Nondynamical calculation of polarization observables in d + d reactions at low energies

The parametrization of cross-section, analysing power and spin-correlation observables in terms of (l, s, J) matrix elements is given for reactions²H(d, p)³H and²H(d, n)³He at low energies. It is shown that a nearly complete set of matrix elements can be obtained from these observables. The feasibility of colliding-beam arrangement for the spin-correlation experiment is estimated.     

Nondynamical calculation of polarization observables in d+d reactions at low energies

The parametrization of polarization observables in terms of (l, s, J) matrix elements is given for²H(d, p)³H and²H(d, n)³He reactions at low energies. It is shown that transverse polarizations of outgoing nucleons are to be measured in order to obtain a complete set of cross-section, analysing powers, spin-correlation and polarization transfer experiments.     

Polarization observables in (γ,NN) reactions

The formalism of ( γ, NN) reactions is given where the incident photon is polarized and the outgoing-nucleon polarization is detected. Sixteen structure functions and fifteen polarization observables are found in the general case, while only eight structure functions and seven polarization observables survive in coplanar kinematics. Numerical examples are presented for the ¹⁶O(γ, np) and ¹⁶O(γ, pp) reactions. The transitions to the ground state of ¹⁴C and ¹⁴N are calculated in a model where realistic short-range and tensor correlations are taken into account for the np pair, while short-range and long-range correlations are included in a consistent way for pp pairs. The effects of the one-body and two-body components of the nuclear current and the role of correlations in cross-sections and polarizations are studied and discussed. Received: 7 June 2001 / Accepted: 26 September 2001     

Relations between polarization observables and complete sets for deuteron photodisintegration

The polarization observables for deuteron photodisintegration are given as Hermitean forms of theT-matrix elementst _i . By inversion we are able to express a given productt _i ^* t _j in terms of polarization observables. This allows (i) to derive linear relations between observables for unpolarized, circularly and linearly polarized photons, (ii) to construct explicitly complete sets of polarization observables, and (iii) to derive quadratic relations between observables.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

Consistent treatment of relativistic corrections in deuteron photodisintegration in a one-pion-exchange model

Using a one-pion-exchange model for the nucleon-nucleon interaction the relativistic corrections to potential and to the electromagnetic operators are derived in a power expansion of (p/M). All corrections up to the order (p/M)³ are consistently included. Numerical results are shown for differential cross section and polarization observables for deuteron photodisintegration. A sizeable influence of relativistic effects on some observables is found even at low energies. A comparison of our operators with the expressions of other authors is given.Supported by Deutsche Forschungsgemeinschaft (SFB 201)     

Relativmessung der longitudinalen Polarisation der β-Teilchen des Eu152

The longitudinal polarizationP of theΒ-rays from the 1.49 MeV transition of Eu¹⁵² (T=13 y) has been measured relatively to P³² using the MØeller-scattering method (electron-electron-scattering). Taking the polarization of P³² asP(P³²)=?(v/c) we getP(Eu¹⁵²)=?(0.959±0.028) (v/c) at a mean energy of 1100 keV. This result is in good agreement with the set of matrix elements taken from measurements of other observables.     

Second-forbidden beta-decay and the effect of (V+A)- andS-interaction admixtures:36Cl

The shapefactor, the logft-value, the electron longitudinal polarization and the distribution of electrons emitted from oriented nuclei of³⁶Cl have been calculated by applying two different nuclear models. Firstly a pure 1d_3/2→1d_3/2 transition has been considered. Secondly a more refined shell model of thes-d shell configuration space has been taken into account. It is shown that there is no great influence of the shell model version to the observables, that the observables depend strongly on the relativistic nuclear matrix elements, that the so-called “two parameter equation” for the shapefactor cannot be used in the case of³⁶Cl and that there is no larger sensitivity of (V+A) admixtures to the electron longitudinal polarization than normally found in allowed decays. Comparisons with the existing experimental data are made.     

General formulae for polarization observables in two-body break-up of deuteron photodisintegration

The formal expressions of all possible polarization observables ind(,N)N with polarized photons and oriented deuterons are derived in terms of thet-matrix elements. Furthermore, using the multipole expansion of thet-matrix, all observables are expanded in terms of Legendre polynomials or associated functions, the coefficients of which are given as bilinear forms of the multipole moments and allow a model independent analysis of experimental data.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

Θ+-Pentaquark parity from associative baryon production in πd collisions, π ± + d → Θ+ + Σ±

