PdLi target produces larger enhanced rates for the reactions 7 Li(p,) 4 He and 6 Li(p,) 3 He, compared with a Li target. We suggest additional experimental tests of this type to be done in order to confirm this theoretical prediction.…”

“…18) For their case of eðR D Þ > kT, the corresponding Poisson equation for ðrÞ is a non-linear equation for which we do not know its solution at present. Furthermore, the classical plasma theory of Debye is valid only if there are enough particles (electrons) in the cloud, N D ) 1, where N D ¼ ð4=3Þn 0 R D 3 . For the above case, N D % 3 Â 10 À5 , and hence the Debye theory may not be applicable for this case as pointed out by Coraddu et al 19) More recently Coraddu et al [19][20][21] used a modified momentum distribution introduced by Galitskii and Yaki-mets, 22) in an attempt to explain the anomalies.…”

“…In 1988, an anomalous enhancement of the low-energy fusion cross-section was observed by Engstler et al for the reaction 3 He(d,p) 4 He, 1) and then in 1995 by Greipe et al for (D+D) fusion. 2) Experimental probes of low-energy nuclear reactions in metals with deuteron beams were first suggested in 1995 by Kasagi et al 3) Anomalously large values of electron screening energies, U e , were observed by Yuki et al 4,5) with ytterbium (Yb) target 4) in 1997, and with palladium (Pd) and palladium oxide (PdO) targets 5) in 1998. Since then, there have been many experimental observations of anomalous values of U e with other metal targets, [6][7][8][9][10][11][12][13][14] which have much larger values than atomic electron screening potential energies, U A .…”

“…IV. Values of f ðE b Þ, ÁxðE b Þ,V int ðE b Þ, V int ðE b ÞR Q ij , R btij ðE b ; U A Þ, and R ij at different values of the beam proton kinetic energy E b for the 6 Li(p,)3 He reaction calculated from eqs (19),. (1b)-(3b), (1),(14),(10), and (16), respectively.E b (keV) f ðE b Þ eq.…”