Nuclear Phase Shifts Research Articles

Microscopic description of the H(α,γ)2Li6 radiative capture reaction

The $^{2}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{6}\mathrm{Li}$ radiative capture responsible for the $^{6}\mathrm{Li}$ production during the big-bang nucleosynthesis is comprehensively studied within a microscopic approach. The approach implements microscopically clustering aspects of nuclear structure and dynamics in an oscillator-basis representation. The total astrophysical $S$ factor of the reaction is calculated. All allowed partial electric quadrupole and magnetic dipole transitions between the $^{4}\mathrm{He}+^{2}\mathrm{H}$ continuum and the $^{6}\mathrm{Li}$ ground state are considered in the standard long-wavelength limit. Isospin-forbidden electric dipole transitions are taken into account in two ways. The first method is based on the expression for the electric dipole operator at the leading order of the long-wavelength approximation with the usage of the exact-mass prescription. In the second method, this operator is written at the first order beyond the leading-order approximation. Contributions of the transitions are compared to each other. The $^{4}\mathrm{He}+^{2}\mathrm{H}$ nuclear phase shifts for the initial channels of the considered reaction are computed. Important properties of the $^{6}\mathrm{Li}$ nucleus, such as the breakup threshold, the asymptotic normalization constants, and the electric quadrupole moment are also described. Deformation effects and their manifestations in $^{6}\mathrm{Li}$ are discussed. The obtained results are shown to be in good agreement with a large set of experimental data.

Elastic Scattering and Radiative Capture in the 4He + 3H and 4He + 3He Systems

The nuclear 4He + 3H and 4He + 3He systems, which are of significant interest to nuclear astrophysics applications, are studied within a microscopic approach. Elastic scattering and radiative capture in these systems are considered over a broad range of energies. Cross sections (astrophysical S-factors) for the radiative capture and nuclear phase shifts for the elastic scattering are calculated. The results are compared with experimental data.

He4+H3 and He4+He3 radiative capture, elastic scattering, and electromagnetic properties within the algebraic version of the resonating group model

The mirror seven-nucleon $^{4}\mathrm{He}+^{3}\mathrm{H}$ and $^{4}\mathrm{He}+^{3}\mathrm{He}$ systems are studied microscopically using the algebraic version of the resonating group model. Astrophysical $S$ factors and branching ratios for the $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ and $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ radiative captures are calculated in a wide energy range from ultralow energies to intermediate ones covering the $^{7}\mathrm{Li}$ and $^{7}\mathrm{Be}$ lowest resonance states. All allowed E1, E2, and M1 captures from $s, p, d$, and $f$ waves are taken into account in the calculations. Nuclear phase shifts for the $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\alpha})^{3}\mathrm{H}$ and $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\alpha})^{3}\mathrm{He} s$-, $p$-, $d$-, and $f$-wave elastic scattering are computed. Properties of the bound and low-lying resonance states of the $^{7}\mathrm{Li}$ and $^{7}\mathrm{Be}$ nuclei are considered. The obtained results are compared with data from experiments.

Fast phase manipulation of the single nuclear spin in solids by rotating fields

We propose fast phase-gates of single nuclear spins interacting with single electron spins. The gate operation utilizes geometric phase shifts of the electron spin induced by fast/slow rotating fields; the path difference depending on nuclear spin states enables nuclear phase shifts. The gate time is inversely proportional to the frequency of the slow rotating field. As an example, we use nitrogen-vacancy centers in diamond, and show the phase-gate time orders of magnitude shorter than previously reported. We also show the robustness of the gate against decoherence and systematic errors.

Analysis of π± – 12C Elastic Scattering Data at 100 MeV Using Inverse Scattering Theory and Klein-Gordon Equation

Our optical potential, determined from available phase shifts within the framework of inverse scattering theory using the full Klein-Gordon equation, is used successfully in this study. This potential is inserted in the radial part of Klein-Gordon equation which is solved numerically using Numerouv integration method. The logarithmic derivatives of the inner and outer solutions are matched at the nuclear surface and phase shifts are obtained for each partial wave. As such, scattering amplitudes and cross sections can easily be calculated. The reliability and success of our potential are examined by accounting for the measured elastic differential cross sections, especially at very large angles, and reaction cross sections for π± – 12C at 100 MeV. The use of full Klein-Gordon equation, and not the truncated one, is very important in explaining large and very large angle data.

