Deep spallation cross sections in high energy protons — Uranium interactions

Cross sections of deep spallation products — from phosphorus to hafnium — formed in uranium by high energy protons (E _p ? 10 GeV) have been calculated with a simple semi-empirical formula. The results are in excellent agreement with experimental data.     

Pairing-energy coefficients of neutron-rich fragments in spallation reactions

The ratio of pairing-energy coefficient to temperature(a_p/T)of neutron-rich fragments produced in spallation reactions has been investigated by adopting an isobaric yield ratio method deduced in the framework of a modified Fisher model.A series of spallation reactions,0.5A and 1A Ge V~(208)Pb+p,1A Ge V~(238)U+p,0.5A Ge V~(136)Xe+d,0.2A,0.5A and 1A Ge V~(136)Xe+p,and~(56)Fe+p with incident energy ranging from 0.3A to 1.5A Ge V,has been analysed.An obvious odd-even staggering is shown in the fragments with small neutron excess(I≡N-Z),and in the relatively small-A fragments which have large I.The values of a_p/T for the fragments,with I from 0 to36,have been found to be in a range from-4 to 4,and most values of a_p/T fall in the range from-1 to 1.It is suggested that a small pairing-energy coefficient should be considered in predicting the cross sections of fragments in spallation reactions.It is also concluded that the method proposed in this article is not good for fragments with A/A_s85%(where A_(s )is the mass number of the spallation system).     

p+56Fe散裂反应中同位素产生截面的规律现象

提出一个经验公式,预测散裂反应中同位素产生的截面值,并且利用现有GSI-FRS实验测量的300,500,750,1 000和1 500 MeV/u能量下p+56Fe散裂反应产物的实验结果进行验证。发现此经验公式预测的同位素截面值与实验值的符合度比较好,但随着质量数与能量的改变,同位素产生截面的计算值与实验值的差距也在变大。通过引入质量与能量修正可使此经验公式计算出的同位素截面值的精确度更高,与实验值的符合程度更好。An empirical formula is proposed to predict the isotopic cross section in spallation reactions. The measured fragments in the 300, 500, 750, 1 000 and 1 500 MeV/u p+56Fe spallation reactions have been adopted to perform the analysis. The cross sections of isotopes predicted by the proposed empirical formula have been compared to the experimental results, which shows that the empirical formula can predict the results well. But with the change of the mass and incident energy, the difference between the calculated results and experimental data is larger. The proposed empirical formula is found to predict the isotopic cross sections better, by incorporating the incident energy and mass dependents of fragments.     

Dynamics of plume and crater formation after action of femtosecond laser pulse

Using microinterferometric method, a transition in laser plume from the regime with spallation to the regime without spallation is experimentally studied for the first time. The transition occurs when the fluence F_inc of incident radiation exceeds a threshold of “evaporation” (F_inc)_ev. It has been shown previously that the spallation layer is formed at fluence above the ablation threshold (F_inc)_abl. Thus the spallation exists within the limits (F_inc)_abl<F_inc<(F_inc)_ev. A laser beam has a maximum fluence (F_inc)_c on the axis of the beam. The threshold F_ev separates two cases with qualitatively different morphology: (1) with unbroken shell covering the crater entirely if F_abl<F_c<F_ev, and (2) with the shell having an aperture in the center (like the volcano muzzle) if F_c>F_ev.     

Some regularities within the Stark widths and shifts of resonance ion lines from Li to Ca

A periodic dependence of the Stark widths and shifts of resonance lines, for singly- and doubly-ionized elements, has been found on nuclear charge number Z. These periodicities were found for Griem's theoretical values of the Stark parameters of resonance lines of some singly charged ions from Li to Ca; for other singly- and doubly- charged ions, this parameter was calculated from Griem's semiempirical formula. The dependence of the Stark parameters of the resonance lines on atomic polarizability X has been determined and used to estimate Stark widths and shifts for other singly-charged ions. These values are compared with estimates derived form Griem's semiempirical formula for the Gaunt factor g = 0.2.     

Comparison of residual nuclei from relativistic ion and antiproton reactions with nuclei

The distribution of residual nuclei after stopped antiproton annihilation in several targets from Cu to Ho has been compared with a recent empirical parametrization of mass and charge yields which is supposed to be valid for relativistic light and heavy ion induced reactions. The basic structure of the proposed formula is also applicable for antiproton induced fragmentation or spallation, but some specific modifications are suggested.     

Directional transport equations for plasmas

The yields of the reactions NUCLEUS (γ,yp xn)²⁴Na have been measured for eleven elements with 13≦Z≦29 at maximum bremsstrahlung energies 100 MeV≦E _{γ max}≦ 1000 MeV. An exponential decrease with increasingZ of the mean cross section calculated from the yield data has been obtained. ThisZ-dependence fits well to the systematics of spallation product cross-sections.     

