LETTER TO THE EDITOR Journal of Radi oanalytical and Nuclear Chemistry, Vol. 231, Nos 1 2 (1998) 15 ~161 An empirical formula for (n, 2n) reaction cross sections in the neutron energy range of about 14.5 MeV Le Hong Khiem, Nguyen Van Do, Pham Duc Khue Institute of Physics, National Centerfor Natural Seience and Technology of Vietnam, P. O.Box 429, BOHO l O000 Hanoi, Vietnam (Received August 12, 1997) The (n,2n) threshold reaction cross-sections, available in the literature are analysed for nuclei with 20_<Z_<92in the neutron energy range of about 14.5 MeV. An empirical formula based on multiple regression technique is proposed for quick estimation of the (n,2n) reaction cross sections. The results obtained are compared with experimental data and those from other empirical formulae as long as by N-Z systematic. The validity of this formula is discussed. Introduction Nuclear reaction cross sections have played an important role in nuclear science and technology. Sometimes the data are not directly determined by measurements or the measured cross-sections are not in very good agreement with each other. In these cases the systematic analysis or the theoretical predictions of the data is very necessary. In a previous paper, 1 we presented an empirical formula for the quick estimation of (n,p) reaction cross sections at 14-15 MeV. Following this direction, in this paper we analyze the dependence of (n,2n) reaction cross sections on general parameters such as the asymmetry factor (N-Z)/A, neutron B n and proton Bp binding energies, threshold energy Ef based on the available experimental data using multiple regression technique. The experimental (n,2n) reaction cross sections are taken from a compilation. 2 The values of B n and Bp are taken from Reference 4. An empirical formula Various semi-empirical and empirical formulae have been used to obtain (n,2n) reaction cross sections at about 14.5 MeV neutron energy. The following formulae were given by BYCHKOV: "~ C~n,Zn (rob) = ( 100+A)[1-exp(-33 (N-Z)/A)[67(N-Z)/A-2] for (n-Z)/A < O.13 8n,2n (mb) = (100+A) [5.7+8.7(N-Z)/A] for (n-Z)/A > O.13 and by CHATTEJEE: 5 C~n,2n (mb) = 45.2(A 1/3+1)2 exp{-O.5(N-Z)/A } and by Lu and FINN: 2 C~n,2n (mb) = =61.6(A 1/3+1 )2 { 1-1.3919 exp [-8,744(N-Z)/A] } In these formulae only the dependence of (n,2n) reaction cross sections on the "asymmetry factor" (N- Z)/A was considered while the dependence on other parameters was adopted. In the present investigation the (n,2n) reaction cross sections were assumed to be a function of many parameters: N, Z, (N-Z)/A, Bn, B and Ef By the use of multiple regression technique tffe following empirical formula is proposed: C~n,2n (rob) = = c~ c {t0+t 1 (N-Z)/A+t2N+t3Z+t4Bn+t5Bp+t6E j} where C~c=(A1/3+1)2 is a neutron absorption cross section, El in MeV; B n and Bp in keV; to= 12.79668, t1=329.6125, t2=-1.557826, t3=2.109632, t4=- 1.7194E-03, t5 =-4.0913E-04, t 6 =-2.8959E-02. Validity and discussion Our formula was used for calculating the (n,2n) reaction cross sections of 107 isotopes. The data calculated by our and other empirical formulae together with the experimental data are listed in Table 1. The relative differences between the experimental and calculated values are given in brackets. From Table 1 it is seen that, when comparing with experimental data, in 47% of all cases our results give the best apl~roximation while BYCHNOV, 3 CHATTERJEE 5 and FINN L are 24%, 8%, 23%, respectively. Furthermore, we also see that calculated data from our formula for 94% of the nuclei agree with experimental results to within 20% but only 92%, 81%, 87% for BYCHNOV, CHATTERJEEand FINN. Those cases with large discrepancies turn out to be the lightest stable isotopes of even Z elements. The deviations between calculated and experimental values were divided into 20 groups with 5% interval. 0236 5731/98/USD 17.00 9 1998 Akad~miai Kiad6, Budapest All rights reserved Elsevier Science B. H, Amsterdam Akad~miai Kiad6, Budapest