A Practical Method of Solving Cutoff Coulomb Problems in Momentum Space: Application to the Lippmann-Schwinger Resonating-Group Method and the pd Elastic Scattering

A practical method of solving cutoff Coulomb problems of two-cluster systems in momentum space is given. When a sharply cut-off Coulomb force with a cutoff radius ρ is introduced at the level of constituent particles, the two-cluster direct potential of the Coulomb force becomes in general a local screened Coulomb potential. The asymptotic Hamiltonian yields two types of asymptotic waves; one is an approximate Coulomb wave with ρ in the middle-range region, and the other a free (no-Coulomb) wave in the longest-range region. The constant Wronskians of this Hamiltonian can be calculated in either region. We can evaluate the Coulomb-modified nuclear phase shifts for the screened Coulomb problem using the matching condition proposed by Vincent and Phatak for the sharply cut-off Coulomb problem. We apply this method first to an exactly solvable model of the αα scattering with the Ali-Bodmer potential and confirm that a complete solution is obtained with a finite ρ. The stability of nuclear phase shifts with respect to the change in ρ within some appropriate range is demonstrated in the αα resonating-group method (RGM) calculation using the Minnesota three-range force. An application to the pd elastic scattering is also discussed.

Simultaneous measurements of thermal conductivity, thermal diffusivity and specific heat by nuclear magnetic resonance imaging

The feasibility of measuring the thermal conductivity ( κ), thermal diffusivity ( α) and specific heat ( c p ) of an aqueous gel noninvasively by nuclear magnetic resonance (NMR) imaging is presented. NMR images acquired with high spatial and temporal resolutions provide the means for a direct evaluation of Fourier's heat conduction relation and the simultaneous measurement of κ, α and c p in a single experiment. An aqueous gel is heated by a diode laser absorbed in a silicon wafer providing a planar constant heat flux boundary condition, and the subsequent spatial and temporal variations of temperature in the gel are measured by changes in the water proton resonance frequency and consequent nuclear spin phase shifts in gradient echo images. The evaluation of the spatial and temporal variations of temperature yields the diffusion length and thermal diffusivity, the ratio of nuclear thermal coefficient to the thermal conductivity; and the temporal variation of the spatially averaged nuclear spin phase shift yields the ratio of heat capacity to the nuclear thermal coefficient. The temporal trajectory of the diffusion length ( λ) is found to be independent of heat flux ( f 0). Furthermore, a direct evaluation of nuclear spin phase shift gradients corresponding to long times and short distances from the heat flux boundary directly yields the ratio of nuclear thermal coefficient to the thermal conductivity per Fourier's heat conduction relation.

Measurement of specific heat and specific absorption rate by nuclear magnetic resonance

We evaluate a nuclear magnetic resonance (NMR) method of calorimetry for the measurement of specific heat ( c p ) and specific absorption rate (SAR) in liquids. The feasibility of NMR calorimetry is demonstrated by experimental measurements of water, ethylene glycol and glycerol using any of three different NMR parameters (chemical shift, spin–spin relaxation rate and equilibrium nuclear magnetization). The method involves heating the sample using a continuous wave laser beam and measuring the temporal variation of the spatially averaged NMR parameter by non-invasive means. The temporal variation of the spatially averaged NMR parameter as a function of thermal power yields the ratio of the heat capacity to the respective nuclear thermal coefficient, from which the specific heat can be determined for the substance. The specific absorption rate is obtained by subjecting the liquid to heating by two types of radiation, radiofrequency (RF) and near-infrared (NIR), and by measuring the change in the nuclear spin phase shift by a gradient echo imaging sequence. These studies suggest NMR may be a useful tool for measurements of the thermal properties of liquids.

