In this study, we have suggested a new empirical formula to reproduce the cross sections of the (n, p) reactions at 14–15 MeV for the neutron incident energy. This formula obtained using the asymmetry parameters represents a modification to the original formula of Levkovskii. The resulting modified formulae yielded cross sections, representing smaller χ2 deviations from experimental values, and values much closer to unity as compared with those calculated using Levkovskii's original formula. The results obtained have been discussed and compared with the existing formulae, and found to be well in agreement, when used to correlate the available experimental σ(n, p) data of different nuclei.

https://iopscience.iop.org/article/10.1088/0954-3899/29/9/311/pdf

A new empirical formula for 14 15 MeV neutron-induced (n, p) reaction cross sections

In this study we propose new semi-empirical formulas by modifying the formula of Levkovskii with the new parameters for (n, 2n) and (n, α) reactions cross-sections at 14–15 MeV neutron incident energy The cross sections have been calculated using the asymmetry parameter depending on empirical formulas for the incoming energies of 14–15 MeV neutrons The parameters obtained by modifying the original formula of Levkovskii and Konno et al have been determined by applying the least squares fitting method to the experimental cross sections, and the systematics of the (n, 2n) and (n, α) reactions have been studied We have also suggested different parameters for the empirical formula to reproduce the cross sections of the (n, 2n) and (n, α) reactions for the neutron incident energy of 14–15 MeV The modified formulas yielded cross sections representing markedly smaller chi-square (χ2) deviations from experimental values, and values much closer to units as compared with those calculated using Levkovskii's and Konno et al original formulas The results obtained have been discussed and compared with the other empirical formulas, and found to be well in agreement when used to correlate the available experimental σ(n, 2n) and σ(n, σ) data of different nuclei

SEMI-EMPIRICAL SYSTEMATICS OF (n, 2n), (n, α) REACTIONS CROSS SECTIONS AT 14–15 MeV NEUTRON ENERGY

We measured activation cross sections via γ-ray spectroscopy using high-purity germanium detectors for 16 reactions induced by (14.4′0.2) MeV neutrons on isotopes of tin. The cross sections are: σ( 1 1 2 Sn(n, 2n) 1 1 1 Sn)= (1104′43) mb, σ( 1 1 2 Sn(n, p) 1 1 2 m In) = (33.6′2.1) mb, σ( 1 1 2 Sn(n, p) 1 1 2 g In) = (42.7′3.1) mb, σ( 1 1 4 Sn(n, 2n) 1 1 3 Sn) = (1270′115) mb, σ( 1 1 4 Sn(n, p) 1 1 4 m 2 In) = (20.5′1.1) mb, σ( 1 1 5 Sn(n, p) 1 1 5 m In) = (35.2′2.6) mb, σ( 1 1 6 Sn(n, p) 1 1 6 m 2 In) = (11.1′0.5) mb, σ( 1 1 7 Sn(n, np) 1 1 6 m 2 In) =(1.35′0.11) mb, σ( 1 1 7 Sn(n, p) 1 1 7 m In) = (4.5′0.4) mb, σ( 1 1 7 Sn(n, p) 1 1 7 g In) = (12.8′0.7) mb, σ( 1 1 7 Sn(n, n') 1 1 7 m Sn) = (246′21) mb, σ( 1 1 8 Sn(n, 2n) 1 1 7 m Sn) = (816′70) mb, σ( 1 1 8 Sn(n, α) 1 1 5 g Cd) = (1.26′0.16) mb, σ( 1 2 0 Sn(n, α) 1 1 7 m Cd) = (0.27 ′ 0.04) mb, σ( 1 2 0 Sn(n, α) 1 1 7 g Cd) = (0.29′0.06) mb and σ( 1 2 4 Sn(n, 2n) 1 2 3 m Sn) = (590′26) mb. Two 1 1 2 Sn targets enriched to 62.5% and 84%, respectively, were used for these measurements in addition to the natural tin. The cross sections were compared with experimental data found in the literature, with published empirical formulae and with model calculations including also the pre-equilibrium contribution. For reactions which do not involve protons from below the closed Z = 50 shell, the agreement to the data is reasonable, it is somewhat weaker for the (n, p) reactions and still worse in the case of (n, a), where, however, the pre-equilibrium component is not described properly by the models included so far. The possibility of production of 1 1 1 Sn → 1 1 1 In generator system is considered.

Activation cross sections for reactions induced by 14 MeV neutrons on natural tin and enriched 112Sn targets with reference to 111In production via radioisotope generator 112Sn(n, 2n)111Sn → 111In

Empirical formulas for the 14 MeV (n, p) and (n, α)cross sections given by Levkovskii were modified separately In three ranges of mass number, in each of which, coefficients modifying Levkovskii's formulas were determined by least-squares fitting to experimental cross sections. The resulting modified formulas yielded cross sections representing markedly smaller chi-square deviations from experimental values, and moreover gathered closer to unity, compared with calculation using Levkovskii's original formulas.

Empirical Formulas for 14-MeV (n, p) and (n, α) Cross Sections

New empirical and semi-empirical formulae have been suggested for the (n, 3He) reaction cross-sections with dependent on asymmetry parameter, S = (N − Z)/A. The (n, 3He) reaction cross-sections at the energy of 14–15 MeV have been investigated for two different parameters groups by the classification of nuclei into 31 ≤ A ≤ 103 and 133 ≤ A ≤ 181. The obtained results have been compared with the other systematics and experimental data for the (n, 3He) reaction cross-sections. Some improvement has been got in describing the (n, 3He) reaction cross-sections compared with the existing relations.

A New Comparison of Empirical and Semi-empirical Formulae for the (n, 3He) Reaction Cross-sections at 14–15 MeV

Levkovskii's and Gardner's empirical formulas for 14 MeV neutron (n,p) cross sections can be shown to be mainly equivalent to the following approximation: subject to modifications from direct interaction. Here T is the nuclear temperature, given by 10/A1/2 and Vp′ is Dostrovsky's value of the effective Coulomb barrier. Qnp′ is the effective Q value calculated using the mass formula in which B and Z0/A are shell-independent parameters.

H. L. Pai

Papers

Empirical formulas for 14 MeV (n,p) cross sections