Non-resonant reactions

Reactions may be either direct , where an energetic particle has such a small wavelength that it only sees one nucleon of the target, or compound nucleus reactions, where the projectile s energy is shared among many nucleons in successive collisions within a compound nucleus which can then decay into one of a number of exit channels (Fig. 2.6). The first case is the more common one in reactions between light nuclei, whereas the second dominates for heavier ones. 

The matrix elements in angle brackets contain nuclear factors and (in the case of charged particles) the Coulomb barrier penetration probabilities or Gamow factors, originally calculated in the theory of a-decay, which can be roughly estimated as follows (Fig. 2.7). 

A particle with energy E moving one-dimensionally along the negative x-axis in a potential V (x) is described quantum-mechanically by a plane wave 

The probability current is conserved for E V. When penetrating the barrier, E — V becomes negative and decays as g-C/ dv i2m(v(x)-E)]8x as particle moves from position x + 5x to position x. The total probability of 

Since a / (typically by a factor of order 100), the factor in brackets is nearly 7r/2 and is quite insensitive to the value of a. Numerically, the barrier penetration probability for 5-waves is thus 

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For non-resonant reactions, the. S -factor defined in Eq. (2.22) is a slowly varying quantity which can be replaced by an appropriate mean value, i.e. 

Stellar nuclear reactions can be either a) charged particle reactions (both target and projectile are nuclei) or b) neutral particle (neutron) induced reactions. Both sets of reactions can go through either a resonant state of an intermediate nucleus or can be a non-resonant reaction. In the former reaction, the intermediate state could be a narrow unstable state, which decays into other particles or nuclei. In general, a given reaction can involve both... 

The experimental determination of the reaction rate 12C(a, 7)lsO has been an important goal in nuclear astrophysics for several decades. Its cross section at the position of the Gamow window for a typical stellar temperature of 2.5 x 108K is comparable to that of weak interaction cross-sections. At those energies, this reaction is practically a non-resonant reaction and its cross-section is determined by the tails of interfering resonance and sub-threshold states [64]. The low cross section and the complexity of low energy contributions to the reaction rate makes a reliable prediction difficult [65,66]. 

Eor a non-resonant nuclear reaction with emission of an ion, a depth scale can be obtained from the measured energy of the emitted ions. If ions emitted from a depth x are lower in energy by AE than ions emitted from the surface, a relationship between AE and x can be found, similarly to RBS and ERDA analysis ... 

A general theory of the aromatic hydrocarbon radical cation and anion annihilation reactions has been forwarded by G. J. Hoytink 210> which in particular deals with a resonance or a non-resonance electron transfer mechanism leading to excited singlet or triplet states. The radical ion chemiluminescence reactions of naphthalene, anthracene, and tetracene are used as examples. 

Pulsed laser-Raman spectroscopy is an attractive candidate for chemical diagnostics of reactions of explosives which take place on a sub-microsecond time scale. Inverse Raman (IRS) or stimulated Raman loss (.1, ) and Raman Induced Kerr Effect (2) Spectroscopies (RIKES) are particularly attractive for singlepulse work on such reactions in condensed phases for the following reasons (1) simplicity of operation, only beam overlap is required (2) no non-resonant interference with the spontaneous spectrum (3) for IRS and some variations of RIKES, the intensity is linear in concentration, pump power, and cross-secti on. 

There is indirect evidence from hydrogen maser studies [221] that the reactions H + H2, HD, D2 (v = 1) show a preference for resonant exchange reactions in the case of H + H2 (v = 1) and H + HD(i> = 1) and for non-resonant exchange for H + D2 (v = 1) in accord with theoretical calculations [222]. With recent experimental developments, particularly UV lasers, it can be expected that spectroscopic methods will be applied to measuring energy disposal for these reactions. 

The effect of non-resonant laser fields upon the cross-section for simple chemical reactions ( laser-assisted collisions ) is currently of theoretical interest, and... 

Non-Resonant Charge Transfer Processes and Ion-Molecular Chemical Reactions of Positive and Negative Ions... 

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