Analysis of refractive effects in 4He + 15N, 18O, 24Mg, 44Ca, and 90Zr scattering processes at energies in the range E(4 He) = 13–15 MeV per nucleon by using smooth monotonic dependences of the nuclear phase shift on the orbital angular momentum

The differential cross sections for the elastic scattering of 4He nuclei on 15N, 18O, 24Mg, 44Ca, and 90Zr nuclei in the energy range E(4He) = 13–15 MeV per nucleon are analyzed on the basis of the model-independent S-matrix approach by using an evolution algorithm. It is shown that a quantitative description of the cross sections under analysis is ensured by smooth monotonic dependences of the real and imaginary parts of the nuclear phase shift on the orbital angular momentum.

Elastic 16O16O scattering at E(16O) = 350 MeV and new method for a model-independent determination of the scattering matrix

A new approach that can be used to extract the scattering matrix S(l) as a complex-valued function of the orbital angular momentum l directly from experimental data on elastic nucleus-nucleus scattering at intermediate energies without resort to additional model assumptions is developed on the basis of the evolutionary algorithm. Owing to the fact that the behavior of the derivatives of S(l) is automatically monitored within this approach, the scattering matrix obtained for 16O16O interaction at an energy of 350 MeV is determined by its absolute value and the nuclear phase shift, which are smooth monotonic functions of the orbital angular momentum. Moreover, the result involves no distortions, the form of the quantum deflection function being typical of the nuclear-rainbow pattern. It is shown that the ultimate form of S(l) is independent of input representations of the scattering matrix, which were usually taken on the basis of various phenomenological models.

Measurement of thermal diffusivity by magnetic resonance imaging

Nuclear magnetic resonance (NMR) may be used for monitoring temperature changes within samples based on measurements of relaxation times, the diffusion coefficient of liquids, proton resonance frequency or phase shifts. Such methods may be extended to the explicit measurement of the thermal diffusivity of materials by NMR imaging. A method based on measuring nuclear spin phase shifts or changes in the equilibrium nuclear magnetization has been developed for measuring transient thermal diffusion effects and thermal diffusivity with potential applications in NMR thermotherapy and materials science. In this method, a thermal pulse is applied to a medium, and the resultant temporal variations of the nuclear spin phase or of the magnitude of the nuclear magnetization produced by the thermal pulse are monitored at a spatial distance. The results obtained on common fluids agree well with the data from other methods.

Star-to-star nitrogen abundances in globular cluster stars

We calculate for the s-, p1/2- and p3/2-waves the electromagnetic corrections which must be subtracted from the nuclear phase shifts obtained from the analysis of low-energy π+p elastic scattering data, in order to obtain hadronic phase shifts. The calculation uses relativised Schrödinger equations containing the sum of an electromagnetic potential and an effective hadronic potential. We compare our results with those of previous calculations and estimate the uncertainties in the corrections.

Electromagnetic corrections to the hadronic phase shifts in low energy [formula omitted] elastic scattering

We calculate for the s-, p 1/2 - and p 3/2 -waves the electromagnetic corrections which must be subtracted from the nuclear phase shifts obtained from the analysis of low-energy π +p elastic scattering data, in order to obtain hadronic phase shifts. The calculation uses relativised Schrödinger equations containing the sum of an electromagnetic potential and an effective hadronic potential. We compare our results with those of previous calculations and estimate the uncertainties in the corrections.

Photodisintegration of 4 He and the Supermultiplet Potential Model of Cluster-Cluster Interactions

p+3H and p+3He elastic collisions are described in terms of a supermultiplet model with [ƒ]-dependent potentials. The phase shifts δ [ƒ] L,t,S (E) with [ƒ] = [4], t = S = 0, L = even are reconstructed from the observable nuclear phase shifts δ L,S (E) of the above collisions. So, the initial-state interaction V [4] L,0,0 (R) of the 4He +Υ→3H +p(3He +n) reaction can be found unambiguously, while the final-state interaction V [31] L, 1, 0 (R) is defined by the observablesδ L,0 (E) of p+3He scattering. The data on the proton momentum distribution in 4He and on the charge-exchange reaction 3H +p→3He +n confirm the model. In calculating the above photonuclear reactions, in addition to the initial-state and final-state antisymmetrizations, preserving the corresponding symmetry [ƒ], the nucleon-nucleon correlations in the 3H (3He) subsystem were also taken into account. The results are in good agreement both with recent experimental data and theoretical investigations by sofianos, Fiedeldey, and Sandhas, who followed a rather different approach.

