Excitation functions of some neutron threshold reactions on isotopes of molybdenum

Cross sections were measured for (n,p) reactions on ^{92, 95, 96, 97, 98}mo, (n, α) reactions on ^{92, 98}Mo, and (n, 2n) reaction on ¹⁰⁰Mo for the first time in the neutron energy range of 5.9 to 9.6 MeV. The quasi-monoenergetic neutrons were produced via the ²H(d, n)³He reaction using a deuterium gas target at a compact cyclotron. Use was made of the activation technique in combination with high-resolution γ-ray spectroscopy. Some systematic trends observed in the excitation functions are discussed. For the various isotopes of molybdenum, with increasing mass of the target nucleus, the thresholds of (n,p) and (n,α) reactions increase and the magnitudes of cross sections near the maxima of the excitation functions appear to decrease. Hauser-Feshbach calculations show that in general the excitation functions of (n, p) and (n, α) reactions are described within a factor of 2 by the statistical model only up to about 8 MeV; the (n,2n) reaction on ¹⁰⁰Mo, however, is reproduced well from threshold up to 15 MeV by this model.     

Reactions on 209Bi induced by intermediate energy protons and the effect of direct reactions

Excitation functions and ranges of recoil nuclei in the ²⁰⁹Bi(p, 3n)²⁰⁷Po, ²⁰⁹Bi(p, 4n) ²⁰⁶Po and ²⁰⁹Bi(p, p3n)²⁰⁶Bi reactions have been measured for incident energies from 18 MeV up to 52 MeV. It has been found that the recoil ranges in (p, p3n) reactions are rather shorter than those in (p, 4n), and that beyond E_p = 40 MeV the high energy tail of the excitation function for (p, p3n) is roughly flat, in contrast to the decreasing tail for (p, 4n). A theoretical analysis of the excitation functions and of the nuclear recoil ranges has been made. It has been found that in (p, p3n) reactions the direct process plays a very important part in the reaction mechanism. It is also found that the reaction mechanisms of (p, 3n) and (p, 4n) reactions should be interpreted by means of an admixture of the equilibrium compound process and the pre-equilibrium decay process at bombarding energies up to 40 MeV and 50 MeV, respectively, and that the direct process seems to appear at bombarding energies higher than these respective energies.     

A study of reaction rates of (n, f ) , (n, \gamma) and (n, 2n) reactions in natU and 232Th by the neutron fluence produced in the graphite set-up (GAMMA-3) irradiated by 2.33 GeV deuteron beam

Spallation neutrons produced in the collision of a 2.33GeV deuteron beam with a large lead target are moderated by a thick graphite block surrounding the target and used to activate the radioactive samples of ^natU and Th put at three different positions, identified as holes “a”, “b” and “c” in the graphite block. Rates of the (n, f), (n, $ \gamma$ and (n, 2n) reactions in the two samples are determined using the gamma spectrometry. The ratios of the experimental reaction rates, R (n, 2n)/R (n, f), for ²³²Th and ^natU are estimated in order to understand the role of the (n, x n) kind of reactions in Accelerator-Driven Sub-critical Systems. For the Th-sample, the ratio is ～ 54 (10)% in the case of hole “a” and ～ 95 (57)% in the case of hole “b” compared to 1.73(20)% for hole “a” and 0.710(9)% for hole “b” in the case of the ^natU sample. Also the ratio of fission rates in uranium to thorium, ^natU (n, f)/ ²³²Th (n, f), is ～ 11.2 (17) in the case of hole “a” and 26.8(85) in hole “b”. Similarly, the ratio ²³⁸U (n, 2n)/ ²³²Th (n, 2n) is 0.36(4) for hole “a” and 0.20(10) for hole “b” showing that ²³²Th is more prone to the (n, x n) reaction than ²³⁸U . All the experimental reaction rates are compared with the simulated ones by generating neutron fluxes at the three holes from MCNPX 2.6c and making use of the LA150 library of cross-sections. The experimental and calculated reaction rates of all the three reactions are in reasonably good agreement. The transmutation power, P _norm as well as P _norm/P _beam of the set-up is estimated using the reaction rates of the (n, $ \gamma$ and (n, 2n) reactions for both the samples in the three holes and compared with some of the results of the “Energy plus Transmutation” set-up and TARC experiment.     