We derive, in model-independent way, the spin structure of the matrix element for the reaction of associative Θ⁺-pentaquark production, π ^± + d → Θ⁺ + Σ^±, in the threshold region and in collinear kinematics. The expressions for the polarization observables in this reaction are found assuming spin 1/2 and different parities for Θ⁺. We have proved that such a reaction can be used for a model-independent determination of the P parity of Θ⁺ only by measuring the Θ⁺ polarization. Other polarization observables, such as the dependence of the Σ^± polarization on the vector and tensor deuteron polarizations, are insensitive to the Θ⁺ parity under the considered kinematical conditions. The linear and quadratic relations between polarization observables in (Θ⁺ is unpolarized) do not depend on the parity of the Θ⁺ pentaquark. The analysis performed for this reaction is also applicable without any modification to the reaction K ⁺ + d → Θ⁺ + p. Using the pole model for the reaction mechanism, we estimated the value of the cross section for the reaction K ⁺ + d → Θ⁺ + p near the threshold. The text was submitted by the authors in English.     

Correlation and polarization characteristics of the nuclear quasi-free (p,dπ<Superscript>+</Superscript>) reaction

An extended set of observables of the nuclear quasi-free (p, dπ⁺) reaction including the triple differential cross-section for coincidence measurements, its analyzing power in case of polarized proton beams and, also, the parameters of the polarization of the excited recoil nucleus and the produced deuteron are considered in the framework of the distorted-wave impulse approximation using the reaction ¹⁶O(p, dπ⁺)¹⁵N at a proton energy of 650 MeV as an example. The calculations show a high sensitivity of the differential cross-section and, especially, of the polarization transfer characteristics of the reaction to the spin-multipole decomposition of the amplitude of the basic two-body pp → dπ⁺ process.     

Polarization in hyperon photo- and electro-production<Superscript>⋆</Superscript>

Multiple polarization observables must be measured to access the amplitude structure of pseudoscalar meson photoproduction off the proton. The hyperon-producing reactions are especially attractive to study, since the weak decays allow straightforward measurement of the induced and recoil polarization observables. In this paper we emphasize γ + p → K ⁺ + Λ , discussing recent measurements of C_x, C_z, and P for this reaction. An empirical constraint on the helicity amplitudes is obtained. A simplified model involving spin-flip and spin-non-flip amplitudes is presented. Finally, a semi-classical model of how the polarization may arise is presented.     

The role of the neutron electric form factor ind(e,e′ N)N including polarization observables

The influence of the neutron electric form factor on various observables in two-body break-up of deuterons by electrons such as differential cross section, beam, target and beam-target asymmetries and outgoing nucleon polarization as well is investigated for different kinematic regions. The electron-deuteron vector asymmetryA _ed ^V and the outgoing nucleon polarization component P′_x(n) are the most promising observables in and off the quasi-free region for a determination ofG _En. Also the single polarization observablesA _d ^T and P_y ⁰(p) and the double polarization observable P′_z(n) show significant influences fromG _En.     

Relativistically invariant analysis of -isobar production in deuteron electrodisintegration: : General analysis of polarization effects

The differential cross-section and the polarization observables for Δ-isobar production in the deuteron electrodisintegration process, e^-+d→e^-+Δ+N, are calculated in a general formalism based on structure functions. The obtained expressions have a general nature, hold for one-photon-exchange, assuming P-invariance of the electromagnetic interaction and the conservation of the hadron electromagnetic current. The dependence of the differential cross-section of the e^-+d→e^-+Δ+N reaction on the vector and tensor polarizations of the deuteron target with unpolarized and longitudinally polarized electrons is considered. The general dependence of the asymmetries on two of five kinematic variables, the azimuthal angle φ and (linear polarization of the virtual photon) is calculated. A similar analysis is performed for the polarization of the nucleon produced in γ^*d→ΔN reaction provided the electron beam is unpolarized or longitudinally polarized. Polarization effects, which are due to the strong ΔN-interaction in the final state are calculated. The photoproduction of the Δ-isobar on the deuteron target has been considered in detail, as a particular case. The differential cross-section and various polarization observables have been derived in terms of the reaction amplitudes. The polarization observables due to the linear and circular polarizations of the photon, when the deuteron target is arbitrarily polarized have been derived in terms of the reaction amplitudes. The polarization of the final nucleon is also considered.     

