Total Transition Amplitude Research Articles

Theoretical oscillator strengths for spin-allowed electric-dipole transitions in Zn-like ions

We have performed a relativistic many-body perturbation theory calculation up to second order to study the transition amplitudes, Einstein $A$ coefficients, and oscillator strengths for the spin-allowed electric-dipole transitions in the Zn-like ions Zn, Ge${}^{2+}$, As${}^{3+}$, Kr${}^{6+}$, Nb${}^{11+}$, and Mo${}^{12+}$. All possible transitions among the first 13 levels of these ions have been studied. The total transition amplitudes obtained in different gauges are in excellent agreement. The gauge dependences of the first and second order, and the total transition amplitudes are derived. A theoretical justification for the small gauge dependence of the total transition amplitude is given. The present calculations agree well with experiment for all ions except for the neutral Zn atom.

High-Order Above-Threshold Ionization of H2+ in Intense Laser Field

The nonperturbative quantum electrodynamics method proposed by Fu et al. [Phys. Rev. A 75 (2007) 063419] is employed to study the high-order above-threshold ionization (ATI) of a diatomic molecule. Based on this frequency-domain theory, the high-order ATI process can be regarded as ATI followed by laser-assisted collision, where the total transition amplitude is the coherent summation of the contributions from each ATI channel. The angular-resolved ATI spectrum, which agrees with the results by Becker et al. based on the time-domain method, is obtained by this frequency domain theory. Furthermore, it is demonstrated that the interference characteristics representing the molecular structure in the ATI spectrum originates from the recollision of the electron with two-centre ion in each ATI channel.

Exploring the 6He continuum sea through proton inelastic collisions

The p-6He inelastic scattering at 700 MeV u-1 is studied using Multiple Scattering expansion of the total Transition amplitude (MST) framework with a pseudo-state representation of 6He continuum. We show that the differential cross sections calculated with two different pseudo-state bases are in good agreement.

Few-body multiple scattering calculations forHe6on protons

The elastic scattering of the halo nucleus $^{6}\mathrm{He}$ from a proton target at 717 MeV/nucleon is investigated within three different multiple-scattering formulations of the total transition amplitude. The factorized impulse approximation (FIA) and the fixed scatterer approximation (FSA) of the multiple-scattering expansion are used to evaluate accurately the single-scattering terms and to test the validity of a few-body Glauber approach. The latter also includes terms beyond single scattering and the importance of these terms is investigated. The differential cross section is calculated for proton scattering from $^{6}\mathrm{He}$ at 717 MeV in inverse kinematics and compared with recent data.

Continuum description with pseudostate wave functions

Benchmark calculations are performed aiming to test the use of two different pseudostate bases on the multiple scattering expansion of the total transition amplitude scattering framework. Calculated differential cross sections for $p\text{\ensuremath{-}}$$^{6}\mathrm{He}$ inelastic scattering at 717 MeV/nucleon show a good agreement between the observables calculated in the two bases. This result gives extra confidence on the pseudostate representation of continuum states to describe inelastic/breakup scattering.

Excitation modes ofHe6from proton collisions

The cross section for inelastic scattering of Borromean halo nuclei from protons is evaluated using the Multiple Scattering expansion of the Total transition amplitude (MST) formalism. Differential cross sections and energy spectra are shown for $p$-$^{6}\mathrm{He}$ at 700 MeV/nucleon. The role of spin flip excitations is analyzed.

Four-body multiple-scattering expansion of the total transition amplitude—MST

The elastic scattering differential cross section is calculated for proton scattering from 6He at 717 MeV, using single-scattering terms of the multiple-scattering expansion of the total transition amplitude. We analyze the effects of different scattering frameworks, specifically the factorized impulse approximation and the fixed scatterer (adiabatic) approximation.

Few body impulse and fixed scatterer approximations for high energy scattering

The elastic scattering differential cross section is calculated for proton scattering from 6He at 717 MeV, using single scattering terms of the multiple scattering expansion of the total transition amplitude (MST). We analyse the effects of different scattering frameworks, specifically the factorized impulse approximation (FIA) and the fixed scatterer (adiabatic) approximation (FSA) and the uncertainties associated with the use different structure models.

Excitation modes of11LiatEx∼1.3MeVfrom proton collisions

The cross section for $p{\ensuremath{-}}^{11}\mathrm{Li}$ inelastic scattering at 68 MeV/nucleon is evaluated using the multiple scattering expansion of the total transition amplitude (MST) formalism, and compared with the breakup in the shakeoff approximation. Three different potential models for ${}^{11}\mathrm{Li}$ are used to calculate the ${}^{11}\mathrm{Li}{(p,p}^{\ensuremath{'}})$ continuum excitations, and all show peaks below 3 MeV of excitation energy, both in resonant and some nonresonant channels. In the most realistic model of ${}^{11}\mathrm{Li},$ there is a strong dipole contribution associated with attractive but not a fully-fledged resonant phase shifts, and some evidence for a ${J}_{\mathrm{nn}}^{\ensuremath{\pi}}{=0}_{2}^{+}$ resonant contribution. These together form a pronounced peak at around 1--2 MeV excitation, in agreement with experiment, and this supports the use of the MST as an adequate formalism to study excited modes of two-neutron nuclear halos.

Perturbative and nonperturbative processes in adiabatic population transfer

With the help of superadiabatic techniques for quantum systems depending slowly on time, we demonstrate how the total transition amplitude, tracked in time in the usual adiabatic basis, can be decomposed into a perturbative part consisting of terms proportional to powers of the adiabaticity parameter, and a nonperturbative component. The interference of both components underlies the oscillations that accompany transitions in the adiabatic basis. Whereas for traditionally considered systems the final nonadiabatic transition probability is determined by the nonperturbative part alone, this is no longer correct for models describing stimulated Raman adiabatic passage (STIRAP). We explain the recently discovered breakdown of the Dykhne-Davis-Pechukas formula on general grounds, and provide simple, but accurate approximations for transition amplitudes in STIRAP systems.

