Temperature effect for an inelastic neutrino scattering cross section

The influence of temperature on inelastic neutrino scattering on hot nuclei is studied with the ⁵⁴Fe nucleus as an example. The strength distribution of charge-neutral Gamov-Teller transitions in ⁵⁴Fe at finite temperature is calculated within the framework of a random phase approximation using the thermo field dynamics formalism. It is shown that for neutrino energies lower than the energy of the Gamov-Teller resonance, the inelastic scattering cross section depends substantially on temperature.     

Thermal effects on neutrino-nucleus inelastic scattering in stellar environments

Thermal effects for inelastic neutrino-nucleus scattering off even-even nuclei in the iron region are studied. Allowed and first-forbidden contributions to the cross sections are calculated within the quasiparticle random-phase approximation, extended to finite temperatures within the Thermo-Field-Dynamics formalism. The GT₀ strength distribution at finite temperatures is calculated for the sample nucleus ⁵⁴Fe. The neutral-current neutrino-nucleus inelastic cross section is calculated for relevant temperatures during the supernova core collapse. The thermal population of the excited states significantly enhances the cross section at low neutrino energies. In agreement with studies using a large scale shell-model approach the enhancement is mainly due to neutrino up-scattering at finite temperatures.     

Statistical theory of nuclear neutrino capture: (II). Inclusion of first-forbidden transitions

The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which ³⁷Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in ³⁷Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states (E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E_v = 50 MeV.     

Nuclear effects in deep inelastic scattering of charged-current neutrino off nuclear target

The nuclear effects in the neutrino–nucleus charged-current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. The structure functions F₂(x,Q²) and xF₃(x,Q²) as well as differential cross sections are calculated by using CTEQ parton distribution functions and the EKRS and HKN nuclear parton distribution functions, and these are compared with the CCFR and NuTeV data. It is found that the corrections of the nuclear effect to the differential cross section for the charged-current antineutrino scattering on the nucleus are negligible, the EMC effect exists in the neutrino structure function F₂(x,Q²) in the large x region, the shadowing and anti-shadowing effect occur in the distribution functions of valence quarks in the small and medium x region, respectively. It is also found that shadowing effects on F₂(x,Q²) in the small x region in the neutrino–nucleus and the charged-lepton–nucleus deep inelastic scattering processes are different. It is clear that the neutrino–nucleus deep inelastic scattering data should further be employed in restricting the nuclear parton distributions. PACS 13.15.+g; 24.85.+p; 25.30.-c     

Nuclear and Coulomb interactions in coherent fragmentation of relativistic nuclei in a photoemulsion

The role of the nuclear and Coulomb interactions in coherent fragmentation of relativistic nuclei is discussed with the cluster-model analysis of the experimental data on the fragmentation of ⁷Li (P = 3A GeV/c) via the ³H + ⁴He channel in photoemulsion used as an example. The calculated electromagnetic contribution of ～10% to the cross section is not in conflict with the photoemulsion data and the upper estimate of ～40% derived from the earlier measurements of total cross sections for fragmentation of light nuclei using the counter technique. The observed irregularities in the differential cross section for ⁷Li fragmentation with a separated Coulomb peak at a very small momentum transfer Q are ascribed to the overlap of nuclear diffraction patterns arising from light (C, N, O) and heavy (Ag, Br) photoemulsion nuclei. The predicted diffraction cross sections in the inelastic channel drastically differ from the usual shape of nuclear diffraction in an elastic channel. For pure targets, they have a shape of oscillations with a few peaks of comparable intensity and show strong dependence on the form of the surface nuclear density and radii of the intranuclear cluster and target nucleus. The probability for two-body clustering in ⁷Li is estimated at about 0.7.     

用高能核子非弹性散射研究核力有效势

本文用扭曲波玻恩近似法及多体高能近似法,处理了原子核对高能核子的非弹性散射现象。在具有可靠的靶核激发态波函数的情况下,可利用这些理论处理方法研究核内两核子间的有效势,本文具体就碳核对185MeV入射核子的非弹性散射进行了计算。在计算中利用了粒子-空穴模型核波函数。在采用了具有各种交换性质并包含自旋轨道耦合项的有效势后,用一组合理的位阱参数,由多体高能近似法计算的理论值可与几个微分截面及极化实验曲线同时符合。     

Distorted wave theory of scattering of nucleons with intermediate energies on nuclei

In the context of nonrelativistic theory in the distorted wave approximation, a three-dimensional form of analytical expression for the differential cross section of scattering of nucleons with intermediate energies on atomic nuclei is derived. In the context of this theory, the main parameters of elastic scattering of protons with incident energy of 1 GeV on the ²⁰⁸Pb nucleus are determined. For inelastic scattering of protons with nuclear surface vibrations, giant multipole resonances in the excited nucleus are investigated for the collective nucleus model. The energy losses of the scattered proton are calculated together with the energies of giant dipole and quadrupole resonances and nuclear surface vibration energy. This allows the deformation parameter of the excited nucleus to be calculated.     