Near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na, K, Rb, Cs; n = 3-6)

The effect of the polarization of the atomic core by the outer electron on near threshold photoionization of excited alkali atoms Ak(np) (Ak = Na-Cs; n=3-6) is investigated. Partial and total cross-sections for photo-ionization of the np-electron were computed utilizing the configuration interaction technique with Pauli-Fock atomic orbitals (CIPF) and including the long range core polarization potential (CP). To calculate the core polarization potential the variational principle is applied. Comparison with previous theoretical results and with available experimental data is made for the total cross-section , for the electron angular distribution parameter , for the ratio of the reduced electric dipole matrix elements and for the phase shift difference , associated with the d-wave and s-wave continua, respectively. In the comparison, new experimental results for , , and , measured for laser-excited, polarized ³⁹K(4p _3/2) atoms, have been included. Received 21 July 1999 and Received in final form 14 October 1999     

Complete Sets of Polarization Observables in Electromagnetic Deuteron Breakup

 For deuteron photo- and electrodisintegration the selection of complete sets of polarization observables is discussed in detail by applying a recently developed new criterion for the check of completeness of a chosen set of observables. The question of ambiguities and their resolution by considering additional observables is discussed for a numerical example, for which the role of experimental uncertainties is also investigated. Furthermore, by inversion of the expressions of the observables as Hermitean forms in the t-matrix elements a bilinear term of the form can be given as a complex linear form in the observables from which an explicit solution for in terms of observables can be obtained. These can also be used to select sets of observables for the explicit representation of the t-matrix. Received May 15, 1999; accepted for publication August 30, 1999     

The Woods-Saxon wave functions and the beta transitions of deformed nuclei

The general expressions for the beta transition matrix elements have been obtained using the Woods-Saxon wave functions for deformed nuclei proposed byFaessler andSheline. As an application the matrix elements for the 1^?(β^?)0⁺ and 1^?(β^?)2⁺ transitions of the¹⁷⁰Tm nucleus have been calculated. The results indicate significant differences between the Nilsson and Woods-Saxon values of the nuclear parameters. Assuming a reasonableK=0 mixture in the ground state of the¹⁷⁰Tm nucleus and a value near the Ahrens-Feenberg estimate for the ∫ α¦ ∫ir ratio it is possible to obtain an important improvement of the theoretical values of the relevant observables and especially of theft values.     

Investigation of the^3 He(\vec d,p)^4 He reaction between 1 and 13 MeV

High-precision measurements of the cross section, the vector analyzing poweriT ₁₁ and the three tensor-analyzing powersT ₂₀,T ₂₁, andT ₂₂ of the³He(d, p)⁴He reaction have been performed in the energy range between 1.0 and 13.0 MeV in steps of 1 or 2 MeV. Angular distributions of the cross section have been obtained between 22.5° and 157.5° in the laboratory system. The polarization observables have been measured between 10° and 170°.     

Asymptotic orbits in a free Fermi gas

We consider the time evolution of local observables and physical states in an infinite system of non-interacting Fermi particles. The orbit of an observable in theC*-algebra of the canonical anticommutation relations is proved to be asymptotic to a set of observables consisting of sums of products of elements of grade two and lower with support in a family of separated cells in ³ (alacunary paving of ³) under time evolution. A space-factorization (clustering) property for primary, even, locally Fock states is established. A class of such states whose space-correlations decay as (logd)^–(1+a) witha positive andd the (space-) separation is, then, proved to be time-asymptotic to their associated quasi-free states.     

sdg Interacting boson model: hexadecupole degree of freedom in nuclear structure

Thesdg interacting boson model (sdgIBM), which includes monopole (s), quadrupole (d) and hexadecupole (g) degrees of freedom, enables one to analyze hexadecupole (E4) properties of atomic nuclei. Various aspects of the model, both analytical and numerical, are reviewed emphasizing the symmetry structures involved. A large number of examples are given to provide understanding and tests, and to demonstrate the predictiveness of thesdg model. Extensions of the model to include proton-neutron degrees of freedom and fermion degrees of freedom (appropriate for odd mass nuclei) are briefly described. A comprehensive account ofsdgIBM analysis of all the existing data on hexadecupole observables (mainly in the rare-earth region) is presented, includingβ ₄ (hexadecupole deformation) systematics,B(IS4; 0 _GS ⁺ →4 _γ ⁺ ) systematics that give information about hexadecupole component in γ-vibration,E4 matrix elements involving few low-lying 4⁺ levels,E4 strength distributions and hexadecupole vibrational bands in deformed nuclei. The survey of literature for this review was concluded in December 1991.     

A theoretical study of the beta decay transitions 0− → 2+ and 0− → 0+ of the Ho166 nucleus

The theoretical beta decay observables are compared with the experimental values for the 0^? → 2⁺ and 0^? → 2⁺ transitions. By considering a Ho¹⁶⁶ ground state configuration infered from (d, p) reaction experiments, and using all the matrix elements, satisfactory results are obtained for the 0^? → 2⁺ transition. For the 0^? → 2⁺ transition an important cancellation effect has been found which determines the failure of the ξ approximation and an energy dependent spectrum shape.