Analytical treatment of heavy-ion elastic scattering at intermediate energies.

The elastic scattering of heavy ions at energies where the eikonal approximation is valid is discussed in detail. The nuclear phase shift and deflection functions for a complex Woods-Saxon interaction are evaluated in closed form. The resulting functions represent extremely well the numerically generated ones, even in cases involving the scattering of loosely bound nuclei. The elastic amplitude is evaluated in closed form, and found to be a reasonable approximation to the optical model one. Applications to the scattering of $^{11}\mathrm{Li}$ and $^{11}\mathrm{C}$ are made.

Coulomb and nuclear excitation in intermediate-energy heavy-ion collisions.

Following previous works where the field of application of Glauber methods were extended to heavy-ion scattering in the energy range of 30--400 MeV/nucleon, we develop here a formalism which includes both Coulomb and nuclear excitation processes and explicitly accounts for the effects arising from the energy difference in different channels. First order inelastic excitations are described in the framework of a distorted wave eikonal approximation; in this connection nuclear phase shifts and form factors are described in terms of microscopic nucleon-nucleon interactions while the Coulomb excitation is described through a proper manipulation of phenomenological form factors. Several specific examples are discussed. The interest is then focused on second-order processes, more specifically on the effects introduced in the elastic channel by the coupling to the inelastic channels, and the corresponding Coulomb and nuclear polarization potentials are derived and discussed. On the ground of these achievements a general formalism is built up, capable of describing coupled-channel problems at any order of scattering. Due to the eikonal propagation, the multichannel multistep series leads to simple algebraic forms for each partial-wave scattering matrix, which involve powers of a channel matrix whose elements only depend on the impact parameter.

Back-angle anomaly and coupling between seven reaction channels of 12C + 24Mg using algebraic scattering theory

We measured six fairly complete angular distributions of elastic, inelastic and α-transfer reactions of the 12C + 24Mg system at E CM=25.2 MeV. We performed coupled channels calculations using algebraic scattering theory with the nuclear algebraic potential derived from nuclear phase shifts and using the available structure information for the inelastic coupling strengths. The back angle rise in the elastic cross section is fully explained by the couplings between elastic and transfer channels.

Semi-classical approach to antiproton-nucleus scattering

The similarities and differences between antiproton-nucleus scattering and heavyion-nucleus scattering are examined. It is found that the one-turning point approach viz Wentzel, Kramers and Brillouin (WKB) approximation can be applied to the analysis of antiproton-nucleus scattering. Using this approximation, a closed form expression for the nuclear phase shift is deduced from the corresponding expression for the heavy-ion scattering phase shift derived by Shastry and the method is illustrated by carrying out the cross-section calculation of\(\bar p + {}^{40}Ca\) atElab = 46·8 MeV.

Polarized neutron interferometry: A survey

A brief summarizing review is given of all those neutron interferometric experiments performed hitherto which explicitly use the spin- 1 2 particle properties of the neutron. It covers topics as the verification of the 4π-periodicity of spinors, the cooperative action of nuclear phase shift and spin-rotation on the neutron wave function, the demonstration of the quantum mechanical principles of fermion spin-state superposition and the more recent double resonance experiments where the two interfering beams propagate through spatially separated oscillatory magnetic fields. Finally a proposal will be presented also for a so-called “late-choice” experiment with polarized neutrons.

The neutron interferometer as a macroscopic quantum device

Neutron interferometry is a unique tool for investigations in the field of particle-wave dualism because massive elementary particles behave like waves within the interferometer. The invention of perfect crystal neutron interferometers providing widely separated coherent beams stimulated a great variety of experiments with matter waves in the field of basic quantum mechanics. The phase of the spatial and spinor wave function become a measurable quantity and can be influenced individually. High degrees of coherence and high order interferences have been observed by this technique. The 4π-symmetry of a spinor wave function and the mutual modulation of nuclear and magnetic phase shifts have been measured in the past. Recent experiments dealt with polarized neutron beams, which are handled to realize the spin-superposition of two oppositionally polarized subbeams resulting in a final polarization perpendicular to both initial beam polarizations. The different actions on the coherent beams of static (DC) and dynamic (HF) flippers have been visualized.