A study of (n,nα) reaction cross sections at 14.7 MeV

Cross sections for (n, nα) reactions induced by 14.7 ± 0.3 MeV neutrons on ⁵¹V, ⁹²Mo, ¹¹⁵In, ¹⁶⁵Ho and ¹⁷⁶Yb have been measured by the activation technique using radiochemical separations and high resolution γ-ray spectroscopy or low-level β⁻counting. A brief summary of the activation data reported in the literature is given and a tentative trend in the data is suggested. The contribution of the (n, nα) process generally amounts to between 10 and 15% of the (n, α) cross section; in some cases, however, it is as low as 0.5%. The summed (n, α) and (n, nα) reaction cross sections obtained by the activation technique are generally in agreement with those deduced from emitted α-particle characterisation as well as mass spectrometry. Detailed Hauser-Feshbach calculations show that the statistical model can describe the (n, nα) cross section only with partial success.     

Isomeric cross-section ratios in (n,t) reactions on some medium- and heavy-mass nuclei at 14.6 MeV

Cross sections were measured for the first time for the reactions ⁷⁹Br(n, t)^77mSe, ⁸⁸Sr(n, t)(^86mRb, ¹¹³In(n, t)^111mCd, ¹²⁷I(n, t)^125mTe, ¹⁴¹Pr(n, t) ^139mCe, ¹⁶⁹Tm(n, t)^167mEr and ¹⁸¹Ta(n, t)^179mHf at 14.6±0.4 MeV using the activation technique, wherever necessary radiochemical separations, and high-resolution γ-ray spectroscopy. The data lie between 10 and 120 μb. A brief review of isomeric cross-section ratios measured in (n, t) reactions is given, and the ratios are compared qualitatively with those obtained in low-energy (n, γ) reactions as well as in high-energy (n, 2n) processes. The isomeric cross-section ratios are influenced by the reaction energy available and are dependent on the spin of the isomeric state. In (n, t) reactions nuclear states with spins between $\text{3}\text{2}$ and 3 seem to be preferentially populated.     

Deconfinement phase transition in a two-dimensional model of interacting 2 × 2 plaquettes

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Activation cross-sections of titanium isotopes at neutron energies of 13.5–14.8 MeV

The cross-sections for ~(46) Ti(n,2 n)~(45) Ti, ~(46) Ti(n,p)~(46 m+g) Sc+~(47) Ti(n,d*)~(46 m+g) Sc, ~(46)Ti(n,p)~(46 m+g) Sc, ~(47) Ti(n,p)~(47) Sc+~(48) Ti(n,d*)~(47) Sc, ~(47) Ti(n,p)~(47) Sc, ~(48) Ti(n,p)~(48) Sc+~(49) Ti(n,d*)~(48) Sc,~(48) Ti(n,p)~(48) Sc, and ~(50) Ti(n,α)~(47) Ca reactions were investigated around neutron energies of 13.5–14.8 Me V by means of the activation technique. Fast neutrons were produced by the~3 H(d,n)~4 He reaction. Neutron energies from different directions in the measurements were obtained in advance using the method of cross-section ratios for ~(90) Zr(n,2 n)~(89 m+g) Zr and ~(93) Nb(n,2 n)~(92 m) Nb reactions. The results obtained are analyzed and compared with the experimental data provided by the literature and verified nuclear data in the JEFF-3.3,CENDL-3.1, ENDF/B-VIII.0 libraries, as well as results calculated by Talys-1.9 code.     

Optimal reactions for the synthesis of superheavy nucleus 270Hs

The superheavy nucleus ²⁷⁰Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions ²⁴⁸Cm(²⁶Mg,4n)²⁷⁰Hs, ²⁴⁴Pu(³⁰Si,4n)²⁷⁰Hs, ²³⁸U(³⁶S,4n)²⁷⁰Hs and ²²⁶Ra(⁴⁸Ca,4n)²⁷⁰Hs using a two-parameter Smoluchowski equation. It is found from our results that ²²⁶Ra(⁴⁸Ca,4n)²⁷⁰Hs and ²³⁸U(³⁶S,4n)²⁷⁰Hs are two optimal reactions for the synthesis of the superheavy nucleus ²⁷⁰Hs due to their large negative Q-values.     

