Statistical theory of precompound reactions: The multistep compound process

doi:10.1016/0003-4916(86)90020-5

Annals of Physics

Volume 172, Issue 1, November 1986, Pages 67-99

https://doi.org/10.1016/0003-4916(86)90020-5 Get rights and content

Abstract

Using a quantum-statistical framework, the method of the generating function involving both commuting and anticommuting variables, and the saddle-point approximation followed by the loop expansion, we derive a theoretical framework for multistep-compound reactions. Our statistical input distinguishes between several classes of states of increasing complexity; this distinction is possible only at the expense of relinquishing the orthogonal invariance of the distribution of Hamiltonian matrix elements usually required in compound-nucleus theories. Our result contains both the compound-nucleus scattering cross section and the theory of Agassi Weidenmüller, and Montzouranis (Phys. Lett. C22 (1975), 145.) developed earlier as special cases. It goes beyond this theory, and extends the framework of precompound theories in general, by allowing the couplings between classes, and to the channels, to be reasonably strong. A self-consistency condition embodied in the saddle-point equation implies in this case that the level densities used in precompound calculations must be modified. We investigate the modification in simple model cases. Our results suggest that the modification may be relevant for the high-energy tail of the spectrum of precompound particles.

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As shown in Fig. 9 (for 30° and 60° angles emission) and 10 (for the calculated angle integrated proton particle emission spectra at 14.8 MeV) the parameters of the optical model for neutrons (N.Yamamuro (1988)) and for protons (Koning and Delaroche (2003)) affect strongly the results. In Fig. 9 (for 120° angle emission) and 11 (for 30°, 60° and 120° angles emission), the obtained of the cross sections values for 60Ni(n, xp) reaction in terms of MSD and MSC models (Tamura et al., 1982; Nishioka et al., 1986) are in a good agreement with the experimental result (Graham et al., 1987; Grimes et al., 1979). The principal input parameters used in the two-component exciton model (Fu, 1984) calculations at the 9.4 and 11 MeV neutron incident energies for (30°, 60° and 120° angles emission) by using TALYS 1.8 code (Koning et al., 2007) are summarized in Table 4.
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^∗: Now at Department of Physics, University of Illinois, Urbana-Champaign, Illinois.

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Annals of Physics

Abstract

References (11)

Phys. Lett. C

Ann. Phys. (N. Y.)

Phys. Lett. C

Nucl. Phys. B

Ann. Phys. (N.Y.)

Cited by (120)

Activation cross section for the (n,2n) and (n,p) reactions on <sup>103</sup>Rh, <sup>48</sup>Ti and <sup>52</sup>Cr from reaction threshold up to 25 MeV energy region

Preequilibrium models for <sup>58</sup>Ni (n, xp) and <sup>60</sup>Ni (n, xp) reactions in neutrons at 8, 9, 9.4, 11 and 14.8 MeV using the EMPIRE and TALYS codes

Isomeric cross sections of the (n, α) reactions on the <sup>90</sup>Zr, <sup>93</sup>Nb and <sup>92</sup>Mo isotopes measured for 13.73 MeV–14.77 MeV and estimated for 10 MeV–20 MeV neutron energies

Calculations for the nuclear reaction cross-sections via α-particle induced reactions on <sup>65</sup>Cu to produce impurity free <sup>67</sup>Ga for medical applications

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Integral cross section of isomeric state formation in (neutron,nucleon) reactions using an Am–Be source