利用MSDM分析p+208Pb散裂反应产物

多步动力学模型(MSDM)研究中、高能质子引起的散裂反应分为3个过程:核内级联、粒子预平衡发射以及通过蒸发粒子和裂变方式的剩余激发核退激发过程.利用Ignatyuk能级密度公式代替MSDM模型中的费米气体能级密度公式,改进其研究质子入射引起散裂产物的形成截面.采用Ignatyuk能级密度公式MSDM研究p+208Pb散裂产物的电荷、质量分布以及产物核形成截面,结果很好地再现了实验数据,且比利用费米气体能级密度的MSDM结果好得多. The level density of Ignatyuk formula is introduced into the Many stages dynamics model ( (MSDM)) instead of Fermi-gas formula to improve the simulation of spallation fragments. The results of (MSDM) with Ignatyuk formula reproduced the experimental data well for the mass and charge distributions, the formation cross sections of isotopic product of proton-induced spallation on~(208)Pb. The calculations are in agreement with the experimental data and better than some simulations by MSDM with Fermi-gas ...     

Spallation reactions in isotopically enriched targets

Yields of ⁴²K and ⁴³K have been measured in spallation reactions at 590 MeV and at 7 GeV in isotopically enriched targets from ⁵⁸Ni to ⁶⁸Zn. The results are correlated with other recent measurements in the development of a new empirical spallation-yield formula which takes into account the isotopic composition of the target. A practical example of the use of this formula is discussed.     

Laser-irradiated thermodynamic behaviors of spallation and recombination at solid-state interface

A microscopic insight of interfacial spallation and recombination behaviors at multilayer thin-film interface induced by incident femtosecond pulsed laser is presented in this paper. Such two different aforementioned behaviors are investigated via the thermodynamic trajectories obtained by using standard Lennard-Jones (L-J) molecular dynamics (MD) simulation. Based on the simulation results, the interfacial damages of multilayer thin film are dominated by a critical threshold that induces an extraordinary expansive dynamics and phase transitions leading to the structural softened and tensile spallation at interface. The critical damage threshold is evaluated at around 8.5 J/m² which governs the possible occurrence of two different regimes, i.e. interfacial spallaiton and recombination. In interfacial damage region, quasi-isothermal thermodynamic trajectories can be observed after the interfacial spallation occurs. Moreover, the result of thermodynamic trajectories analyses indicates that, the relaxation of pressure wave may cause the over-heated interfacial zone to reduce volumetric density, thus leading to structural softness and even weaken interfacial structural strength. The crucial effect leading to the phenomenon of low tension spallation is identified.     

Isotopic temperature in spallation reactions

The possibility of applying the double-isotope-ratio method for calculating temperature to spallation products formed by high-energy protons is discussed. It is concluded that, at a specific incident-particle energy, spallation is characterized by a single temperature of the formation of products for targets in the mass range 56 ≤ A ≤ 208. No energy dependence of the temperature that was calculated by the double-isotope-ratio method was observed in the energy range 0.3 ≤ E ≤ 300 GeV.     

Molecular dynamics simulation of femtosecond ablation and spallation with different interatomic potentials

Fast heating of target material by femtosecond laser pulse (fsLP) with duration τ_L∼40-100 fs results in the formation of thermomechanically stressed state. Its unloading may cause frontal cavitation of subsurface layer at a depth of 50 nm for Al and 100 nm for Au. The compression wave propagating deep into material hits the rear-side of the target with the formation of rarefaction wave. The last may produce cracks and rear-side spallation. Results of MD simulations of ablation and spallation of Al and Au metals under action fsLP are presented. It is shown that the used EAM potentials (Mishin et al. and our new one) predict the different ablation and spallation thresholds on absorbed fluence in Al: ablation F_a=60{65} mJ/cm²and spallation F_s=120{190} mJ/cm², where numbers in brackets { } show the corresponding values for Mishin potential. The strain rate in spallation zone was 4.3×10⁹ 1/s at spallation threshold. Simulated spall strength of Al is 7.4{8.7} GPa, that is noticeably less than 10.3{14} GPa obtained from acoustic approximation with the use of velocity pullback on velocity profile of free rear surface. The ablation threshold F_a≈120 mJ/cm² and crater depth of 110 nm are obtained in MD simulations of gold with the new EAM potential. They agree well with experiment.     

Semiempirical relation between λ and 2Δ/ktC of superconductors

A simple formula relating the electron-phonon coupling constant λ and 2Δ/kT_C is proposed. The formula allows one to estimate λ on the basis of experimental Δ and T_C.     

Abrupt changes in the temperature dependence of the ESR linewidth of La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript> Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> MnO<Subscript>3</Subscript> single crystals

The temperature dependence of the ESR linewidth in La_{1 ? x} Ca _x MnO₃ single crystals with various dopant concentrations (x = 0.18, 0.2, 0.22, 0.25, and 0.3) has been studied. An abrupt decrease in the ESR linewidth has been observed in the samples with a dopant concentration of x = 0.18 and 0.2 near the respective temperatures T _OO′ ≈ 260 and 240 K of the orthorhombic to pseudocubic structural phase transition. The abrupt decrease in the ESR linewidth by approximately 180 Oe has been also observed in the whole temperature range when the concentration is increased from x = 0.2 to x = 0.22. The formula for the fourth moment of the ESR line has been derived including both crystal fields and isotropic exchange interactions and taking into account the difference between the exchange coupling of a spin to its nearest in-plane and out-of-plane neighbors. The formula has been used to estimate the parameter D of the crystalline field on Mn³⁺ ions.     