贫铀球壳中D-T中子诱发的铀反应率的测量与分析

为校验次临界能源堆的概念设计,在R19.4/30.0 cm的贫铀球壳装置上采用活化法开展14 MeV中子学积分实验.布放6片贫铀活化片于球壳中与入射D离子束90°方向上的不同位置处活化,用HPGe探测器测量238U(n,γ)反应、238U(n,f)及235U(n,f)反应和238U(n,2n)各反应产物发射的特征γ射线,得到了相应的反应率.238U(n,γ)反应率的不确定度为3.6％-3.7％,238U(n,D和235U(n,f)反应率的不确定度为5.1％-5.9％,238U(n,2n)反应率的不确定为4.3％-4.7％.用MCNP5程序在ENDF66c数据库下进行模拟计算,238U(n,γ)反应率的计算值/实验值(C/E)为0.972-1.034,238U(n,f)和235U(n,f)反应率的C/E为0.983-1.058,238U(n,2n)反应率的C/E为0.979-1.019.     

Critical consideration of the statistical model analysis of photonuclear isomeric cross-section ratios

We have measured isomeric cross-section ratios for the photonuclear reactions ¹⁸¹Ta(γ, 3n) ^178m,gTa, ¹⁴²Nd(γ, n)^141m,gNd, ¹¹⁰Pd(γ, n)^{109m₁,m₂,g}Pd, ¹⁰⁸Pd(γ, n)^107m₁,m₂Pd, ¹⁰⁰Mo(γ, n) ^99m,gMo, ⁹²Mo(γ, n)^91m,gMo and ⁸⁹Y(γ, n)^88m₁,m₂Y. The experimental results were compared with statistical model calculations according to the method of Huizenga and Vandenbosch. The applicability and limits of this method, especially the simple decision model for the population of the isomeric state and the ground state of the residual nucleus, were tested and discussed. Additionally, it is shown that for photonuclear reactions on magic nuclei, contributions of a direct reaction mechanism are not negligible.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

A systematic study of (n,d), (n,n' p) and (n,pn) reactions at 14.7 MeV

Cross sections for [(n, d) + (n, n′p) + (n, pn)] reactions induced by 14.7 ± 0.3 MeV neutrons on ⁴⁴Ca, ⁴⁹Ti, ⁵⁰Cr, ^{67, 68}Zn, ⁹²Zr and ^{97, 98}Mo have been measured by the activation technique using enriched isotopes as target materials, modern radiochemical separations and high-resolution counting methods. A brief summary of the literature data and our own earlier measurements is given. Our activation data are generally in agreement with those deduced from emitted charged particle characterisation. Some systematic trends in the activation cross-section data were analysed. Similar to other (n, charged particle) reactions, the [(n, d) + (n, n′p) + (n, pn)] reaction cross section decreases as a function of (N?Z)/A; the data, however, fall on two curves, one for nuclei with neutron separation energies (S_n higher than the proton separation energies (S_p) and the other for nuclei with S_n < S_p. For nuclei with S_n ? S_p the (n, n′p) process is very important. Detailed Hauser-Feshbach calculations show that in general contributions of statistical processes to the (n, d) reaction cross section are very small.     

Study of the excitation of high-spin isomers in <Superscript>190</Superscript>Ir and <Superscript>196,198</Superscript>Au in the near-threshold region

The isomeric ratios of the yields for ^190m,g Ir and ^196m,g Au have been measured in the (γ,n) reaction in the near-threshold region at γ-ray energies of 12 and 12.5 MeV. The isomeric ratios for ^198m,g Au have been measured in the (d,p) and (n,γ) reactions. The statistical nature of the (γ,n) and (n,γ) reactions is shown.     

