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Kinematics of Open Cycle Mechanisms
Published in Ilie Talpasanu, Alexandru Talpasanu, Mechanics of Mechanisms and Machines, 2019
Ilie Talpasanu, Alexandru Talpasanu
With the skew-symmetric product shown in Equation (2.274): L˜EB0∗uB0=[0−zEByEBzEB0−xEB−yEBxEB0]∗{001}={0−xEB0}
The Basic Formalism of Field Theory
Published in A.N. Vasiliev, Patricia A. Millard, Functional Methods in Quantum Field Theory and Statistical Physics, 2019
A.N. Vasiliev, Patricia A. Millard
If a product of operator functionals appears inside some kind of symmetric product it is automatically symmetrized, and the usual expressions (1.45) and (1.46) can be used. For example, () T{∑i=1nFi(φ^)}=N{exp(12⋅δδφΔδδφ)∏i=1nFi(φ)}|φ=φ^.
Electrons and anti-symmetry
Published in David K Ferry, Quantum Mechanics, 2001
where P is the total number of permutations required to reach the configuration of the wave function on the left from that on the right of (9.20). Thus, if we have for example Ψ4ξ1,ξ2,ξ3,ξ4, then to get to Ψ4ξ4,ξ3,ξ2,ξ1 requires a total of six permutations (three to get ξ4 moved to the beginning, then two to bring ξ3 adjacent to it, and finally one more to interchange ξ2 and ξ1). Hence, this new example yields a symmetric product after the six interchanges. The general permuted wave function (9.20) then has the inner product with the original of () ΨNξ1',ξ2',…,ξN'∣ΨNξ1,ξ2,…,ξN=(-1)P.
Post-Neutron Mass Yield Distribution in the Epi-Cadmium Neutron–Induced Fission of 238Pu
Published in Nuclear Science and Engineering, 2023
H. Naik, R. J. Singh, S. P. Dange, W. Jang
It can be also seen from Fig. 4 that the mass yields of fission products in the epi-cadmium neutron–induced fission of 238Pu near the symmetric region are significantly higher than in the thermal neutron–induced fission of 238Pu. The higher yields of symmetric fission products are with the cost of yields of asymmetric fission products. This difference is due to the difference in excitation energy, which reflects in the peak-to-valley (P/V) ratio. Table I shows that the highest YA value for the asymmetric product of A = 134 is 7.331% ± 0.160% whereas for A = 102, it is 6.350% ± 0.043%. The average of these two values is 6.841% ± 0.491%. On the other hand, the yield of nearly symmetric products of A = 117 is 0.0957% ± 0.0156%. From the average YA values of 6.841% ± 0.491% and 0.0957% ± 0.0156%, the value of the P/V ratio was obtained as 71.5 ± 12.7 for the first time. If the yield of 0.0930% ± 0.0093% for an exact symmetric product with A = 118 is considered, then the P/V ratio will be 73.6 ± 9.1.
Post-Neutron Mass Yield Distribution in the Epi-Cadmium Neutron-Induced Fission of 245Cm
Published in Nuclear Science and Engineering, 2023
H. Naik, R. J. Singh, W. Jang, S. P. Dange
It can be seen from Fig. 1 that the mass yields of symmetric fission products in the epi-cadmium neutron-induced fission are significantly higher than in the thermal neutron–induced fission of 245Cm. The higher yields of symmetric fission products are with the cost of yields of asymmetric fission products. This difference is due to the difference in excitation energy, which reflects in the P/V ratio. Table I shows that the highest YA value for the asymmetric product of A = 134 is 7.204% ± 0.082% whereas for A = 103, it is 6.480% ± 0.221%. The average of these two values is 6.842% ± 0.221%. On the other hand, the yield of nearly symmetric products of A = 123 is 0.165% ± 0.031%. From the average YA values of 6.842% ± 0.221% and 0.165% ± 0.031%, the value of the P/V ratio was obtained as 41.5 ± 7.9. If the exact symmetric product around A = 121 is considered, then the yield will be around 0.130% ± 0.013%. Based on the average YA values of 6.842% ± 0.221% and 0.130% ± 0.013%, the value of the P/V ratio was obtained as 52.6 ± 5.5. Thus, the P/V value in the 245Cm(nf,f) reaction is ~53, which is about three times lower than the value of 153 to 155 (Refs. 32 and 35) in the 245Cm(nth,f) reaction. This indicates the effect of excitation energy. The P/V ratios from the present work and for other epi-cadmium neutron-induced fissioning systems36–51 are given in Table II and plotted in Fig. 2.
Post-Neutron Mass Yield Distribution in the Epi-Cadmium Neutron-Induced Fission of 241Pu
Published in Nuclear Science and Engineering, 2023
H. Naik, R. J. Singh, S. P. Dange, W. Jang
If the exact symmetric product around A = 119 is considered, then the yield will be around 0.089 ± 0.009%. Based on the average YA values of 7.330 ± 0.659% and 0.089 ± 0.009%, a P/V ratio of 82.4 ± 11.1 was obtained. Thus, the P/V value in the 241Pu(nf, f) reaction is ~82, which is about three times lower than the value of 230 (Ref. 37) in the 241Pu(nth, f) reaction. This indicates the effect of excitation energy. The P/V ratio from the present work and for other epi-cadmium neutron–induced fissioning systems38–54 are given in Table II. The P/V ratio in the epi-cadmium neutron–induced fission from Table II and in the thermal and spontaneous fission of actinides from Refs. 37 and 55 and their back references are plotted in Fig. 4. The P/V ratio in the fissioning system 236U* shown in Fig. 4 is based on data in the 2-MeV neutron–induced fission of 235U (Refs. 56 and 57), which is discussed in Refs. 53 and 54.