Measurement of cross sections for gamma transitions induced in excited nuclei by the interaction of 1.1-GeV protons with silicon nuclei

The cross sections for the production of excited nuclei were measured in the reaction ²⁸Si(p, xpyn)A* followed by a gamma transition to a state of lower excitation energy or to the ground state. The experiment was performed in an extracted proton beam from the accelerator of the Institute of Theoretical and Experimental Physics (ITEP, Moscow). The reaction in question was identified by a Ge(Li)-NaI(Tl) anticoincidence spectrometer that recorded prompt gamma radiation emitted by the excited final nucleus. The sensitivity of the experiment was 1.5 mb. The cross-section values were obtained for 24 gamma transitions in 17 nuclear products. The cross sections for spallation reactions were estimated. A comparison was performed with known experimental data and with the results of calculations by a semiempirical formula, as well as with the results obtained by simulating hadron interactions on the basis of the GEANT and INUCL codes.     

Spallative ablation of dielectrics by X-ray laser

A short laser pulse in wide range of wavelengths, from infrared to X-ray, disturbs electron–ion equilibrium and increases pressure in a heated layer. The case where the pulse duration τ _L is shorter than acoustic relaxation time t _s is considered in the paper. It is shown that this short pulse may cause thermomechanical phenomena such as spallative ablation regardless of wavelength. While the physics of electron–ion relaxation strongly depends on wavelength and various electron spectra of substances: there are spectra with an energy gap in semiconductors and dielectrics opposed to gapless continuous spectra in metals. The paper describes entire sequence of thermomechanical processes from expansion, nucleation, foaming, and nanostructuring to spallation with particular attention to spallation by X-ray pulse.     

Heavy density liquid metal spallation target studies for indian ADS programme

Department of Atomic Energy, India has taken up the development of ADS in view of many attractive features like inherent safety, capability to transmute large quantities of nuclear waste, better utilization of thorium etc. A roadmap has been finalized for the development of ADS. One of the key components of the ADS is the spallation target. Considering the neutron yield, thermal-hydraulics and radiation damage issues, we are proposing to develop spallation target based on heavy density liquid metals like lead and lead-bismuth-eutectic (LBE). Both window and windowless target configurations are presently being studied. In view of the various advantages we are also studying liquid metal flow circulation based on gas lift mechanism. An R&D programme has been initiated to address various physics and technology issues of ADS target. Under this programme, mercury and LBE experimental facilities are presently being set up. Along with these facilities, computational tools related to spallation physics (FLUKA) and CFD are being developed, and the existing ones are utilized to design the entire target loop as well as sub-systems. In this presentation the details of these activities are presented.      

New isotope159Lu and decay of158Lu,159,158Yb isotopes

Lutetium and ytterbium isotopes with masses A=159,158 have been produced by proton induced spallation reaction, and investigated by on-line mass separation and subsequent decay spectroscopy. A new isotope¹⁵⁹Lu (T_1/2=12.3±1 s) has been identified, and newγ-ray data have been obtained for the decay of¹⁵⁸Lu and^{159, 158}Yb.     

A method for estimating the sound power radiated from plates with prescribed excitation in the multi-mode region

In a well known textbook on structure-borne sound by Cremer et al., a formula for estimating the sound power emitted from a finite, baffled and point-excited plate is derived. The steps used in this derivation can be made the basis of a general estimation method. Such a method is described in this paper. This general method can be applied to estimate the sound power emitted from finite, baffled plates with any type of prescribed excitation. The method has been applied to a test case and the results compared with experiments. The agreement between theory and measurement is satisfactory and it seems that the suggested method should be useful in noise control work.     

质子入射散裂产物理论研究方法探讨

简要介绍了几种关于中高能质子入射引起散裂反应产物理论计算的方法,以及这些方法的最新发展.比较了这些方法在理论计算中的特点,指出经典外推方法有局限性,量子分子动力学方法和改进后的M C方法的计算结果与实验数据有较好的符合,但是计算量大,而且量子分子动力学方法在与宏观输运理论连接上存在不少的困难.半经验计算方法已经取得了初步的成果,需要根据新的实验结果来对其进行发展. The analysis on spallation product of proton-induced reaction with intermediate energy has important applications, such as astrophysics, biophysics, spallation neutron source, and accelerator-driven system (ADS) etc. In recent year, some theoretical models have been developed to investigate this reaction processes. At present work, we introduce the extrapolated classic theory, the quantum molecule dynamic (QMD) plus statistical decay and fission models, the method of Mento-Carlo and Smiempirical method for...