Ground and γ-vibrational bands in even Os isotopes (A = 182–188) studied by (α, χnγ) and (p, χnγ) reactions

Gamma rays following ¹⁸²W(α, 2n)¹⁸⁴Os, ¹⁸⁴W(α, 2n)¹⁸⁶Os, ¹⁸⁶W(α, 2n)¹⁸⁸Os, ¹⁸⁵Re (p, 2n)¹⁸⁴Os, ¹⁸⁵Re(p, 4n)¹⁸²Os, ¹⁸⁷Re(p, 2n)¹⁸⁶Os and ¹⁸⁷Re(p, 4n)¹⁸⁴Os reactions have been measured to study the ground and γ-vibrational bands in even Os isotopes (A = 182–188). In addition to the ground-state levels the γ-vibrational bands have been identified up to the 5⁺ members. The K = 4 band head is proposed in ¹⁸⁶Os and ¹⁸⁸Os.     

The excitation functions and Isomer ratios for neutron-induced reactions on Mo and Zr

Absolute cross sections of the reactions ⁹²Mo(n, 2n)^91m,91gMo, ⁹²Mo(n, p)⁹²Nb and ⁹²Mo(n, α)^{89m, 89g}Zr, relative cross sections of the reaction ⁹⁰Zr(n, 2n) ^89mZr and isomer ratios of the ⁹⁰Zr(n, 2n) reaction have been measured in the neutron energy range 13–15 MeV. The results for the (n, 2n) reactions are in good agreement with those of the previous studies. The present results for the (n, p) and (n, α) reactions are in disagreement with the previous works. The experimental data are analysed by the statistical model to determine the level-density parameter a, the moment of inertia ? and the strength of the γ-ray transition S_l in order to simultaneously reproduce the experimental data on the excitation function and the isomer ratio in the (n, 2n) reaction. The γ-ray competition, the yrast level and the experimental information on the excited levels of the residual nucleus in the (n, 2n) reaction are taken into account. The obtained values of a, ? and S_l are consistent with those deduced from other types of nuclear data.     

Cross-sections for the formation of isomeric pair Ge through (n, 2n), (n, p) and (n, α) reactions measured over 13.73 MeV to 14.77 MeV and calculated from near threshold to 20 MeV neutron energies

The cross-sections for formation of isomeric pair, ⁷⁵Ge^m(σ_m) and ⁷⁵Ge^g(σ_g), through ⁷⁶Ge(n, 2n), ⁷⁵As(n, p) and ⁷⁸Se(n, α) reactions were measured at 13.73 MeV, 14.42 MeV and 14.77 MeV neutrons and also estimated using EMPIRE-II and TALYS codes over neutron energies from near threshold to 20 MeV. For each (n, 2n), (n, p) and (n, α) reaction, the cross-section initially increases with neutron energy, but starts decreasing as the neutron energy exceeds the respective threshold of (n, 3n), (n, pn) and (n, αn) reactions. The higher values of σ_m relative to σ_g reveal that the transitions of the excited ⁷⁵Ge from higher energy levels to metastable state (7⁺/2) are favored as compared to unstable ground state (1⁻/2). The present values of cross sections for formation of ⁷⁵Ge^m,g through (n, 2n) and (n, α) reactions are lower, and that of (n, p) reaction are higher compared to most of the corresponding literature cross-sections.     

Application of hyperspherical close-coupling method to antiproton collisions with muonic hydrogen

The cross sections for p^- + (Hμ^-)_1s (H = p, d, t) are calculated in the hyperspherical close-coupling method for collision energies below the (Hp^-)_n=4 threshold. The results show good convergence with respect to basis size. The formation cross section of (Hp^-)_n=2 is dominant and two orders of magnitude larger than that of (Hp^-)_n=1 below the (Hp^-)_n=3 threshold, while the (Hp^-)_n=3 formation cross-section exceeds that for (Hp^-)_n=2 formation above the (Hp^-)_n=3 threshold. Resonance parameters are also calculated below thresholds of (Hp^-)_n=2-4.     

Effect of high density of states in the presence of interchain coupling on the transition temperature

The combinationN(0)I ² (N(0)-electronic density of states at the Fermi level,I ²-electron-phonon coupling constant) is calculated in the tight-binding approximation for the ₂ band of V₃Si. In this model the density of states can be very high even when strong interchain coupling is present. It is found thatI ² is almost insensitive to changes in the interchain coupling, and that a significant increase inN(0)I ² of this model can be achieved only for low occupation numbers of the ₂ band.Work supported by a grant from the National Council for Research and Development, Israel and KfK (Kernforschungszentrum, Karlsruhe, FRG)