Application of a folding-model optical potential to analyzing inelastic pion–nucleus scattering and the in-medium effect on a pion–nucleon amplitude

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π ^±-mesons on ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, and ²⁰⁸Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2⁺ and 3^? collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β ₂) and octupole (β ₃) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Experimental estimate of the diffractive-dissociation phenomenon following neutrino interaction with photoemulsion nuclei

The first experimental estimate of the diffractive-dissociation (DD) cross section for muon-neutrino interaction with nuclei is presented. Eleven events that satisfy the DD criteria (x _B<0.1, Δη>2) are found among 207 events induced by neutrino interactions with Ag and Br nuclei of nuclear photoemulsion and borrowed from the database of the E-564 experiment (FNAL). The ratio of the DD cross section to the total deep-inelastic cross section for the charged current is 0.29±0.09. Four of the 11 events proved to be candidates for events of coherent DD.     

Magnetic neutrino scattering on atomic electrons revisited

We reexamine the role of electron binding effects in the inelastic neutrino–atom scattering induced by the neutrino magnetic moment. The differential cross section of the process is presented as a sum of the longitudinal and transverse components, according to whether the force that the neutrino magnetic moment exerts on electrons is parallel or perpendicular to momentum transfer. The atomic electrons are treated nonrelativistically. On this basis, the recent theoretical predictions concerning the magnetic neutrino-impact ionization of atoms are critically discussed. Numerical calculations are performed for ionization of a hydrogenlike Ge⁺³¹ ion by neutrino impact.     

Muo-production of neutrino pairs and the number of generations

The cross section for production of neutrino pairs by high energy muons in the nuclear Coulomb field is calculated analytically. For right (left)-handedμ ^?(μ ⁺) helicity, the process is only mediated by neutral currents, which opens the possibility to look for the number of generations. Assuming three generations, the calculated cross section turns out to be 1.1×10^?40 cm² for⁵⁶Fe and 6.6×10^?40cm² for²⁰⁸Pb at an incident muon energy of 300 GeV. Some comments about the equivalent photon approximation are made.     

Scaling of the F2 structure function in nuclei and quark distributions at x>1

We present new data on electron scattering from a range of nuclei taken in Hall C at Jefferson Lab. For heavy nuclei, we observe a rapid falloff in the cross section for x>1, which is sensitive to short-range contributions to the nuclear wave function, and in deep inelastic scattering corresponds to probing extremely high momentum quarks. This result agrees with higher energy muon scattering measurements, but is in sharp contrast to neutrino scattering measurements which suggested a dramatic enhancement in the distribution of the "superfast" quarks probed at x>1. The falloff at x>1 is noticeably stronger in 2H and 3He, but nearly identical for all heavier nuclei.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

Phenomenological local potential analysis of π+ scattering

π⁺-nucleus scattering cross section are calculated by solving a Schrödinger equation reduced from the Klein-Gordon equation. Local potentials are assumed, and phenomenological potential parameters are searched energy dependently for π⁺ scattering from ¹²C, ⁴⁰Ca, and ²⁰⁸Pb to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at 800 MeV/c pion laboratory momentum. The collective model is used to calculate the angular distributions of differential inelastic cross sections for pions leading to the lowest 2⁺ and 3^? states of ¹²C. The deformation parameters and lengths are extracted and compared to the corresponding ones from other works. Local potentials well describe the scattering of pions from nuclei.     

Neutrino absorption cross sections in the supernova environment

We study charged-current neutrino cross sections on neutron-rich nuclei in the mass A∼60 region. Special attention is paid to environmental effects, i.e., finite temperature and density, on the cross sections. As these effects are largest for small neutrino energies, it is sufficient to study only the Gamow–Teller (GT) contributions to the cross sections. The relevant GT strength distributions are derived from large-scale shell model calculations. We find that the low-energy cross sections are enhanced at finite temperatures. However, for (ν_e,e⁻) reactions Pauli blocking of the electrons in the final state makes the cross sections for low-energy neutrinos much smaller than for the competing inelastic scattering on electrons at moderate and large densities. Absorption cross sections for low-energy antineutrinos are strongly enhanced at finite temperatures.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.     

Nuclear effects in the structure functions

By using a relativistic framework and accurate nuclear spectral function the structure functions F_2A andF _3A of deep inelastic charged lepton and neutrino scattering are calculated in nuclei and results are presented.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

Scattering of polarized electrons on oriented light nuclei

For a series of parameter values characterizing an axially symmetric nuclear orientation, the differential cross sections of electrical excitation of oriented⁷Li,¹⁰B nuclei by completely polarized ultrarelativistic electrons with nuclear transition to the first excited states are calculated as a function of the transmitted momentum q. The nucleus is described by a multiparticle oscillator shell model in intermediate coupling. The contribution to the cross section due to nuclear polarization is calculated; it is compared with the influence of the alignment of the nuclei. It is shown that the cross sections calculated for these two cases may differ significantly, both in magnitude and in the character of the dependence on q. For a series of transitions to low-lying levels of the⁷Li,¹⁰B nuclei, systems of equations in terms of reduced nuclear matrix elements of multipole transitions and statistical solutions are obtained; their solution, with cross sections measured in different kinematic conditions but for fixed q as parameters, allows not only the absolute values of the desired quantities to be established, but also the relative phases of the reduced matrix elements.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 84–88, May, 1990.