Hyperfine-structure measurements on trapped Pb II.

The 6${\mathit{P}}_{3/2}$-6${\mathit{P}}_{1/2}$ magnetic dipole resonance transition in ${\mathrm{Pb}}^{+}$ has been observed by cw laser excitation of an ion cloud stored in a Paul trap and subsequent detection of the fluorescence radiation. From the hyperfine-structure splitting of the spectrum we determine the A factor for the ground state, A(${\mathit{P}}_{1/2}$)=12.967(13) GHz, and the excited state, A(${\mathit{P}}_{3/2}$)=0.580(3) GHz. From a contamination of $^{208}\mathrm{Pb}$ in our sample we derived the $^{207}\mathrm{Pb}^{+}$${\mathrm{\ensuremath{-}}}^{208}$${\mathrm{Pb}}^{+}$ isotope shift [\ensuremath{\Delta}\ensuremath{\nu}=311(14) MHz]. A small electric quadrupole admixture giving rise to a \ensuremath{\Delta}F=2 component in the spectrum has been determined to be 6.4(0.5)% of the total transition amplitude.

Third quantization formalism for Hamiltonian cosmologies

Within the ADM technique of Hamiltonian cosmology, in the case of Bianchi class A models, we introduce a Fock-like, field theoretical approach to the description of quantum cosmology. We then calculate the total transition amplitude between two quantum states of the state functional of the ADM geometry.

Semiclassical approach to the theory of atomic excitation processes associated with heavy-ion collisions

Starting from a quantum-mechanical description of the total system consisting of an electron and two nuclei, the semiclassical equation for the transition amplitude between electronic adiabatic basis states is derived for the case of the Rutherford scattering. This method is then generalized to include the effect of nuclear elastic and inelastic collisions. The total transition amplitude for a reaction in which both the electron and nuclei are excited is expressed as products of three factors summed over the intermediate atomic states. Of these three factors, the first and the third are the semiclassical atomic transition amplitudes before and after the nuclear collision, respectively, and the second is the $S$-matrix element for the nuclear collision.

Theory of radiative muon capture byC12

The theory of radiative muon capture, as formulated in a previous paper on the basis of the conservation of the hadronic electromagnetic current, the conservation of the hadronic weak polar current, the partial conservation of the hadronic weak axial-vector current, the SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) current algebra for the various hadronic currents, and the "linearity hypothesis," is applied to the process ${\ensuremath{\mu}}^{\ensuremath{-}}^{12}\mathrm{C}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}^{12}\mathrm{B}\ensuremath{\gamma}$. The resultant total transition amplitude is worked out explicitly and used to calculate various observable quantities.RADIOACTIVITY ${\ensuremath{\mu}}^{\ensuremath{-}}^{12}\mathrm{C}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}^{12}\mathrm{B}\ensuremath{\gamma}$; application of a general theory of radiative muon capture to nuclear spin and isospin [${0}^{+}$, 0] \ensuremath{\rightarrow} [${1}^{+}$, 1] transitions.

Investigation of the mechanism of ρ-induced four-nucleon pick-up reactions

In the first part of this paper, the α-transfer character of the (τ, 7Be) reaction which is shown to be direct is examined in the light of two particular experimental features: (i) the variation of the cross section with the mass of the target nucleus, and (ii) the hindrance of ΔT ≠ 0 or ΔS ≠ 0 transitions. The experimental evidence indicates that the dominant mechanism in the (τ, 7Be) reaction to low-lying states is a direct α-transfer. However, in the second part of the paper we investigate the possibility of a mechanism in which the two protons and two neutrons transferred are in a T = 1 state through an experimental study of the analogue process, the transfer of a 4H-like fragment. The corresponding reaction, (τ, 7Li), is found to proceed through a direct mechanism at forward angles. It is concluded, for the 19F(τ, 7Be)15N ground state transition, that the magnitude of the T = 1 transfer amplitude is approximately √0.2 times the total transition amplitude. A simple estimate of the (τ, 7Li) and (ρ, 7Be) reaction strengths. D0, suggests that 2p+2n, T = 1 clustering in light and medium nuclei is less probable than T = 0 α-clustering by almost two orders of magnitude.

Final-State Interactions among Three Particles. II. Explicit Evaluation of the First Rescattering Correction

The lowest approximation to the three-body final-state interaction problem is a simple superposition of 3 two-body interaction terms, as given by the Watson final-state formula. The first rescattering correction corresponds to the graph of perturbation and dispersion theory; for example, the process $W\ensuremath{\rightarrow}2+(13)\ensuremath{\rightarrow}1+(23)\ensuremath{\rightarrow}1+2+3$, i.e., where first particles 1 and 3 interact strongly, then separate in such a way that 2 and 3 come together and interact strongly. For the case in which the (13) interaction is dominated by a resonance, we discuss the kinematic conditions under which such a rescattering correction will contribute appreciably to the total transition amplitude. We then evaluate this term exactly in the non-relativistic (N.R.) case; that is, we evaluate the N.R. triangle graph. An analogous expression is proposed for the relativistic case, with suitable reinterpretation of the variables. The method is generalized to include spin and angular momentum, and to incorporate (23) rescattering to all orders, for the cases in which this can be parametrized either by a scattering length or by a resonance. Specific application is made to the $\ensuremath{\pi}\ensuremath{\pi}N$ case.